How to Dunk a Doughnut: The Science of Everyday Life

Copyright © 2 0 0 2 by Len Fisher All rights reserved. No part of this book m a y be r e p r o d u c e d in a n y form ...

Author: Len Fisher

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Copyright © 2 0 0 2 by Len Fisher All rights reserved. No part of this book m a y be r e p r o d u c e d in a n y form or by a n y electronic or m e c h a n i c a l m e a n s , including information storage and retrieval systems, w i t h o u t permission in writing from t h e publisher, except by a reviewer, w h o m a y q u o t e brief passages in a review. 2003

FIRST U . S . EDITION

First published in 2 0 0 2 in Great Britain by Weidenfeld & Nicolson Library of Congress Cataloging-in-Publication Data Fisher, Len. H o w to d u n k a d o u g h n u t : t h e science of e v e r y d a y life / Len Fisher. —1st U.S. ed. p. cm. Includes bibliographical references a n d index. ISBN 1-55970-680-5 1. Science—popular w o r k s . I. Title. Q162.F53 2003 00—dc21

2003052418

Published in t h e United States by Arcade Publishing, Inc., N e w York Distributed by AOL Time W a r n e r Book G r o u p Visit o u r Web site at w w w . a r c a d e p u b . c o m 1 0

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contents

vii

Preface to the American Edition Introduction

ix 1

1 The Art a n d Science of D u n k i n g 2 H o w Does a Scientist Boil an Egg?

23

3 The Tao of Tools

42

4 H o w to Add Up Your S u p e r m a r k e t Bill

77

5 H o w to T h r o w a B o o m e r a n g

92 108

6 Catch as Catch Can 7 Bath Foam, Beer Foam, a n d t h e M e a n i n g of Life

121 146

8 A Question of Taste 9 The Physics of Sex Coda Appendices Notes and References Index

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171 189 195 205 245

preface to the a m e r i c a n edition

W h e n I b e g a n t o use e v e r y d a y activities like d u n k i n g t o s h o w h o w scientists t h i n k a b o u t t h e w o r l d , I h a d n ' t e x p e c t e d m y a c tivities to be televised live in A m e r i c a a n d r e p o r t e d in s u c h p r e s t i g i o u s places as t h e Wall Street Journal a n d t h e San Francisco Chronical, n o r to receive letters from A m e r i c a n s c h o o l c h i l d r e n w a n t i n g h e l p w i t h t h e i r school science projects. T h e s e t h i n g s h a p p e n e d , t h o u g h , a n d so I w a s p a r t i c u l a r l y pleased to be a s k e d to p r e p a r e an e d i t i o n of this b o o k on t h e science of e v e r y d a y life lor an A m e r i c a n a u d i e n c e . I h a v e s p e n t m a n y h a p p y h o u r s w o r k i n g w i t h A m e r i c a n scientists, scientists from o t h e r c o u n t r i e s n o w living i n A m e r i c a , a n d especially A m e r i c a n chefs a n d food w r i t e r s . I h o p e t h e y will forgive m e for t h e stories t h a t I tell a b o u t t h e m h e r e .

how to dunk a doughnut

1 the art a n d science of d u n k i n g

O n e o f t h e m a i n p r o b l e m s t h a t scientists h a v e i n s h a r i n g t h e i r p i c t u r e of t h e w o r l d w i t h a w i d e r a u d i e n c e is t h e k n o w l e d g e g a p . O n e d o e s n ' t n e e d to be a w r i t e r to read a n d u n d e r s t a n d a n o v e l , o r t o k n o w h o w t o p a i n t before b e i n g able t o a p p r e c i a t e a p i c t u r e , b e c a u s e b o t h t h e p a i n t i n g a n d t h e n o v e l reflect o u r c o m m o n e x p e r i e n c e . S o m e k n o w l e d g e of w h a t science is a b o u t , t h o u g h , is a p r e r e q u i s i t e for b o t h u n d e r s t a n d i n g a n d a p p r e c i a t i o n , b e c a u s e science is largely b a s e d on c o n c e p t s w h o s e detail is u n f a m i l i a r to m o s t p e o p l e . That detail starts w i t h t h e b e h a v i o r o f a t o m s a n d m o l e c u l e s . T h e n o t i o n t h a t s u c h t h i n g s exist is p r e t t y familiar t h e s e days, a l t h o u g h t h a t did n o t s t o p o n e of my c o m p a n i o n s at a d i n n e r party from g u s h i n g , " O h , y o u ' r e a scientist! I d o n ' t k n o w m u c h a b o u t science, b u t I d o k n o w t h a t a t o m s a r e m a d e o u t o f m o l e c u l e s ! " T h a t r e m a r k m a d e m e realize j u s t h o w difficult i t can b e for p e o p l e w h o d o n o t s p e n d t h e i r professional lives d e a l i n g w i t h m a t t e r a t t h e a t o m i c o r m o l e c u l a r level t o visualize h o w i n d i v i d u a l a t o m s a n d m o l e c u l e s a p p e a r a n d b e h a v e i n their miniaturized world. S o m e o f t h e first e v i d e n c e a b o u t t h a t b e h a v i o r c a m e from scientists w h o w e r e t r y i n g t o u n d e r s t a n d t h e forces t h a t suck liquids i n t o p o r o u s m a t e r i a l s . O n e o f t h e m o s t c o m m o n m a n ifestations of this effect is w h e n coffee is d r a w n i n t o a d u n k e d d o u g h n u t or tea or milk i n t o a d u n k e d c o o k i e , so I w a s d e lighted w h e n a n English a d v e r t i s i n g firm a s k e d m e t o h e l p publicize t h e science of c o o k i e d u n k i n g b e c a u s e it g a v e me an opportunity to explain s o m e of t h e behavior of a t o m s and m o l e c u l e s in t h e c o n t e x t of a familiar e n v i r o n m e n t , as well as a n o p p o r t u n i t y t o s h o w h o w scientists o p e r a t e w h e n t h e y a r e confronted with a n e w problem.

2

h o w to d u n k a d o u g h n u t

I w a s less d e l i g h t e d w h e n I w a s a w a r d e d t h e spoof IgNobel Prize for my efforts. Half of t h e s e a r e a w a r d e d e a c h y e a r for "science t h a t c a n n o t , o r s h o u l d n o t , b e r e p r o d u c e d . " T h e o t h e r half a r e a w a r d e d for projects t h a t " s p a r k p u b l i c i n t e r e s t in scie n c e . " T h e o r g a n i z e r s h a v e n o w c h a n g e d t h e s e confusing d e scriptions for t h e s i m p l e "First t h e y m a k e y o u l a u g h ; t h e n t h e y m a k e you think." It w a s a p l e a s u r e , t h o u g h , to r e c e i v e letters from s c h o o l c h i l d r e n w h o h a d b e e n e n t h u s e d b y t h e publicity s u r r o u n d i n g b o t h t h e prize a n d t h e project. O n e A m e r i c a n s t u d e n t s o u g h t m y h e l p t o t a k e t h e w o r k f u r t h e r i n his s c h o o l s c i e n c e project, i n w h i c h h e s t u d i e d h o w d o u g h n u t s differ from c o o k i e s . H e s u b s e q u e n t l y r e p o r t e d w i t h p r i d e t h a t h e h a d received a n "A" for his efforts. This c h a p t e r tells t h e story of t h e d u n k i n g project a n d of t h e u n d e r l y i n g science, w h i c h i s u s e d t o tackle p r o b l e m s r a n g i n g from t h e e x t r a c t i o n of oil from u n d e r g r o u n d r e s e r v o i r s to t h e w a y t h a t w a t e r r e a c h e s t h e leaves i n t r e e s . D o u g h n u t s m i g h t h a v e b e e n d e s i g n e d for d u n k i n g . A d o u g h n u t , like b r e a d , is h e l d t o g e t h e r by an elastic n e t of t h e p r o t e i n g l u t e n . T h e g l u t e n m i g h t stretch, a n d e v e n t u a l l y e v e n b r e a k , w h e n t h e d o u g h n u t i s d u n k e d i n h o t coffee, b u t i t d o e s n ' t swell or dissolve as t h e liquid is d r a w n i n t o t h e n e t w o r k of h o l e s a n d c h a n n e l s t h a t t h e g l u t e n s u p p o r t s . This m e a n s t h a t t h e d o u g h n u t d u n k e r can t a k e his o r h e r t i m e , p a u s i n g o n l y t o let t h e excess liquid d r a i n back i n t o t h e c u p b e f o r e raising t h e d o u g h n u t to the waiting m o u t h . The only problem that a d o u g h n u t d u n k e r faces is t h e selection of t h e d o u g h n u t , a m a t t e r o n w h i c h science h a s s o m e s u r p r i s i n g advice t o offer, a s I will s h o w later in t h e c h a p t e r . C o o k i e d u n k e r s face m u c h m o r e of a c h a l l e n g e . If r e c e n t m a r k e t r e s e a r c h i s t o b e believed, o n e c o o k i e d u n k i n e v e r y f i v e e n d s i n disaster, w i t h t h e d u n k e r f i s h i n g a r o u n d i n t h e b o t t o m of t h e c u p for t h e soggy r e m a i n s . T h e p r o b l e m for ser i o u s c o o k i e d u n k e r s is t h a t h o t tea or coffee dissolves t h e sugar, m e l t s t h e fat, a n d swells a n d softens t h e starch grains in

the art and

science of dunking

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t h e c o o k i e . T h e w e t t e d c o o k i e e v e n t u a l l y collapses u n d e r its own weight. C a n science d o a n y t h i n g t o b r i n g t h e d e d i c a t e d c o o k i e d u n k e r i n t o p a r i t y w i t h t h e d u n k e r o f d o u g h n u t s ? C o u l d science, w h i c h has added that extra edge to the a c h i e v e m e n t s of a t h l e t e a n d a s t r o n a u t alike, b e used t o e n h a n c e u l t i m a t e c o o k i e d u n k i n g p e r f o r m a n c e a n d s a v e t h a t f i f t h , vital d u n k ? These questions were p u t to me by an advertising c o m p a n y wanting to p r o m o t e "National Cookie-Dunking Week." As s o m e o n e w h o u s e s t h e science u n d e r l y i n g c o m m o n p l a c e o b jects a n d activities to m a k e science m o r e publicly accessible, I w a s h a p p y to give "The Physics of C o o k i e D u n k i n g " a try. T h e r e was, it s e e m e d , a fair c h a n c e of p r o d u c i n g a l i g h t - h e a r t e d piece o f r e s e a r c h t h a t w o u l d s h o w h o w science actually w o r k s , a s well as p r o d u c i n g s o m e m e d i a publicity on behalf of b o t h science and the advertisers. T h e a d v e r t i s e r s clearly t h o u g h t t h a t t h e r e w o u l d b e k e e n public i n t e r e s t . T h e y little realized j u s t h o w k e e n . T h e " c o o k i e d u n k i n g " story t h a t e v e n t u a l l y b r o k e i n t h e British m e d i a rapidly s p r e a d w o r l d w i d e , e v e n r e a c h i n g A m e r i c a n breakfast television, w h e r e I p a r t i c i p a t e d in a l e a r n e d discussion of t h e relative p r o b l e m s o f d o u g h n u t a n d c o o k i e d u n k e r s . T h e e x t e n t of p u b l i c i n t e r e s t in u n d e r s t a n d a b l e science w a s strikingly r e v e a l e d w h e n I talked a b o u t t h e physics of c o o k i e d u n k i n g on a call-in science s h o w in Sydney, A u s t r a l i a . T h e s w i t c h b o a r d of Triple-J, t h e rock r a d i o s t a t i o n , r e c e i v e d seven thousand calls in a q u a r t e r of an h o u r . The advertisers had their o w n preconceptions about h o w science w o r k s . T h e y w a n t e d n o t h i n g less t h a n a " d i s c o v e r y " t h a t w o u l d attract n e w s p a p e r h e a d l i n e s . A d v e r t i s e r s a n d j o u r nalists a r e n ' t t h e o n l y p e o p l e w h o see science i n t e r m s o f "discoveries." E v e n s o m e scientists d o . S h o r t l y after t h e Royal Society w a s f o u n d e d i n 1660, R o b e r t H o o k e w a s a p p o i n t e d a s "curator of e x p e r i m e n t s " and charged with the job of m a k i n g " t h r e e o r four c o n s i d e r a b l e e x p e r i m e n t s " (i.e., discoveries) e a c h w e e k a n d d e m o n s t r a t i n g t h e m t o t h e Fellows o f t h e Society. G i v e n this p r e s s u r e , it is no w o n d e r that H o o k e is

4


r e p o r t e d to h a v e b e e n of irritable disposition, w i t h h a i r h a n g ing in d i s h e v e l e d locks o v e r his h a g g a r d c o u n t e n a n c e . He did i n fact m a k e m a n y discoveries, o r i g i n a t i n g m u c h but perfecting little. I h a d to tell t h e a d v e r t i s e r s in q u e s t i o n that H o o k e m a y h a v e b e e n able to do it, but 1 c o u l d n ' t . Science d o e s n ' t usually w o r k that way. Scientists d o n ' t set out to m a k e discoveries; t h e y set out to u n cover stories. T h e stories are about h o w things w o r k . S o m e t i m e s t h e story might result in a totally n e w piece of k n o w l e d g e , or a n e w w a y of v i e w i n g t h e n a t u r e of things. But not often. 1 t h o u g h t t h a t , w i t h t h e h e l p of my friends a n d c o l l e a g u e s in physics a n d food science, t h e r e w o u l d be a good c h a n c e of u n c o v e r i n g a story a b o u t c o o k i e d u n k i n g , but that it w a s h a r d l y likely to result in a "discovery." To t h e i r credit, t h e a d v e r t i s e r s a c c e p t e d m y r e a s o n i n g , a n d w e set t o w o r k . T h e first q u e s t i o n that we asked w a s " W h a t does a cookie look like from a physicist's point of v i e w ? " It's a typical scientist's q u e s t i o n , to be read as " H o w can we simplify this p r o b l e m so thai we can a n s w e r it?" The a p p r o a c h can s o m e t i m e s be t a k e n to e x t r e m e s , as w i t h t h e f a m o u s physicist w h o w a s asked to calculate t h e m a x i m u m possible speed of a r a c e h o r s e . His res p o n s e , according to legend, w a s that he could do so, but only it h e w a s p e r m i t t e d t o a s s u m e that t h e h o r s e w a s spherical. Most scientists d o n ' t go to q u i t e such lengths to r e d u c e complicated p r o b l e m s to solvable form, but we all do it in s o m e w a y — t h e w o r l d is just too complicated to u n d e r s t a n d all at o n c e . Critics call us reductionists, but, no m a t t e r w h a t t h e y call us, t h e m e t h o d w o r k s . Francis Crick a n d J a m e s Watson, discoverers of t h e s t r u c t u r e of DNA, d i d n ' t find t h e s t r u c t u r e by looking at t h e complicated living cells w h o s e destiny DNA drives. Instead, they took a w a y all of t h e p r o t e i n s a n d o t h e r m o l e c u l e s that m a k e up life a n d looked at t h e DNA a l o n e . Biologists in the fifty years following t h e i r discovery h a v e gradually put the p r o t e i n s back to find out h o w real cells use t h e DNA s t r u c t u r e , but t h e y w o u l d n ' t h a v e k n o w n w h a t t h a t s t r u c t u r e w a s had it not b e e n for t h e original reductionist a p p r o a c h . W e decided t o b e r e d u c t i o n i s t a b o u t cookies, a t t e m p t i n g t o

the art and

science of dunking

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u n d e r s t a n d t h e i r r e s p o n s e t o d u n k i n g i n s i m p l e physical t e r m s a n d leaving t h e c o m p l i c a t i o n s until later. W h e n w e e x a m i n e d a cookie u n d e r a m i c r o s c o p e , it a p p e a r e d to consist of a t o r t u ous set of i n t e r c o n n e c t e d holes, cavities, a n d c h a n n e l s (so d o e s a d o u g h n u t ) . In t h e case of a c o o k i e , t h e c h a n n e l s a r e t h e r e b e c a u s e it consists ol d r i e d - u p starch g r a n u l e s imperfectly glued t o g e t h e r w i t h s u g a r a n d fat. To a scientist, t h e c o o k i e d u n k i n g p r o b l e m is to w o r k o u t h o w h o t tea or coffee gets i n t o these channels and what h a p p e n s w h e n it does. With this p i c t u r e of d u n k i n g in m i n d , I sat d o w n w i t h s o m e of my c o l l e a g u e s in t h e Bristol U n i v e r s i t y Physics D e p a r t m e n t and proceeded to examine the question experimentally. Solemnly, w e d i p p e d o u r cookies i n t o o u r d r i n k s , t i m i n g h o w long t h e y t o o k t o collapse. This w a s B a c o n i a n science, n a m e d alter Sir Francis Bacon, t h e E l i z a b e t h a n c o u r t i e r w h o d e c l a r e d that science w a s simply a m a t t e r of collecting a sufficient n u m b e r of facts to m a k e a p a t t e r n . B a c o n i a n science lost us a lot of c o o k i e s b u t did n o t p r o v i d e a scientific a p p r o a c h to c o o k i e d u n k i n g . Serendipity, t h e art of m a k i n g f o r t u n a t e discoveries, c a m e t o t h e r e s c u e w h e n I d e cided to try h o l d i n g a c o o k i e horizontally, w i t h just o n e side in c o n t a c t w i t h t h e surface of t h e tea. I w a s a m a z e d to find t h a t this c o o k i e beat t h e p r e v i o u s record for longevity by a l m o s t a factor of four. Scientists, like sports fans, a r e m u c h m o r e i n t e r e s t e d i n t h e exceptional than they are in the average. The times of greatest e x c i t e m e n t i n science a r e w h e n s o m e o n e p r o d u c e s a n observ a t i o n that c a n n o t h e e x p l a i n e d b y t h e established r u l e s . This i s w h e n " n o r m a l science" u n d e r g o e s w h a t T h o m a s K u h n called a p a r a d i g m shift, a n d all p r e v i o u s ideas m u s t be recast in t h e light o f t h e n e w k n o w l e d g e . E i n s t e i n ' s d e m o n s t r a t i o n t h a t m a s s m is actually a form of e n e r g y E, t h e t w o b e i n g linked by t h e s p e e d of light c in t h e f o r m u l a E = mc , is a classic e x a m p l e of a p a r a d i g m shift. P a r a d i g m shifts often arise from u n e x p e c t e d o b s e r v a t i o n s , b u t t h e s e o b s e r v a t i o n s n e e d t o h e verified. T h e m o r e u n e x p e c t e d t h e o b s e r v a t i o n , t h e h a r s h e r t h e testing. I n t h e w o r d s 2

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of Carl S a g a n : " E x t r a o r d i n a r y claims r e q u i r e e x t r a o r d i n a r y proof." No o n e is going to discard t h e w h o l e of m o d e r n physics j u s t b e c a u s e s o m e o n e h a s c l a i m e d t h a t Yogic flying is possible, or b e c a u s e a m a g i c i a n h a s b e n t s p o o n s on t e l e v i s i o n . If levitation did p r o v e to be a fact, t h o u g h , or s p o o n s could really be b e n t w i t h o u t a force b e i n g applied, t h e n physics w o u l d h a v e to take it on t h e chin and reconsider. O n e long-lived h o r i z o n t a l c o o k i e d u n k w a s h a r d l y likely t o r e q u i r e a p a r a d i g m shift lor its e x p l a n a t i o n . For t h a t r a r e e v e n t t o h a p p e n , t h e n e w o b s e r v a t i o n m u s t b e i n e x p l i c a b l e b y curr e n t l y k n o w n rules. E v e n m o r e i m p o r t a n t l y , t h e effect o b s e r v e d h a s to be a real o n e , a n d n o t t h e result of s o m e u n i q u e circumstance. O n e t h i n g t h a t c o n v i n c e s scientists t h a t an effect is real is r e p r o d u c i b i l i t y — finding t h e s a m e result w h e n a test is r e p e a t e d . T h e long-lived c o o k i e could h a v e b e e n e x c e p t i o n a l b e c a u s e i t h a d b e e n h a r d e r b a k e d t h a n o t h e r s w e h a d tried, o r for a n y n u m b e r o f r e a s o n s o t h e r t h a n t h e m e t h o d o f d u n k i n g . We repeated t h e e x p e r i m e n t s with other cookies and other c o o k i e t y p e s . T h e result w a s a l w a y s t h e s a m e — c o o k i e s t h a t w e r e d u n k e d b y t h e " h o r i z o n t a l " t e c h n i q u e lasted m u c h longer than those that w e r e d u n k e d conventionally. It seemed t h a t t h e m e t h o d really w a s t h e key. W h a t w a s t h e e x p l a n a t i o n ? O n e possibility w a s diffusion, a process w h e r e b y e a c h i n d i v i d u a l m o l e c u l e i n t h e p e n e t r a t i n g liquid m e a n d e r s from p l a c e to place in a r a n d o m fashion, e x ploring t h e c h a n n e l s a n d cavities i n t h e c o o k i e w i t h n o a p p a r e n t m e t h o d o r p a t t e r n t o its w a n d e r i n g s . T h e m o v e m e n t i s similar t o t h a t o f a d r u n k e n m a n w a l k i n g h o m e from t h e p u b , n o t k n o w i n g in w h i c h direction h o m e lies. E a c h step is a h a p h a z a r d l u r c h , w h i c h could b e f o r w a r d s , b a c k w a r d s o r sidew a y s . T h e c o m p l i c a t e d statistics of s u c h m o v e m e n t (called a stochastic process) h a s b e e n w o r k e d o u t b y m a t h e m a t i c i a n s . I t s h o w s t h a t his p r o b a b l e d i s t a n c e from t h e p u b d e p e n d s o n t h e s q u a r e root of t h e t i m e . Put simply, if he t a k e s an h o u r to get a mile a w a y from t h e p u b , it is likely to t a k e h i m four h o u r s to get t w o miles a w a y .

the art and science of dunking

7

If t h e s a m e m a t h e m a t i c s applied to t h e flow of liquid in t h e r a n d o m c h a n n e l s of p o r o u s m a t e r i a l s s u c h as cookies, t h e n it w o u l d t a k e four t i m e s as l o n g for a c o o k i e d u n k e d by o u r fort u i t o u s m e t h o d to get fully w e t as it w o u l d for a c o o k i e d u n k e d " n o r m a l l y . " T h e r e a s o n for this is t h a t in a n o r m a l d u n k t h e liquid o n l y h a s to get as far as t h e m i d - p l a n e of t h e c o o k i e for t h e c o o k i e to be fully w e t t e d , since t h e liquid is c o m i n g from b o t h sides. If t h e c o o k i e is laid flat at t h e t o p of t h e c u p , t h e liquid h a s to travel t w i c e as far (i.e., from o n e side of t h e c o o k i e to t h e o t h e r ) b e f o r e t h e c o o k i e is fully w e t t e d , w h i c h w o u l d t a k e four t i m e s a s long a c c o r d i n g t o t h e m a t h e matics of diffusion (Figure 1.1).

Figure 1.1: H o w to D u n k a Cookie. Left-hand diagram: Disaster — a cookie dunked in the "conventional" manner, with liquid entering from both sides. Right-hand diagram: Triumph — a cookie dunked in the "scientific" manner. The liquid takes four times as long to penetrate the width of the cookie, and the cookie will remain intact so long as the upper surface stays dry.

T h e A m e r i c a n scientist E. W. W a s h b u r n f o u n d a similar factor of four w h e n he s t u d i e d t h e d u n k i n g of b l o t t i n g p a p e r — a m a t of cellulose fibers t h a t is also full of r a n d o m c h a n n e l s . W a s h b u r n ' s e x p e r i m e n t s , p e r f o r m e d s o m e e i g h t y y e a r s ago, w e r e simplicity itself. He m a r k e d off a p i e c e of blotting p a p e r w i t h lines at e q u a l i n t e r v a l s , t h e n d i p p e d it vertically i n t o ink (easier t o see t h a n w a t e r ) w i t h t h e lines a b o v e a n d parallel t o t h e liquid surface, a n d w i t h o n e line e x a c t l y a t t h e surface. H e t h e n t i m e d h o w l o n g i t t o o k t h e ink t o r e a c h successive lines. He f o u n d t h a t it t o o k four t i m e s as l o n g to r e a c h t h e s e c o n d


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line as it did to r e a c h t h e first, a n d n i n e t i m e s as l o n g to r e a c h t h e t h i r d line. I a t t e m p t e d to r e p e a t W a s h b u r n ' s e x p e r i m e n t s w i t h a r a n g e of different c o o k i e s p r o v i d e d by my c o m m e r c i a l s p o n s o r . I d u n k e d t h e cookies, e a c h m a r k e d w i t h a pencil in fivem i l l i m e t e r steps, vertically i n t o h o t tea, a n d t i m e d t h e rise of t h e liquid w i t h a s t o p w a t c h . T h e cookies t u r n e d o u t t o b e v e r y similar t o b l o t t i n g p a p e r w h e n i t c a m e t o t a k i n g u p liquid. J u s t h o w similar b e c a m e o b v i o u s w h e n I d r e w o u t t h e results i n a g r a p h . If t h e d i s t a n c e p e n e t r a t e d follows t h e l a w of diffusion, t h e n a g r a p h of t h e s q u a r e of t h e d i s t a n c e t r a v e l e d v e r s u s t i m e s h o u l d be a s t r a i g h t line. If it t o o k five s e c o n d s for t h e liquid to rise four m i l l i m e t e r s , it s h o u l d t a k e t w e n t y s e c o n d s for t h e liquid to rise eight m i l l i m e t e r s . A n d so it p r o v e d , for up to t h i r t y s e c o n d s , after w h i c h t h e s o d d e n p a r t of t h e c o o k i e d r o p p e d off i n t o t h e tea (Figure 1.2).

Time (seconds) Figure 1.2: D i s t a n c e ( S q u a r e d ) of Hot Tea P e n e t r a t i o n into Different Kinds of Cookies versus Time. The boxes represent individual measurements, with the lengths of the vertical and horizontal sides representing the probable error in the measurement of (distance) or time respectively. 2


9

T h e s e results look v e r y c o n v i n c i n g . N u m e r i c a l a g r e e m e n t w i t h p r e d i c t i o n is o n e of t h e t h i n g s t h a t i m p r e s s e s scientists m o s t . E i n s t e i n ' s G e n e r a l T h e o r y of Relativity, for e x a m p l e , p r e d i c t e d t h a t t h e s u n ' s g r a v i t a t i o n w o u l d b e n d light rays from a d i s t a n t star by 1.75 s e c o n d s of arc ( a b o u t five t e n t h o u s a n d t h s of a d e g r e e ) as t h e y p a s s e d close by. A s t r o n o m e r s h a v e n o w f o u n d t h a t E i n s t e i n ' s p r e d i c t i o n w a s correct t o within o n e percent. If astrology could provide such accurate forecasts, e v e n physicists m i g h t believe it. That's n o t t h e e n d of t h e story. In fact, it is h a r d l y t h e b e g i n n i n g . E v e n t h o u g h t h e e x p e r i m e n t a l results followed t h e p a t t e r n of b e h a v i o r p r e d i c t e d by a diffusion m o d e l , closer r e a s o n i n g s u g g e s t e d t h a t diffusion w a s a n u n l i k e l y e x p l a n a t i o n . Diffusion applies t o s i t u a t i o n s w h e r e a n object ( w h e t h e r it is a d r u n k e n m a n or a m o l e c u l e in a liquid) h a s an e q u a l c h a n c e o f m o v i n g i n a n y d i r e c t i o n , w h i c h s e e m s u n l i k e l y for liquid p e n e t r a t i n g a cookie, since t h e r e t r e a t is b l o c k e d by t h e o n c o m i n g liquid. Diffusion m o d e l s , t h o u g h , a r e n o t t h e o n l y o n e s to p r e d i c t e x p e r i m e n t a l l y o b s e r v e d p a t t e r n s of b e h a v i o r . W a s h b u r n p r o v i d e d a different e x p l a n a t i o n , b a s e d o n t h e forces t h a t p o r o u s m a t e r i a l s e x e r t o n liquids t o d r a w t h e m in. T h e i m b i b i t i o n p r o c e s s is called capillary rise, a n d w a s k n o w n t o t h e ancient Egyptians, w h o used the p h e n o m e n o n t o fill t h e i r r e e d p e n s w i t h i n k m a d e from c h a r c o a l , w a t e r , a n d g u m arabic. T h e q u e s t i o n of h o w capillary rise is d r i v e n , t h o u g h , w a s first c o n s i d e r e d o n l y t w o h u n d r e d y e a r s ago w h e n t w o scientists, a n E n g l i s h m a n a n d a F r e n c h m a n , i n d e pendently asked the question: "What is doing the pulling?" T h e E n g l i s h m a n , T h o m a s Young, w a s t h e y o u n g e s t o f t e n c h i l d r e n in a Q u a k e r family. By t h e age of f o u r t e e n , he h a d t a u g h t himself s e v e n l a n g u a g e s , i n c l u d i n g H e b r e w , Persian, a n d Arabic. H e b e c a m e a practicing p h y s i c i a n a n d m a d e i m portant contributions to our understanding of h o w the heart and the eyes work, showing that there m u s t be three kinds of r e c e p t o r a t t h e b a c k o f t h e e y e ( w e n o w call t h e m c o n e s ) t o p e r m i t color vision. G o i n g o n e better, h e p r o d u c e d t h e t h e o r y t h a t light itself is w a v e - l i k e in c h a r a c t e r . In his s p a r e t i m e he

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laid t h e g r o u n d w o r k for m o d e r n life i n s u r a n c e a n d c a m e close t o i n t e r p r e t i n g t h e h i e r o g l y p h s o n t h e Rosetta s t o n e . T h e F r e n c h m a n , t h e M a r q u i s d e Laplace, also c a m e from r u r a l origins (his f a t h e r w a s a f a r m e r in N o r m a n d y ) a n d his t a l e n t s , too, s h o w e d t h e m s e l v e s early o n . H e e v e n t u a l l y b e c a m e k n o w n as " T h e N e w t o n of F r a n c e " on a c c o u n t of his i n c r e d i b l e t e n v o l u m e w o r k called Mecanique celeste. In this w o r k he s h o w e d t h a t t h e m o v e m e n t s o f t h e p l a n e t s w e r e stable a g a i n s t p e r t u r b a t i o n . In o t h e r w o r d s , a c h a n g e in t h e orbit of o n e p l a n e t , s u c h a s m i g h t b e c a u s e d b y a m e t e o r collision, w o u l d o n l y c a u s e m i n o r a d j u s t m e n t s t o t h e orbits o f t h e o t h e r s , r a t h e r t h a n t h r o w t h e m catastrophically out of synchrony. Young a n d Laplace i n d e p e n d e n t l y w o r k e d o u t t h e t h e o r y o f capillary rise — in Laplace's case, as an u n l i k e l y a p p e n d i x to his work on the m o v e m e n t s of the planets. Both had observed that w h e n w a t e r is d r a w n i n t o a n a r r o w glass t u b e by capillary a c tion, t h e surface of t h e w a t e r is c u r v e d . T h e c u r v e d liquid surface is called t h e meniscus, a n d if t h e glass is perfectly clean t h e m e n i s c u s will a p p e a r to j u s t graze t h e glass surface (Figure 1.3).

F i g u r e 1.3: W a t e r R i s e in a N a r r o w G l a s s T u b e .

Laplace's ( a n d Young's) brilliantly s i m p l e t h o u g h t w a s t h a t it a p p e a r e d a s t h o u g h t h e c o l u m n o f w a t e r w a s b e i n g lifted a t t h e e d g e b y t h e m e n i s c u s . B u t w h a t w a s d o i n g t h e lifting? I t

the art and

science of dunking

11

could o n l y be t h e glass wall, w i t h t h e m o l e c u l e s of t h e glass pulling o n t h e n e a r b y w a t e r m o l e c u l e s . B u t h o w could s u c h a h o r i z o n t a l a t t r a c t i o n p r o v i d e a vertical lift? Laplace c o n c l u d e d that e a c h w a t e r m o l e c u l e i n t h e surface i s a t t r a c t e d p r i m a r i l y to its n e a r e s t n e i g h b o r s , so t h a t t h e w h o l e surface is like a r o p e hammock, w h e r e each knot is a water molecule and the l e n g t h s of r o p e in b e t w e e n r e p r e s e n t t h e forces h o l d i n g t h e m o l e c u l e s t o g e t h e r (Figure 1.4).

F i g u r e 1.4: F o r c e s B e t w e e n M o l e c u l e s i n a M e n i s c u s . The molecules (circles) are held together by attractive forces (arrows). Molecules near the tube walls also experience attractive forces between themselves and the walls.

A h a m m o c k s u p p o r t e d at e a c h e n d sags in t h e m i d d l e . A simplistic p i c t u r e of capillary rise is t h a t t h e w a t e r c o l u m n is being lifted in a similar m a n n e r . M o r e accurately, t h e forces of local m o l e c u l a r a t t r a c t i o n t e n d t o s h r i n k t h e liquid surface t o t h e m i n i m u m possible a r e a . If t h e surface is c u r v e d , t h e t e n d e n c y of t h e surface to s h r i n k ( k n o w n as surface tension) p r o d u c e s a p r e s s u r e difference b e t w e e n t h e t w o sides, j u s t a s t h e s t r e t c h e d r u b b e r surface of a b a l l o o n c r e a t e s a h i g h i n t e r n a l p r e s s u r e . It is t h e p r e s s u r e difference across a m e n i s c u s t h a t drives capillary rise. Laplace w a s able to u s e his p i c t u r e of local m o l e c u l a r a t t r a c tion to w r i t e d o w n an e q u a t i o n describing t h e s h a p e of a

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meniscus so accurately that the equation has never needed to b e m o d i f i e d since. B y t h i n k i n g a b o u t t h e c o m m o n p l a c e p h e n o m e n o n o f capillary rise, h e h a d also u n e x p e c t e d l y f o u n d a n a n s w e r to o n e of t h e big q u e s t i o n s in science at t h a t t i m e : " H o w far d o t h e forces b e t w e e n a t o m s o r m o l e c u l e s e x t e n d ? " A r e t h e y l o n g r a n g e , like t h e force of a m a g n e t on a n e e d l e , or t h e force o f gravity b e t w e e n t h e S u n a n d t h e E a r t h ? O r a r e t h e y v e r y s h o r t r a n g e , s o t h a t o n l y n e a r b y a t o m s a r e affected? Laplace s h o w e d t h a t o n l y v e r y s h o r t - r a n g e forces could e x plain t h e s h a p e of a m e n i s c u s a n d t h e e x i s t e n c e of surface t e n sion. K n o w i n g h o w m a n y m o l e c u l e s a r e p a c k e d t o g e t h e r i n a g i v e n v o l u m e of liquid, he w a s e v e n able to m a k e a c r e d i t a b l e e s t i m a t e of t h e a c t u a l r a n g e of t h e i n t e r m o l e c u l a r forces. His e x p e r i e n c e s h o w s t h a t t h e science o f t h e familiar i s m o r e t h a n a w a y of m a k i n g science accessible or illustrating scientific principles. M a n y o f t h e principles t h e m s e l v e s h a v e arisen from efforts to u n d e r s t a n d e v e r y d a y t h i n g s like t h e fall of an a p p l e , t h e s h a p e a n d color of a s o a p b u b b l e , or t h e u p t a k e of liquid by a p o r o u s m a t e r i a l . Scientists e x p l o r i n g s u c h a p p a r e n t l y m u n d a n e q u e s t i o n s h a v e u n c o v e r e d s o m e o f N a t u r e ' s d e e p e s t laws. Laplace a n d Young s h o w e d t h a t t h e r e l a t i o n s h i p b e t w e e n surface c u r v a t u r e , surface t e n s i o n , a n d t h e p r e s s u r e across a meniscus was an extraordinarily simple o n e — the pressure difference across t h e m e n i s c u s a t a n y p o i n t i s j u s t t w i c e t h e surface t e n s i o n divided by t h e m e a n r a d i u s of c u r v a t u r e at that p o i n t . This r e l a t i o n s h i p , w h i c h n o w b e a r s t h e i r j o i n t n a m e s , s h o w s (for e x a m p l e ) t h a t capillary a c t i o n a l o n e c a n raise a colu m n of water no m o r e t h a n fourteen millimeters in a tube w i t h a r a d i u s of o n e m i l l i m e t e r . As t h e t u b e r a d i u s b e c o m e s smaller, t h e w a t e r c a n rise h i g h e r in p r o p o r t i o n . For a t u b e o n e t h o u s a n d t i m e s n a r r o w e r , t h e w a t e r c a n rise o n e t h o u sand times higher. S u c h tiny c h a n n e l s a r e p r e s e n t in t h e leaves of t r e e s . N a t u r e p r o v i d e s a s p e c t a c u l a r e x a m p l e in t h e G i a n t S e q u o i a , f o u n d in t h e Sierra N e v a d a r a n g e in California. T h e leafy c r o w n of t h e largest k n o w n s p e c i m e n , t h e " G e n e r a l S h e r m a n , " t o w e r s eighty-three meters above the tourists passing below. The w a -

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ter s u p p l y for t h e leaves is d r a w n up from t h e soil by capillary action. T h e m e n i s c i of t h e s e h u g e c o l u m n s of w a t e r reside in t h e leaves, a n d a q u i c k c a l c u l a t i o n s h o w s t h a t t h e capillary c h a n n e l s c o n t a i n i n g t h e m e n i s c i c a n b e n o m o r e t h a n 0.2 m i c r o m e t e r s w i d e — a b o u t o n e t w o - h u n d r e d - a n d - f i i t i e t h of t h e d i a m e t e r of a h u m a n hair. T h e p r e s s u r e across such a tiny m e n i s c u s c a n s u p p o r t a c o n t i n u o u s c o l u m n of w a t e r , of w h i c h t h e r e a r e m a n y i n t h e b u n d l e s o f t u b e s called t h e x y l e m , w h i c h r u n u p t h e t r u n k b e l o w t h e b a r k . I f t h e c o l u m n o f liquid b r e a k s , h o w e v e r , a n airlock d e v e l o p s a t a p o i n t w h e r e t h e t u b e i s m u c h wider, a n d w h e r e t h e n e w m e n i s c u s c a n n o t s u p port a n y t h i n g like s u c h a tall c o l u m n of liquid. S u c h b r e a k s a r e frequent e v e n t s — t h e o c c u r r e n c e of e a c h n e w b r e a k is signified by a "click" t h a t c a n be h e a r d w i t h a s t e t h o s c o p e . O n c e a column has broken, it seemingly cannot re-form. Eventually, a c c o r d i n g t o t h e a c c e p t e d t h e o r y , all c o l u m n s s h o u l d b r e a k a n d t h e t r e e s h o u l d die. Yet m a s s i v e t r e e s c o n t i n u e t o grow, s o m e t i m e s for t h o u s a n d s of y e a r s , p r o v i d i n g b o t a n i s t s a n d biophysicists w i t h a p r o b l e m t h a t is a l o n g w a y from b e i n g solved. The Young-Laplace equation nevertheless provides the only r e a s o n a b l e e x p l a n a t i o n for t h e u p t a k e of w a t e r by t r e e s . It a p plies e q u a l l y to t h e u p t a k e of coffee by d o u g h n u t s , since t h e coffee is h e l d in p l a c e in t h e p o r o u s m a t r i x by t h e p r e s s u r e across t h e m e n i s c u s i n t h e smallest o f t h e p o r e s a t t h e u p p e r level of t h e coffee, j u s t as w a t e r is h e l d up in t h e x y l e m of a tree b y t h e p r e s s u r e across t h e m e n i s c u s i n t h e smallest o f t h e p o r e s i n t h e leaves. This leads t o t h e p a r a d o x i c a l c o n c l u s i o n t h a t m o r e f i n e l y t e x t u r e d d o u g h n u t s s h o u l d b e able t o r e t a i n m o r e coffee t h a n t h e i r c o a r s e r - t e x t u r e d c o u s i n s , p r o v i d e d t h a t b o t h h a v e t h e s a m e total p o r e v o l u m e . T h e Y o u n g - L a p l a c e e q u a t i o n h a s b e e n applied t o m a n y serio u s practical q u e s t i o n s , s u c h a s t h e p r e v e n t i o n o f rising d a m p in b u i l d i n g s a n d t h e e x t r a c t i o n of oil from p o r o u s rocks, as well as to t h e slightly less s e r i o u s q u e s t i o n s of c o o k i e a n d d o u g h n u t d u n k i n g . It tells us h o w far liquids will rise up a t u b e or p e n e t r a t e i n t o a p o r o u s m a t e r i a l , b u t it d o e s n ' t say h o w fast. This is a key piece of i n f o r m a t i o n w h e n it c o m e s to

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c o o k i e d u n k i n g . It w a s p r o v i d e d by a F r e n c h p h y s i c i a n , J e a n L o u i s - M a r i e Poiseuille, w h o p r a c t i c e d i n Paris i n t h e 1830s. Poiseuille w a s i n t e r e s t e d i n t h e r e l a t i o n s h i p b e t w e e n t h e r a t e of flow of b l o o d a n d t h e p r e s s u r e in v e i n s a n d a r t e r i e s . He w a s t h e first t o m e a s u r e b l o o d p r e s s u r e u s i n g a m e r c u r y m a n o m e ter, a t e c h n i q u e still u s e d by d o c t o r s today. He tested h o w fast b l o o d a n d o t h e r liquids c o u l d flow t h r o u g h t u b e s o f different d i a m e t e r s u n d e r t h e p r e s s u r e s t h a t h e h a d m e a s u r e d i n living p a t i e n t s , a n d f o u n d t h a t t h e r a t e o f flow d e p e n d e d n o t o n l y o n t h e p r e s s u r e , b u t also o n t h e d i a m e t e r o f t h e t u b e a n d t h e viscosity of t h e liquid (i.e., its r e s i s t a n c e to flow: h o n e y , for e x a m p l e , i s m u c h m o r e viscous t h a n w a t e r ) . Poiseuille's c o n t r i b u t i o n to science w a s to describe t h e d e p e n d e n c e of r a t e of flow on t u b e d i a m e t e r a n d liquid viscosity by m e a n s of a v e r y s i m p l e e q u a t i o n ( t h e details o f w h i c h a r e i n t h e n o t e s t o this chapter). Poiseuille's e q u a t i o n c a n b e c o m b i n e d w i t h t h e Y o u n g Laplace e q u a t i o n to p r e d i c t rates of capillary rise. W a s h b u r n w a s t h e f i r s t t o d o this, p r o d u c i n g a n e q u a t i o n t h a t p r e d i c t s h o w far a liquid d r a w n i n t o a cylindrical t u b e by capillary a c t i o n will t r a v e l in a given t i m e . T h e a c t u a l e q u a t i o n is:

w h e r e L is t h e d i s t a n c e t h a t t h e liquid travels in t i m e t, R is t lie r a d i u s of t h e t u b e , a n d -y (surface t e n s i o n ) a n d r\ (viscosity) a r e n u m b e r s t h a t d e p e n d o n t h e n a t u r e o f t h e liquid. W a s h b u r n ' s v e r y s i m p l e e q u a t i o n p r e d i c t s an e q u a l l y s i m p l e effect — t h a t to d o u b l e t h e d i s t a n c e of t r a v e l will t a k e four t i m e s as long, a n d t o triple i t will t a k e n i n e t i m e s l o n g e r ; e x a c t l y t h e e x p e r i m e n t a l result t h a t W a s h b u r n o b t a i n e d for b l o t t i n g p a p e r , a n d t h a t I o b t a i n e d for c o o k i e s . In t h e a b s e n c e of g r a v i t a t i o n a l effects ( w h i c h w e r e negligible for b o t h W a s h b u r n ' s a n d m y o w n e x p e r i m e n t s ) , t h e W a s h b u r n equation is extremely accurate, as I found w h e n studying it as a p a r t of my P h . D thesis s o m e t w e n t y y e a r s ago. By

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t i m i n g t h e flow of liquid d o w n glass t u b e s ( s o m e of t h e m t w e n t y t i m e s n a r r o w e r t h a n a h u m a n hair) I f o u n d t h a t t h e e q u a t i o n is correct for t u b e d i a m e t e r s as small as t h r e e m i c r o m e t e r s . S u c h t u b e s , t h o u g h , a r e a far cry from t h e i n t e r i o r s of blotting paper or cookies. There seemed to be no theoretical r e a s o n w h y an e q u a t i o n d e r i v e d for a v e r y s i m p l e s i t u a t i o n s h o u l d a p p l y to s u c h a c o m p l i c a t e d m e s s . T h e r e still isn't. No o n e , t o m y k n o w l e d g e , u n d e r s t a n d s w h y a liquid d r a w n b y surface t e n s i o n i n t o a t o r t u o u s set of i n t e r c o n n e c t e d c h a n n e l s s h o u l d follow t h e s a m e s i m p l e d y n a m i c s a s a liquid d r a w n i n t o a single cylindrical t u b e . All t h a t we can say is t h a t m a n y p o r o u s m a t e r i a l s b e h a v e i n this way. T h e " d r u n k a r d ' s w a l k " diffusion e q u a t i o n , w h i c h p r e d i c t s a similar r e l a t i o n s h i p b e t w e e n d i s t a n c e p e n e t r a t e d a n d t i m e t a k e n , m a y h a v e a role t o play. Despite e x t e n s i v e c o m p u t e r m o d e l i n g studies, t h o u g h , we still d o n ' t h a v e a full a n d satisfactory a n s w e r . W h a t w e d o k n o w i s t h a t t h e W a s h b u r n e q u a t i o n w o r k s . It's n o t t h e o n l y e q u a t i o n t h a t w o r k s w h e n it's n o t s u p p o s e d t o . T h e e q u a t i o n t h a t describes h o w a t h i n s t r e a m o f w a t e r d r i p ping from a t a p b r e a k s up i n t o d r o p l e t s , for e x a m p l e , h a s b e e n applied v e r y successfully t o describe t h e b r e a k u p o f a n a t o m i c nucleus during radioactive disintegration. That doesn't m e a n t h a t an a t o m i c n u c l e u s is like a w a t e r d r o p l e t in all o t h e r r e spects, a n y m o r e t h a n a c o o k i e or piece of b l o t t i n g p a p e r is e x actly like a n a r r o w t u b e . It s i m p l y h a p p e n s t h a t an e q u a t i o n derived for an idealized s i t u a t i o n also applies in p r a c t i c e to m o r e c o m p l i c a t e d s i t u a t i o n s , a n d h e n c e c a n b e used t o give guidance and predictions in these circumstances. Such equations are called s e m i - e m p i r i c a l , a n d often arise w h e n scientists are in t h e t h r o e s of t r y i n g to u n d e r s t a n d a c o m p l e x p h e n o m e n o n . T h e y a r e m o s t useful a t a n i n t e r m e d i a t e stage i n t h e u n d e r s t a n d i n g of a p r o b l e m . W h e n a m o r e c o m p l e t e e x p l a n a t i o n e v e n t u a l l y b e c o m e s available, s e m i - e m p i r i c a l e q u a t i o n s a r e u s u a l l y discarded, a l t h o u g h t h e y s o m e t i m e s r e t a i n a v a l u e as teaching instruments. T h e W a s h b u r n e q u a t i o n , a p p l i e d t o cylindrical t u b e s , h a s a s o u n d t h e o r e t i c a l basis. Applied to c o o k i e s or b l o t t i n g p a p e r ,

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h o w to dunk a d o u g h n u t

t h o u g h , it is s e m i - e m p i r i c a l . To u s e it in t h e s e c i r c u m s t a n c e s , we n e e d to be a b l e to i n t e r p r e t R. R is a r a d i u s , b u t of w h a t ? T h e best t h a t we c a n do is to i n t e r p r e t it as an "effective" radius, a sort of a v e r a g e r a d i u s of all t h e p o r e s a n d c h a n n e l s . O n e c a n try to assess t h e v a l u e of this effective r a d i u s by m e a s u r i n g a s m a n y c h a n n e l s a s possible u n d e r a m i c r o s c o p e a n d t a k i n g an a v e r a g e , b u t t h e r e is a s i m p l e r way, using t h e e x p e r i m e n t a l g r a p h for c o o k i e d u n k i n g . T h e slope of this g r a p h can b e u s e d t o c a l c u l a t e t h e effective r a d i u s via t h e W a s h b u r n e q u a t i o n . W h e n I tried t h e c a l c u l a t i o n , t h o u g h , t h e results didn't seem to m a k e sense. T h e effective radii of t h e c h a n n e l s in d u n k e d cookies, calculated from t h e W a s h b u r n e q u a t i o n , w e r e 6 8 , 8 8 , a n d 110 n a n o m e t e r s for t h e soft a n d c r u m b l y , m e d i u m , a n d h a r d c o o k ies respectively. T h e s e radii are v e r y small. T h e calculated dia m e t e r s are h u n d r e d s , o r e v e n t h o u s a n d s o f t i m e s s m a l l e r t h a n t h e size of t h e h o l e s t h a t c a n be s e e n in a dry c o o k i e u n der the microscope, w h i c h are measurable in micrometers (a m i c r o m e t e r i s o n e t h o u s a n d t i m e s bigger t h a n a n a n o m e t e r ) . So what's going o n ? The answer seems to be that the structure of a w e t c o o k i e is v e r y different from t h a t of a dry c o o k i e . In a dry c o o k i e , t h e starch is in t h e form of s h r u n k e n , d r i e d - u p g r a n u l e s . T h e s e a r e q u i t e tiny. In rice ( w h i c h is a l m o s t p u r e s t a r c h ) , for e x a m p l e , t h e r e a r e t h o u s a n d s of tiny g r a n u l e s in e v e r y single visible g r a i n . W h e n t h e s e g r a n u l e s c o m e into c o n tact w i t h h o t w a t e r , t h e y swell dramatically, t a k i n g in w a t e r as avidly as an a t h l e t e d u r i n g a m a r a t h o n . As it h a p p e n s , my coll e a g u e s a n d I h a d s t u d i e d t h e swelling p r o c e s s , w h i c h is v e r y i m p o r t a n t i n t h e p r e s e r v a t i o n , processing, a n d r e c o n s t i t u t i o n of s t a r c h y foods. We h e l d single p o t a t o starch g r a n u l e s in w a ter w h i l e w e g r a d u a l l y raised t h e t e m p e r a t u r e o f t h e w a t e r , watching w h a t h a p p e n e d t h r o u g h a microscope. At a r o u n d 60°C t h e g r a n u l e s s u d d e n l y i n c r e a s e d t h e i r v o l u m e b y u p t o s e v e n t y t i m e s , p r o d u c i n g w h a t I s u b s e q u e n t l y described in a r a d i o i n t e r v i e w a s t h e w o r l d ' s smallest p o t a t o p a n c a k e s . T h e starch g r a n u l e s i n cookies swell similarly w h e n t h e c o o k i e s a r e d i p p e d i n t o h o t tea. T h e s w o l l e n , c r i n k l e d g r a n u l e s

the art a n d s c i e n c e of d u n k i n g

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b e c o m e v e r y soft, w h i c h is o n e of t h e r e a s o n s w h y a d u n k e d cookie puffs u p a n d e v e n t u a l l y d i s i n t e g r a t e s ( t h e o t h e r r e a s o n i s t h a t t h e fat a n d s u g a r " g l u e " b e t w e e n t h e g r a n u l e s m e l t s a n d dissolves). T h e g r a n u l e s t h a t w e w e r e s t u d y i n g b e c a m e s o soft t h a t t h e y c o u l d b e s u c k e d i n t o glass t u b e s w h o s e d i a m e t e r s w e r e t h r e e t i m e s smaller. This d e f o r m a b i l i t y s e e m s t o b e t h e e x p l a n a t i o n for t h e e x t r a o r d i n a r i l y l o w v a l u e s of t h e effective c h a n n e l r a d i u s calculated from t h e W a s h b u r n e q u a t i o n for d u n k e d c o o k i e s — t h e softened g r a n u l e s s q u e e z e u p against e a c h o t h e r like rock fans at a c o n c e r t , l e a v i n g o n l y t h e n a r r o w e s t of g a p s in b e t w e e n . In practice, it's j u s t as well. If t h e p o r e s stayed a t t h e i r original "dry c o o k i e " size, t h e W a s h b u r n e q u a t i o n predicts t h a t a c o o k i e w o u l d fill up w i t h tea or coffee in a fraction of a s e c o n d , a n d c o o k i e d u n k i n g , u n l i k e d o u g h n u t d u n k i n g , w o u l d b e c o m e a m a t t e r of s p l i t - s e c o n d t i m i n g . As il is, t h e W a s h b u r n e q u a t i o n n o t o n l y e x p l a i n s w h y c o o k ies d u n k e d b y t h e "flat-on" scientific m e t h o d can b e d u n k e d lor l o u r t i m e s as l o n g as w i t h t h e c o n v e n t i o n a l m e t h o d — it can also be used to predict h o w l o n g a c o o k i e m a y safely be d u n k e d b y t h o s e w h o prefer a m o r e c o n v e n t i o n a l a p p r o a c h . O n l y o n e a s s u m p t i o n is n e e d e d — t h a t t h e c o o k i e will n o t fall apart so long as a t h i n layer r e m a i n s dry a n d sufficiently s t r o n g t o s u p p o r t t h e w e i g h t o f t h e w e t part. B u t h o w t h i n can this layer b e ? T h e r e w a s o n l y o n e w a y t o f i n d o u t , a n d t h a t w a s b y m e a s u r i n g t h e b r e a k i n g s t r e n g t h o f d r y cookies t h a t h a d b e e n t h i n n e d d o w n . I c o n s e q u e n t l y g r o u n d d o w n a r a n g e of c o o k ies on t h e Physics D e p a r t m e n t ' s belt sander, a process t h a t covered m e w i t h c o o k i e d u s t a n d c a u s e d m u c h a m u s e m e n t a m o n g w o r k s h o p staff, w h o w e r e m o r e u s e d t o m a n u f a c t u r ing precision p a r t s for a s t r o n o m i c a l i n s t r u m e n t s . W h o l e dry cookies, I f o u n d , could s u p p o r t up to t w o kilograms of weight w h e n clamped horizontally at one end with t h e w e i g h t placed o n t h e o t h e r e n d . T h e t h i n n e d - d o w n d r y cookies w e r e s t r o n g i n p r o p o r t i o n t o t h e i r w e i g h t , a n d c o u l d be r e d u c e d to t w o p e r c e n t of t h e i r original t h i c k n e s s a n d still be strong e n o u g h to support the weight of an otherwise saturated cookie ( b e t w e e n t e n a n d t w e n t y g r a m s , d e p e n d i n g o n

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t h e c o o k i e t y p e ) . All t h a t w a s n e e d e d n o w w a s t o calculate h o w l o n g t h e cookies could h e d u n k e d w h i l e still leaving a t h i n d r y layer, e i t h e r in t h e m i d - p l a n e of t h e c o o k i e for a c o n v e n t i o n a l d u n k or on t h e u p p e r surface of t h e c o o k i e for a "scientific" d u n k . T h e calculation w a s easily d o n e u s i n g t h e W a s h b u r n e q u a t i o n p l u s t h e v a l u e s o f t h e effective c h a n n e l r a d i u s for different c o o k i e s . For m o s t cookies, t h e a n s w e r c o m e s o u t at b e t w e e n 3.5 s e c o n d s a n d 5 s e c o n d s for a c o n v e n t i o n a l d u n k , a n d b e t w e e n 14 a n d 20 s e c o n d s for a "scientific" d u n k . Was t h e r e a n y t h i n g else t o c o n s i d e r ? T h e o n l y t h i n g r e m a i n ing w a s to e x a m i n e t h e b r e a k i n g p r o c e s s itself. T h e physics of h o w m a t e r i a l s ( i n c l u d i n g cookies) b r e a k i s q u i t e c o m p l i c a t e d . T h e u n d e r l y i n g c o n c e p t , t h o u g h , is relatively s i m p l e (as a r e q u i t e a few scientific c o n c e p t s — t h e e x p e r t i s e conies in w o r k ing o u t t h e i r c o n s e q u e n c e s i n d e t a i l ) . T h e c o n c e p t h e r e i s t h a t w h e n a crack starts all of t h e stress is c o n c e n t r a t e d at t h e s h a r p tip o f t h e crack, i n t h e s a m e w a y t h a t w h e n s o m e o n e w e a r i n g stiletto h e e l s steps on y o u r t o e , all of t h e painful p r e s s u r e is c o n c e n t r a t e d at t h e tip of t h e h e e l . If t h e stress is sufficient to start a crack, it is sufficient to finish t h e j o b . T h a t is w h y brittle m a t e r i a l s ( i n c l u d i n g dry cookies) b r e a k c o m p l e t e l y o n c e a b r e a k h a s s t a r t e d . T h e stress t h a t is n e e d e d to d r i v e a crack d e p e n d s o n t h e s h a r p n e s s o f t h e crack tip. T h e s h a r p e r t h e tip, t h e less stress is n e e d e d , in t h e s a m e w a y t h a t a light p e r s o n w e a r i n g a stiletto h e e l c a n p r o d u c e as m u c h p a i n as a h e a v i e r person wearing a wider heel. It would seem, then, that even t h e tiniest scratch could p o t e n t i a l l y g r o w i n t o a c a t a s t r o p h i c b r e a k , n o m a t t e r h o w s t r o n g t h e m a t e r i a l , s o long a s t h e tip o f t h e scratch w a s sufficiently s h a r p . E n g i n e e r s u p t o t h e e n d o f t h e S e c o n d World W a r k n e w from practical e x p e r i e n c e t h a t t h e r e m u s t b e s o m e t h i n g w r o n g w i t h this theory, or else a s a b o t e u r could h a v e c a u s e d L o n d o n ' s Tower Bridge to collapse i n t o t h e T h a m e s by s c r a t c h i n g it w i t h a pin. E v e n t h o u g h e x p e r i e n c e s h o w e d t h a t this w o u l d n ' t h a p p e n , e n g i n e e r s still m a s s i v e l y o v e r - d e s i g n e d s t r u c t u r e s like bridges a n d ships — j u s t in case. E v e n so, t h e r e w e r e occasions


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w h e n t h e t h e o r y t o o k over. O n e s u c h e x a m p l e w a s w h e n a n additional p a s s e n g e r e l e v a t o r w a s f i t t e d t o t h e W h i t e Star liner Majestic in 1 9 2 8 . Stresses c o n c e n t r a t e d at t h e s h a r p c o r n e r of the n e w , s q u a r e h o l e i n t h e deck w h e r e t h e e l e v a t o r w a s situated d r o v e a crack across t h e deck a n d d o w n t h e side of t h e ship, w h e r e it fortuitously s t r u c k a p o r t h o l e (providing a r a t h e r m o r e r o u n d e d tip), w i t h o u t w h i c h t h e ship c a r r y i n g 3,000 p a s sengers w o u l d h a v e b e e n lost s o m e w h e r e b e t w e e n N e w York a n d S o u t h a m p t o n . In o t h e r cases, s u c h as t h a t of t h e USS Schenectady, ships h a v e actually b e e n t o r n in half (Figure 1.5).

F i g u r e 1.5: C r a c k F o r m a t i o n o n a G r a n d S c a l e : the Schenectady D i s a s t e r . In January 1943 the one-day-old 12 tanker SS Schenectady had just returned to harbor after sea trials when there was a huge bang, and the vessel fractured from top to bottom, jackknifing so that the bow and stern settled to the river bottom while the center rose clear of the water. Photograph reproduced with permission from B, B, Rath, Naval Research Institute.

S h a r p c o r n e r s a r e n o w r o u n d e d w h e r e possible t o avoid stress c o n c e n t r a t i o n effects. W e also u n d e r s t a n d m o r e a b o u t

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h o w to d u n k a

doughnut

t h e m e c h a n i s m s t h a t s t o p small cracks from g r o w i n g , w h i c h i n v o l v e plastic (i.e. plasticine-like) flow of t h e m a t e r i a l at t h e tip of t h e crack, so t h a t t h e tip b e c o m e s slightly r o u n d e d a n d less s h a r p . T h e p r o c e s s c a n b e e n c o u r a g e d b y t h e i n c o r p o r a t i o n of c r a c k - s t o p p e r s . T h e s e a r e soft c o m p o n e n t s in a m i x e d ( c o m p o s i t e ) m a t e r i a l w h o s e f u n c t i o n is to stop cracks from g r o w i n g . W h e n a t r a v e l i n g crack hits a particle of crackstopper, t h e c r a c k - s t o p p e r "gives," t u r n i n g t h e crack tip from s h a r p t o b l u n t a n d r e d u c i n g t h e stress c o n c e n t r a t i o n t o b e l o w a safe limit. T h e u l t i m a t e c r a c k - s t o p p e r is an a c t u a l h o l e , s u c h as t h e p o r t h o l e in t h e Majestic. M o d e r n composite materials, such as those used for t h e m a n u facture of jet e n g i n e s , r o u t i n e l y c o n t a i n " c r a c k - s t o p p e r s . " C o o k i e s are also c o m p o s i t e m a t e r i a l s , a n d also c o n t a i n cracks t o p p e r s . T h e c r a c k - s t o p p e r s a r e n a t u r a l m a t e r i a l s like sugar, starch, a n d (especially) fat, w h i c h , a l t h o u g h h a r d , still h a v e s o m e "give." As a result, m o s t c o o k i e s a r e r e m a r k a b l y r o b u s t , u n t i l t h e y a r e t h i n n e d t o o far. T h e n t h e " g r a i n i n e s s " o f t h e c o o k i e t a k e s over. W h e n a c o o k i e b e c o m e s as t h i n as t h e dia m e t e r of t h e i n d i v i d u a l g r a i n s , t h e s e p a r a t i o n of a n y t w o g r a i n s is sufficient to reveal t h e void below, a n d t h e c o o k i e falls a p a r t . T h e r e is a s o l u t i o n e v e n to this p r o b l e m — a t w o d i m e n s i o n a l c r a c k - s t o p p e r . T h a t c r a c k - s t o p p e r is c h o c o l a t e , a m a t e r i a l t h a t "gives" slightly w h e n a n a t t e m p t i s m a d e t o b r e a k it, a n d w h i c h can be ( a n d is) often used to c o v e r part or all of a c o o k i e surface. Our eventual r e c o m m e n d a t i o n to the advertisers was that basic physics p r o v i d e s t h e u l t i m a t e a n s w e r t o t h e perfect c o o k i e d u n k . T h a t a n s w e r is to u s e a c o o k i e c o a t e d on o n e side w i t h c h o c o l a t e , k e e p t h e c h o c o l a t e side u p p e r m o s t a s y o u d u n k t h e physicists' w a y , a n d t i m e t h e d u n k s o t h a t t h e t h i n layer of c o o k i e u n d e r t h e c h o c o l a t e stays dry. T o m y c o n s i d e r a b l e surprise, t h e story w a s t a k e n u p avidly by the media, with the Washburn equation as the centerpiece. T h e idea of a p p l y i n g an e q u a t i o n to s o m e t h i n g as h o m e l y as c o o k i e d u n k i n g m a d e a great hit w i t h j o u r n a l i s t s . T h o s e w h o


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p u b l i s h e d t h e e q u a t i o n took g r e a t c a r e to get it right; s o m e even t e l e p h o n e d several times to double-check. Only o n e failed t o c h e c k , a n d t h e y got i t w r o n g , p r o v o k i n g t h e following letter: D e a r Sir, 1 think there is something w r o n g with y o u r cookie-dunking e q u a t i o n . Please s e n d m e s o m e c o o k i e s for n o t i c i n g t h i s . C h a o Q u a n (aged 12)

U n f o r t u n a t e l y , b y t h e t i m e t h e letter arrived, m y c o l l e a g u e s a n d I h a d e a t e n all t h e c o o k i e s . W h y should an eighty-year-old equation become the center of a n e w s s t o r y ? At t h e i n v i t a t i o n of t h e j o u r n a l Nature, I tried t o find a n a n s w e r . M y c o n c l u s i o n w a s : S u c h j o u r n a l i s t i c e x c i t e m e n t o v e r a n e q u a t i o n c o n t r a d i c t s thenormal publisher's advice to a u t h o r s — that every additional e q u a t i o n h a l v e s t h e sales o f a p o p u l a r s c i e n c e h o o k . W h y w a s this so? Let m e s u g g e s t a n a n s w e r , r e l e v a n t t o t h e s h a r i n g o f m o r e s e r i o u s s c i e n c e . Scientists a r e s e e n b y m a n y a s t h e i n h e r i tors o f t h e a n c i e n t p o w e r o f t h e k e y s , t h e o w n e r s a n d c o n t r o l l e r s of seemingly forbidden k n o w l e d g e . Equations are o n e key to that k n o w l e d g e . The excitement of journalists in gaining control of a k e y w a s s u r e l y a m a j o r factor in t h e i r s y m p a t h e t i c p r o m o t i o n of t h e story. By m a k i n g t h e W a s h b u r n e q u a t i o n accessible, I w a s able t o e n s u r e t h a t j o u r n a l i s t s u n f a m i l i a r w i t h s c i e n c e c o u l d use the key to unlock Pandora's box.

T h e science o f d u n k i n g m a y s e e m trivial, a n d i n o n e s e n s e i t is. Scientists' q u e s t i o n s often s e e m like a child's idle curiosity, t h e sort o f t h i n g t h a t w e s h o u l d h a v e o u t g r o w n w h e n w e r e a c h e d a d u l t h o o d , s o t h a t w e could c o n c e n t r a t e o n m o r e serious t h i n g s like m a k i n g m o n e y o r w a g i n g war. T o myself a n d o t h e r scientists, t h o u g h , a s k i n g " w h y ? " i s o n e o f t h e m o s t

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s e r i o u s t h i n g s t h a t w e c a n d o . S o m e t i m e s w e try t o justify i t b y practical o u t c o m e s . To m e , t h a t is a big m i s t a k e , w h e t h e r t h e o u t c o m e is landing a m a n on the m o o n or finding a better w a y to d u n k a c o o k i e . T h e real r e a s o n t h a t a scientist asks " w h y ? " i s b e c a u s e h e o r s h e s h a r e s w i t h t h e rest o f t h e c o m m u n i t y t h e m o s t basic of h u m a n a s p i r a t i o n s — w a n t i n g to u n d e r s t a n d t h e w o r l d a n d h o w it w o r k s . As m e m b e r s of a t h i n k i n g species, we all h a v e s u c h a s p i r a t i o n s , a n d e x p r e s s t h e m e v e r y t i m e w e p o n d e r religious beliefs, o r o u r r e l a t i o n s h i p s w i t h o t h e r p e o p l e , or feelings of a n y k i n d . Scientists find a similar s e n s e of e x c i t e m e n t in a d d r e s s i n g a p a r t i c u l a r a r e a of life's g r e a t c a n vas — t h e b e h a v i o r of t h e m a t e r i a l w o r l d . In c o m p e n s a t i o n for t h e n a r r o w n e s s of o u r c o m p a s s , scientists h a v e g o t t e n f u r t h e r i n u n d e r s t a n d i n g t h e m a t e r i a l w o r l d t h a n psychologists, p h i l o s o p h e r s , a n d t h e o l o g i a n s h a v e i n their attempts to u n d e r s t a n d people and their relationships w i t h e a c h o t h e r o r w i t h t h e w o r l d . I t h a s often h a p p e n e d (as i n t h e case o f Laplace) t h a t q u e s t i o n s a b o u t c o m m o n p l a c e p h e n o m e n a h a v e p r o d u c e d answers to other, and sometimes m o r e i m p o r t a n t , q u e s t i o n s . I n t h e rest o f this b o o k , t h e science of t h e c o m m o n p l a c e is u s e d to o p e n d o o r s for n o n - s c i e n t i s t s . It h a s often o p e n e d d o o r s for scientists as well.

2 how d o e s a scientist boil a n e g g ? T h e single egg, in t h e dark blue egg cup with a gold ring a r o u n d t h e top, was boiled for three dud a third m i n u t e s . It was a very fresh, speckled b r o w n egg from French M a r a n s b e n s o w n e d by s o m e friends of M a y in t h e country. Bond disliked w h i t e eggs a n d , faddish as he was in m a n y small things, it a m u s e d h i m to m a i n t a i n that t h e r e w a s such a thing as t h e perfect boiled egg. Ian Fleming, From Russia with Love

Energy, we n o w b e l i e v e , is t h e u l t i m a t e stuff of t h e u n i v e r s e . It c o m e s in v a r i o u s f o r m s — h e a t , light, m i c r o w a v e s , electricity, a n d so o n . All of t h e s e forms h a v e o n e t h i n g in c o m m o n : t h e y can b e u s e d t o m o v e t h i n g s . This e v e n applies t o d o m e s t i c c o o k i n g , w h e r e t h e e n e r g y (usually in t h e form of h e a t ) t h a t we p u t i n t o t h e food d o e s its j o b b y m o v i n g t h e m o l e c u l e s i n t h e food, w h i c h wiggle a n d r e a r r a n g e t h e m s e l v e s t o m a k e food m o r e digestible a n d w i t h a m o r e p a l a t a b l e t e x t u r e . H o w it d o e s this w a s t h e subject of a very i n t e r e s t i n g m e e t i n g t h a t I a t t e n d e d in Sicily, w h e r e scientists a n d chefs w o r k e d j o i n t l y to establish t h e best w a y s of d e livering h e a t e n e r g y to t h e p a r t s of t h e food w h e r e it m a t t e r e d . This c h a p t e r gives t h e story of t h a t m e e t i n g , a n d t h e story of e n e r g y itself. For t h o s e r e a d e r s w i t h a n e y e t o w a r d s practical v a l u e , it also gives t h e scientific rules for t h e best w a y to boil an egg. James Bond is not the only g o u r m e t to h a v e pursued t h e perfect boiled egg. If he h a d d r i v e n his 1930 4/2-liter gray s u p e r c h a r g e d B e n t l e y c o u p e u p t h e tightly folded m o u n t a i n r o a d t h a t scars t h e e a s t e r n flank of Sicily's M o n t e San G i u l i a n o , t h e fluttering g r o w l of its t w i n e x h a u s t s w o u l d e v e n t u a l l y h a v e e c h o e d from t h e a n c i e n t walls of t h e village of Erice, r u m o r e d t o b e t h e f o r m e r h e a d q u a r t e r s o f t h e Mafia. T h e s e days, B o n d

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w o u l d h a v e e n c o u n t e r e d a different sort of mafia — t h e gast r o n o m i c k i n d , a n i n t e r n a t i o n a l g r o u p o f chefs a n d scientists w h o m e e t e v e r y t w o y e a r s i n t h e E t t o r e M a j o r a n a C e n t e r lor Scientific C u l t u r e to look for w a y s of u s i n g science to e x t e n d t h e h o r i z o n s of g a s t r o n o m y . T h e r e , in t h e y e a r 1997, B o n d w o u l d h a v e f o u n d t h e a n s w e r t o his q u e s t . B o n d w o u l d h a v e b e e n s e v e n t y - n i n e y e a r s old; t e n y e a r s y o u n g e r t h a n Nicholas Kurti, t h e f o r m e r Oxford p h y s i c s p r o lessor w h o i n s p i r e d t h e m e e t i n g s . Nicholas, a t e i g h t y - n i n e , w a s still l o o k i n g for n e w c h a l l e n g e s w i t h an e n e r g y t h a t w a s a t r i b u t e to his lifetime's d e v o t i o n to t h e p l e a s u r e s of t h e table. I h a d t r a v e l e d w i t h h i m from E n g l a n d , puffing in t h e w a k e of his small, b a l d i n g figure as we raced across t h e c o n c o u r s e of Milan airport to catch a c o n n e c t i n g flight to P a l e r m o . His p r o g r e s s s e e m e d u n i m p e d e d by a b a c k p a c k lull of t h e r m o c o u p l e s a n d r e c o r d e r s lor following t h e t e m p e r a t u r e c h a n g e s in food as it w a s c o o k e d . Nicholas w a s fond of d e c l a i m i n g t h a t " w e k n o w m o r e a b o u t t h e t e m p e r a t u r e d i s t r i b u t i o n i n t h e atm o s p h e r e of V e n u s t h a n we do a b o u t t h e i n t e r i o r of a souffle," a n d this m e e t i n g w a s a n o p p o r t u n i t y t o correct t h e b a l a n c e . I t w a s not Nicholas's f i r s t v e n t u r e i n t o c o m b i n i n g science w i t h c o o k i n g . H e w a s o n e o f t h e f i r s t television c o o k s i n t h e U.K., p r e s e n t i n g as e a r l y as 1969 on b l a c k - a n d - w h i t e television a live p r o g r a m called The Physicist in the Kitchen, in w h i c h he produced some surprising variants on traditional cooking m e t h o d s . He u s e d a h y p o d e r m i c syringe, for e x a m p l e , to inject b r a n d y directly i n t o h o t m i n c e pies s o a s t o avoid d i s t u r b i n g t h e crust. H e also d e m o n s t r a t e d a n original t e c h n i q u e for m a k i n g m e r i n g u e s , w h e r e h e p u t dollops o f c r e a m y m e r i n g u e m i x t u r e o n t o plates i n a v a c u u m j a r a n d t h e n t u r n e d o n t h e p u m p . T h e dollops f o a m e d u p t o p r o d u c e m e r i n g u e s t h a t w e r e a s h a r d a n d brittle a s a n y p r e p a r e d i n a n o v e n , b u t w h i c h t o o k a q u a r t e r of t h e t i m e to m a k e a n d m e l t e d in t h e m o u t h . 1

Nicholas w a s a l o w - t e m p e r a t u r e physicist, f a m o u s for o n c e 1

Nicholas Kurti, CBE, FRS, died in November 1998, shortly after his ninetieth birthday. This chapter is dedicated to his memory.

h o w d o e s a scientist boil an e g g ?

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h a v i n g held t h e w o r l d r e c o r d for t h e l o w e s t t e m p e r a t u r e e v e r a c h i e v e d in t h e l a b o r a t o r y . His fame a m o n g scientists p r o v e d useful w h e n it c a m e to p r o m o t i n g a series of m e e t i n g s on t h e science of g a s t r o n o m y , c o n c e i v e d as a result of a c o n v e r s a t i o n b e t w e e n t h e San Francisco c o o k i n g t e a c h e r Elizabeth T h o m a s a n d a n Italian scientist w h o h a p p e n e d t o b e a t t e n d i n g a m e e t ing w i t h Elizabeth's h u s b a n d at t h e E t t o r e M a j o r a n a C e n t e r , a sel of c o n v e r t e d m o n a s t e r i e s in Erice, on q u i t e a different s u b ject. T h e d i r e c t o r w a s k e e n o n t h e idea, a n d p r o m p t l y a s k e d Elizabeth to o r g a n i z e s u c h a m e e t i n g . Elizabeth suggested t h a t Nicholas, an old friend a n d a l e a d i n g figure at m a n y Erice m e e t i n g s , w o u l d b e t h e ideal scientific link. T h e o n l y p r o b l e m w a s t h e title. A series on "The Science of C o o k i n g " s e e m e d r a t h e r out of k e e p i n g in a place used for h o s t i n g discussions on major q u e s t i o n s like " P l a n e t a r y E m e r g e n c i e s " a n d "The M a t h ematics of D e m o c r a c y . " Nicholas, e v e r t h e p r a g m a t i s t , suggested t h e m o r e i m p r e s s i v e title " M o l e c u l a r a n d Physical G a s t r o n o m y , " a n d t h e Erice series of m e e t i n g s w a s b o r n . The M a j o r a n a C e n t e r t u r n e d o u t t o b e a n excellent e n v i r o n m e n t . T h e m e e t i n g r o o m , w h i c h holds a b o u t forty (the u p p e r limit for o u r m e e t i n g s ) , lies on o n e side of a flagstone c o u r t y a r d . On t h e opposite side of t h e c o u r t y a r d is t h e old m o n a s t e r y k i t c h e n , n o w m o d e r n i z e d so t h a t ideas arising in t h e c o u r s e of t h e m e e t i n g o r t h o s e p r o p o s e d b e f o r e h a n d could b e tried o u t . T h e m e e t i n g title h a s also t u r n e d o u t to be a g o o d o n e , a n d h a s b e e n w i d e l y a d o p t e d o u t s i d e t h e c o n f i n e s of Erice. Its v a l u e is that it a c c u r a t e l y reflects o u r a p p r o a c h to g a s t r o n o m y , w h i c h is to focus n o t on t h e w h o l e g a s t r o n o m i c e x p e r i e n c e ( t h a t is t h e responsibility of t h e chef), but on w h a t is h a p p e n i n g to t h e food at t h e m o l e c u l a r level. T h e p r o b l e m of p r o d u c i n g a perfect boiled egg, for e x a m p l e , is a p r o b l e m of c o n v i n c i n g t h e string-like a l b u m i n p r o t e i n m o l e c u l e s in t h e w h i t e of t h e egg t o b e c o m e e n t a n g l e d w h i l e leaving similar m o l e c u l e s i n t h e yolk in t h e i r n a t i v e , u n e n t a n g l e d state. This is a m a t t e r of getting t h e right a m o u n t o f h e a t t o t h e right place. J u s t h o w t o d o this is t h e c e n t r a l p r o b l e m , not just of egg-boiling ( w h i c h w a s

26


n o t e v e n o n t h e a g e n d a w h e n w e b e g a n o u r 1997 m e e t i n g ) , b u t of c o o k i n g in g e n e r a l . T h e t r a n s p o r t of h e a t is a m a t t e r of physics, b u t its r u l e s a r e so s i m p l e t h a t no scientific t r a i n i n g is n e e d e d to u n d e r s t a n d t h e m . T o w o r k o u t h o w t h e rules a p p l y t o practical c o o k i n g p r o b l e m s , t h o u g h , it is n e c e s s a r y to u n d e r s t a n d h o w h e a t affects food flavor a n d t e x t u r e , a n d this i n t u r n m e a n s u n d e r s t a n d i n g w h a t h e a t is. U n f o r t u n a t e l y for e a s e of c o m m u n i c a tion b e t w e e n chefs a n d scientists, t h e t r u e n a t u r e o f h e a t i s n o t readily u n d e r s t a n d a b l e i n c o m m o n s e n s e t e r m s . I t w a s t i m e for a s h o r t h i s t o r y lesson. Luckily, it w a s o n e in w h i c h food e n tered in unexpected a n d even entertaining ways. Until t h e m i d d l e o f t h e n i n e t e e n t h c e n t u r y , h e a t w a s believed to be an actual fluid. This w a s a perfectly r e a s o n a b l e , c o m m o n sense view, since h e a t is clearly able to "flow" from h o t t e r to colder places, a n d it is difficult to i m a g i n e this h a p p e n i n g u n less h e a t is a real fluid. T h e fluid e v e n h a d a n a m e — caloric — a n d it w a s believed t h a t " t h e s e n s a t i o n of h e a t is c a u s e d by particles of caloric passing i n t o o u r bodies." T h e c o m m o n s e n s e pict u r e of h e a t as caloric a c c o u n t e d for a lot of t h e k n o w n facts. Addition of caloric to an u n c o o k e d piece of m e a t w o u l d , likewise, p r o d u c e a different m a t e r i a l : t h e c o o k e d v e r s i o n . A l t h o u g h caloric lived o n i n t o t h e m i d - n i n e t e e n t h c e n t u r y , its d e a t h knell w a s s o u n d e d s o m e f i f t y y e a r s earlier b y t h e American adventurer Benjamin Thompson, a man w h o s e pers o n a l a n d scientific lives w e r e b o t h i n f l u e n c e d b y s o m e u n usual e n c o u n t e r s w i t h food. W h e n h e w a s i n his t w e n t i e s , a n d in c o m m a n d of British t r o o p s d u r i n g t h e A m e r i c a n W a r of Ind e p e n d e n c e , his soldiers u s e d t o m b s t o n e s from a c e m e t e r y to build a b r e a d o v e n . S o m e of t h e loaves w e r e d i s t r i b u t e d to m e m b e r s o f t h e local c o m m u n i t y , u n f o r t u n a t e l y w i t h t h e epit a p h s o f t h e i r d e a d relatives b a k e d b a c k w a r d s i n t o t h e crusts. After this "it w a s c o n s i d e r e d p r u d e n t t h a t h e s h o u l d seek a n early o p p o r t u n i t y o f l e a v i n g t h e c o u n t r y . " H e m o v e d t o E n gland, w h e r e his t a l e n t for p e r s o n a l a d v a n c e m e n t p r o v e d s o g r e a t t h a t h e b e c a m e u n d e r s e c r e t a r y o f state w i t h i n four


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years, a n d a Fellow of t h e Royal Society for his r e s e a r c h i n t o g u n p o w d e r , firearms, a n d n a v a l signaling. M o v i n g t o m a i n l a n d E u r o p e , h e a c q u i r e d t h e title o f C o u n t R u m f o r d , C o u n t o f t h e Holy R o m a n E m p i r e , a n d b e c a m e M i n ister of W a r for B a v a r i a . It w a s in this capacity t h a t he c a m e to be in charge of the M u n i c h arsenal w h e n he m a d e the famous o b s e r v a t i o n s t h a t led to his d e v a s t a t i n g dismissal of caloric. In his o w n w o r d s : Being engaged . . . in superintending the boring of cannon, I was struck with the very considerable degree of Heat which a brass gun acquires, in a short time, in being bored; and with the still more intense Heat (much greater than that of boiling water, as I found by experiment) of the metallic chips . . . the source of the Heat generated by friction, in these Experiments, appears to be inexhaustible. It is hardly necessary to add, that anything which any insulated body . . . can continue to furnish without limitation, cannot possibly be a material substance; and it appears to me to be extremely difficult, if not quite impossible, to form any distinct idea of anything, capable of being excited and communicated, in the manner that Heat was excited and communicated in these Experiments, except it be MOTION. Rumford's c o n c e p t i o n of h e a t as m o t i o n is n o w c o m m o n p l a c e a m o n g scientists. We t h i n k of t h e effect of h e a t on a food, for instance, largely in t e r m s of t h e i n c r e a s e d mobility of t h e m o l ecules i n t h e food, w h i c h c o n s e q u e n t l y b e c o m e r e a r r a n g e d a n d d i s r u p t e d . T h e l o n g a l b u m i n m o l e c u l e s in t h e w h i t e of a boiled egg, for e x a m p l e , w h i c h exist as loosely folded balls at r o o m t e m p e r a t u r e , unfold a n d w a v e a r o u n d a s t h e egg gets hotter, e v e n t u a l l y b e c o m i n g e n t a n g l e d a n d c r e a t i n g a t h r e e d i m e n s i o n a l n e t w o r k w h i c h t r a p s t h e w a t e r i n t h e egg w h i t e , t u r n i n g it from liquid to solid a n d from t r a n s p a r e n t to o p a q u e . C o m p u t e r s i m u l a t i o n s are n o w available t h a t d e m o n s t r a t e such m o l e c u l a r r e a r r a n g e m e n t s i n g r a p h i c detail. N o a m o u n t °f p i c t u r e s q u e detail, t h o u g h , will a n s w e r a f u n d a m e n t a l

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h o w to d u n k a

doughnut

question. Heat is o n e thing. Motion seems to be something totally different. H o w could t h e t w o possibly b e r e l a t e d ? T h e s o l u t i o n to this p r o b l e m r e q u i r e d a l e a p of i m a g i n a t i o n at least as brilliant as t h a t r e q u i r e d for t h e d e v e l o p m e n t of q u a n t u m m e c h a n i c s or t h e T h e o r y of Relativity. Yet, w h i l e e v e r y o n e h a s h e a r d of Einstein, few h a v e h e a r d of J u l i u s M a y e r , t h e failed G e r m a n p h y s i c i a n w h o l i n k e d h e a t a n d m o tion t h r o u g h t h e c o n c e p t of energy. T h e full story of M a y e r ' s d e s p a i r i n g efforts to get his ideas accepted, c u l m i n a t i n g in his a t t e m p t e d suicide, is given in A p p e n d i x 1 at t h e e n d of this b o o k . Suffice it to say h e r e t h a t his ideas w e r e e v e n t u a l l y a c c e p t e d , e v e n t h o u g h t h e credit often goes t o o t h e r s , a n d t h e n o t i o n o f " e n e r g y " n o w u n d e r p i n s t h e w h o l e of s c i e n c e . W h a t is " e n e r g y " ? Luckily for e a s e of c o m m u n i c a t i o n , t h e scientist's definition i s v e r y close t o t h e w a y i n w h i c h w e u s e t h e w o r d i n e v e r y d a y s p e e c h . P u t simply, " e n e r g y " i s a n y t h i n g t h a t c a n b e m a d e t o p e r f o r m physical w o r k , i.e., t o m o v e s o m e t h i n g . T h e m o r e e n e r g y w e h a v e , t h e m o r e w e can m o v e , a n d t h e f u r t h e r we c a n m o v e it. A b e a m of light, for e x a m p l e , c a n be used to spin a t i n y w i n d m i l l k n o w n as a C r o o k e ' s rad i o m e t e r . Light, t h e n , is a form of e n e r g y , j u s t as h e a t , electricity, m a g n e t i s m , a n d gravity a r e also f o r m s of e n e r g y , all of w h i c h can be u s e d to d r i v e different t y p e s of e n g i n e . M o v e m e n t itself is a f o r m of e n e r g y , since o n e m o v i n g object m a y be u s e d to m o v e a s e c o n d o n e . E n e r g y of m o t i o n h a s its o w n n a m e — kinetic e n e r g y . W h e n we h e a t food, as Nicholas Kurti pointed out, t h e increased kinetic energy of the individual food m o l e c u l e s lets t h e m w o r k h a r d e r t o v i b r a t e , wriggle, a n d strive t o b r e a k free from t h e i r m o o r i n g s , e v e n t u a l l y u n d e r g o ing c h a n g e s t h a t u s u a l l y m a k e t h e food m o r e p a l a t a b l e . T h e c o n c e p t of h e a t as t h e e n e r g y of m o l e c u l a r m o t i o n lets us understand m a n y of the events in cooking that would have b e e n a p u z z l e to believers in caloric. If it is t r u e t h a t caloric + r a w food = c o o k e d food, t h e n t h e a d d i t i o n of caloric at a n y t e m p e r a t u r e s h o u l d e v e n t u a l l y cook t h e food. Yet a n egg c a n be left in w a t e r at 50°C for h o u r s w i t h o u t t h e w h i t e setting,


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w h i l e if t h e t e m p e r a t u r e is raised to 70°C t h e w h i t e will set w i t h i n a q u a r t e r of an h o u r ; a t i m e t h a t r e d u c e s to t h e classic t h r e e m i n u t e s or so if t h e t e m p e r a t u r e is raised to iOO°C, t h e t e m p e r a t u r e of boiling w a t e r . This t e m p e r a t u r e effect — i n e x p l i c a b l e u s i n g t h e c o m m o n sense caloric p i c t u r e of old — is easily a c c o u n t e d for u s i n g t h e c o n c e p t of h e a t as t h e e n e r g y of m o l e c u l a r m o t i o n . T h e s t r i n g like a l b u m i n m o l e c u l e s in t h e egg w h i t e h a v e a loosely folded ball s t r u c t u r e (technically k n o w n as a r a n d o m coil). This s t r u c t u r e i s held t o g e t h e r b y w e a k a t t r a c t i v e forces b e t w e e n t h o s e p a r t s of t h e m o l e c u l a r c h a i n t h a t cross close to e a c h o t h e r . T h e s t r u c t u r e is a d y n a m i c o n e , f l u c t u a t i n g a n d w o b bling as it is b o m b a r d e d from all sides by s u r r o u n d i n g w a t e r m o l e c u l e s . As t h e t e m p e r a t u r e is i n c r e a s e d , t h e e n e r g y of t h e b o m b a r d i n g m o l e c u l e s c o r r e s p o n d i n g l y increases, a s d o e s t h e e n e r g y of i n t e r n a l v i b r a t i o n of t h e a l b u m i n c h a i n itself. T h e r e c o m e s a p o i n t w h e r e t h a t e n e r g y is sufficient to d i s r u p t t h e w e a k l i n k a g e s t h a t h o l d t h e s t r u c t u r e t o g e t h e r . This h a p p e n s at a fairly precise t e m p e r a t u r e ( a r o u n d 6 8 ° C ) . B e l o w t h a t t e m p e r a t u r e , n o a m o u n t o f c o o k i n g will d i s r u p t t h e s t r u c t u r e . A b o v e it, t h e a l b u m i n m o l e c u l e s unfold a n d b e c o m e free t o e n tangle t h e m s e l v e s w i t h other, similarly u n f o l d e d , a l b u m i n m o l ecules, c r e a t i n g a n e w s t r u c t u r e — a t h r e e - d i m e n s i o n a l n e t . J u s t o n e t h i n g n e e d s t o b e clarified a b o u t this (slightly simplified) p i c t u r e — t h e difference b e t w e e n t h e w o r d s " h e a t " a n d " t e m p e r a t u r e . " Einstein, w r i t i n g i n f 9 3 8 , b e l i e v e d t h a t "these c o n c e p t s a r e n o w familiar t o e v e r y o n e , " b u t E i n s t e i n w a s w r o n g . Most p e o p l e o u t s i d e science ( a n d a s u r p r i s i n g n u m b e r inside) w o u l d still be h a r d - p r e s s e d to spell o u t t h e difference b e t w e e n h e a t a n d t e m p e r a t u r e . W e n e e d e d t o b e clear a b o u t t h e d i s t i n c t i o n i n o u r discussion o f c o o k i n g . W i t h t h e c o n c e p t o f e n e r g y u n d e r o u r belts, t h e clarification ( p r e s e n t e d by Nicholas) l o o k a b o u t t h i r t y s e c o n d s . T h e distinction, as Nicholas p o i n t e d o u t , is very s i m p l e . Hear refers to total e n e r g y . The temperature of a m a t e r i a l , on t h e o t h e r h a n d , is a practical m e a s u r e of t h e average e n e r g y p e r m o l e c u l e in t h e m a t e r i a l . In cooking, t h e total e n e r g y t h a t i s d e l i v e r e d t o t h e dish b e i n g

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c o o k e d d e p e n d s o n t h e c o o k i n g device. H o t p l a t e s a n d grills d e liver h e a t e n e r g y at a r a t e w h i c h is m o r e or less c o n s t a n t for a p a r t i c u l a r setting, s o t h e a m o u n t d e l i v e r e d t o t h e dish d e p e n d s o n t h e t i m e a n d t h e setting. M i c r o w a v e o v e n s d e l i v e r e n e r g y i n i n t e r m i t t e n t b u r s t s o f c o n s t a n t p o w e r , w i t h t h e relative " o n " a n d "off" t i m e s b e i n g d e t e r m i n e d b y t h e setting. T h e a m o u n t of e n e r g y t h a t is a c t u a l l y a b s o r b e d by t h e food d e p e n d s o n h o w m u c h m o i s t u r e i s p r e s e n t a n d its p o s i t i o n i n t h e spatially u n e v e n m i c r o w a v e f i e l d i n t h e o v e n . T h e effect o f t h e total a m o u n t o f h e a t e n e r g y d e l i v e r e d o n t h e t e m p e r a t u r e d e p e n d s o n h o w m u c h food t h e r e i s ( t h e m o r e food, t h e m o r e m o l e c u l e s ) , o n t h e t y p e o f food, a n d o n h o w t h e h e a t e n e r g y is d i s t r i b u t e d w i t h i n t h e food, ft is t h e t e m p e r a t u r e , r a t h e r t h a n the total a m o u n t of heat energy added, that d e t e r m i n e s w h a t h a p p e n s in c o o k e d food at a m o l e c u l a r level. O n e (usually m i n o r ) effect arises from t h e fact t h a t m o r e e n e r g e t i c m o l e c u l e s , like m o r e e n e r g e t i c p e o p l e , n e e d m o r e space, jostling e a c h o t h e r aside t o get it, w h i c h i s w h y m a t e r i a l s e x p a n d as t h e t e m p e r a t u r e i n c r e a s e s (e.g., t h e liquid in a t h e r m o m e t e r ) . A s t h e t e m p e r a t u r e i n c r e a s e s , m o l e c u l e s also c h a n g e t h e i r s h a p e s , m o v e t o different places, b r e a k apart, a n d j o i n c h e m i c a l l y w i t h o t h e r m o l e c u l e s . All of t h e s e c h a n g e s (see A p p e n d i x 2) alter t h e flavor a n d t e x t u r e of t h e food. T h e aim of c o o k i n g is to direct t h o s e c h a n g e s in a g a s t r o n o m i c a l l y appropriate manner. The main problem in cooking is h o w to achieve the approp r i a t e t e m p e r a t u r e d i s t r i b u t i o n i n t h e food. T h e r e a r e s i m p l e physical l a w s t h a t c a n b e u s e d t o p r e d i c t t h e t e m p e r a t u r e dist r i b u t i o n . O u r a i m a t t h e 1997 Erice m e e t i n g w a s t o find o u t w h e t h e r t h e s e laws w o r k i n practice d u r i n g c o o k i n g , o r w h e t h e r s o m e foods m i g h t h a v e n a s t y s u r p r i s e s i n s t o r e . The two m a i n processes by which heat energy might be t r a n s p o r t e d w i t h i n food a r e conduction a n d convection. All m a t e rials c o n d u c t h e a t ; t h e difference b e t w e e n " c o n d u c t o r s " a n d " i n s u l a t o r s " lies o n l y i n t h e rate a t w h i c h t h e y c o n d u c t h e a t . M e a t , for e x a m p l e , is a l m o s t as efficient an i n s u l a t o r as t h e r u b b e r in a w e t s u i t , b u t its l o w h e a t c o n d u c t i v i t y is n e v e r t h e -


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less sufficient to p e r m i t t h e c e n t e r to r e a c h a r e a s o n a b l e t e m perature during cooking. If t h e h o t m a t e r i a l in a food can m o v e , c o n v e c t i o n also b e c o m e s a possibility. A l t h o u g h t h e n o t i o n n o w s e e m s familiar (as in c o n v e c t o r h e a t e r s ) , it w a s in fact d i s c o v e r e d by C o u n t R u m f o r d little m o r e t h a n t w o h u n d r e d y e a r s ago, after a n o t h e r u n f o r t u n a t e e n c o u n t e r w i t h food: When dining, I had often observed that some particular dishes retained their heat much longer than others, and that apple pies . . . remained hot for a surprising length of time . . . I never burnt my m o u t h with them, or saw others meet with the same misfortune, without endeavouring, but in vain, to find out some way of accounting . . . for this surprising p h e n o m e n o n . Twelve y e a r s later, he h a d a similar e n c o u n t e r w i t h thick rice soup, which had been brought to him hot but which he had left for an h o u r . His first s p o o n f u l , t a k e n from t h e t o p , w a s cold a n d u n p l e a s a n t . T h e s e c o n d , t a k e n from d e e p e r d o w n , again b u r n e d his m o u t h . R u m f o r d w a s still p u z z l e d . His p u z z l e m e n t w a s d u e t o t h e fact t h a t w a t e r w a s believed a t t h e t i m e to be a good c o n d u c t o r of h e a t . Why, t h e n , did t h e s e w a t e r l a d e n dishes n o t cool d o w n faster? As so often in c u l i n a r y m a t ters, alcohol e v e n t u a l l y s u p p l i e d t h e a n s w e r . T h e alcohol w a s in t h e h u g e ( 4 - i n c h ) b u l b of a specially c o n s t r u c t e d t h e r m o m e t e r that Rumford had taken to a high t e m p e r a t u r e during an e x p e r i m e n t a n d t h e n left on a w i n d o w s i l l to cool. To his i n t e n s e surprise, he s a w " t h e w h o l e m a s s of liquid in a m o s t rapid m o t i o n , r u n n i n g swiftly in t w o o p p o s i t e directions, up, a n d down, at t h e s a m e t i m e . " L o o k i n g m o r e closely, he discovered t h a t " t h e a s c e n d i n g c u r r e n t o c c u p i e d t h e [central] axis of the tube, a n d t h a t it d e s c e n d e d by t h e sides of the tube." This process, w h i c h R u m f o r d called convection, is c o m m o n p l a c e in c o o k i n g . W h e n w a t e r is h e a t e d in a s a u c e p a n , for e x a m p l e , the heated water at the bottom, which expands and becomes less d e n s e t h a n t h e c o l d e r w a t e r a b o v e , rises t o t h e t o p , a n d i s replaced by an inflow of cold w a t e r , w h i c h is a g a i n h e a t e d in

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t u r n , so t h a t t h e r e is a c o n t i n u a l c i r c u l a t i o n of w a t e r c a r r y i n g heat to all p a r t s of t h e s a u c e p a n (Figure 2 . 1 ) .

Figure 2 . 1 : H o w Convection Works. The movement of water in a saucepan.

C o n v e c t i o n is vastly m o r e efficient t h a n c o n d u c t i o n as a m o d e of t r a n s p o r t i n g h e a t . W a t e r w a s t h o u g h t to be a good c o n d u c t o r o n l y b e c a u s e n o o n e before R u m f o r d h a d recognized t h a t c o n v e c t i o n existed. R u m f o r d g u e s s e d t h a t w a t e r i s really a p o o r c o n d u c t o r of h e a t , a n d t h a t his p r o b l e m s w i t h a p p l e pies a n d rice s o u p h a d o c c u r r e d b e c a u s e t h e free m o v e m e n t o f t h e w a t e r w a s s o m e h o w b l o c k e d i n t h e s e dishes. T o check his g u e s s , he d e l i b e r a t e l y b l o c k e d c o n v e c t i o n in t w o p a n s of h o t w a t e r , dissolving s t a r c h in o n e a n d stuffing an eiderdown in the second. He found that the water in these pans cooled m u c h m o r e slowly t h a n did t h e h o t w a t e r i n a p a n t o which nothing had been added to hinder the convection process. R u m f o r d s p e c u l a t e d (correctly) t h a t , in d i s h e s s u c h as s t e w e d a p p l e s a n d thick rice s o u p , c o n v e c t i o n c u r r e n t s a r e s l o w e d d o w n o r blocked b y t h e p r e s e n c e o f f i b e r a n d dissolved s u b s t a n c e s t h a t a r e released d u r i n g c o o k i n g . T h e surface layer m a y cool d o w n , b u t t h e h o t m a t e r i a l inside c a n n o t b e t r a n s p o r t e d by c o n v e c t i o n to t h e surface. C o n v e c t i o n is likely to be similarly b l o c k e d in an egg t h a t is b e i n g boiled, since t h e h e a t - i n d u c e d d e n s i t y g r a d i e n t s i n t h e


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w h i t e a r e u n l i k e l y t o b e large e n o u g h t o c a u s e s u b s t a n t i a l m a terial m o v e m e n t of s u c h a viscous m a t e r i a l . C o n v e c t i o n is e v e n less likely in d i s h e s like v e g e t a b l e s or roast m e a t , w h e r e t h e w a t e r is held t r a p p e d in a m a t r i x of fibers. C o n d u c t i o n , t h o u g h slow, is likely to be t h e d o m i n a n t m o d e of h e a t t r a n s port in s u c h foods. T h e d i s a d v a n t a g e of this, from t h e p o i n t of v i e w of a chef, is t h a t m e a t a n d large v e g e t a b l e pieces t a k e a relatively l o n g t i m e t o c o o k . T h e a d v a n t a g e , t h o u g h , i s t h a t t h e s e foods ( o n c e c o o k e d ) r e t a i n t h e i r h e a t lor a long t i m e . A n o t h e r a d v a n t a g e is t h a t its basic r u l e s are easy to w r i t e d o w n . T h o s e rules, t h o u g h , a r e n o t a l w a y s t h e o n e s t h a t a r e given in c o o k b o o k s or b e l i e v e d by chefs. Take t h e s i m p l e case of a large, flat slab of m e a t , s u c h as a steak, c o o k e d in a vertical grill so t h a t it is b e i n g h e a t e d equally from b o t h sides. If t h e t h i c k n e s s of t h e m e a t is doubled, w h a t does that do to the cooking time? A consensus of chefs (not t h o s e at Erice!) got t h e w r o n g a n s w e r . M a n y t h o u g h t t h a t it m i g h t n o t t a k e e v e n t w i c e as l o n g to cook t h e thicker piece. T h e correct a n s w e r , p r o v e d by e x p e r i m e n t , is thai it will t a k e four times as long to cook t h e t h i c k e r piece, if o n e defines " c o o k e d " a s " r e a c h i n g t h e s a m e t e m p e r a t u r e a t t h e center." This is o n e e x a m p l e of t h e fact t h a t h e a t t r a n s f e r by c o n d u c t i o n g e n e r a l l y follows a " s q u a r e r u l e . " To get t h e h e a t twice as far t a k e s l o u r t i m e s as l o n g . " W h y a s q u a r e r u l e ? " a s k e d t h e chefs a t Erice. T h e a n s w e r lies in t h e w a y t h a t k i n e t i c e n e r g y is t r a n s f e r r e d b e t w e e n m o l ecules in food. T h e p r o c e s s starts i n c o o k i n g w h e n h e a t e n e r g y r e a c h e s t h e food surface, i n c r e a s i n g t h e k i n e t i c e n e r g y of t h e surface m o l ecules. T h e s e m o l e c u l e s t h e n pass s o m e o f t h a t e n e r g y o n t o their less e n e r g e t i c n e i g h b o r s by a " k n o c k - o n " effect. T h e e n ergy c o n t i n u e s to be p a s s e d on to f u r t h e r m o l e c u l e s in relay fashion. T h e rules t h a t g o v e r n this p r o c e s s a r e statistical, a n d based o n t h e idea t h a t t h e e n e r g y m a y b e p a s s e d i n a n y direction w i t h e q u a l probability, so t h a t t h e g o v e r n i n g e q u a t i o n is t h e s a m e a s t h a t w h i c h describes t h e r a n d o m diffusion o f m o l ecules in a liquid (see c h a p t e r o n e ) . This e q u a t i o n s h o w s t h a t

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t h e t i m e t a k e n for h e a t e n e r g y to travel a g i v e n d i s t a n c e by c o n d u c t i o n d e p e n d s o n t h e s q u a r e o f t h e d i s t a n c e . T o travel t w i c e as far t a k e s , on a v e r a g e , four t i m e s as l o n g . T h e e q u a t i o n s for c o n d u c t i v e h e a t t r a n s f e r w e r e w r i t t e n d o w n b y t h e F r e n c h m a t h e m a t i c i a n J e a n Baptiste Fourier, o n e o f t h e s a v a n t s w h o a c c o m p a n i e d N a p o l e o n t o Egypt i n 1 7 9 8 . T h e s q u a r e r u l e is a s o l u t i o n to F o u r i e r ' s e q u a t i o n t h a t is a c c u r a t e for flat pieces of food w h e r e t h e w i d t h is v e r y m u c h g r e a t e r t h a n t h e t h i c k n e s s . W o u l d it w o r k for a food s u c h as an i r r e g u l a r l y s h a p e d r o a s t ? T h e r e is e v e r y r e a s o n to e x p e c t it to. S o l u t i o n s of F o u r i e r ' s e q u a t i o n for s h a p e s o t h e r t h a n a flat slab a r e c o m p l i c a t e d , b u t all c o n t a i n a t e r m i n w h i c h t h e t i m e d e pends on the square of the distance. Theory, t h o u g h , is no s u b s t i t u t e for e x p e r i m e n t , especially w h e r e c o o k i n g i s c o n c e r n e d . W e d e c i d e d a t Erice t o test t h e t h e o r y w i t h a g e n u i n e roast, lovingly p r e p a r e d by chef Fritz Blank, p r o p r i e t o r o f t h e f a m o u s P h i l a d e l p h i a r e s t a u r a n t D e u x C h e m i n e e s . M y task w a s t o lace t h e roast w i t h f i n e w i r e t h e r mocouples, inserted so as to monitor the temperature changes a t different d e p t h s i n t h e m e a t . T h e w i r e s from t h e s e t h e r m o c o u p l e s trailed across t h e k i t c h e n from t h e o v e n to a m u l t i c h a n n e l r e c o r d e r , w h e r e Fritz a n d I sat w a t c h i n g w h i l e w e sipped a reflective glass of w i n e . Two h o u r s later, t h e c e n t e r of t h e roast h a d r e a c h e d Fritz's prescribed v a l u e of 45°C, a n d c o n f e r e n c e talks w e r e f o r g o t t e n a s t h e s p e a k e r s c r o w d e d w i t h t h e rest, e a g e r for a t a s t e . First, t h o u g h , Fritz insisted t h a t t h e roast h a d to be left for forty m i n u t e s to "settle." f c o u l d n ' t u n d e r s t a n d t h e r e a s o n for this bit of chef's folklore, t h o u g h I w a s s o o n t o find o u t w h y . T h e d e l a y g a v e m e a n o p p o r t u n i t y t o k e e p m o n i t o r i n g t h e t e m p e r a t u r e of t h e roast as it cooled d o w n , w h i l e a n a l y z i n g t h e data o b t a i n e d so far. If t h e s q u a r e r u l e held, t h e n a g r a p h of d i s t a n c e s q u a r e d against t i m e to r e a c h a n y p a r t i c u l a r t e m p e r a t u r e w o u l d be a straight line. 1 tried it for a few different t e m p e r a t u r e s . W h e n 1 s a w t h e r e sults, I felt t h a t t h e glass of w i n e h a d b e e n justified. T h e t e m p e r a t u r e s i n t h e m e a t d u r i n g r o a s t i n g followed t h e s q u a r e r u l e beautifully.


35

T h e roast, m e a n w h i l e , h a d a little s u r p r i s e in s t o r e for u s . The t h e r m o c o u p l e s n e a r t h e surface s h o w e d t h a t t h e t e m p e r a t u r e h a d b e g u n t o d r o p a s s o o n a s t h e roast w a s r e m o v e d from t h e o v e n . T h o s e n e a r e r t h e center, t h o u g h , s h o w e d t h e t e m p e r a t u r e still rising! T h e c e n t e r t e m p e r a t u r e c o n t i n u e d to rise for t h e n e x t forty m i n u t e s , e v e n t u a l l y r e a c h i n g 55°C, a t e m p e r a t u r e a p p r o p r i a t e for s o m e w h e r e b e t w e e n m e d i u m and well-done. Does meat, t h e n , disobey t h e n o r m a l rules of conduction? I quickly realized t h a t t h e n o r m a l r u l e s of c o n d u c t i o n w e r e in fact r e s p o n s i b l e . T h e cool c e n t e r of a roast is s u r r o u n d e d by h o t t e r m e a t , e v e n after t h e roast h a s b e e n r e m o v e d from t h e o v e n . T h e l a y e r o f h i g h e s t t e m p e r a t u r e will b e s o m e w h e r e b e t w e e n t h e o u t s i d e a n d t h e m i d d l e , a n d h e a t will flow from this layer to c o o l e r places, w h i c h m e a n s t h a t it will flow b o t h to t h e o u t s i d e a n d t h e inside o f t h e m e a t . Later a n a l y s i s s h o w e d t h a t t h e r a t e a t w h i c h this p r o c e s s o c c u r s f i t s v e r y closely w i t h t h e p r e d i c t i o n s of F o u r i e r ' s e q u a t i o n . T h e analysis also s h o w e d t h a t t h e chef's h a b i t of a l l o w i n g large r o a s t s to "settle" b e f o r e b r i n g i n g t h e m to t h e t a b l e h a s a v e r y solid scientific f o u n d a tion. T h e c e n t e r o f t h e m e a t goes o n c o o k i n g , a n d t h e t e m p e r a t u r e profile also flattens o u t , s o t h a t t h e m e a t i s m o r e e v e n l y cooked. M e a t will also be m o r e e v e n l y c o o k e d if it is r o a s t e d for l o n g e r at a l o w e r t e m p e r a t u r e . B u t h o w c a n this be achieved w h e n we w a n t high t e m p e r a t u r e s to p r o m o t e the b r o w n i n g r e a c t i o n s a t t h e surface, giving t h a t lovely crispy t e x t u r e a n d flavor? T h e a n s w e r is s i m p l e . Start t h e o v e n off at a h i g h t e m p e r a t u r e , t h e n t u r n t h e t e m p e r a t u r e right d o w n after a s h o r t t i m e . This is w h a t professional chefs like Fritz do w h e n t h e y a r e n o t collaborating in e x p e r i m e n t s . T h e s q u a r e r u l e still applies, t h o u g h t h e a c t u a l t i m e s a r e different b e c a u s e o f t h e l o w e r o v e n t e m p e r a t u r e s . In fact, t h e s q u a r e r u l e is a g o o d g u i d e for m a n y foods. T h e differences b e t w e e n c o o k i n g t i m e s b a s e d o n t h e s q u a r e r u l e a n d t h o s e c a l c u l a t e d from s u c h t r a d i t i o n a l m e t h o d s a s " 2 0 m i n u t e s p e r p o u n d p l u s 2 0 m i n u t e s " o r "25 minutes per p o u n d plus 25 m i n u t e s " are interesting:


36

Table 2 . 1 : Calculated Times to Cook a Piece of Roast Beef to "Rare" Perfection in an Oven at 190"C (375*F).

Weight of Piece

Square rule

Mrs. Beetorfs time

My m o t h e r ' s time

(kg)

(lb)

time (min)*

( 2 0 min/lb + 20 min)

( 2 5 min/lb + 25 min)

0.1

V V

30 47 86 140 181 219

24 28 42 64 86 108

31 36 53 80 108 135

4

0.2 0.5 1 1.5

2V 37

2

4 /

a

1 B

4

1

a

* Adapted from Peter Barham's original calculations in The Science of Cooking.

The traditional rule inevitably overestimates cooking times for s m a l l e r pieces o f m e a t a n d u n d e r e s t i m a t e s t h e t i m e s r e q u i r e d to c o o k larger pieces. T h e r e will be a c r o s s o v e r p o i n t w h e r e t h e t w o rules a g r e e exactly for a g i v e n w e i g h t of m e a t , usually the weight with which the writer r e c o m m e n d i n g the p a r t i c u l a r rule h a s h a d t h e m o s t c o o k i n g e x p e r i e n c e . T h e a g r e e m e n t b e t w e e n t h e t w o rules for a r a n g e of w e i g h t s on eit h e r side of this c r o s s o v e r p o i n t is r e a s o n a b l e . T h e r e is an int e r e s t i n g m a t h e m a t i c a l r e a s o n for this r a n g e of a g r e e m e n t , w i t h t h e m a i n p o i n t for t h e practical c o o k b e i n g t h a t t h e calc u l a t e d c o o k i n g t i m e s d i v e r g e m o r e rapidly for w e i g h t s b e l o w t h e c r o s s o v e r p o i n t t h a n t h e y d o for larger w e i g h t s . Top-class chefs a r e v e r y g o o d at e s t i m a t i n g c o o k i n g t i m e s , and h o w these times change with weight, without recourse to t h e s q u a r e r u l e , w i t h w h i c h t h e i r e s t i m a t e s u s u a l l y accord q u i t e closely. T h e r u l e for t h e i n t e l l i g e n t d o m e s t i c cook is: Practice u n t i l y o u p r o d u c e t h e perfect result, a n d k e e p a n o t e of the weight of the portion and the time that produced the result. T h e n u s e t h e s q u a r e r u l e t o alter t h e c o o k i n g t i m e s for p o r t i o n s w i t h different w e i g h t s . This s o u n d s v e r y straightforw a r d , b u t t h e r e is a t r a p . T h e s q u a r e r u l e applies to d i a m e t e r s , n o t t o w e i g h t s . T o c o n v e r t from o n e t o t h e o t h e r i s tricky u n less y o u a r e m a t h e m a t i c a l l y i n c l i n e d . I n m a t h e m a t i c a l t e r m s , t h e c o o k i n g t i m e scales w i t h t h e s q u a r e o f t h e d i a m e t e r b u t


37

with the two-thirds p o w e r of the weight. The conversion is doable b u t m a t h e m a t i c a l l y c o m p l i c a t e d , so forget it u n l e s s y o u are a d a b h a n d w i t h a calculator. I n s t e a d , j u s t a d d fifty p e r c e n t to the cooking time if you double the weight, and proportionately less or m o r e o t h e r w i s e (e.g., if t h e w e i g h t i n c r e a s e is fifty p e r c e n t , a d d t w e n t y - f i v e p e r c e n t t o t h e c o o k i n g t i m e ) . This simple a p p r o x i m a t i o n to t h e a c t u a l r u l e is surprisingly a c c u rate, as tests w i t h t h e figures in t h e table a b o v e will quickly s h o w . It's p r o b a b l y t h e r u l e t h a t top-class chefs h a v e i n t u itively w o r k e d o u t for t h e m s e l v e s . T h e s q u a r e r u l e , w h i c h applies t o s o m a n y foods, s h o u l d surely a p p l y to boiled eggs — a n d it d o e s . We d i d n ' t n e e d to do t h e e x p e r i m e n t at Erice, t h o u g h . R i c h a r d G a r d n e r , Professor of Cell Biology at t h e U n i v e r s i t y of Oxford, h a d a l r e a d y d o n e it n i n e years earlier w h e n t r y i n g t o u n d e r s t a n d w h y his t w o year-old s o n M a t t h e w w a s able to eat t h e yolk of a freshly o p e n e d boiled egg, b u t s t e e r e d clear of t h e w h i t e u n t i l it h a d cooled d o w n . S t i m u l a t e d by scientific curiosity, Professor G a r d n e r i n s e r t e d a pair of t h e r m o c o u p l e s i n t o an egg, o n e in t h e w h i t e a n d o n e i n t h e yolk, a n d set t h e egg t o boil. Professor G a r d n e r did n o t i n t e r e p r e t his d a t a in t e r m s of t h e s q u a r e rule, b u t w e w e r e able to, b e c a u s e h e p u b l i s h e d his results i n a n e x t r a o r d i n a r y a n t h o l o g y o n food a n d d r i n k b y F e l l o w s a n d Foreign M e m b e r s of t h e Royal Society. T h e e d i t o r of t h e a n t h o l o g y w a s (of course!) Nicholas K u r t i . A g r a p h of t h e results is s h o w n in Figure 2.2. T h e l o w e r "wiggle" (A) in t h e c u r v e for t h e t e m p e r a t u r e of t h e w h i t e is a n artifact, arising from m o v i n g t h e t h e r m o c o u p l e after t h e m e a s u r e m e n t s h a d s t a r t e d . T h e u p p e r "wiggle" (B), h o w e v e r , has real m e a n i n g , ft o c c u r s at t h e t e m p e r a t u r e ( a n d t i m e ) w h e n t h e w h i t e sets, a n d s e t t i n g t a k e s energy, t h e r e f o r e t h e t e m p e r a t u r e of t h e w h i t e stays c o n s t a n t (if e n e r g y is c o m i n g in by c o n d u c t i o n as fast as it is b e i n g u s e d to r e a r r a n g e m o l e cules) or e v e n d r o p s (if m o r e e n e r g y is r e q u i r e d to r e a r r a n g e t h e a l b u m i n m o l e c u l e s t h a n i s available from c o n d u c t i o n ) . Professor G a r d n e r a l l o w e d his egg to cook for t h i r t y m i n utes, an a p p r o p r i a t e p r o c e d u r e for a l o v e r of v e r y h a r d - b o i l e d

38


Figure 2.2: Internal T e m p e r a t u r e of an Egg During Boiling. Redrawn from Richard Gardner, "On Boiling Eggs," in Kurti, N. and G. (eds), But the Crackling Is Superb.

eggs, a n d also for a scientist i n t e r e s t e d in t e s t i n g t h e applicat i o n of t h e s q u a r e r u l e , w h i c h gives an e x c e l l e n t fit to Professor G a r d n e r ' s d a t a . T h e p r o d u c t i o n of a perfect soft-boiled breakfast egg, t h o u g h , r e q u i r e s t h e c o o k i n g to stop after a m u c h s h o r t e r t i m e , fn fact, if Professor G a r d n e r h a d r e m o v e d t h e egg after t h r e e a n d a half m i n u t e s ( t h e t i m e at t h e e n d of t h e s e c o n d "wiggle") a n d o p e n e d it i m m e d i a t e l y , his egg w o u l d h a v e b e e n perfectly c o o k e d ( a s s u m i n g t h a t t h e t h e r m o couple in the white had been measuring the temperature at a p o i n t v e r y close t o t h e y o l k ) . W e k n o w t h a t t h e egg w o u l d h a v e b e e n perfectly soft-boiled b e c a u s e a t t h e t e m p e r a t u r e w h e n t h e w h i t e sets, t h e yolk i s still r u n n y . This i s d u e t o t h e fact t h a t t h e p r o t e i n m o l e c u l e s i n t h e yolk a r e e a c h w r a p p e d a r o u n d a t i n y c o r e of oil. It t a k e s m o r e e n e r g y to r e l e a s e t h e p r o t e i n from t h e oil surface t h a n i t d o e s t o u n w i n d a n a l b u m i n m o l e c u l e in t h e a q u e o u s e n v i r o n m e n t of t h e w h i t e — t h e yolk

h o w d o e s a s c i e n t i s t boil an e g g ?

39

p r o t e i n s a r e n o t free t o m o v e a r o u n d a n d b e c o m e e n t a n g l e d until t h e yolk r e a c h e s a h i g h e r t e m p e r a t u r e t h a n t h e w h i t e . The yolk, in fact, o n l y sets a b o v e a t e m p e r a t u r e of 68°C, so t h e p r o b l e m of boiling an egg b e c o m e s a m a t t e r of g e t t i n g t h e w h i t e a b o v e 63°C, w h i l e k e e p i n g t h e yolk b e l o w 6 8 ° C . For t h e c o o k w i t h o u t a t h e r m o c o u p l e , it's a m a t t e r of delicate t i m i n g . T h e s q u a r e r u l e lets us calculate t h e l e n g t h of t i m e r e q u i r e d , w h i c h is a s t o n i s h i n g l y sensitive to t h e size of t h e egg c o n c e r n e d . T h e c a l c u l a t i o n w a s p e r f o r m e d b y Dr. C h a r l e s Williams of E x e t e r U n i v e r s i t y in 1 9 9 8 . He p r e s e n t e d his results in t h e form of an e q u a t i o n , from w h i c h I h a v e calculated t h e figures b e l o w :

Table 2.2: C a l c u l a t e d T i m e s t o Boil t h e P e r f e c t E g g . Egg diameter at

Cooking time (min)

widest lateral point (mm)

Initial temp. 2 0 ' C

Initial temp. 4 " C

small

39

3.34

3.75

small

40

3.5

4.0

medium

42

3.9

4.4

medium

44

4.25

4.8

medium

46

4.6

5.2

large

48

5

5.7

large

50

5.5

6.2

These f i g u r e s s h o w t h a t J a m e s B o n d w a s right — s o l o n g a s t h e F r e n c h M a r a n s h e n s laid a t least s o m e eggs t h a t w e r e 3 9 millimeters i n d i a m e t e r , a n d t h a t t h e s e eggs w e r e k e p t a t r o o m t e m p e r a t u r e . B o n d , in his fastidious way, w o u l d of c o u r s e h a v e h a d a m e t a l ring available w i t h a d i a m e t e r of 39 m i l l i m e ters, a n d w o u l d o n l y h a v e u s e d eggs t h a t j u s t f i t t h r o u g h this ring, so t h a t a c o o k i n g t i m e of t h r e e a n d o n e - t h i r d m i n u t e s w o u l d h a v e b e e n perfect. F o r m e d i u m eggs a t r o o m t e m p e r a t u r e , place directly i n t o boiling w a t e r , a n d a l l o w a r o u n d four m i n u t e s c o o k i n g t i m e . T h e t i m e s will s h o r t e n if t h e egg is allowed t o "settle" b e f o r e b e i n g o p e n e d , since t h e c e n t e r will c o n t i n u e c o o k i n g e v e n after t h e egg i s r e m o v e d from t h e

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boiling water, just as t h e c e n t e r of a roast j o i n t k e e p s on c o o k i n g after it h a s b e e n r e m o v e d from t h e o v e n . S u c h a p r o c e d u r e will p r o d u c e a m o r e delicately t e x t u r e d egg, w i t h t h e w h i t e n o t q u i t e s o r u b b e r y , since f e w e r cross-links will h a v e b e e n formed b e t w e e n the a l b u m i n molecules. A sophisticated w a y of t a c k l i n g this p r o b l e m , devised by Fritz B l a n k a n d u s e d in his r e s t a u r a n t , is to c o o k t h e eggs for a s h o r t e r t i m e t h a n n o r m a l a n d t h e n t o roll t h e m i n c r u s h e d ice w h i l e t h e inside goes o n cooking, so that the residual internal heat goes towards cooking t h e c e n t e r b u t d o e s n o t o v e r c o o k t h e o u t s i d e o f t h e w h i t e a n d c r e a t e a r u b b e r y t e x t u r e . H o w e v e r , as Nicholas p o i n t e d o u t , t h e r e i s a n e v e n b e t t e r w a y . His a p p r o a c h , later e l a b o r a t e d by H e r v e This in a letter to t h e m a g a z i n e New Scientist, w a s b a s e d o n t h e k n o w l e d g e t h a t t h e w h i t e sets a t a l o w e r t e m p e r a t u r e t h a n t h e yolk. All t h a t is n e e d e d , t h e n , is to boil t h e egg i n a liquid w h o s e boiling p o i n t i s b e t w e e n t h e t w o s e t t i n g t e m p e r a t u r e s . T h e w h i t e will e v e n t u a l l y set, b u t t h e yolk n e v e r will. A n d t h e egg c a n be boiled for as l o n g as t h e cook likes. S o m e o n e w i t h t h e r e s o u r c e s of a scientific l a b o r a t o r y c a n a c h i e v e t h e a p p r o p r i a t e t e m p e r a t u r e ( b e t w e e n 63°C a n d 68°C) b y boiling t h e w a t e r u n d e r r e d u c e d p r e s s u r e . This r e quires elaborate (and expensive) apparatus, together with app r o p r i a t e safety m e a s u r e s . T h e a l t e r n a t i v e is to u s e a different liquid a l t o g e t h e r , o n e w i t h a boiling p o i n t of 6 4 - 6 6 ° C . T h e r e a r e a few s u c h liquids. O n e , c o m m o n i n c h e m i c a l l a b o r a t o r i e s , i s m e t h a n o l (also k n o w n a s w o o d a l c o h o l ) , w h i c h h a s a boiling p o i n t of 6 4 . 6 ° C . T h e r e a r e o n l y t h r e e p r o b l e m s . T h e first is t h e f l a v o r t h a t t h e m e t h a n o l i s likely t o i m p a r t t o t h e egg t h r o u g h its p o r o u s shell. T h e s e c o n d is availability — w o o d alc o h o l is available to c h e m i s t s for scientific p u r p o s e s , b u t its c o m m e r c i a l u s e is m o s t l y as a p o i s o n o u s a d u l t e r a n t in m e t h y lated spirits. I t i s t h e t h i r d p r o b l e m , t h o u g h , t h a t p r e s e n t s t h e m o s t difficulty. M e t h a n o l v a p o r is h i g h l y i n f l a m m a b l e , a n d liable t o c a t c h f i r e e v e n o n a n electric h o t p l a t e . T h e c o n c l u s i o n is t h a t t h e r e is an ideal, scientific, g u a r a n t e e d m e t h o d to boil t h e perfect egg, b u t d o n ' t , w h a t e v e r y o u d o , try i t a t h o m e . J a m e s B o n d m i g h t h a v e b e e n able t o get a w a y w i t h it, d o u s i n g

h o w d o e s a scientist boll an e g g ?

t h e r e s u l t i n g flames w i t h o n e of Q's special g a d g e t s t h a t he doubtless carried i n t h e t r u n k o f his Bentley. H e m a y e v e n h a v e b e e n able to u s e t h e flaming egg as a M o l o t o v cocktail. For a p r o p e r g a s t r o n o m i c e x p e r i e n c e , t h o u g h , t h e rest of us will do far b e t t e r by sticking to a c o m b i n a t i o n of w a t e r a n d simple a r i t h m e t i c .

3 t h e t a o of t o o l s

O n e of my greatest p r o b l e m s as a s t u d e n t l e a r n i n g a b o u t scie n c e w a s w a n t i n g to u n d e r s t a n d t h e logical basis of t h e ideas t h a t w e r e b e i n g p r e s e n t e d to m e . It s o u n d s like just t h e sort of p r o b l e m t h a t a scientist o u g h t to h a v e , b u t m a n y of t h e m o s t f u n d a m e n t a l ideas w e r e simply p r e s e n t e d to us as facts to be a c c e p t e d a n d u s e d . M y m o r e successful c o n t e m p o r a r i e s accepted this a p p r o a c h , got o n w i t h t h i n g s , a n d i n d u e c o u r s e b e c a m e professors a n d e v e n vice c h a n c e l l o r s . I, in t h e m e a n t i m e , s p e n t e n d l e s s h o u r s trying t o figure o u t w h e r e t h i n g s like t h e S c h r o d i n g e r e q u a t i o n ( w h i c h g o v e r n s all of q u a n t u m m e c h a n i c s ) c a m e from, o r h o w t h e c o n c e p t o f e n e r g y a r o s e . I eventually found out that the Schrodinger equation was a c o m p l e t e g u e s s , p e r h a p s t h e m o s t brilliant g u e s s i n t h e h i s t o r y of science, a n d t h a t t h e c o n c e p t of e n e r g y g r e w g r a d u a l l y from efforts t o u n d e r s t a n d w h a t h e a t w a s . W h e n I l o o k e d m o r e closely, t h o u g h , I f o u n d t h a t e n e r g y w a s a l w a y s defined in t e r m s of its ability to p e r f o r m physical w o r k , so w o r k , t h e r e fore, w a s a n e v e n m o r e f u n d a m e n t a l c o n c e p t t h a n e n e r g y . W h e r e did this c o n c e p t c o m e f r o m ? I t t o o k m e thirty-five y e a r s to find o u t . W h e n I did, t h e a n s w e r c a m e as a c o m p l e t e s h o c k . T h e definition o f " w o r k , " t h e m o s t f u n d a m e n t a l q u a n tity i n science, c a m e e n t i r e l y from i n t u i t i o n . W e d o n ' t e v e n k n o w w h o s e i n t u i t i o n . W e d o k n o w , t h o u g h , t h a t t h e definition can b e u s e d t o figure o u t h o w best t o u s e t h e tools t h a t s u p p o s e d l y s a v e u s w o r k . T h e y d o n ' t , o f c o u r s e . W h a t tools d o i s t o m a k e w o r k possible, b y c h a n g i n g t h e b a l a n c e b e t w e e n t h e force w e n e e d t o e x e r t a n d t h e d i s t a n c e t h r o u g h w h i c h w e h a v e to m o v e t h e p o i n t of a p p l i c a t i o n of t h a t force to do a given j o b . This c h a p t e r describes h o w t h a t principle a r o s e , a n d h o w p e o p l e from A r c h i m e d e s o n w a r d s h a v e used i t t o a c h i e v e

the tao of tools

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objectives r a n g i n g from lifting a R o m a n galley o u t of t h e w a ter t o r e m o v i n g recalcitrant nails from h a r d w o o d . T h e s a m e principle can b e used t o w o r k o u t t h e m o s t efficient w a y t o u s e tools. As t h e r e a d e r will find, this is n o t a l w a y s t h e w a y t h a t t h e y are u s u a l l y used b y h a n d y m e n a n d t r a d e s m e n . Is it best to d r i v e a nail i n t o a p i e c e of w o o d w i t h a series of light b l o w s r a t h e r t h a n a few h e a v i e r b l o w s ? W h e n r e m o v i n g a nail w i t h a c l a w h a m m e r , d o e s it h e l p to place a small block of wood u n d e r the head of the h a m m e r ? Are long screwdrivers easier t o u s e t h a n s h o r t e r s c r e w d r i v e r s w i t h t h e s a m e blade size? H o w s h a r p d o e s a chisel really n e e d to b e ? F r o m practical e x p e r i e n c e , t h e a n s w e r s t o t h e s e q u e s t i o n s a r e : yes, yes, yes, a n d very. T h e r e is a right a n d a w r o n g w a y of u s i n g tools; a n effective a n d a n ineffective w a y ; a w a y t h a t m a k e s the w o r k easier a n d a w a y t h a t m a k e s w o r k h a r d e r . Practical e x p e r i e n c e is codified in b o o k s s u c h as M o r g a n ' s classic Woodworking Tools and How to Use Them, a b o o k t h a t I d e voured eagerly w h e n young, partly in t h e h o p e of showing my l a t h e r t h a t s o m e aspect o f his w o r k s h o p t e a c h i n g h a d b e e n w r o n g . Sadly for m y y o u t h f u l h o p e s , t h e r u l e s w e r e j u s t a s h e had said (1 later f o u n d t h a t he t o o h a d read M o r g a n ' s b o o k ) . N o w h e r e , t h o u g h , did t h e b o o k s say why t h e r u l e s w e r e as they w e r e . I n this t h e y differed from t h e o t h e r b o o k s t h a t w e r e shaping my f u t u r e life — t h e p o p u l a r science b o o k s t h a t a d dressed t h e q u e s t i o n of why i n s t e a d of how. T h e w o r l d p o r trayed i n t h o s e b o o k s s e e m e d t o m e a m o r e i m p o r t a n t o n e , dealing w i t h t h i n g s t h a t really m a t t e r e d , a n d far r e m o v e d b o m t h e m u n d a n e l y practical. 1 did n o t realize h o w t h e t w o worlds feed off e a c h o t h e r , a n d h o w t h e y a r e b o t h p a r t of o n e larger, i n t e r c o n n e c t e d w o r l d of u n d e r s t a n d i n g . 1 was n o t t h e first to m a k e s u c h a m i s t a k e . A r c h i m e d e s , b o r n nearly t h r e e h u n d r e d y e a r s b e f o r e Christ, s h a r e d m y m i s c o n ception t h a t practical t h i n g s a r e m u c h less i m p o r t a n t t h a n 'deas. Even t h o u g h h e i n v e n t e d m a n y practical devices, h e seld o m t h o u g h t t h e m sufficiently i m p o r t a n t t o w r i t e d o w n t h e i r details for posterity, ft is b e c a u s e of this a t t i t u d e t h a t he left no

44


d e s c r i p t i o n of t h e first h a n d tool to be d e s i g n e d from scientific principles. As h a n d tools go, it w a s r a t h e r large; large e n o u g h , in fact, to lift a R o m a n galley clear of t h e w a t e r a n d s h a k e t h e frightened soldiers o u t like weevils from a sailor's biscuit. Despite its size, t h o u g h , it still fitted t h e Oxford Dictionary definition of a tool as "a m e c h a n i c a l i m p l e m e n t for w o r k i n g u p o n s o m e t h i n g . . . held i n a n d o p e r a t e d directly b y t h e h a n d , b u t also i n c l u d i n g s o m e simple m a c h i n e s . " This p a r t i c u l a r o n e p r o b a b l y r e q u i r e d q u i t e a few h a n d s to o p e r a t e . We k n o w from historical r e c o r d s t h a t i t t o o k t h e form o f a n a s y m m e t r i c lever, m o u n t e d o n t h e seawall of A r c h i m e d e s ' h o m e t o w n of S y r a c u s e as p r o t e c t i o n against a n i n v a d i n g R o m a n fleet. T h e l e v e r a r m m u s t h a v e b e e n like a l o n g tree t r u n k . T h e s h o r t e n d h u n g o v e r t h e sea, w i t h a claw-like grab s u s p e n d e d from it. O n c e t h e grab h a d h o o k e d i n t o s o m e p a r t of an a t t a c k i n g ship, t e a m s of m e n or a n i m a l s pulling d o w n on t h e long e n d of t h e lever could lift t h e ship clear of t h e w a t e r . T h e device w a s so effective, a c c o r d i n g to t h e G r e e k h i s t o r i a n Plutarch, t h a t if a t t a c k i n g R o m a n s s a w a piece of w o o d projecting over t h e seawall it w a s e n o u g h to m a k e t h e m t u r n tail a n d h e a d for t h e o p e n sea (Figure 3.1). Archimedes' great m a c h i n e w o r k e d first time because he u n d e r s t o o d n o t j u s t how levers w o r k ( t h e a n c i e n t E g y p t i a n s k n e w t h a t ) b u t why t h e y f u n c t i o n i n t h e w a y t h a t t h e y d o . H e h a d w o r k e d o u t t h e l a w o f t h e lever y e a r s earlier, a n d d e scribed it in a b o o k e n t i t l e d On Balances or Levers, a b o o k t h a t is u n f o r t u n a t e l y n o w lost. P u t m a t h e m a t i c a l l y , a s A r c h i m e d e s w o u l d h a v e d o n e , t h e l a w simply states t h a t t h e p r o d u c t o f t h e load a n d t h e l e n g t h o f t h e lever a r m i s t h e s a m e for b o t h l o a d s . A n earlier writer, m y s t e r i o u s l y called t h e p s e u d o - A r i s t o t l e , w o r k e d out t h e law intuitively and put it in a m o r e unders t a n d a b l e w a y : ". . . as t h e w e i g h t m o v e d is to t h e w e i g h t m o v ing it, so, inversely, is t h e l e n g t h of t h e a r m b e a r i n g t h e w e i g h t to the length of the lever arm nearer the power." I d i s c o v e r e d t h e l e v e r principle e x p e r i m e n t a l l y , as m a n y c h i l d r e n d o , w h e n I f o u n d t h a t I w a s able to lift my father's w e i g h t on a seesaw, p r o v i d e d t h a t he sat sufficiently close to

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Figure 3 . 1 : Hypothetical Reconstruction of A r c h i m e d e s ' Ship-Lifting

Lever.

t h e m i d d l e w h i l e I sat on o n e e n d . He w e i g h e d t h r e e t i m e s as m u c h as I did, so I h a d to sit t h r e e t i m e s as far a w a y from t h e middle (Figure 3.2).

Figure 3.2: B a l a n c i n g on a S e e s a w . The fulcrum, or balance point, is the point about which rotation occurs. Technically, a seesaw is a first-order lever, since the loads are on opposite sides of the fulcrum.

46


I quickly l e a r n e d to apply t h e lever principle to o t h e r situations, i n c l u d i n g t h e m e m o r a b l e occasion w h e n I u s e d o n e of m y father's carefully s h a r p e n e d chisels t o j i m m y o p e n t h e tightly stuck lid of a tin of c a n d i e s . My father said t h a t he w o u l d t e a c h me to u s e his chisels in t h a t way, b u t I a l r e a d y k n e w , a n d a v o i d e d t h e painful lesson b y h i d i n g i n t h e w a r d r o b e . As t i m e w e n t on I l e a r n e d t h a t t h e r e a r e o t h e r forms of lever, s u c h a s t h e w h e e l b a r r o w . M y struggling a t t e m p t s a t age t w e l v e to u s e o n e to shift a load of w e t c e m e n t led a friend's m o t h e r to s c r e a m in a l a r m : " O h , Lenny, d o n ' t do t h a t ; y o u ' l l bust a kafoops valve!" T h e lever principle w o r k e d fine, t h o u g h , a n d 1 d i d n ' t b u s t a kafoops valve, w h a t e v e r t h a t is (Figure 3.3). It w a s n ' t u n t i l I r e a c h e d h i g h school t h a t I l e a r n e d t h e v e r y s i m p l e m a t h e m a t i c s u n d e r l y i n g t h e u s e of levers, a n d realized t h a t this could b e u s e d t o calculate i n a d v a n c e , a s A r c h i m e d e s h a d , j u s t w h e r e t o p u t a f u l c r u m a n d h o w t o design a lever t o d o a g i v e n j o b . I n o w u s e this k n o w l e d g e i n t h e design a n d c o n s t r u c t i o n o f scientific m e a s u r i n g i n s t r u m e n t s for m y o w n

Figure 3.3: The Wheelbarrow. Technically, a wheelbarrow is a second-order lever, since the load and the lifting force are on the s a m e side of the fulcrum, with the lifting force being further away than the load.

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and o t h e r p e o p l e ' s r e s e a r c h . O n l y recently, t h o u g h , did I start to w o n d e r w h e t h e r I could a p p l y this a n d a few o t h e r e q u a l l y simple physical principles t o i m p r o v e m y efficiency i n u s i n g h a n d tools to tackle s i m p l e d o m e s t i c j o b s . T h e s t i m u l u s for t h e t h o u g h t w a s a c o n v e r s a t i o n o v e r earlym o r n i n g coffee in t h e Physics D e p a r t m e n t at Bristol University, w h e r e I raised t h e q u e s t i o n of w h y long-shafted s c r e w d r i v e r s a p p e a r t o b e easier t o u s e t h a n s h o r t e r s c r e w d r i v e r s o f t h e s a m e b l a d e w i d t h . It's a typical scientist's " w h y ? " q u e s t i o n . C o n t r a r y to p o p u l a r belief, t h e r e is no p r e s c r i b e d , r i g o r o u s , logical p a t h lor finding t h e "scientific" a n s w e r to s u c h a q u e s tion. It's v e r y m u c h a m a t t e r of style, w i t h i n d i v i d u a l scientists following o n e of t h r e e b r o a d a p p r o a c h e s . T h e first is to w o r k o u t a n a n s w e r based o n f u n d a m e n t a l principles, n o t a c c e p t i n g or e v e n caring w h a t o t h e r s m i g h t h a v e said b e f o r e . S o m e of t h e scientists b e s t - k n o w n t o t h e public, s u c h a s A r c h i m e d e s , N e w t o n , a n d Einstein, w o r k e d i n this w a y . T h o s e w h o a r e capable of u s i n g this a p p r o a c h t e n d to be t h e gadflies of t h e scientific c o m m u n i t y , r e s p e c t e d , a n d s o m e t i m e s feared, b y t h e i r fellow scientists. O n e s u c h w a s J o h n C o n r a d Jaeger, t h e A u s t r a l i a n c o a u t h o r of an influential applied m a t h e m a t i c s t e x t b o o k . A friend of m i n e w a s p r e s e n t w h e n J a e g e r w a s i n t h e a u d i e n c e for a s e m inar given by a s t u d e n t just finishing his P h . D at t h e U n i v e r s i t y of T a s m a n i a . It w a s in t h e e a r l y d a y s of c o m p u t e r s , a n d t h e s t u d e n t w a s r e p o r t i n g his success in u s i n g o n e to tackle a p a r ticularly c o m p l i c a t e d p r o b l e m . M y friend describes h o w t h e s t u d e n t e n d e d his s e m i n a r w i t h a flourish a s h e p r o d u c e d t h e c o m p l e t e s o l u t i o n t o t h e p r o b l e m , t h e n stood back w i t h his s u pervisor, b a s k i n g in t h e a d u l a t i o n . J a e g e r a s k e d if he m i g h t c o m e t o t h e b l a c k b o a r d , w h i c h w a s still c o v e r e d w i t h t h e s t u d e n t ' s e q u a t i o n s . Picking u p a piece o f chalk, h e b e g a n m u m bling to himself, "The limit of this f u n c t i o n is s o - a n d - s o ; t h a t expression is a p p r o x i m a t e d as this; t h e s e t w o t e r m s cancel . . ." After a m i n u t e o r so, h e p r o d u c e d t h e s o l u t i o n t o t h e p r o b l e m , glanced o v e r at t h e s t u d e n t ' s results, said, "Yes, t h a t ' s right," a n d sat d o w n .

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Science could h a r d l y s u r v i v e w i t h o u t p e o p l e like Jaeger, w h o h a v e t h e capacity to see straight t h r o u g h to t h e h e a r t of a p r o b l e m . 1 h a v e b e e n privileged to w o r k w i t h a few s u c h p e o p l e in t h e c o u r s e of my scientific career. O n e w a s a m a t h e m a t i c i a n w h o c o u l d solve p r o b l e m s w h e r e 1 w o u l d n ' t e v e n k n o w h o w t o start. I could a t least u n d e r s t a n d t h e a n s w e r s , since I h a d o n c e d o n e a d e g r e e in p u r e m a t h e m a t i c s . 1 i n c a u tiously r e v e a l e d this fact o n e day, w h e r e u p o n h e t u r n e d , l o o k e d a t m e w i t h a s t o n i s h m e n t , a n d said, "You?!" A t Bristol t h e y w e r e m o r e polite, b u t e q u a l l y forthright, w h e n 1 raised the problem of the screwdriver. My a r g u m e n t was that longer s c r e w d r i v e r s m u s t b e easier t o u s e b e c a u s e t h e y can b e tilted slightly w i t h o u t t h e h e a d c o m i n g o u t o f t h e slot, t h u s p r o v i d ing a d d e d l e v e r a g e . My c o l l e a g u e Jeff Odell calculated, in t h e t i m e t h a t it t o o k for o n e sip of coffee, t h a t a tilt of a few d e grees w o u l d a d d little t o t h e r o t a t i o n a l force, a n d c o m m e n t e d t h a t , in a n y case, l e v e r a g e h a d little to do w i t h it. "A firmly h e l d s c r e w d r i v e r , " he c o m m e n t e d , "is s i m p l y an e x t e n s i o n of t h e a r m . The ease of rotating the forearm is t h e only thing that c o u n t s . L o n g e r s c r e w d r i v e r s a r e p r o b a b l y easier t o u s e b e c a u s e t h e h a n d l e s a r e bigger a n d easier t o grip w i t h o u t slipping." I h a d n o a n s w e r t o t h a t o t h e r t h a n t o g o a w a y a n d try t h e e x p e r i m e n t . T h e results of this a p p r o a c h a r e given later in this c h a p t e r . It's t h e a p p r o a c h t h a t f h a v e m o s t often u s e d i n m y scientific career, a n d o n e t h a t p u t s m e f i r m l y i n t h e s e c o n d c a m p of scientists — t h o s e w h o s e first instinct is to m e a s u r e something and think about the results afterwards. My favorite e x a m p l e of this style of tackling scientific q u e s tions is t h a t of Lord R u t h e r f o r d , t h e bluff N e w Z e a l a n d e r w h o d o m i n a t e d British physics early in t h e last c e n t u r y . R u t h e r f o r d w a s s t u d y i n g a l p h a - p a r t i c l e s — h e a v y , positively c h a r g e d p a r ticles t h a t a r e e m i t t e d from s o m e r a d i o a c t i v e m a t e r i a l s like bullets a n d w h i c h travel at an a p p r e c i a b l e fraction of t h e speed of light. He l a t e r recalled t h a t " O n e d a y Geiger [his r i g h t - h a n d m a n , a n d t h e i n v e n t o r o f t h e Geiger c o u n t e r ] c a m e t o m e a n d said, ' D o n ' t y o u t h i n k y o u n g M a r s d e n w h o m I a m t r a i n i n g i n r a d i o a c t i v e m e t h o d s o u g h t to begin a small r e s e a r c h ? ' N o w I

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had t h o u g h t so too, so I said, ' W h y not let h i m see if a n y a l p h a particles c a n be s c a t t e r e d t h r o u g h a large a n g l e [from a t h i n piece of gold foil]?'" On t h e face of it, this w a s a crazy e x p e r i m e n t , w i t h no realistic c h a n c e of success. At t h e t i m e , a t o m s w e r e b e l i e v e d to be like tiny i n d i v i d u a l p l u m p u d d i n g s , w i t h n e g a t i v e l y c h a r g e d electrons ( t h e raisins) d o t t e d r a n d o m l y a b o u t in a spherical haze of positive c h a r g e (the p u d d i n g ) . S p e e d i n g a l p h a - p a r t i c l e s s h o u l d pass s t r a i g h t t h r o u g h a m a t e r i a l built from s u c h a t o m s w i t h no m o r e t r o u b l e t h a n a rifle b u l l e t t h r o u g h a real p l u m p u d d i n g . Yet w h e n M a r s d e n tried t h e e x p e r i m e n t , m a n y alpha-particles w e r e deviated widely from their paths, a n d s o m e w e r e e v e n reflected back i n t h e d i r e c t i o n from w h i c h t h e y h a d c o m e . A c c o r d i n g t o R u t h e r f o r d , this w a s " q u i t e t h e m o s t incredible e v e n t t h a t h a s e v e r h a p p e n e d t o m e i n m y life . . . I t w a s a l m o s t as i n c r e d i b l e as if y o u fired a fifteen-inch shell at a piece of tissue p a p e r a n d it c a m e back a n d hit y o u . " R u t h e r f o r d h a d no r e a s o n to e x p e c t s u c h a s p e c t a c u l a r effect, b u t h e h a d d o n e w h a t m a n y scientists w i t h a g o o d e x p e r i m e n t a l instinct do; t h a t is, to try s o m e t h i n g t h a t could be i m p o r t a n t if it worked, a n d n o t b o t h e r i n g t o o m u c h a b o u t w h e t h e r it w a s a c t u a l l y likely to w o r k . T h e less likely an e x p e r i m e n t is to w o r k , t h e m o r e significant t h e result is likely to be. I n this case, t h e result w a s v e r y significant, a n d led R u t h e r ford t o d e v e l o p t h e m o d e r n p i c t u r e o f t h e a t o m , w i t h t h e " h a z e of positive c h a r g e " a c t u a l l y c o n c e n t r a t e d as a c e n t r a l l u m p ( t h e a t o m i c n u c l e u s ) , s u b s t a n t i a l e n o u g h t o deflect a l p h a - p a r t i c l e s t h a t a p p r o a c h t o o closely. R u t h e r f o r d ' s a p p r o a c h of trying out an i n s t i n c t i v e idea w a s probably t h e o n e used b y t h e early i n v e n t o r s o f h a n d tools, including t h e u n k n o w n p e r s o n w h o f i r s t t h o u g h t o f t y i n g a h a n d l e t o t h e piece o f rock u s e d t o s m a s h a n i m a l b o n e s , t h u s t u r n i n g t h a t piece of rock i n t o a h a m m e r . T h e real R u t h e r f o r d o f t h e h a m m e r w o r l d , t h o u g h , w a s t h e p e r s o n w h o , after several t h o u s a n d y e a r s of p o o r l y tied h e a d s flying off h a m m e r h a n d l e s , c o n c e i v e d t h e idea of p u t t i n g a h o l e in t h e h e a d a n d fitting the handle into that.

50

h o w to d u n k a

doughnut

M a n y varieties of h a m m e r h a v e since b e e n d e v e l o p e d . I w a s i n t e r e s t e d t o find o u t w h e t h e r a n y o n e h a d t a k e n R u t h e r f o r d ' s n e x t step, t h e o n e t h a t m a r k s a t r u e scientist, of a s k i n g why h a m m e r s , s c r e w d r i v e r s , a n d o t h e r h a n d tools w o r k i n t h e w a y t h a t t h e y d o a n d , i f so, w h e t h e r this i n f o r m a t i o n h a d b e e n o r could b e u s e d t o o p t i m i z e t h e w a y t h a t w e n o w design a n d u s e t h e s e tools. To do so, I e n r o l l e d myself in t h e t h i r d a n d largest scientific c a m p — t h a t c o m p o s e d of scientists w h o , sensibly, look t o find w h a t o t h e r s h a v e d o n e b e f o r e t h e y g o o n t o c o n sider a q u e s t i o n f u r t h e r t h e m s e l v e s . S o m e of t h e v e r y best scientists b e l o n g in this c a m p , providing t h e m o r t a r t h a t h o l d s t h e w h o l e s t r u c t u r e of science together. T h e y a r e p e o p l e like my early collaborator J a c o b Israelachvili ( n o w a t Santa B a r b a r a ) , t h e scientist w h o f i r s t m e a s u r e d t h e forces b e t w e e n surfaces so closely spaced t h a t no m o r e t h a n a few a t o m s could h a v e fitted b e t w e e n t h e m — an e x p e r i m e n t t h a t m a n y , i n c l u d i n g myself, h a d t h o u g h t impossible. He perf o r m e d t h e s e e x p e r i m e n t s for his Ph.D, a n d later told me t h a t he h a d s p e n t t w o a n d t h r e e - q u a r t e r years o u t o f t h e allotted t h r e e i n s t u d y i n g w h a t o t h e r s h a d d o n e a n d using this k n o w l e d g e t o design a n d build e q u i p m e n t t o d o t h e j o b better. H e t h e n took just t w o m o n t h s t o p e r f o r m t h e m e a s u r e m e n t s t h a t m a d e h i m f a m o u s , b u t his success w a s d u e in large part to t h e f o r e k n o w l edge w i t h w h i c h h e h a d a r m e d himself. The design of Jacob's e q u i p m e n t was based on an intimate u n d e r s t a n d i n g of t h e scientific principles i n v o l v e d . Is t h e s a m e t r u e for t h e d e v e l o p m e n t of h a n d tools? I w e n t in search of t h e w r i t t e n e v i d e n c e a n d q u i c k l y f o u n d , w i t h t h e h e l p of a friendly e n g i n e e r i n g librarian, t h a t c o m p a r a t i v e l y little h a s b e e n w r i t t e n a b o u t t h e science u n d e r p i n n i n g t h e u s e o f h a n d tools. O n l y a few s c a t t e r e d r e f e r e n c e s b o r e r e l a t i o n to t h e s u b ject. E v e n t h e closely p r i n t e d t h i r t y - t w o - p a g e article e n t i t l e d "Tool" in t h e f a m o u s 1911 edition of t h e Encylopaedia Britannica ( a n article still referred to by t h e m o d e r n e d i t i o n ) failed to say a single w o r d on why tools a r e d e s i g n e d a n d u s e d as t h e y a r e . I s o u g h t o u t S t u a r t Burgess, a design e x p e r t w h o r u n s a s e c o n d - y e a r c o u r s e o n m a c h i n e tools a t Bristol University.

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Could h e h e l p ? H e w a s o n l y t o o p l e a s e d . Not t o h e l p , b u t t o find t h a t I w a s w r i t i n g s o m e t h i n g on t h e subject. T h e r e w a s n o t h i n g o f this n a t u r e available, h e said, a n d p r o m i s e d t o reco m m e n d m y b o o k t o his s t u d e n t s w h e n i t w a s f i n i s h e d . Perhaps, I t h o u g h t , h a n d tools w o u l d f e a t u r e in physics c o u r s e s as e x e m p l i l i e r s of s i m p l e m e c h a n i c a l p r i n c i p l e s . I a s k e d my physicist friends a n d f o u n d t h a t , w h i l e t h e basic principles a r e taught, such applications are not. 1 was on my o w n . Well, n o t entirely on my o w n . A lifetime in science has given me plenty of p e o p l e to talk to a n d w i t h w h o m to try o u t ideas. That's h o w science usually w o r k s — n o t by p e o p l e sitting a l o n e in ivory t o w e r s , b u t by p e o p l e s h a r i n g ideas, talking a b o u t results, a n d suggesting n e w a p p r o a c h e s i n e n v i r o n m e n t s t h a t a r e s o m e t i m e s iar r e m o v e d from t h e traditional lab. Science, in other words, is a c o m m u n i t y activity, a n d I h a v e m o r e t h a n my fair s h a r e of friends a n d colleagues w h o a r e willing to offer help, ideas, a n d criticism, in v a r y i n g p r o p o r t i o n s , ft w a s to t h e s e people, a n d t o m y h a n d y m a n a n d t r a d e s m a n friends, t h a t I t u r n e d in my quest to u n d e r s t a n d t h e scientific tao of tools. M y first q u e s t i o n w a s " W h y d o w e u s e t o o l s ? " Galileo b e rated t r a d e s m e n four h u n d r e d y e a r s a g o for h o l d i n g t h e m i s t a k e n belie! t h a t w e u s e tools b e c a u s e t h e y m a k e j o b s easier. Despite Galileo's strictures, I s u s p e c t e d t h a t t h e s a m e belief w o u l d still be c u r r e n t today. I w a s w r o n g . Every o n e of my practical friends g a v e m e t h e scientist's a n s w e r , w h i c h i s t h a t tools d o n ' t s o m u c h m a k e j o b s easier a s m a k e j o b s possible, b y r e d u c i n g t h e b r u t e force r e q u i r e d t o m a n a g e a b l e p r o p o r t i o n s . An e x a m p l e is t h e u s e of a car j a c k . A p e r s o n u s i n g an a v e r a g e car jack can lift a 5 0 0 - k i l o g r a m car w i t h a force t h a t w o u l d only lift 5 k i l o g r a m s directly. T h e w e i g h t lifted is a h u n d r e d times t h e lorce applied, a n d so t h e j a c k is said to give a 1

Scientists are used to thinking ol lorce in terms of Newtons. To lift 5 kilograms would take a force of 49 Newtons, a quantity that most people outside science would find hard to visualize. To make life easier for the reader, I will henceforth refer to forces in terms of the mass that they would lift. W h e n I say, for example, lorce of 5 kilograms," I mean "a force that would lift 5 kilograms at the Earth's surface" (the same force w o u l d lift more on the M o o n ) , with a brief nod of apology toward those w h o would prefer more exactitude of nomenclature. 1

a

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mechanical advantage of 100:1. W h e n I used my childhood weight of 25 kilograms to lift my 75-kilogram father from t h e g r o u n d on a seesaw, I w a s e x e r t i n g a m e c h a n i c a l a d v a n t a g e of 3:1. T h e d o w n s i d e of a m e c h a n i c a l a d v a n t a g e is t h a t t h e r e d u c tion in force m u s t be paid for by an i n c r e a s e in t h e d i s t a n c e o v e r w h i c h t h e p o i n t of a p p l i c a t i o n of t h e force is m o v e d . W h a t e v e r h e i g h t t h e car i s raised to, t h e j a c k h a n d l e m u s t b e p u m p e d t h r o u g h a h u n d r e d t i m e s t h a t d i s t a n c e . T h e r e ' s n o escape. W h y is t h e r e no escape? The reason was discovered by Galileo, w h o u s e d a series of v e r y clever a r g u m e n t s to s h o w that, in the performance of any job requiring the application of force, force multiplied by the distance through which its point of application is moved is a c o n s t a n t q u a n t i t y t h a t c a n ' t be c h a n g e d , n o m a t t e r h o w m u c h w e wriggle o r h o w cleverly w e design o u r tool o r m a c h i n e . Scientists n o w call force X distance by a n o t h e r n a m e — work. It is a basic p r i n c i p l e of science, d e r i v e d t h e s e d a y s from t h e notion that energy can neither be created nor destroyed, that t h e w o r k t h a t w e h a v e t o d o i n p e r f o r m i n g a j o b i s unaffected by the way in which we do the job. Galileo k n e w n o t h i n g of t h e principle of t h e c o n s e r v a t i o n of e n e r g y , a n d 1 h a d n o t e v e n s e e n his a p p r o a c h t o t h e q u e s t i o n until I b e g a n p u t t i n g t o g e t h e r t h e m a t e r i a l for this b o o k . W h e n I e v e n t u a l l y did find his a r g u m e n t , w r i t t e n for a lay a u d i e n c e , I w i s h e d t h a t I could w r i t e like t h a t . It w a s so a u d a ciously s i m p l e t h a t I b u r s t o u t l a u g h i n g w h i l e r e a d i n g it. In his o w n w o r d s : " . . . t h e a d v a n t a g e a c q u i r e d from t h e l e n g t h o f t h e lever is n o t h i n g b u t t h e ability to m o v e all at once [ m y italics] t h a t h e a v y b o d y w h i c h could b e c o n d u c t e d o n l y i n pieces b y t h e s a m e force . . . a n d w i t h e q u a l m o t i o n , w i t h o u t t h e benefit of t h e lever." In o t h e r w o r d s , if we cut o u r 5 0 0 - k i l o g r a m car into a h u n d r e d e q u a l pieces, e a c h w e i g h i n g 5 kilograms, a n d t h e n lifted e a c h of t h e s e pieces t h r o u g h 30 c e n t i m e t e r s by h a n d , we w o u l d be d o i n g t h e s a m e w o r k (5 kg X 30 cm X 100) as if we h a d p u m p e d t h e j a c k h a n d l e t h r o u g h 30 m e t e r s to lift t h e w h o l e car a t o n c e ( w h e r e t h e w o r k w o u l d b e 5 0 0 k g X 3 0

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cm). All t h a t t h e j a c k h a s d o n e is to let us c h a n g e t h e b a l a n c e b e t w e e n force a n d d i s t a n c e . T h e p r o d u c t o f t h e t w o r e m a i n s t h e s a m e . Galileo w e n t o n t o s h o w t h a t t h e s a m e a r g u m e n t h o l d s for a n y tool. Galileo's principle t h a t a tool c a n ' t c h a n g e t h e a c t u a l a m o u n t of w o r k n e e d e d to do a j o b , b u t o n l y c h a n g e t h e b a l a n c e b e t w e e n force a n d d i s t a n c e , h o l d s g o o d so l o n g as all of t h e w o r k goes i n t o d o i n g t h e j o b . If d o i n g t h e j o b w i t h o u t a tool i n v o l v e s wasting s o m e of t h e w o r k , t h e n t h e u s e of a tool o b v i o u s l y does save w o r k . If, for e x a m p l e , we try to slide a load of bricks along a p a t h by h a n d , t h e n a lot of t h e w o r k t h a t we do goes into o v e r c o m i n g friction b e t w e e n t h e bricks a n d t h e p a t h r a t h e r t h a n m o v i n g t h e bricks. T h e e x t r a w o r k i s t u r n e d i n t o h e a t e n e r g y t h a t i s t h e n dissipated i n t o t h e s u r r o u n d i n g s a n d c a n n o t be r e c o v e r e d . If we c a r r y t h e s a m e load of bricks a l o n g t h e p a t h i n a w h e e l b a r r o w , w e avoid t h e friction, a n d save t h e extra w o r k . I t follows from t h e discussion a b o v e t h a t t h e r e a r e t w o q u e s tions to be a n s w e r e d w h e n it c o m e s to t h e effective u s e of h a n d tools: 1. Is t h e m e c h a n i c a l a d v a n t a g e as h i g h as it c o u l d or s h o u l d be? 2. Is t h e w a s t e of e n e r g y (e.g., in friction) as l o w as it c o u l d be? 1 decided to ask t h e s e q u e s t i o n s of s o m e of t h e c o m m o n h a n d tools used by t r a d e s m e n , h a n d y m e n , a n d do-it-yourselfers. Even in t h e limited t i m e available, I e n d e d up w i t h e n o u g h m a t e r i a l to m a k e a w h o l e b o o k in its o w n right. W h a t follows is a selection of t h e p o i n t s t h a t 1 f o u n d m o s t i n t e r e s t i n g a n d w h i c h h a n d y m e n a n d do-it-yourselfers m i g h t f i n d m o s t useful. In o r d e r to categorize t h e tools in s o m e way, I t u r n e d a g a i n to t h e article "Tool" in t h e a u t h o r i t a t i v e Encyclopaedia Britannica of 1 9 1 1 . A c c o r d i n g to t h e writer, t h e Victorian a u t h o r i t y J o s e p h G. H o r n e r , tools fall i n t o j u s t five g r o u p s :


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I II III IV V

Chisels T h e s h e a r i n g g r o u p (e.g., scissors) Scrapers T h e p e r c u s s i v e g r o u p (e.g., h a m m e r s ) T h e m o l d i n g g r o u p (e.g., t r o w e l s )

T h e r e w a s n o m e n t i o n o f tools b a s e d o n t h e lever principle, a n d n o m e n t i o n o f a n o t h e r i m p o r t a n t g r o u p : tools t h a t u s e a w e d g e a c t i o n . At t h e risk of i n c u r r i n g t h e w r a t h of Mr. H o r n e r ' s ghost, I d e c i d e d to e x a m i n e just o n e of his categories, b u t to a d d t w o of my o w n . My full list is t h u s : 1. Tools b a s e d on t h e lever principle 2 . Tools t h a t u s e t h e w e d g e principle 3. Percussive tools

T o o l s B a s e d o n the Lever Principle

The Claw Hammer

A c c o r d i n g t o p u b l i s h e d tables, t h e initial force n e e d e d t o w i t h d r a w a 2 - i n c h ( 5 0 - m i l l i m e t e r ) nail d r i v e n i n t o t h e side grain of a block of s e a s o n e d h a r d w o o d is e q u i v a l e n t to lifting a w e i g h t of 26 k i l o g r a m s . T h a t is w h y it is so difficult to pull a nail o u t w i t h a pair of pliers, a n d w h y we use a c l a w h a m m e r as a lever to do the job. T h e design of a typical d o m e s t i c c l a w h a m m e r m a k e s it v e r y easy t o start t h e p u l l . T h e m e c h a n i c a l a d v a n t a g e i s e n o r m o u s , since t h e f u l c r u m i s v e r y close t o t h e nail. M y o w n 7 0 0 - g r a m claw h a m m e r h a s a h a n d l e l e n g t h of 330 m i l l i m e t e r s , w i t h t h e initial c o n t a c t p o i n t o f t h e h a m m e r h e a d w i t h t h e w o o d b e i n g o n l y 10 m i l l i m e t e r s from t h e nail axis. A m e c h a n i c a l a d v a n lage of 3 3 0 / t 0 = 33 m e a n s t h a t I o n l y h a v e to a p p l y a force of less t h a n a k i l o g r a m to get t h e nail s t a r t e d (Figure 3.4). T h e m e c h a n i c a l a d v a n t a g e d r o p s v e r y fast a s t h e nail starts

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Fulcrum Figure 3.4: C l a w H a m m e r U s e d as a Lever to R e m o v e a Nail.

t o lift, b e c a u s e t h e c o n t a c t p o i n t o f t h e h e a d w i t h t h e w o o d m o v e s f u r t h e r a w a y from t h e nail a s t h e h a m m e r rocks o n its c u r v e d s p u r s . E v e n t u a l l y , t h e e d g e o f t h e h a m m e r face, 110 millimeters a w a y from t h e nail for m y h a m m e r , c o n t a c t s t h e w o o d , b y w h i c h stage t h e m e c h a n i c a l a d v a n t a g e h a s d r o p p e d t o a m e r e t h r e e a n d t h e nail h a s b e e n lifted o n l y 2 0 m i l l i m e ters. If t h e h a m m e r is r o c k e d a n y further, t h e h e a d will m a k e a d e n t i n t h e w o o d . T h e force t h a t w a s originally pulling t h e nail straight u p i s also n o w p u l l i n g i t a t a n a n g l e , w i t h t h e p o tential for f u r t h e r d a m a g e . Is this t h e best t h a t can be d o n e ? Professional t r a d e s m e n s o m e t i m e s i m p r o v e t h e situation by placing a small block of w o o d u n d e r t h e h a m m e r h e a d . M y father used t o explain that this w a s t o p r e v e n t d a m a g e t o t h e w o r k , a n a d v a n t a g e t h a t has to be paid for by loss of t h e initial m e c h a n i c a l a d v a n t a g e , since t h e fulcrum is n o w further from t h e nail at t h e start of t h e pull (Figure 3.5).

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Fulcrum Figure 3.5: U s e of a S m a l l Block of W o o d to Improve the R a n g e of M o v e m e n t of a C l a w H a m m e r .

T h e m e c h a n i c a l a d v a n t a g e is still q u i t e good, h o w e v e r , a n d also d o e s n o t c h a n g e v e r y m u c h t h r o u g h t h e w h o l e lilting process. If t h e piece of w o o d is a 10-millimeter cube, for e x a m p l e , a n d placed n e a r t h e base o f t h e h a n d l e , t h e m e c h a n i c a l a d v a n t a g e w i t h my o w n h a m m e r d r o p s from f 0: f to 8: f d u r i n g a single pull, w h i c h m e a n s that 1 h a v e to e x e r t an initial force of 2.6 k i l o g r a m s , a v a l u e t h a t is still satisfactorily low. F u r t h e r m o r e , t h e j o b gets easier a s t h e h a m m e r i s rocked, e v e n t h o u g h t h e m e c h a n i c a l a d v a n t a g e is d r o p p i n g . This is b e c a u s e t h e pulling force t h a t is n e e d e d is p r o p o r t i o n a l to t h e l e n g t h of e m b e d d e d nail; w i t h half t h e nail w i t h d r a w n , o n l y half t h e force is n e e d e d . T h e real a d v a n t a g e of t h e little block of w o o d , t h o u g h , is t h a t t h e nail c a n be lifted t h r o u g h a full 35 m i l l i m e t e r s in a single pull. W i t h o n l y 1 5 millimeters left e m b e d d e d , t h e j o b can n o w be finished off by a direct pull w i t h a pair of pliers, since this n o w r e q u i r e s a force of o n l y 26 X ( 1 5 / 5 0 ) = 7.8 kg.

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In t h i n k i n g all of this t h r o u g h , I c a m e up w i t h a n o t h e r idea, w h i c h I will claim as my o w n until s o m e o n e c o m e s a l o n g a n d tells me that t r a d e s m e n h a v e b e e n d o i n g it lor ages. M a k e a stepped block o u t of several pieces of w o o d , a n d slip it p r o g r e s sively f u r t h e r u n d e r t h e h a m m e r h e a d as t h e nail is lifted. T h e stepped block can be k e p t as part of a r e g u l a r tool kit, a n d e n ables nails of a n y l e n g t h to be w i t h d r a w n in a single o p e r a t i o n .

The Wrench

T h e ideal w r e n c h is o n e t h a t e x e r t s p u r e t o r q u e — in o t h e r w o r d s , all t h e force e x e r t e d g o e s i n t o r o t a t i n g t h e bolt or t h e n u t . M y i l l - r e m e m b e r e d c o u r s e s i n applied m a t h e m a t i c s t a u g h t me t h a t this is o n l y possible if t h e w r e n c h is s y m m e t r i cal, as in t h e design s h o w n in Figure 3.6. An a d v a n t a g e of s u c h a design for a h a n d w r e n c h is t h a t b o t h h a n d s can be used to exert force.

T h e forces o n t h e t w o e n d s a r e e q u a l , b u t act i n o p p o s i t e directions. If t w o s u c h forces lie in t h e s a m e line, as t h e y w o u l d , for e x a m p l e , if g e n e r a t e d by t w o e q u a l l y s t r o n g i n d i v i d u a l s pulling o n a r o p e , t h e n t h e y w o u l d b e i n b a l a n c e a n d n o t h i n g w o u l d m o v e . S e p a r a t e d laterally i n space, t h o u g h , t h e forces c o n s t i t u t e a couple. T h e t o r q u e , or t w i s t i n g force, e x e r t e d by a couple is simply t h e force m u l t i p l i e d by t h e s e p a r a t i o n dist a n c e ( m y s c h o o l physics t e a c h e r , well a t t u n e d t o t h e p r e o c c u -

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h o w to d u n k a

doughnut

p a t i o n s o f t h e a d o l e s c e n t m i n d , t a u g h t u s t h a t " t h e closer t h e c o u p l e , t h e less t h e t o r q u e " ) . It is n o t so easy to w o r k o u t t h e m e c h a n i c a l a d v a n t a g e t h a t t h e w r e n c h a b o v e w o u l d c o n v e y o v e r t u r n i n g t h e bolt w i t h t h e f i n g e r s , b e c a u s e t h e grip a n d t h e a c t u a l m o v e m e n t o f t h e m u s c l e s a r e q u i t e different i n u s i n g t h e f i n g e r s o r g r a s p i n g t w o e n d s o f a b a r a n d pulling o n o n e e n d w h i l e p u s h i n g o n t h e o t h e r . A b e t t e r c o m p a r i s o n is w i t h w r a p p i n g a c o u p l e of pieces o f t a p e , o n e a b o v e t h e o t h e r , a r o u n d t h e bolt h e a d i n o p p o s i t e d i r e c t i o n s a n d p u l l i n g on t h e free e n d s ( q u i t e a g o o d trick, incidentally, if no w r e n c h is h a n d y ) . In this case, t h e s a m e force can b e e x e r t e d a s i n u s i n g t h e w r e n c h . T h e m e c h a n i c a l a d v a n tage from using t h e w r e n c h is j u s t t h e r a t i o of t h e t o r q u e s i n t h e t w o cases. Since t h e forces a r e e q u a l , t h e m e c h a n i c a l a d v a n t a g e is s i m p l y t h e ratio of t h e d i s t a n c e s by w h i c h t h e forces a r e s e p a r a t e d laterally in t h e t w o cases, i.e., t h e ratio of t h e overall l e n g t h of t h e w r e n c h to t h e d i a m e t e r of t h e bolt head. U n f o r t u n a t e l y for t h e p e a c e of m i n d of c a l c u l a t i n g p h y s i cists, m o s t w r e n c h e s h a v e o n l y o n e h a n d l e , a n d w o r k i n g o u t t h e m e c h a n i c a l a d v a n t a g e is n o t so easy. A s i n g l e - h a n d l e d w r e n c h d o e s n o t e x e r t p u r e t o r q u e — it also e x e r t s a lateral force w h i c h t e n d s t o m o v e a n u n s e c u r e d j o b s i d e w a y s . I f t h e j o b is s e c u r e d by a c l a m p or o t h e r m e a n s , t h e s i d e w a y s force is still t h e r e , p u s h i n g o n t h e bolt o r n u t a n d i n c r e a s i n g t h e frictional r e s i s t a n c e t h a t h a s t o b e o v e r c o m e , t h u s d e c r e a s i n g t h e real m e c h a n i c a l a d v a n t a g e . For t h e p u r p o s e s of a s i m p l e analysis, a s i n g l e - h a n d l e d w r e n c h can be v i e w e d as a lever, w h e r e t h e n e a r e s t p o i n t o f c o n t a c t o n t h e n u t o r bolt h e a d i s the fulcrum, and the furthest point of contact transmits t h e force t o t u r n t h e n u t a b o u t t h a t f u l c r u m (Figure 3.7). This p i c t u r e is oversimplified (since t h e f u l c r u m c a n m o v e ) , b u t it d o e s let us calculate t h e m e c h a n i c a l a d v a n t a g e for s u c h a w r e n c h , w h i c h is s i m p l y t h e d i s t a n c e from t h e e n d of t h e h a n d l e t o t h e p o i n t o f f i r s t c o n t a c t w i t h t h e n u t o r bolt h e a d divided by t h e l e n g t h of o n e side of t h e n u t or bolt h e a d . In t h e e x a m p l e a b o v e , t h e m e c h a n i c a l a d v a n t a g e is 2 5 / 5 = 5:1. This

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Figure 3.7: Lever Action of a S i n g l e - H a n d l e d W r e n c h .

is half t h e m e c h a n i c a l a d v a n t a g e t h a t a similar w r e n c h w i t h two handles w o u l d provide. A n easier w a y o f t h i n k i n g a b o u t t h e difference b e t w e e n one-handled and two-handled wrenches, and one that is very r e p r e s e n t a t i v e of h o w physicists t h i n k , is to fall back on Galileo's p r i n c i p l e t h a t t h e t o t a l w o r k d o n e i s n o t affected b y h o w it is d o n e . This m e a n s t h a t force X distance m u s t be t h e s a m e i n t h e t w o cases. W i t h t h e t w o - h a n d l e d w r e n c h , t h e t w o points of a p p l i c a t i o n m o v e a total of t w i c e as far as t h e single point of a p p l i c a t i o n for t h e o n e - h a n d l e d w r e n c h . Since t h e distance i s d o u b l e d , t h e force m u s t b e h a l v e d , w h i c h m e a n s that t h e t w o - h a n d l e d w r e n c h is t w i c e as efficient, i.e., it h a s twice t h e m e c h a n i c a l a d v a n t a g e o f t h e o n e - h a n d l e d w r e n c h . Even so, a s i n g l e - h a n d l e d w r e n c h is a p r e t t y effective w e a p o n . But w h y d o w e n e e d s u c h a w e a p o n ? W h a t i s t h e a c t u a l a d v a n t a g e of t i g h t e n i n g a n u t or bolt u s i n g a w r e n c h ? T h e r e a son, as I f o u n d o u t in p r a c t i c e w h e n d e s i g n i n g h i g h - p r e c i s i o n e q u i p m e n t , is t h a t t h e use of a w r e n c h lets us a p p l y e n o u g h force to a c t u a l l y s t r e t c h t h e bolt. T h e s t r e t c h e d bolt acts as a very s t r o n g spring, g e n e r a t i n g a force t h a t i n c r e a s e s t h e friction b e t w e e n t h e m a t i n g m a l e a n d f e m a l e t h r e a d s , a n d w h i c h also increases t h e friction b e t w e e n t h e h e a d a n d t h e n u t (if t h e r e is o n e ) w i t h t h e c o r r e s p o n d i n g surfaces of t h e w o r k , m a k i n g it m o r e difficult for t h e bolt to w o r k loose. T h e a m o u n t

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by w h i c h a bolt n e e d s to be s t r e t c h e d in o r d e r to stay tight d e p e n d s v e r y m u c h o n its e n v i r o n m e n t . T h e bolts i n a v i b r a t i n g car e n g i n e , for e x a m p l e , o b v i o u s l y n e e d t o b e d o n e u p m o r e tightly t h a n t h o s e h o l d i n g a w o o d e n b e n c h t o g e t h e r . Bolts h o l d i n g m e t a l pieces t o g e t h e r c a n also b e d o n e u p m o r e tightly t h a n t h o s e passing t h r o u g h w o o d w i t h o u t risk o f d e f o r m i n g o r damaging the work. But h o w tightly? H o w is the t o r q u e that is u s e d to do up a bolt r e l a t e d to its d e g r e e of s t r e t c h i n g a n d to t h e spring force t h a t i t e x e r t s ? W h a t spring force s h o u l d o n e a i m for? A r e t h e r e s i m p l e r u l e s t h a t t h e h a n d y m a n can follow? I s e a r c h e d for t h e a n s w e r s in e n g i n e e r i n g r e f e r e n c e b o o k s , a n d rapidly f o u n d myself i m m e r s e d in a m o r a s s of f o r m u l a e w h i c h d e s c r i b e d t h e effects of bolt d i a m e t e r , bolt m a t e r i a l , pitch, s h a p e a n d d e p t h o f t h e t h r e a d , a n d e v e n w h e t h e r t h e bolt is likely to be s u b j e c t e d to e x t r a forces after it is d o n e u p (e.g., bolts h o l d i n g t h e h e a d o n t o a car e n g i n e b l o c k ) . Typical o f t h e f o r m u l a e t h a t c o n f r o n t e d m e w a s t h a t o f t h e m i n i m u m length of engagement between two mating threads to avoid stripping t h e e x t e r n a l t h r e a d before t h e bolt actually breaks:

I find it d e p r e s s i n g e n o u g h w h e n I am forced to u s e s u c h form u l a e i n a professional c o n t e x t , a n d w o u l d b e t h e last p e r s o n t o inflict t h e m o n a h a n d y m a n . I l o o k e d t o see w h e t h e r t h e r e m i g h t be a b e t t e r w a y . T h e r e w a s . H i d d e n a m o n g t h e f o r m u l a e a n d tables w a s t h e i n f o r m a t i o n t h a t " e x p e r i m e n t s m a d e a t C o r n e l l U n i v e r s i t y [on behalf of t h e car i n d u s t r y ] . . . s h o w e d t h a t e x p e r i e n c e d m a chinists t i g h t e n n u t s w i t h a pull r o u g h l y p r o p o r t i o n a l t o t h e bolt d i a m e t e r , " a n d t h a t " t h e stress d u e t o n u t t i g h t e n i n g w a s often sufficient to b r e a k a half-inch bolt, b u t n o t larger sizes." As a result of this study, e n g i n e e r i n g practice w a s c h a n g e d —

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n o t t o r e d u c e t h e force a p p l i e d t o t h e bolts, b u t t o u s e larger bolts t h a t t h e m e c h a n i c s c o u l d n ' t b r e a k ! It is possible, t h o u g h , to u s e t h e i n f o r m a t i o n in a different way. T h e t e n s i l e s t r e n g t h of t h e bolts in q u e s t i o n w a s a r o u n d 10,000 k i l o g r a m s (in o t h e r w o r d s , a rod m a d e of t h e bolt m a terial could s u p p o r t a w e i g h t of 1 0 , 0 0 0 k i l o g r a m s ) . A b o x w r e n c h d e s i g n e d to t i g h t e n s u c h a bolt typically h a s a l e n g t h of 20 c e n t i m e t e r s (0.2 m e t e r s ) , a n d by e x p e r i m e n t I h a v e found t h a t a r e a s o n a b l y s t r o n g m a n c a n pull o n t h e e n d o f such a w r e n c h w i t h a m a x i m u m force of a r o u n d 30 k i l o g r a m s . A t o r q u e of 30 kg X 0.2 m ( = 15 k g . m ) is t h u s sufficient to b r e a k a half-inch ( 1 2 - m i l l i m e t e r ) steel bolt. Bolts m a d e from w e a k e r m a t e r i a l s s u c h as brass or a l u m i n u m will r e q u i r e a correspondingly lower torque to generate the same breaking t e n s i o n . A practical c o m p r o m i s e to fasten a h a l f - i n c h bolt as tightly as possible w i t h o u t t h e risk of b r e a k a g e is to u s e a t o r q u e o f n o m o r e t h a n 8 k g . m . T h e limiting t o r q u e d e p e n d s on t h e cross-sectional area of t h e bolt. T h e limit for o n e - i n c h ( 2 5 - m i l l i m e t e r ) bolts, a c c o r d i n g t o t h e c r i t e r i o n a b o v e , i s t h u s 32 kg.m, w h i l e t h a t for q u a r t e r - i n c h ( 6 - m i l l i m e t e r ) bolts is 2 kg.m. This m e a n s t h a t t h e " e x p e r i e n c e d m a c h i n i s t s " got i t w r o n g — to g e n e r a t e t h e s a m e t e n s i o n in bolts of different dia m e t e r s , t h e y s h o u l d h a v e b e e n p u l l i n g w i t h a force p r o p o r tional, n o t t o t h e d i a m e t e r , b u t t o t h e s q u a r e o f t h e d i a m e t e r . I f you k n o w t h e m a x i m u m force t h a t y o u c a n e x e r t o n e h a n d e d (this can b e e s t i m a t e d b y f i n d i n g t h e h e a v i e s t w e i g h t that can b e lifted o n e - h a n d e d ) , y o u c a n u s e this i n f o r m a t i o n t o w o r k o u t w h e r e t o grip a w r e n c h s o a s t o p r o d u c e t h e m a x i m u m safe t o r q u e . Table 3.1 p r o v i d e s s o m e s a m p l e v a l u e s , w i t h t h e a s s u m p t i o n t h a t t h e l o n g e s t w r e n c h available i s 2 5 0 millimeters i n l e n g t h . Undoing a bolt is a different story. It takes m o r e force to u n d o even a clean, well-oiled bolt t h a n it does to do o n e u p , b e c a u s e the initial force to o v e r c o m e friction a n d get t h e m a t i n g surfaces sliding ( h e a d a n d n u t surfaces against t h e w o r k , a n d t w o threads against e a c h o t h e r ) i s g r e a t e r t h a n t h a t r e q u i r e d t o k e e p t h e m sliding, so w r e n c h e s will n e e d to be h e l d a little further


62

Table 3 . 1 : W h e r e to Grip a W r e n c h .

M a x i m u m force that operator

Bolt diameter ( m m )

10

20

30

40

Distance of grip from bolt h e a d ( m m )

can generate (kg) 4

88

6

200

8

Full length

10

Full length

12

Full length

4

44

6

100

8

170

10

250

12

Full length

4

30

6

67

8

113

10

170

12

Full length

4

22

6

50

8

85

10

125

12

200

o u t . W h e n it c o m e s to u n d o i n g a rusted bolt, t h e p r o b l e m is n o t that t h e t w o t h r e a d s are "stuck t o g e t h e r " b y t h e rust. T h e real p r o b l e m is that, as iron t u r n s to rust (a c o m p l e x reaction p r o d uct of iron, o x y g e n , a n d w a t e r ) it e x p a n d s , g e n e r a t i n g e n o r m o u s p r e s s u r e s t h a t increase t h e frictional forces b e t w e e n t h e t h r e a d s . O n e c a n see h o w high t h e p r e s s u r e s can b e b y looking at a s t o n e i n t o w h i c h iron spikes h a v e b e e n d r i v e n . As t h e iron rusts, it is n o t u n c o m m o n for t h e p r e s s u r e s g e n e r a t e d to be so high t h a t t h e s t o n e is split. Oil is of little u s e in r e d u c i n g t h e frictional forces c a u s e d by rust. A b e t t e r trick (if y o u h a v e t h e time) is to use a w e a k acid such as v i n e g a r to gradually p e n e t r a t e a n d dissolve t h e rust. Alternatively, if t h e j o i n t is accessible to heat, application of a p r o p a n e torch will e x p a n d t h e bolt, t h e n u t , a n d t h e gap in b e t w e e n to relieve s o m e of t h e p r e s s u r e .

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The Wheelbarrow

B a r r o w s did n o t a l w a y s h a v e w h e e l s . Before t h e f o u r t e e n t h century, a E u r o p e a n b a r r o w consisted of "a flat r e c t a n g u l a r frame of t r a n s v e r s e bars, h a v i n g shafts or ' t r a m s ' before a n d b e h i n d , by w h i c h it is carried [by t w o or m o r e m e n ] . " O n l y after A . D . 1 300 did t h e idea of p u t t i n g a w h e e l b e t w e e n t h e front shafts, i n v e n t e d a t h o u s a n d y e a r s earlier in C h i n a , finally m a k e its w a y t o t h e West a n d p e r m i t t h e c o n t r i v a n c e t o b e o p e r a t e d b y j u s t o n e m a n . This w a s o n e o f t h o s e i n c o n s p i c u o u s a d v a n c e s i n t e c h n o l o g y t h a t h e l p e d t o m a k e possible s u c h conspicuous m a r k e r s of progress as t h e great Gothic cathedrals of E u r o p e . W i t h it, a single w o r k e r could n o w shift large blocks of stone. W h e n some u n k n o w n genius put a box between the shafts i n s t e a d of a flat tray, b u i l d i n g r u b b l e a n d m o r t a r could also be carried. T h e load t h a t a single p e r s o n c a n shift u s i n g a w h e e l b a r r o w d e p e n d s on t h e p o s i t i o n of t h e w h e e l . In t e c h n i c a l t e r m s , a w h e e l b a r r o w is a s e c o n d - o r d e r lever, w i t h t h e load b e t w e e n t h e fulcrum ( t h e axle) a n d t h e p o i n t of a p p l i c a t i o n of t h e force (the h a n d l e s ) . If t h e axle w e r e placed directly u n d e r t h e load, as it w a s in flat-trayed m e d i e v a l b a r r o w s d e s i g n e d to c a r r y piles o f b o d i e s d u r i n g t h e p l a g u e years, t h e m e c h a n i c a l a d v a n tage w o u l d t h e o r e t i c a l l y be infinite, a n d a single p e r s o n c o u l d m o v e a n y load at all so long as t h e b a r r o w did n o t collapse. Such b a r r o w s , w h i c h s u r v i v e i n s o m e places a s m o r t u a r y trolleys, h a d a w h e e l on e i t h e r side, r a t h e r t h a n a single w h e e l in t h e center. T h a t single w h e e l m a k e s t h e b a r r o w m o r e m a n e u verable, a n d is essential if t h e b a r r o w is to be w h e e l e d a l o n g n a r r o w p l a n k s o r m a n i p u l a t e d i n tight c o r n e r s . B u t w h y d o n ' t m o d e r n w h e e l b a r r o w d e s i g n e r s p u t i t i n t h e m i d d l e , directly u n d e r t h e load, i n s t e a d o f a t o n e e n d ? T h e a n s w e r lies i n stability. So as l o n g as t h e d o w n w a r d force t h r o u g h t h e c e n t e r of gravity o f t h e load d o e s n o t m o v e o u t s i d e t h e t r i a n g l e defined by the operator's t w o hands and the point w h e r e the wheel contacts t h e g r o u n d , t h e w h e e l b a r r o w will n o t tip. T h e r e a s o n for this is t h a t t h e d o w n w a r d force of t h e load, a n d t h e total

64


Center of Load Inside Triangle Wheelbarrow Stable

Center of Load Outside Triangle - Wheelbarrow Tips

Figure 3.8a a n d 3.8b: Balancing the Load in a Wheelbarrow.

u p w a r d force p r o v i d e d b y t h e o p e r a t o r ' s h a n d a n d t h e r e a c tion force of t h e g r o u n d on t h e w h e e l , c o n s t i t u t e a c o u p l e thai t e n d s t o r o t a t e t h e b a r r o w back i n t h e d i r e c t i o n from w h i c h i t c a m e . If t h e c e n t e r of gravity of t h e load m o v e s o u t s i d e a line between the operator's h a n d and t h e wheel, the situation bec o m e s u n s t a b l e , since t h e c o u p l e i s n o w t e n d i n g t o r o t a t e t h e b a r r o w f u r t h e r still. To a v e r t disaster, t h e o p e r a t o r m u s t exert a c o u n t e r - c o u p l e b y lifting o n t h e n e a r h a n d l e a n d p u s h i n g d o w n o n t h e far h a n d l e . T h e a c t i o n m u s t b e fast, a n d t h e furt h e r t h e b a r r o w tilts t h e m o r e difficult it b e c o m e s , as I f o u n d early on as a t w e l v e - y e a r - o l d . T h e p r o b l e m w i t h p u t t i n g t h e w h e e l i n t h e c e n t e r o f t h e bar-

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row, w i t h t h e load directly a b o v e , is t h a t t h e s i t u a t i o n is alw a y s u n s t a b l e , since t h e load is n o w at t h e a p e x of t h e i m a g i n a r y triangle f o r m e d b y t h e h a n d s a n d t h e w h e e l , a n d any load shift or w h e e l b a r r o w tilt is sufficient to t a k e t h e c e n t e r of gravity o u t s i d e t h a t i m a g i n a r y t r i a n g l e . T h e o n l y w a y t o get a r o u n d this s i t u a t i o n is to c o n s t r u c t t h e w h e e l b a r r o w in s u c h a w a y t h a t t h e c e n t e r of gravity of t h e load is b e l o w t h e level of t h e p o i n t of c o n t a c t of t h e w h e e l w i t h t h e g r o u n d . T h e n t h e c o u p l e c r e a t e d w h e n t h e w h e e l b a r r o w i n e v i t a b l y tilts will act t o r e s t o r e t h e original p o s i t i o n r a t h e r t h a n t o tilt t h e b a r r o w further. It m a y s e e m impossible to m a k e s u c h a w h e e l b a r r o w , b u t I h a v e m a n a g e d t o design o n e t h a t s h o u l d w o r k w h e n w h e e l e d along a p l a n k , w i t h t w o e q u a l loads h a n g i n g d o w n o n e i t h e r side of t h e p l a n k . My design ( p a t e n t n o t p e n d i n g ) is s h o w n in cross-section ( v i e w e d from t h e front) in Figure 3.9.

Figure 3.9: D e s i g n for a W h e e l b a r r o w that C a n N e v e r Tip Over.

For t h e m o m e n t , t h o u g h , I a m stuck w i t h using a n o r d i n a r y w h e e l b a r r o w . Is it possible to u s e s u c h a b a r r o w m o r e efficiently? It's a c o m p r o m i s e b e t w e e n m e c h a n i c a l a d v a n t a g e a n d stability, w h i c h really d e p e n d s o n t h e load t h a t t h e u s e r w a n t s to shift. For m a x i m u m m e c h a n i c a l a d v a n t a g e , t h e c e n t e r of gravity of t h e load s h o u l d be as close to t h e front of t h e b a r r o w

66


as possible. For m a x i m u m stability, t h e load s h o u l d be as far back as possible (so t h a t t h e c e n t e r of gravity stays w i t h i n t h e i m a g i n a r y triangle e v e n w h e n t h e w h e e l b a r r o w i s badly tilted), a n d s p r e a d so as to k e e p t h e c e n t e r of gravity as l o w as possible. In t h e e n d , it's up to t h e user. T h e o n l y extra tip t h a t I h a v e received from my t r a d e s m a n friends is to k e e p a c o u p l e of lengths of h o l l o w pipe h a n d y t h a t can be slipped o v e r t h e h a n d l e s to increase t h e i r effective length, a n d h e n c e increase t h e m e c h a n i c a l a d v a n t a g e , if an e x t r a - h e a v y load n e e d s to be m o v e d .

T o o l s that U s e the W e d g e P r i n c i p l e

Wedges

T h e w e d g e is a v e r y a n c i e n t tool. As w i t h o t h e r tools, its action is b a s e d on a trade-off b e t w e e n force a n d d i s t a n c e . T h e action i s s i m p l e t o u n d e r s t a n d b y visualizing t h e w e d g e b e i n g used t o lift s o m e t h i n g , s u c h as a slab of rock. T h e m e c h a n i c a l a d v a n tage is s i m p l y t h e ratio of t h e d i s t a n c e t h a t t h e w e d g e has to be d r i v e n divided b y t h e h e i g h t t h r o u g h w h i c h t h e rock i s lifted. I n t h e e x a m p l e s h o w n i n Figure 3.10, t h e m e c h a n i c a l a d v a n t a g e i s 6 : 1 . T h e w e d g e t h u s a l l o w s t h e rock t o b e lifted w i t h o n e - s i x t h of t h e force t h a t it w o u l d t a k e to do t h e j o b directly, at t h e e x p e n s e of h a v i n g to m o v e t h e p o i n t of a p p l i c a t i o n of t h a t force (i.e., t h e b a s e of t h e w e d g e ) six t i m e s as far. So far, so s i m p l e . T h e real a d v a n t a g e of a w e d g e , t h o u g h , is t h a t it lets us c h a n g e t h e d i r e c t i o n of t h e force. We drive t h e w e d g e s i d e w a y s , b u t t h e rock i s lifted u p w a r d ( t h e s a m e t h i n g h a p p e n s w h e n w e force a c l a w h a m m e r u n d e r t h e h e a d o f a

Figure 3.10: M e c h a n i c a l A d v a n t a g e of a W e d g e .

the tao of tools

67

nail). T h e m a t h e m a t i c a l r e a s o n lor this is e x p l a i n e d later, in c h a p t e r six. All t h e i n f o r m a t i o n t h a t is n e e d e d h e r e is t h a t t h e mechanical advantage depends on the wedge angle, but only b e c o m e s r e a s o n a b l y h i g h for v e r y s h a l l o w angles, as Table 3.2 s h o w s . This i s w h y m o s t w e d g e s a r e c o n s t r u c t e d w i t h relatively s h a l l o w a n g l e s . Table 3.2: Mechanical Advantage Generated by a W e d g e . W e d g e angle (degrees)

5 10 15 20 25 30 35 40 45

Mechanical advantage

11.4 5.7 3.7 2.7 2.1 1.7 1.4 1.2 1

Chisels

Cutting tools, in t h e form of s t o n e or (lint Hakes, a r e t h e oldest tools k n o w n t o m a n . M o s t p e o p l e ( i n c l u d i n g t h e a u t h o r o f t h e Britannica article m e n t i o n e d earlier) v i e w chisels as t h e i r m o d e r n e q u i v a l e n t . This is correct if t h e chisel is b e i n g u s e d to cut w o o d across t h e g r a i n . Often, t h o u g h , chisels act a l o n g t h e grain, a n d h e r e a chisel is not p r i m a r i l y a c u t t i n g tool. It is a w e d g e . O n c e t h e chisel h a s e n t e r e d t h e w o o d , t h e s h a p e o f the o p e n i n g crack e n s u r e s t h a t t h e chisel e d g e is virtually floating free in space, t a k i n g little f u r t h e r p a r t in t h e action (Figure 3.1 f). Typical w o o d chisels h a v e a w e d g e a n g l e of a r o u n d 30°. This gives t h e m a m e c h a n i c a l a d v a n t a g e of a p p r o x i m a t e l y 2:1 w h i c h t h e y d o n ' t n e e d after t h e initial stages, since t h e p r o c e s s °f c u t t i n g a l o n g t h e grain is a n a l o g o u s to o p e n i n g up a crack in a n y m a t e r i a l . T h e w o r k r e q u i r e d t o d o this d e p e n d s o n t h e s h a r p n e s s of t h e crack tip, n o t t h e s h a r p n e s s of t h e chisel.

68

h o w to d u n k a

doughnut

Figure 3 . 1 1 : Chisel Cutting End-Grain (Showing "Floating" Edge).

e x c e p t a t t h e v e r y start, w h e n t h e s h a r p n e s s o f t h e chisel defines h o w easy it is to start t h e crack. After t h a t , t h e s h a r p e r t h e crack tip, t h e less t h e w o r k , as we s a w earlier in t h e case of the dry cookie. If t h e chisel tip is n o t sufficiently s h a r p , it can " c a t c h " in t h e o p e n i n g split a n d t e a r a t t h e w o o d f i b e r s , m a k i n g t h e j o b m u c h m o r e difficult. So, h o w s h a r p d o e s t h e chisel tip h a v e t o be? That depends on the shape of the bent part of the wood n e a r t h e tip — t h e p a r t t h a t i s u n d e r t h e m o s t stress. To find t h e o p t i m u m s h a p e , I t u r n e d to Formulas for Stress and Strain, a b o o k of e n g i n e e r i n g f o r m u l a e t h a t I d i s c o v e r e d in t h e p s y c h o l o g y section of a s e c o n d h a n d b o o k s t o r e . T h e calculat i o n s w e r e c o m p l i c a t e d , b u t i n t h e e n d I f o u n d t o m y surprise t h a t a chisel e d g e m u s t b e n o m o r e t h a n 0.15 m i c r o m e t e r s thick if it is n o t to catch t h e a d j a c e n t w o o d . T h r e e h u n d r e d s u c h edges c o u l d fit side by side on a h u m a n hair. It is no w o n d e r t h a t m y f a t h e r w a s s o a n g r y w h e n I used o n e o f his c a r e fully s h a r p e n e d chisels as a lever. W h e n a p r o p e r l y s h a r p e n e d chisel is u s e d to split w o o d a l o n g t h e grain, its m a i n task ( o n c e t h e c u t h a s s t a r t e d ) is to slice a n y w o o d fibers t h a t h a p p e n t o h a v e s p a n n e d across t h e g a p . This a c t i o n is m o r e efficient if t h e e d g e is v e r y s h a r p a n d if t h e chisel m o v e s across t h e fiber in a s h e a r i n g a c t i o n , w h i c h i s w h y m y f a t h e r t a u g h t m e t o slide t h e chisel slightly s i d e w a y s as it p r o g r e s s e d t h r o u g h t h e w o o d . That's all t h a t t h e r e is to u s ing a chisel to cut a l o n g t h e grain. T h e trick is to stop t h e s h a r p e d g e from c u t t i n g i n t o t h e a d j a c e n t w o o d , since this will t a k e t h e d e v e l o p i n g split off line. T h e slightest tilt of t h e h a n d l e

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69

t o w a r d s t h e b e v e l e d side will result i n t h e e d g e " c a t c h i n g " t h e w o o d . T h e o b v i o u s r e m e d y is a l w a y s to e x e r t a slight force in t h e o p p o s i t e d i r e c t i o n , so t h a t t h e tip r e m a i n s in free space, o u t of c o n t a c t w i t h t h e w o o d .

The Screwdriver

Screwdrivers, o n e o f t h e few h a n d tools t h a t w e r e n o t i n v e n t e d until m e d i e v a l times, a r e difficult to categorize. If a s c r e w d r i v e r blade is used w i t h a b r a c e a n d bit, t h e a s s e m b l y acts as a lever in t h e s a m e w a y t h a t a w r e n c h d o e s . M o s t s c r e w d r i v e r s , t h o u g h , are h a n d h e l d , a n d t h e i r sole p u r p o s e , as Jeff Odell p o i n t e d o u t in o u r coffee-room c o n v e r s a t i o n , is to p r o v i d e a convenient linkage b e t w e e n the screw and the h a n d of the user. A s c r e w d r i v e r t h u s u s e d acts as a rigid e x t e n s i o n to t h e o p e r a t o r ' s a r m , b u t d o e s n o t of itself c o n v e y a m e c h a n i c a l advantage if p r o p e r l y aligned w i t h t h e screw. W h a t it does do is to permit t h e u s e r to a t t a c h himself or herself firmly to s o m e t h i n g that does c o n v e y a m e c h a n i c a l a d v a n t a g e — n a m e l y , t h e screw. A screw d r i v e n i n t o t h e s i d e - g r a i n of a piece of w o o d acts as a w e d g e , w h i c h is w h y f h a v e listed t h e s c r e w d r i v e r in this section. T h e w e d g e h a p p e n s to be w r a p p e d as a spiral a r o u n d a central shaft, b u t it is n e v e r t h e l e s s a w e d g e , w i t h t h e j o b of levering t h e w o o d fibers a p a r t . This is a v e r y difficult task to p e r f o r m directly (try p u l l i n g a piece of w o o d in half across t h e grain w i t h y o u r b a r e h a n d s ) . E v e n a s o f t w o o d s u c h a s w h i t e spruce h a s a b r e a k i n g t e n s i o n across t h e g r a i n of 33 k g / c m ; h a r d w o o d s c a n r e q u i r e t h r e e o r four t i m e s a s m u c h . T h e m e chanical a d v a n t a g e t h a t a w o o d s c r e w p r o v i d e s can be w o r k e d out b y i m a g i n i n g t h e t h r e a d t o b e u n w r a p p e d a n d s t r e t c h e d out at t h e s a m e a n g l e as t h e original pitch. A "typical" w o o d screw from my collection, for e x a m p l e , h a s a pitch of 5 t u r n s per c e n t i m e t e r a n d a m e d i a n d i a m e t e r of 5 m i l l i m e t e r s . F r o m simple g e o m e t r y , t h e total t h r e a d l e n g t h (per c e n t i m e t e r l e n g t h of screw) is 7.8 c e n t i m e t e r s , a n d t h e m e c h a n i c a l a d v a n t a g e is t h u s 7.8 (Figure 3.12). 2

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h o w to d u n k a

doughnut

Figure 3.12: " U n w r a p p e d " S c r e w Thread

T h e a r e a of w o o d p e n e t r a t e d by this s c r e w is 0.2 sq. cm, a n d t h e force n e e d e d t o s e p a r a t e t h e w o o d f i b e r s across this a r e a i s t h u s 0.2 X 33 = 6.6 kg. T h e m e c h a n i c a l a d v a n t a g e of 7.8 p r o vided by t h e s c r e w r e d u c e s this figure to 6.6 / 7.8 = 0.85 kg, a figure t h a t w o u l d rise to several k i l o g r a m s if t h e s c r e w w e r e being driven into h a r d w o o d . I w o n d e r e d w h e t h e r I could g e n e r a t e s u c h a force u s i n g a t w i s t i n g m o t i o n of my a r m only. To find o u t , I w r a p p e d a r o p e several t i m e s a r o u n d my wrist, a n d tied t h e free e n d to a series of progressively h e a v i e r b o u l d e r s . I f o u n d t h a t f could lift b o u l d e r s w e i g h i n g up to 3 k i l o g r a m s fairly easily w i t h a twist of t h e wrist ( c o r r e s p o n d i n g to a t o r q u e w i t h my 7 - c e n t i m e t e r d i a m e t e r wrist of 0. f k g . m ) , b u t t h a t t h e j o b t h e r e a f t e r b e c a m e progressively h a r d e r , w i t h iO k i l o g r a m s b e i n g a b o u t my limit. F r o m this e x p e r i m e n t , i t s e e m s t h a t t h e m e c h a n i c a l a d v a n t a g e p r o v i d e d by w o o d s c r e w s is p r e t t y well o p t i m a l for t h e j o b . T h e figures a b o v e a r e a p p r o x i m a t e , c o m i n g from a "back-oft h e - e n v e l o p e " calculation t h a t t a k e s n o a c c o u n t o f i n c r e a s i n g friction b e t w e e n s c r e w a n d w o o d ; t h e fact t h a t t h e c e n t r a l core of t h e s c r e w is n o t p a r t of t h e w e d g e ; or t h e w o r k n e e d e d to displace t h e w o o d t o m a k e w a y for this c o r e . T h e last p r o b l e m can, of c o u r s e , be a v o i d e d in practice by drilling t h e w o o d first to m a k e w a y for t h e c o r e of t h e screw. C a n t h e j o b also b e m a d e easier b y tilting t h e s c r e w d r i v e r t o p r o v i d e e x t r a l e v e r a g e ? It w a s t i m e for a n o t h e r e x p e r i m e n t . I selected a w o o d s c r e w w i t h a slotted h e a d 7 m i l l i m e t e r s in dia m e t e r , a n d t w o s c r e w d r i v e r s of different shaft l e n g t h , but e a c h w i t h a tip t h a t w a s a n e a t fit to t h e s c r e w slot, a n d p r o ceeded to use each screwdriver in turn to drive the screw into a piece of s o f t w o o d . T h e r e w a s no d o u b t t h a t t h e l o n g e r ( 2 5 -

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c e n t i m e t e r ) s c r e w d r i v e r w a s m u c h easier t o use t h a n t h e shorter (10-centimeter) screwdriver, and that as the screw bec a m e m o r e difficult to drive I f o u n d myself s p o n t a n e o u s l y tilting t h e s c r e w d r i v e r s up to 2 0 ° from t h e vertical, in a d i r e c t i o n p e r p e n d i c u l a r to t h a t of t h e slot (Figure 3.13). H o w m u c h e x tra t o r q u e did this tilt p r o v i d e ? A 20° tilt will t a k e t h e h a n d l e of t h e l o n g e r s c r e w d r i v e r s o m e 9 c e n t i m e t e r s from t h e s c r e w axis, but t h e lateral force t h a t I m i g h t h a v e b e e n a p p l y i n g to g e n e r a t e a t u r n i n g c o u p l e is difficult to e s t i m a t e . E v e n if t h a t force w a s o n l y 0.5 k i l o g r a m s , t h e t o r q u e g e n e r a t e d w o u l d h a v e b e e n 0.02 k g . m , w h i c h a d d s t w e n t y p e r c e n t t o t h a t provided simply by r o t a t i n g t h e wrist — a n o t - i n s i g n i f i c a n t i m p r o v e m e n t . A similar calculation s h o w s t h a t t h e c o r r e s p o n d i n g i m p r o v e m e n t lor t h e s h o r t e r s c r e w d r i v e r i s o n l y eight p e r c e n t , w h i c h e x p l a i n s t h e difference b e t w e e n l o n g and short-handled screwdrivers. W h a t , t h o u g h , is t h e c h a n c e of t h e s c r e w d r i v e r slipping w h e n used in this w a y ? Not m u c h , as t h e scale d i a g r a m b e l o w shows. What about the chance of bending the screwdriver tip? If t h e lateral force on t h e h a n d l e is half a k i l o g r a m , t h e m e c h a n i c a l a d v a n t a g e is of t h e o r d e r of 2 5 0 (!) for a 2 5 c e n t i m e t e r s c r e w d r i v e r in a 1-millimeter slot, w h i c h m e a n s

Figure 3.13: Screwdriver Tip in Slotted S c r e w H e a d , with Screwdriver Tilted at 20°. Scale diagram. The screwdriver tip would be a neat fit to the screw slot if the screwdriver were held vertically. The diagram shows that such a tip is unlikely to skp out even if tilted at 20 to the vertical.

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t h a t t h e s c r e w d r i v e r is p r e s s i n g on t h e side of t h e slot w i t h a force of 125 k i l o g r a m s . It s o u n d s like a d i s a s t r o u s s c e n a r i o ( w h i c h it m i g h t be for t h e s c r e w h e a d ) , b u t t h e s c r e w d r i v e r is u n l i k e l y to be affected, since m o d e r n s c r e w d r i v e r s (so S t u a r t Burgess i n f o r m s m e ) a r e d e s i g n e d t o b e s t r o n g e n o u g h t o lever t h e lid off a c a n of p a i n t . T h e screw, u s u a l l y m a d e of a soft m e t a l , i s m o r e likely t o b e d a m a g e d . M y a r g u m e n t w i t h Jeff Odell e n d e d u p a s a n h o n o r a b l e d r a w so far as u s i n g a h a n d h e l d s c r e w d r i v e r is c o n c e r n e d . T h e best w a y to d r i v e in a r e c a l c i t r a n t screw, t h o u g h ( a p a r t from using a h a m m e r ) , is to u s e a b r a c e a n d bit fitted w i t h a s c r e w driver h e a d . T h e s p a n of a typical b r a c e a n d bit is a r o u n d 20 c e n t i m e t e r s , w h i c h is a b o u t t h e s a m e as t h a t of a large w r e n c h , a n d p r o v i d e s a m e c h a n i c a l a d v a n t a g e of a r o u n d 30 for t h e s c r e w t h a t I h a v e b e e n discussing. T h e o n l y d i s a d v a n t a g e of a b r a c e a n d bit, so l o n g as it can fit in t h e w o r k i n g space, is t h a t i t m a k e s t h e j o b t o o easy.

P e r c u s s i v e Tools

Hammers

With t h r e e of my four initial q u e s t i o n s a n s w e r e d , it w a s t i m e to t u r n to t h e f o u r t h — w h a t is t h e best w a y to use a h a m m e r ? Is t h e r e a best w e i g h t of h a m m e r for a given nail? H o w h a r d s h o u l d y o u s w i n g a h a m m e r at each b l o w ? Certainly n o t as h a r d as I did w h e n l e a r n i n g as a child. T h e r e s u l t a n t b l o w on t h e t h u m b n a i l c r e a t e d a n e x c r u c i a t i n g p r e s s u r e w h i c h m y lat h e r released by using a n e e d l e w a r m e d in a b l o w t o r c h flame to red h e a t to drill a h o l e in t h e nail. To this d a y I am grateful for t h a t rapid piece of a m a t e u r d o c t o r i n g , b u t it w o u l d h a v e b e e n b e t t e r if I h a d n ' t tried to hit t h e nail so h a r d in t h e first place. T h e p r o b l e m w a s t h a t I w a s t r y i n g to start t h e nail off w i t h a single h e a v y b l o w . E x p e r i e n c e rapidly t a u g h t me t h a t a nail n e e d s to be s t a r t e d off w i t h a series of light b l o w s . T h e r e a s o n

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for this is t h a t , u n l e s s t h e b l o w is a b s o l u t e l y a c c u r a t e , t h e r e will be a small s i d e w a y s c o m p o n e n t to t h e force g e n e r a t e d by t h e blow, sufficient t o k n o c k t h e nail s i d e w a y s o r for t h e h a m m e r to g l a n c e off t h e nail h e a d if t h e b l o w is t o o h a r d . T h e idea t h a t a force, or a m o v e m e n t , can be s e p a r a t e d i n t o two independent c o m p o n e n t s is o n e that is not intuitively obv i o u s . I o n c e c h e c k e d o u t t h e q u e s t i o n w i t h a g r o u p in o u r village p u b , a n d f o u n d t h a t s o m e 30 p e r c e n t b e l i e v e d t h a t , if f f r e e w h e e l on a bicycle at c o n s t a n t s p e e d d o w n a hill a n d t h r o w a s t o n e vertically as f ride, t h e s t o n e will l a n d b e h i n d me (for a lull a c c o u n t of this story see c h a p t e r six). T h e correct a n s w e r is t h a t it will l a n d b e s i d e m e , b e c a u s e its f o r w a r d velocity at t h e m o m e n t of l e a v i n g my h a n d is totally i n d e p e n d e n t of t h e u p w a r d velocity w i t h w h i c h I t h r o w it, a n d s o t h e s t o n e will k e e p m o v i n g f o r w a r d a t t h e s a m e s p e e d a s t h e bicycle e v e n after it h a s left my h a n d . Scientists a r e n o w a c c u s t o m e d t o t h e idea t h a t a n y m o v e m e n t , o r a n y force, c a n b e r e g a r d e d a s t h e s u m o f t w o o t h e r forces at right a n g l e s to e a c h o t h e r . Luckily, it is easy to w o r k o u t h o w large t h e t w o different c o m p o n e n t s a r e w i t h t h e aid of a simple d i a g r a m . T h e trick is simply to r e g a r d t h e original force or m o v e m e n t as t h e l o n g side ( t h e h y p o t e n u s e ) of a r i g h t - a n g l e d triangle, a n d j u s t f i t t h e o t h e r t w o sides t o it. T h e result of a nail b e i n g struck at a slight a n g l e is s h o w n in F i g u r e 3.14, w h e r e t h e direction of t h e a r r o w s gives t h e d i r e c t i o n of t h e forces, a n d t h e l e n g t h o f t h e a r r o w s s h o w s h o w s t r o n g t h o s e forces a r e . O n c e t h e nail h a s b e e n d r i v e n a few m i l l i m e t e r s i n t o t h e w o o d , t h e h o r i z o n t a l c o m p o n e n t of an off-axis s w i n g will be b a l a n c e d b y t h e r e s t o r i n g elasticity o f t h e w o o d r a t h e r t h a n t h e grip o f t h e f i n g e r s o n t h e nail, a n d t h e h a m m e r n e e d n o t be s w u n g q u i t e so slowly. B u t h o w fast s h o u l d it be s w u n g ? Is t h e r e a n o p t i m u m velocity? W h e n a h a m m e r is s w u n g , s o m e of t h e e n e r g y goes i n t o r e coil as t h e h a m m e r h e a d b o u n c e s back off t h e h e a d of t h e driven nail. M y f i r s t t h o u g h t w a s t h a t t h e h a m m e r s h o u l d t h e r e f o r e b e s w u n g slowly for m a x i m u m efficiency, w i t h less

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how to dunk a

doughnut

Figure 3.14: Triangle of F o r c e s for a H a m m e r S w u n g "Off-Vertical."

recoil a n d m o r e t i m e in contact w i t h t h e h e a d of t h e nail. This t i m e , I d i d n ' t n e e d Jeff Odell to tell me t h a t I w a s w r o n g . I w o r k e d it o u t for myself, realizing t h a t e v e n if s o m e of t h e e n ergy t h a t goes i n t o t h e s w i n g is e x p e n d e d in t h e recoil, it is still n o t w a s t e d , since it saves an e q u i v a l e n t a m o u n t of t h e w o r k i n v o l v e d i n lifting t h e h a m m e r for t h e n e x t blow. S o m e h a m m e r s a r e n o w d e s i g n e d w i t h a layer of polyu r e t h a n e o n t h e h e a d t h a t "gives" slightly w h e n t h e nail i s struck, k e e p i n g t h e h e a d in c o n t a c t w i t h t h e nail for a l o n g e r t i m e a n d a l l o w i n g m o r e o f t h e e n e r g y t o b e t r a n s f e r r e d . Acc o r d i n g to t h e a b o v e a r g u m e n t , this is a g i m m i c k . T h e o n l y p r o b l e m in d r i v i n g a nail in is to m a x i m i z e t h e d o w n w a r d c o m p o n e n t o f t h e force a n d m i n i m i z e t h e s i d e w a y s c o m p o n e n t . E v e n this b e c o m e s less of a p r o b l e m as t h e nail p r o g r e s sively e n t e r s t h e w o o d ; so t h e correct t e c h n i q u e is to g r a d u a l l y i n c r e a s e t h e p o w e r of t h e b l o w s , w h i c h is s o m e t h i n g t h a t most c a r p e n t e r s do by instinct. Most c a r p e n t e r s also drill a lead hole,

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slightly s m a l l e r in d i a m e t e r t h a n that of t h e nail. This h a s t h e a d v a n t a g e of e n s u r i n g t h a t t h e nail is aligned m o r e rapidly by t h e initial b l o w s , a n d also t h a t t h e w o o d is less likely to split. A n o t h e r s u r p r i s i n g a d v a n t a g e to drilling a lead h o l e is that t h e driven nail is h a r d e r to r e m o v e from t h e w o o d t h a n if no h o l e had b e e n drilled. T h e r e a s o n i s t h a t , w i t h n o lead h o l e , t h e w o o d is o n l y in a c t u a l c o n t a c t w i t h t h e nail on t w o sides. If a lead h o l e h a s b e e n drilled, t h e c o n t a c t is all t h e w a y a r o u n d a n d t h e frictional force is c o r r e s p o n d i n g l y g r e a t e r (Figure 3.15).

Figure 3.15: C o n t a c t of Driven Nail in W o o d W i t h o u t (Left) a n d W i t h (Right) a L e a d Hole.

Only o n e r e f i n e m e n t r e m a i n s — w h i c h part of t h e h a m m e r h e a d s h o u l d be used to strike t h e nail? Most p e o p l e w o u l d say t h e m i d d l e — a n d m o s t p e o p l e w o u l d b e w r o n g . H a m m e r s actually h a v e a " s w e e t spot" (very similar to t h e " s w e e t spot" in a cricket or baseball bat or a t e n n i s racket), w h e r e t h e j a r r i n g is least a n d t h e m o m e n t u m transfer is at its m a x i m u m , its t e c h nical n a m e is t h e " c e n t e r of p e r c u s s i o n , " a n d its e x i s t e n c e arises from t h e fact t h a t t h e h a m m e r h e a d is s w i n g i n g in an arc r a t h e r t h a n straight u p a n d d o w n . F o r m u l a e exist lor calculating t h e c e n t e r of p e r c u s s i o n , w h i c h , for s o m e t h i n g like a bat, can be a lot farther from t h e h a n d t h a n t h e c e n t e r of gravity. For a h a m mer, h o w e v e r , m y r o u g h calculations s h o w e d t h a t t h e differe n c e was negligible, a n d t h a t t h e m a i n p r o b l e m w i t h using a h a m m e r r e m a i n s in s w i n g i n g it a c c u r a t e l y in t h e first place.

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At t h e e n d of my s u r v e y of h a n d tools, I w a s d i s a p p o i n t e d to find that their development, unlike m a n y other c o m m o n place activities, h a s c o n t r i b u t e d c o m p a r a t i v e l y little t o o u r u n d e r s t a n d i n g of scientific principles. I w a s v e r y p l e a s e d to find, h o w e v e r , t h a t scientific principles a r e v e r y useful w h e n i t c o m e s t o u s i n g t h e tools i n t h e m o s t efficient m a n n e r .

4 h o w t o a d d u p your s u p e r m a r k e t bill

Physical c o n c e p t s a r e n o t t h e o n l y b a r r i e r b e t w e e n scientists a n d n o n - s c i e n t i s t s . N u m b e r s a n d c a l c u l a t i o n s can p r o v i d e a n e v e n g r e a t e r barrier. Scientists a r e u s u a l l y a t e a s e w i t h t h e m , but m a n y other people are not. T h e scientist's e a s e c o m e s p a r t l y from familiarity, b u t also from t h e s h o r t c u t s h e o r s h e h a s l e a r n e d , w h i c h m a k e i t relatively easy t o j u g g l e w i t h n u m b e r s . Scientists a p p l y t h e s e s h o r t c u t s to scientific c a l c u l a t i o n s . 1 w o n d e r e d w h e t h e r it m i g h t be possible to a p p l y t h e m to o t h e r a r e a s of life, a n d d e cided t o try m y h a n d a t u s i n g t h e m t o c h e c k bills a n d assess t h e pricing policies of my local s u p e r m a r k e t s . I w a s a m a z e d at w h a t t h e c a l c u l a t i o n s r e v e a l e d . T h e tricks a r e s o s i m p l e t h a t a n y o n e can use t h e m , b o t h to b e c o m e m o r e at ease with h a n dling n u m b e r s a n d t o c h e c k u p o n w h a t i s g o i n g o n i n t h e i r own supermarket. My wife, W e n d y , a n d I live in a small r u r a l English village, b u t w e h a v e several s u p e r m a r k e t s nearby, a n d t h a t i s w h e r e w e d o o u r s h o p p i n g . W e n d y actually d o e s m o s t o f t h e s h o p ping, a n d w h e n f sat d o w n to w r i t e this chapter, f told h e r t h a t I h a d devised a statistically based, scientific, s i m p l e - t o - u s e m e t h o d to let h e r k e e p a r o u g h track of w h a t s h e h a d b e e n s p e n d i n g a s s h e w e n t a r o u n d b u y i n g . S h e l a u g h e d a n d replied t h a t she a l r e a d y h a d a m e t h o d , w h i c h w a s to r o u n d d o w n all of t h e prices e n d i n g in " . 4 9 " or less, r o u n d up t h e rest, a n d k e e p a r u n n i n g total of t h e results. 1 told h e r t h a t it s o u n d e d like an interesting a p p r o a c h , b u t t h a t I w a s s u r e m y m e t h o d w o u l d b e m o r e a c c u r a t e . You c a n p r o b a b l y g u e s s t h e n e x t bit. W h e n I checked t h e t w o m e t h o d s o u t , W e n d y ' s w a s a clear w i n n e r , ft looked as if this w a s going to be a v e r y s h o r t c h a p t e r . H o p i n g to s a v e s o m e t h i n g from t h e w r e c k , f sat d o w n to

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a n a l y z e just w h y h e r m e t h o d w o r k e d w h i l e m i n e d i d n ' t . T h e first clue c a m e from a friend's s u p e r m a r k e t bill, b u t t h e final piece of t h e puzzle w a s p u t in place only after I h a d s u r v e y e d nearly a t h o u s a n d s u p e r m a r k e t prices. It t r a n s p i r e d that W e n d y ' s a p p r o a c h t o o k a l m o s t perfect a c c o u n t of t h e fact that s u p e r m a r k e t s distribute t h e i r prices in a very selective way. My s u p p o s e d l y m o r e r i g o r o u s statistical a p p r o a c h h a d failed to cope with this factor, w h i c h , as f will s h o w later in this chapter, applies equally t o s o m e m a j o r A m e r i c a n s u p e r m a r k e t s . A r m e d w i t h this k n o w l e d g e , f w a s able t o a d a p t m y a p p r o a c h t o give t h e right a n s w e r , a l t h o u g h W e n d y still a r g u e s t h a t h e r m e t h o d i s easier t o u s e . T h a t i s u p t o t h e r e a d e r t o d e cide. M o r e i m p o r t a n t , 1 f o u n d t h a t t h e pricing policies used by s o m e s u p e r m a r k e t s can be turned, judo-like, against t h e m by t h e s h o p p e r in p u r s u i t of t h e best v a l u e for m o n e y .

Taking Care of the Pounds

S u p e r m a r k e t bills i n E n g l a n d look p r e t t y m u c h t h e s a m e a s t h e y d o i n A m e r i c a , e x c e p t t h a t t h e English prices a r e i n p o u n d s a n d p e n c e , r a t h e r t h a n dollars a n d c e n t s . Luckily, t h e n u m e r i c a l a d d i t i o n s a r e j u s t a s easy, since t h e r e a r e o n e h u n dred pence in t h e p o u n d , just as there are o n e h u n d r e d cents in t h e dollar. So £ 1 . 4 9 + £2.51 = £ 4 . 0 0 , just as $ 1 . 4 9 + $2.51 = $ 4 . 0 0 . I will talk in dollars a n d c e n t s w h e r e it is possible to do so w i t h o u t a m b i g u i t y , b u t t h e a c t u a l bills t h a t W e n d y a n d I l o o k e d a t will o b v i o u s l y b e i n p o u n d s a n d p e n c e . T h e English w o r d pounds p e r m i t t e d Lewis Carroll to p e r p e t r a t e o n e o f t h e m o r e o u t r a g e o u s p u n s i n t h e English l a n g u a g e . In c h a p t e r 9 of Carroll's Alice in Wonderland, t h e D u c h e s s advises Alice to " t a k e c a r e of t h e s e n s e a n d t h e s o u n d s will t a k e care of t h e m s e l v e s , " w h i c h is a w o n d e r f u l m u l t i p l e p u n on t h e old English saying, "Take care of t h e p e n c e a n d t h e p o u n d s will t a k e c a r e of t h e m s e l v e s . " Poorly paid English scientists, t h o u g h , k n o w t h a t p o u n d s a r e w o r t h a lot m o r e t h a n p e n c e , and concentrate on the p o u n d s first w h e n it comes to adding

h o w t o a d d u p y o u r s u p e r m a r k e t bill

79

up t h e i r bills. W e n d y a n d I b o t h used this as o u r starting p o i n t . VVe i g n o r e d t h e figures t h a t d i d n ' t m a t t e r a n d c o n c e n t r a t e d on t h o s e t h a t did. T h e figures t h a t m a t t e r a r e called significant figures. If a sup e r m a r k e t bill c o m e s t o $ 4 5 . 2 1 , for e x a m p l e , t h e m o s t significant figure is t h e 4, r e p r e s e n t i n g forty dollars of t h e s h o p p e r ' s h a r d - e a r n e d m o n e y . T h e n e x t m o s t significant f i g u r e i s t h e 5 — that e x t r a five dollars m a t t e r s to m o s t p e o p l e . T h e 2 a n d t h e 1 h a r d l y m a t t e r at all — few p e o p l e w o u l d w o r r y a b o u t t h e extra 21 c e n t s . So far as significant figures a r e c o n c e r n e d , we can just call t h e bill $45 a n d be d o n e w i t h it. T h e principle of significant figures is v e r y useful in k e e p i n g a r u n n i n g total of w h a t y o u h a v e spent in a s u p e r m a r k e t . Dollars are m o r e significant t h a n c e n t s , a n d p o u n d s a r e m o r e i m portant t h a n p e n c e , so a s i m p l e w a y to k e e p a r o u g h r u n n i n g total is to i g n o r e t h e c e n t s or t h e p e n c e entirely. T h e process is called truncation — literally " c u t t i n g s h o r t . " It could also be called g u i l l o t i n i n g . T h e a d v a n t a g e of t r u n c a t i o n is t h a t it is an easy feat of m e n tal a r i t h m e t i c . Its d i s a d v a n t a g e is t h a t it o n l y gives w h a t scientists call a first-order a p p r o x i m a t i o n to t h e real total. In o t h e r w o r d s , it p r o v i d e s a r o u g h first g u e s s w i t h t h e m e n t a l p r o v i s o "could do b e t t e r . " In t h e real bill s h o w n in Figure 4 . 1 , for e x a m p l e ( t h e r e a d e r will g u e s s t h a t t h e flowers w e r e for m y wife), t r u n c a t i o n gives a total of £ 5 , i.e., 0 + 0 + 2 + 3, c o m pared to t h e real price of £ 7 . 3 8 .

Figure 4 . 1 : S h o r t S u p e r m a r k e t Bill.

80


T h e basis of my statistical a p p r o a c h is t h a t t r u n c a t i o n can lead to b e t t e r t h i n g s . T h a t r o u g h first g u e s s is a lower bound to t h e real total, i.e., t h e real total could n o t possibly be less, ft is also possible, a n d e q u a l l y simple, t o u s e t r u n c a t i o n t o calculate a n u p p e r b o u n d t o t h e real total, s i m p l y b y a d d i n g t h e n u m b e r of i t e m s p u r c h a s e d . In t h e s a m p l e bill, t h e total o b t a i n e d by t r u n c a t i o n i s £ 5 , a n d t h e r e a r e four i t e m s i n t h e bill. T h e u p p e r b o u n d is t h e r e f o r e £ ( 5 + 4) = £ 9 . This t o t a l is t h e s a m e t h a t w o u l d h a v e b e e n o b t a i n e d b y r o u n d i n g u p t h e price o f e a c h item to the next highest p o u n d before adding, because every t i m e y o u r o u n d up t h e price of an i t e m , all y o u a r e d o i n g is a d d i n g " o n e " t o t h e price t h a t y o u w o u l d h a v e g o t t e n b y t r u n cation. K n o w i n g t h e u p p e r b o u n d t o y o u r e x p e c t e d bill p r o v i d e s q u i t e a h a n d y test at t h e c h e c k o u t . If t h e c h e c k o u t price is higher than the one you worked out in your head, then the c h e c k o u t total i s w r o n g . A n i t e m m a y h a v e b e e n e n t e r e d t w i c e , o r a price m a y h a v e b e e n w r o n g l y k e y e d in. W h a t e v e r t h e c a u s e , it's w o r t h c h e c k i n g . U p p e r a n d l o w e r b o u n d s "box in" t h e real total b e t w e e n t h e m . B e c a u s e t h e y a r e often relatively s i m p l e t o calculate, scientists f r e q u e n t l y use t h e m in t h e m a n n e r of a p i n c e r m o v e m e n t t o isolate a n d t r a p a n o t h e r w i s e elusive n u m b e r t h a t w o u l d b e difficult t o pin d o w n i n h a n d - t o - h a n d c o m b a t . A r c h i m e d e s , for e x a m p l e , w h e n n o t e n g a g e d i n d e s i g n i n g a n d b u i l d i n g w a r m a c h i n e s , u s e d t h e " b o x i n g in" t e c h n i q u e i n his relentless p u r s u i t of t h e v a l u e of TT ( p r o n o u n c e d "pie"), a n u m b e r t h a t h e n e e d e d t o k n o w a c c u r a t e l y s o t h a t h e could w o r k o u t t h e a r e a s of circular spaces a n d objects. T h e a n c i e n t B a b y l o n i a n s h a d k n o w n t h a t t h e area of a circle of r a d i u s R is TT X R , a n d t o o k t h e v a l u e of TT to be 3, a l t h o u g h t h e y w e r e n ' t s u r e w h e t h e r TT w a s t h e s a m e for big a n d small circles. G r e e k m a t h e m a t i c i a n s p r i o r to A r c h i m e d e s p r o v e d t h a t TT h a d a c o n s t a n t v a l u e , b u t w e r e n o t m u c h closer t o k n o w i n g w h a t t h a t v a l u e w a s . Two t h o u s a n d y e a r s later, t h e I n d i a n a state legislature is said to h a v e c o m e w i t h i n o n e v o t e of r e s o l v i n g t h e difficulty by d e c l a r i n g t h e v a l u e of TT to be 3.2. U n f o r t u n a t e l y for e a s e of 2


81

Figure 4.2: Circle Inscribed a n d C i r c u m s c r i b e d by a Pair of EightSided Polygons (Octagons).

calculation, circles are m o r e w o n t t o o b e y t h e l a w s o f N a t u r e t h a n t h e laws of I n d i a n a . A r c h i m e d e s did m u c h b e t t e r by d r a w i n g t w o p o l y g o n s , o n e c i r c u m s c r i b i n g t h e circle a n d o n e circumscribed by t h e circle. It is easy to calculate t h e area of a p o l y g o n , since a p o l y g o n can a l w a y s be divided up i n t o a set of triangles, a n d t h e form u l a for t h e a r e a of a t r i a n g l e is well k n o w n . A r c h i m e d e s t o o k a d v a n t a g e of this e a s e of calculation, t o g e t h e r w i t h t h e facts that t h e a r e a of t h e o u t e r p o l y g o n is larger t h a n t h e a r e a of t h e circle ( a n d h e n c e p r o v i d e s a n u p p e r b o u n d t o t h e v a l u e o f I T ) , while t h e a r e a of t h e i n n e r p o l y g o n is l o w e r t h a n t h a t of t h e circle ( a n d h e n c e p r o v i d e s a l o w e r b o u n d to I T ) . By d r a w i n g p o l y g o n s w i t h m o r e a n d m o r e sides, a p p r o x i m a t i n g m o r e a n d m o r e closely to t h e s h a p e of t h e circle, A r c h i m e d e s a p p r o a c h e d TT from a b o v e a n d below, e v e n t u a l l y finding (after d r a w i n g a p o l y g o n w i t h 96 [!] sides) t h a t IT could n o t be m o r e t h a n 3.1429 or less t h a n 3 . 1 4 0 8 . T h e a c t u a l v a l u e (correct to five significant figures) is 3 . 1 4 1 6 .

Supermarket Mathematics

A r c h i m e d e s could h a v e d o n e e v e n b e t t e r b y a v e r a g i n g his u p per a n d l o w e r b o u n d s . This gives an a n s w e r of 3 . 1 4 1 8 — close

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e n o u g h for m o s t practical p u r p o s e s . My p l a n w a s to u s e a similar a p p r o a c h to e s t i m a t e t h e total of a s u p e r m a r k e t bill. In t h e bill a b o v e , for e x a m p l e , t h e a v e r a g e o f t h e u p p e r a n d l o w e r b o u n d s (£9 a n d £5 respectively) is £ 7 , an a n s w e r t h a t is satisfactorily close to t h e t r u e total of £ 7 . 3 8 . A simple, practical w a y to do this calculation is to k e e p track of t h e dollars or p o u n d s (i.e., t r u n c a t e ) w h i l e going a r o u n d a sup e r m a r k e t or a d d i n g a bill, a n d t h e n add half t h e n u m b e r of items in t h e bill to t h a t total. This is m a t h e m a t i c a l l y e q u i v a l e n t to a v e r a g i n g t h e u p p e r a n d l o w e r b o u n d s ( t h e r e a s o n is given in t h e n o t e s to this c h a p t e r ) , but is m u c h easier to do in practice. It

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83

also s e e m e d to w o r k at least as well as W e n d y ' s m e t h o d — or so I t h o u g h t . My confidence in this a p p r o a c h w a s such t h a t 1 m a d e a small bet on its a c c u r a c y w h i l e h a v i n g a drink w i t h a friend. He i m m e d i a t e l y p r o d u c e d a c r u m p l e d bill from his pocket a n d challenged me to h a v e a go. 1 h a v e kept t h a t bill as a r e m i n d e r that hubris, an o c c u p a t i o n a l disease a m o n g scientists, can strike at a n y t i m e . As Figure 4.3 s h o w s , t h e bill c o n t a i n e d t h i r t y - o n e items. Half of t h i r t y - o n e is fifteen a n d a half, a n d t h e total in t h e " p o u n d s " c o l u m n is £ 2 5 , so, according to my rapid a p p r o x i m a tion t e c h n i q u e , t h e overall total s h o u l d h a v e b e e n £ 4 0 . 5 0 . U n fortunately, t h e real total w a s £ 4 5 . 6 0 . E v e n m o r e gallingly, Wendy's a p p r o a c h predicted a total of £ 4 6 .

Supermarket Statistics

W h y w a s m y a n s w e r s o w r o n g ? M o r e t o t h e point, w h y w a s Wendy's so right? B o t h m e t h o d s , after all, s e e m e d to rely on t h e same a s s u m p t i o n , w h i c h w a s t h a t t h e a v e r a g e price i n t h e "pence" c o l u m n over a large n u m b e r of items w o u l d be close to 50p ("p" is s h o r t for " p e n c e , " just as "£" is short for "cents"). In m y m e t h o d , this a s s u m p t i o n m e a n t t h a t t h e p e n c e total (expressed in p o u n d s ) w o u l d be e q u a l to hall t h e n u m b e r of i t e m s . I n W e n d y ' s case, t h e a s s u m p t i o n m e a n t t h a t h e r errors from r o u n d i n g up w o u l d cancel o u t t h o s e from r o u n d i n g d o w n , fn any case, we b o t h s e e m e d to be in t h e s a m e statistical b o a t . Things b e c a m e e v e n m o r e puzzling w h e n 1 looked at t h e actual average of t h e p e n c e c o l u m n in t h e bill. This t u r n e d o u t to be 66p. Prices in t h e p e n c e c o l u m n w e r e t h u s clearly biased towards t h e u p p e r e n d o f t h e r a n g e . I t w a s n o w o n d e r t h a t m y m e t h o d bad given an a n s w e r t h a t w a s far too low. W h y , t h o u g h , didn't W e n d y ' s a p p r o a c h give a n a n s w e r t h a t w a s equally l o w ? It could only be t h a t t h e errors i n t r o d u c e d in r o u n d i n g up w e r e still being b a l a n c e d by t h e errors i n t r o d u c e d in r o u n d i n g d o w n . W h e n I l o o k e d at t h e bill in detail, I f o u n d t h a t this w a s i n d e e d the case. I n h e r r o u n d i n g - u p r a n g e ( 5 0 p - 9 9 p ) , t h e a v e r a g e Pence price w a s 81p, so that e a c h r o u n d e d - u p price w o u l d be

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in e r r o r by 19p on a v e r a g e . T h e a v e r a g e price in h e r r o u n d i n g d o w n r a n g e ( 0 p - 4 9 p ) w a s 35p, s o t h a t e a c h r o u n d i n g d o w n w o u l d , on a v e r a g e , be in e r r o r by 35p — a l m o s t twice as m u c h a s t h e e r r o r i n t r o d u c e d b y r o u n d i n g u p . This i m b a l a n c e , w h i c h might have been expected to wreck her method, was almost exactly c o m p e n s a t e d for by t h e fact t h a t t h e r e w e r e twice as m a n y items t o b e r o u n d e d u p a s t h e r e w e r e t o b e r o u n d e d d o w n . I w o n d e r e d w h e t h e r this w a s a o n e - t i m e e v e n t , or w h e t h e r t h e s a m e p a t t e r n w a s followed by o t h e r bills from this superm a r k e t . T h e r e w a s o n l y o n e w a y t o f i n d out, a n d t h a t w a s t o e x a m i n e a r a n g e of bills, preferably from different s h o p p e r s . With t h e h e l p of my village n e i g h b o r s , I b e g a n to a m a s s a collection. Over t h e n e x t w e e k piles of bills p o u r e d in t h r o u g h t h e mailbox, to t h e b e m u s e m e n t of o u r cat, w h o s e cat d o o r is situated directly below. I also c h e c k e d t h e prices for a different s u p e r m a r k e t c h a i n in a different t o w n , w h e r e u n f o r t u n a t e l y I h a d no friendly n e i g h b o r s to h e l p m e . I solved t h a t p r o b l e m by rooting a r o u n d in t h e w a s t e b a s k e t s o u t s i d e t h e c h e c k o u t c o u n t e r s for discarded bills. In t h e e n d , I w a s able to e n t e r n e a r l y a t h o u s a n d individual prices in my Excel s p r e a d s h e e t — over six h u n d r e d from t h e first store, a n d t h r e e h u n d r e d a n d fifty from t h e second, w h e r e suspicious looks from t h e m a n a g e r e v e n t u a l l y forced me to give up my search of his w a s t e b a s k e t s . As a p a t t e r n b e g a n to e m e r g e , I e x p e r i e n c e d t h e s a m e sense of m o u n t i n g e x c i t e m e n t t h a t I h a v e often felt in t h e scientific laboratory — t h e special thrill of chasing d o w n a n d e v e n t u a l l y m a k i n g sense of a set of results. T h a t feeling, far r e m o v e d from t h e often sterile w a y in w h i c h results a r e e v e n t u a l l y p r e s e n t e d for p u b l i c c o n s u m p tion, is t h e u l t i m a t e r e w a r d in science. I h a v e s e e n t h e m o s t s o b e r - m i n d e d of scientists on t h e s e o c c a s i o n s sing, d a n c e , a n d , o n o n e m e m o r a b l e occasion, strip n a k e d a n d d o h a n d s t a n d s for t h e s h e e r u n i n h i b i t e d j o y o f t h e m o m e n t . T h e s e m o m e n t s h a p p e n b e c a u s e o f t h e t e n s i o n t h a t builds u p d u r i n g a n e x p e r i m e n t o r series o f e x p e r i m e n t s . T h a t t e n s i o n w o u l d n ' t b e t h e r e i f science o p e r a t e d i n t h e w a y t h a t m a n y p e o p l e s e e m t o t h i n k it d o e s , w i t h t h e scientist p a t i e n t l y a n d objectively collecting " d a t a , " a n d o n l y t h e n t h i n k i n g a b o u t w h a t t h o s e data might

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u p y o u r s u p e r m a r k e t bill

m e a n . But t h a t ' s not t h e w a y m o s t e x p e r i m e n t a l scientists o p erate. Most of us start off w i t h a p i c t u r e t h a t we a r e t r y i n g to check o u t . T h e p i c t u r e m a y b e v a g u e , o r i t m a y b e v e r y p r e cise. E i t h e r way, e v e r y fresh result is s o m e t h i n g to be t h o u g h t a b o u t a n d i n c o r p o r a t e d , e i t h e r as r e i n f o r c e m e n t or as a step in a n e w d i r e c t i o n . A s m o r e results c o m e i n t h e e x c i t e m e n t builds, r e a c h i n g a p e a k w h e n q u i c k c a l c u l a t i o n s s h o w t h a t t h e results are g o i n g a c c o r d i n g to p l a n . T h e n o t e b o o k s of R o b e r t Millikan, w h o w a s a w a r d e d t h e f 9 2 3 N o b e l Physics Prize for m e a s u r i n g t h e v a l u e of t h e c h a r g e on t h e e l e c t r o n , a r e full of c o m m e n t s like " B e a u t y . Publish this surely, beautiful!" a n d "This is a l m o s t e x a c t l y r i g h t a n d t h e best o n e 1 e v e r had!!!" My o w n n o t e b o o k s a r e full of similar c o m m e n t s , a l t h o u g h I h a v e t a k e n m o r e care w i t h t h e m since t h e occasion w h e n m y h a b i t u a l A u s t r a l i a n adjectival e x p r e s s i o n s w e r e faithfully r e corded b y m y assistant a l o n g s i d e t h e r e s u l t s . The picture that I was trying to check out with my superm a r k e t bills w a s w h e t h e r t h e p e n c e prices o f t h e g o o d s i n o u r local s u p e r m a r k e t w e r e really biased t o w a r d s t h e u p p e r e n d o f the scale, a n d w h e t h e r t h e r e w e r e m o r e a c t u a l g o o d s priced in t h e u p p e r half of t h e scale t h a n t h e r e w e r e in t h e l o w e r half. The act of e n t e r i n g a l o n g string of prices i n t o a s p r e a d s h e e t m a y s e e m b o r i n g to s o m e , b u t I felt a q u i c k e n i n g p u l s e as I n o t e d t h e n u m b e r o f prices t h a t w e r e n o t o n l y i n t h e u p p e r half of t h e scale b u t a c t u a l l y e n d e d in . 9 9 . As I c o n t i n u e d to list the prices from different bills I also n o t i c e d t h a t m a n y of t h e prices t h a t did not e n d in .99 e n d e d in .49, a n d of t h o s e t h a t did neither, m a n y still e n d e d in 9. This w a s h a r d l y an original o b s e r v a t i o n , b u t t h e scale of this pricing policy w a s staggering, with 67 p e r c e n t of all prices e n d i n g in 9. T h e n I b e g a n to n o t i c e gaps. Prices n e v e r s e e m e d to e n d in a 0, 1, or 2, a n d prices e n d i n g in 3, 4, 6, a n d 7 w e r e n o t i c e a b l y rare. W h e n 1 t u r n e d to bills from t h e s e c o n d s u p e r m a r k e t , f found a similar p a t t e r n . To v i e w t h e d a t a as a w h o l e , a n d to look for o t h e r p a t t e r n s a n d for differences b e t w e e n t h e s u p e r m a r k e t s , I d r e w a f r e q u e n c y d i s t r i b u t i o n of t h e prices for e a c h store (Figure 4 . 4 ) .

86


Figure 4.4a a n d 4.4b: Distribution of Prices of G o o d s Bought from Two Different S u p e r m a r k e t s .

If t h e prices in t h e p e n c e c o l u m n s h a d b e e n r a n d o m l y dist r i b u t e d , t h e n t h e g r a p h s s h o u l d n o t h a v e h a d a n y p e a k s , let alone t h e h u g e ones that actually appeared at regular intervals ( £ 0 . 9 9 , £ 1 . 9 9 , £ 2 . 9 9 , etc.), d e c r e a s i n g i n h e i g h t w i t h i n c r e a s ing price, a n d w i t h s m a l l e r p e a k s d i s t r i b u t e d a b o u t t h e m . I t a p p e a r e d t h a t b o t h s u p e r m a r k e t s priced m a n y o f t h e i r g o o d s a s close t o e a c h w h o l e p o u n d a s t h e y could m a n a g e w i t h o u t a c t u a l l y t o u c h i n g o r g o i n g o v e r t h a t barrier. L o o k i n g m o r e closely, I o b s e r v e d a s e c o n d set of p e a k s , a l m o s t invariably h i g h e r t h a n t h e i r n e i g h b o r s , b u t n o t as h i g h as t h e first set. T h e s e a r e t h e p e a k s a t £ 0 . 4 9 , £ 1 . 4 9 . £ 2 . 4 9 , etc. T h e y o c c u r j u s t b e l o w t h e m i d d l e of t h e r a n g e ( £ 0 . 5 0 , £ 1 . 5 0 , £ 2 . 5 0 , etc.) for

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87

a n y p a r t i c u l a r p o u n d b a n d . W i t h a h i g h p r o p o r t i o n of prices c o n c e n t r a t e d in t h e s e t w o sets of p e a k s , it a p p e a r s t h a t t h a t t h e f u n d a m e n t a l u n i t of price is a c t u a l l y 50p, a n d t h a t t h e price of m a n y g o o d s c h a n g e s on a v e r a g e by 50p at a t i m e , w i t h t h e rest o f t h e prices r a n d o m l y s c a t t e r e d a b o u t this m e a n . A t t h e h i g h e r e n d o f t h e s u p e r m a r k e t price r a n g e ( n o t s h o w n i n t h e g r a p h s ) , this c o n c l u s i o n p r o v e d t o b e exactly right. For i t e m s priced a b o v e £6, t h e r e w e r e n o prices t h a t did not e n d in .49 or .99 in t h e bills t h a t I e x a m i n e d . L o o k i n g at the l o w e r prices, t h o u g h , it a p p e a r e d t h a t t h e r e w a s a third series of p e a k s , s e p a r a t e d by lOp, w i t h m a n y prices at 2 9 p , 39p, 49p, 59p, etc. This p a t t e r n w a s especially e v i d e n t for prices b e tween £1 and £2. I t s e e m s fairly o b v i o u s , t h e n , a n d c o m e s a s n o surprise, t h a t t h o s e w h o set s u p e r m a r k e t prices p e r c e i v e prices e n d i n g i n zero a s b a r r i e r s n o t t o b e passed, o r e v e n t o u c h e d , b u t t o b e a p p r o a c h e d as closely as possible from b e l o w . T h e m a j o r b a r r i ers a r e t h e w h o l e p o u n d s . Less i m p o r t a n t , b u t still significant, are prices e n d i n g i n £ 0 . 5 0 . E v e n prices e n d i n g i n o t h e r m u l tiples of lOp, t h o u g h , still n e e d to be t a k e n i n t o a c c o u n t for a full p i c t u r e . The psychological rationale b e h i n d this sort of pricing policy is presumably that we tend to truncate but not to round up w h e n looking at prices. I w a s m o r e interested, t h o u g h , to see w h e t h e r the p e n c e a v e r a g e in t h e s u p e r m a r k e t bill t h a t I h a d started w i t h was r e p r e s e n t a t i v e of local s u p e r m a r k e t bills generally. It w a s . The average p e n c e price for goods b e l o w £2 ( r e p r e s e n t i n g 80 percent of t h e p u r c h a s e s of t h e a v e r a g e s h o p p e r ) w a s 6 0 p for the first s u p e r m a r k e t a n d 6 3 p for t h e s e c o n d s u p e r m a r k e t , w i t h 55 percent of t h e prices in t h e u p p e r half of t h e r a n g e for t h e first s u p e r m a r k e t a n d 64 p e r c e n t in t h e u p p e r half of t h e r a n g e for t h e s e c o n d s u p e r m a r k e t . This suggested t h a t t h e s e c o n d sup e r m a r k e t w a s t h e m o r e e x p e n s i v e , a c o n c l u s i o n t h a t w a s later b o r n e out. T h e figures also s h o w e d t h a t W e n d y ' s calculation t e c h n i q u e w o u l d be expected to w o r k a l m o s t perfectly for bills from t h e s e c o n d s u p e r m a r k e t , a n d w o u l d still be b e t t e r t h a n mine for bills from t h e first s u p e r m a r k e t .

88


I w a s not b e a t e n yet, since I could modify my a p p r o a c h to t a k e a c c o u n t o f t h e n e w statistical i n f o r m a t i o n . T h e overall p e n c e a v e r a g e for b o t h s u p e r m a r k e t s w a s 6 1 p , w h i c h m e a n t t h a t I c o u l d get a m o r e a c c u r a t e total t h a n b e f o r e by a d d i n g up t h e p o u n d s c o l u m n a n d t h e n a d d i n g 0.61 t i m e s t h e total n u m b e r of i t e m s i n s t e a d of half t h e n u m b e r . This is n o t a p r o c e d u r e t h a t is likely to a p p e a l to t h e a v e r a g e s h o p p e r , b u t a r e a s o n a b l e a p p r o x i m a t i o n to it is to a d d t w o - t h i r d s of t h e n u m b e r of i t e m s t o t h e p o u n d s t o t a l . I n t h e s u p e r m a r k e t hill o n p a g e 8 2 , for e x a m p l e , t h e total n u m b e r o f w h o l e p o u n d s i s £ 2 5 , a n d t h e r e a r e t h i r t y - o n e i t e m s . T w o - t h i r d s of $] is a p p r o x i m a t e l y 20 ( 2 0 . 6 7 , to be m o r e e x a c t ) , a n d £ 2 5 + £ 2 0 . 6 7 = £ 4 5 . 6 7 , w h i c h is p l e a s ingly, if a little luckily, close to t h e actual total of £ 4 5 . 6 0 . Usually t h e o v e r e s t i m a t e of t h e total will be slightly g r e a t e r — b u t t h e n , it is o n l y an e s t i m a t e .

Will It Work for American Supermarkets?

M y basic ideas lor c h e c k i n g a n d c o m p a r i n g s u p e r m a r k e t prices s h o u l d w o r k a n y w h e r e , b u t t h e exact n u m b e r s t o use obviously d e p e n d on t h e pricing strategy of t h e p a r t i c u l a r s u p e r m a r k e t . I l o o k e d up t h e price lists lor t e n different A m e r i c a n s u p e r m a r k e t c h a i n s o n t h e f n t e r n e t , a n d e x a m i n e d t h e prices of a r o u n d a t h o u s a n d i t e m s overall, to see w h e t h e r t h e s e sup e r m a r k e t s a d o p t e d similar pricing strategies t o British s u p e r m a r k e t s . T h e r e w e r e s o m e very i n t e r e s t i n g differences. T h e A m e r i c a n c h a i n s c o n c e n t r a t e d s o m e of t h e i r prices in a similar w a y t o British s u p e r m a r k e t s , w i t h m a j o r price p e a k s just b e l o w e a c h w h o l e dollar (e.g., 9 9 c , $ 1 . 9 9 , $ 2 . 9 9 , etc.). T h e s e p e a k s a c c o u n t lor s o m e 30 p e r c e n t of i t e m s in British s u p e r m a r k e t s b u t for a r o u n d 5 4 p e r c e n t i n t h e a v e r a g e A m e r ican s u p e r m a r k e t . In s o m e cases t h e p e r c e n t a g e is e v e n higher. For o n e large s u p e r m a r k e t c h a i n , every unit price e n d e d in .99! Clearly my " t w o - t h i r d s " f o r m u l a for quickly c h e c k i n g a bill w o u l d n ' t w o r k h e r e . O n t h e o t h e r h a n d , this pricing policy lets t h e b u y e r e s t i m a t e t h e bill simply by r o u n d -

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ing u p e a c h price t o t h e n e x t dollar a n d a d d i n g . Alternatively, just a d d t h e dollars c o l u m n a n d t h e n a d d t h e n u m b e r o f i t e m s . For o t h e r s u p e r m a r k e t s , t h e r e w e r e t w o m a j o r p e a k s i n t h e prices — o n e w h e r e t h e price e n d e d i n .99, a n d o n e w h e r e t h e price w a s in w h o l e dollars, i.e., e n d i n g in .00. For m o s t of these s u p e r m a r k e t s t h e r e w e r e n e a r l y t w i c e a s m a n y i t e m s with prices e n d i n g in .99 as t h e r e w e r e w i t h prices e n d i n g in .00. My " t w o - t h i r d s " trick for q u i c k l y c h e c k i n g a bill s h o u l d work well in t h e s e cases.

Comparing Prices

Consumer organizations, and supermarkets themselves, compare prices u s i n g a " s t a n d a r d s h o p p i n g b a s k e t " of t h e s a m e goods. This can b e c o m e a g a m e of m i n i m i z i n g t h e prices in t h e standard b a s k e t , w h i l e raising o t h e r prices t o c o u n t e r b a l a n c e the loss. T h e i n d i v i d u a l c o n s u m e r , a r m e d w i t h t h e i n f o r m a tion from my s u r v e y s , c a n do b e t t e r in a n u m b e r of w a y s . The first is to c o m p a r e t h e a v e r a g e prices in t h e " c e n t s " colu m n for bills from different s u p e r m a r k e t s . This c o m p a r i s o n t e c h n i q u e w o r k s best if it is c o n f i n e d to i t e m s priced u n d e r $ 5 , since t h e prices of g o o d s t h a t a r e m o r e costly a l m o s t invariably end in " . 9 9 . " It h a s t h e a d v a n t a g e t h a t t h e s h o p p e r c a n u s e his o r h e r o w n " s h o p p i n g b a s k e t " ( w h i c h n e e d n o t b e identical b e t w e e n the t w o stores for t h e p r o c e d u r e t o w o r k satisfactorily) t o m a k e t h e c o m p a r i s o n . T h e difference i n t h e " c e n t s " a v e r a g e s might, of c o u r s e , reflect differences in t h e quality of t h e g o o d s . It might also reflect different prices for t h e s a m e q u a l i t y — t h a t is up to t h e s h o p p e r to decide. At least, w i t h t h e s e calculations, the s h o p p e r will b e b e t t e r a r m e d t o m a k e t h e decision. For a fair c o m p a r i s o n , at least fifty i t e m s s h o u l d be i n c l u d e d •n t h e total. This u s u a l l y m e a n s saving a n u m b e r of bills, a n d the a v e r a g e s h o p p e r m a y n o t t h i n k that it is w o r t h t h e effort. Is there an easier w a y ? T h e r e is, b a s e d on t h e fact t h a t 90 p e r c e n t of t h e prices in a typical A m e r i c a n s u p e r m a r k e t e n d in " . 9 9 " or '•00." This simple pricing strategy m e a n s t h a t , if a s u p e r m a r k e t

90


is going to raise t h e price of an i t e m m a r k e d in w h o l e dollars, it has virtually n o choice, m a t h e m a t i c a l l y s p e a k i n g , b u t t o j u m p t h e price all t h e w a y up to t h e n e x t ".99." If t h e original price e n d s in ".99," t h e store h a s t h e o p t i o n of raising t h e price by just o n e c e n t to t h e n e x t w h o l e dollar, w h i c h is a m u c h l o w e r p e r c e n t a g e i n c r e a s e in price. So t h e c h e a p e s t s u p e r m a r k e t is likely t o b e t h e o n e w i t h t h e h i g h e s t p r o p o r t i o n o f i t e m s m a r k e d i n w h o l e dollars, b e c a u s e t h e big price j u m p s for t h e s e i t e m s h a v e n ' t h a p p e n e d yet. It's t h a t simple. F l o r e n c e N i g h t i n g a l e b e l i e v e d t h a t "to u n d e r s t a n d God's t h o u g h t s , w e m u s t s t u d y statistics, for t h e s e a r e t h e m e a s u r e o f His p u r p o s e . " Be t h a t as it m a y , t h e r e is no b e t t e r w e a p o n t h a n statistics for u n d e r s t a n d i n g a n d d e f e a t i n g t h e p u r p o s e s of sup e r m a r k e t pricing c o n t r o l l e r s . T h e q u i c k m e t h o d s t h a t I h a v e suggested for c h e c k i n g a n d c o m p a r i n g s u p e r m a r k e t prices rely o n v e r y s i m p l e statistics. I a m a w a r e t h a t i n s u g g e s t i n g t h e i r u s e in s h o p p i n g I am in t h e p o s i t i o n of a m a n w h o h a s l e a r n e d t o s w i m from a b o o k b u t h a s n o t yet tried o u t his m e t h o d i n practice. T h e r e is a s i m p l e r e a s o n for this — I h a t e s h o p p i n g , a n d will p a y a n y t h i n g to get o u t of t h e s t o r e as q u i c k l y as p o s sible. For t h o s e w i t h m o r e p a t i e n c e , t h e s i m p l e c h e c k s t h a t I h a v e o u t l i n e d in this c h a p t e r s h o u l d be of s o m e v a l u e . K e e p in m i n d t h a t t h e differences in prices m i g h t reflect g e n u i n e differences in t h e q u a l i t y of t h e g o o d s , r a t h e r t h a n different prices for t h e s a m e quality. T h a t i s u p t o t h e s h o p p e r t o d e c i d e . W i t h t h e s e s i m p l e tests, h o w e v e r , a t least t h e s h o p p e r n o longer needs to shop in the dark.

Summary

To Quickly Check the Addition of a Supermarket Bill

Add t w o - t h i r d s of t h e n u m b e r of i t e m s to t h e total in t h e "dollars" c o l u m n ( u n l e s s it's o n e o f t h o s e s u p e r m a r k e t s w h e r e everything ends in " . 9 9 " ) .


9 1

To Compare Prices Between Supermarkets

If m o s t of t h e prices at t h e s u p e r m a r k e t e n d in " . 0 0 " or ".99," check w h a t p r o p o r t i o n a c t u a l l y e n d i n " . 0 0 . " T h e h i g h e r t h e p r o p o r t i o n , t h e c h e a p e r t h e s u p e r m a r k e t is likely to b e . If t h e price s p r e a d a t y o u r local s u p e r m a r k e t i s m o r e u n i f o r m , j u s t look a t t h e prices e n d i n g i n " . 9 9 . " T h e h i g h e r t h e p r o p o r t i o n , t h e m o r e e x p e n s i v e t h e s u p e r m a r k e t i s likely t o b e .

h o w to t h r o w a b o o m e r a n g

Not m a n y p e o p l e gel to i n v e n t a n e w c a t e g o r y lor t h e Guinness Book of World Records. I w a s lucky e n o u g h to do so w h e n I w a s briefly affiliated w i t h a television science p r o g r a m a n d asked to c o m e up w i t h an idea for a s c i e n c e - b a s e d n a t i o n a l c o m p e t i tion that w o u l d attract p u b l i c a t t e n t i o n . " W h y not," I suggested, "get t h e m to design a n d lly t h e i r o w n b o o m e r a n g s ? " T h e p r o d u c e r patiently p o i n t e d out that o u t d o o r filming w a s very e x p e n s i v e , a n d that t h e idea was to h a v e a c o m p e t i t i o n w h e r e t h e final could be held in a TV s t u d i o . "Fine," I said, "we'll get t h e m to m a k e t h e b o o m e r a n g s out of c a r d b o a r d , a n d h a v e a race to see h o w m a n y t i m e s t h e y can t h r o w t h e m a r o u n d a pole a n d catch t h e m i n o n e m i n u t e . " T h e c o m p e t i t i o n w a s a great success, a n d a " n e w " work! record w a s d u l y established by t h e British t h r o w e r L a w r e n c e West, w h o zipped his b o o m e r a n g a r o u n d a pole t h r e e m e t e r s a w a y a staggering t w e n t y times in o n e m i n u t e . O u r a t t e m p t s to explain just w h y b o o m e r a n g s c o m e back w e r e frustrated, t h o u g h , w h e n t h e p r o d u c e r w o u l d allow o n l y a lew s e c o n d s of a i r t i m e for t h e e x p l a n a t i o n . This w a s a pity, b e c a u s e t h e explan a t i o n is fascinating in itself, a n d goes far b e y o n d t h e confines of s p i n n i n g b o o m e r a n g s . In fact, it applies to a n y s p i n n i n g o b ject, from t h e a t o m s in o u r brain to t h e w h e e l s of a bicycle a n d t h e Earth in its orbit. All of t h e s e r e s p o n d in t h e s a m e w a y w h e n s o m e t h i n g tries to tilt t h e m over. In t h e case of a b o o m e r a n g , t h e tilting force c o m e s from t h e air r u s h i n g o v e r t h e " w i n g s . " H o w it h a p p e n s , a n d h o w it m a k e s t h e b o o m e r a n g c o m e back, a r e t h e subjects of this c h a p t e r . As a b o n u s , t h e r e is e v e n a design for a "world record" c a r d b o a r d b o o m e r a n g to try. " B o o m e r a n g s ? You m e a n t h e t h i n k i n g p e r s o n ' s F r i s b e e ? "

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T h e s p e a k e r w a s Sean Slade, secretary of t h e British B o o m e r a n g Society. I h a d called h i m in d e s p e r a t i o n for h e l p w i t h a o n e - d a y c o u r s e o n " B o o m e r a n g s : Physics a n d Flying," w h e r e I p l a n n e d t o s h o w n o n - s c i e n t i s t s h o w t o design, build, a n d fly their o w n b o o m e r a n g s . I h a d r e a d up on t h e physics of b o o m e r a n g s , b u t , w i t h o n l y a w e e k to go, I still h a d n ' t m a n aged to fly o n e . No m a t t e r h o w h a r d I tried, my b o o m e r a n g w o u l d n ' t c o m e back. S e a n w a s s u r p r i s e d , to p u t it mildly, to encounter an Australian w h o didn't k n o w h o w to t h r o w a b o o m e r a n g , a n d offered t o i n t r o d u c e m e t o t h e art. I t i s a n art t h a t A u s t r a l i a n Aborigines h a v e u n d e r s t o o d for at least ten t h o u s a n d years, a l t h o u g h m o d e r n science i s o n l y j u s t starting to c o m e to grips w i t h it. T h e n e x t day, S e a n t u r n e d u p o n m y d o o r s t e p w i t h a bag c o n t a i n i n g m o r e t h a n 150 b o o m e r a n g s . S o m e w e r e m a d e o f wood, the traditional material, but m a n y m o r e w e r e m a d e from t h e m a t e r i a l s of m o d e r n science — brightly colored plastics, c a r b o n f i b e r - r e i n f o r c e d c o m p o s i t e s , a n d e v e n m e t a l s like t i t a n i u m . T h e longest w a s a l m o s t as tall as h i m , a n d l o o k e d a fearsome w e a p o n . R e t u r n i n g b o o m e r a n g s w e r e , in fact, h a r d l y e v e r used as w e a p o n s . A u s t r a l i a n Aborigines, like m o d e r n - d a y b o o m e r a n g t h r o w e r s , u s e d (and still use) t h e m for sport. T h e sport could be quite bloodthirsty, as t h e following a c c o u n t from 1881 s h o w s : Ten o r t w e l v e w a r r i o r s , p a i n t e d w i t h w h i t e stripes a c r o s s t h e c h e e k a n d n o s e , a n d a r m e d w i t h shields a n d b o o m e r a n g s , a r e m e t by an equal n u m b e r at a distance of about t w e n t y paces. E a c h i n d i v i d u a l h a s a r i g h t t o t h r o w his b o o m e r a n g a t a n y o n e o n t h e o t h e r side, a n d steps o u t o f r a n k i n t o t h e i n t e r v e n i n g space t o d o so. T h e o p p o s i t e p a r t y t a k e t h e i r t u r n , a n d s o o n a l t e r n a t e l y , u n t i l s o m e o n e i s hit, o r all a r e satisfied . . . A s t h e b o o m e r a n g i s t h r o w n w i t h g r e a t force, i t r e q u i r e s v e r y g r e a t d e x terity a n d q u i c k sight t o avoid s u c h a n e r r a t i c w e a p o n , a n d affords a fine o p p o r t u n i t y for d i s p l a y i n g t h e r e m a r k a b l e activity of t h e a b o r i g i n e s . This activity is, n o d o u b t , c o n s i d e r a b l y r o u s e d b y fear of t h e s e v e r e cut w h i c h is inflicted by t h e b o o m e r a n g .

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S o m e m o d e r n b o o m e r a n g s can b e e q u a l l y f r i g h t e n i n g . S e a n told m e t h a t a n e w w o r l d d i s t a n c e r e c o r d h a d j u s t b e e n e s t a b lished — not by an Aboriginal t h r o w e r , b u t by a F r e n c h m a n c o m p e t i n g in a c o n t e s t at S h r e w s b u r y in E n g l a n d . T h e record d i s t a n c e w a s a n i n c r e d i b l e 149 m e t e r s , b u t t h e t r i u m p h w a s n e a r l y a c a t a s t r o p h e b e c a u s e a g o o d d i s t a n c e b o o m e r a n g is like a flying r a z o r b l a d e , b e i n g v e r y t h i n a n d s h a r p - e d g e d to r e d u c e a e r o d y n a m i c d r a g a n d to p e r m i t it to travel as far as possible before r e t u r n i n g , ft is practically invisible to t h e t h r o w e r a s i t r e t u r n s , e d g e - o n , a n d this o n e n e a r l y r e m o v e d t h e t h r o w e r ' s h e a d , e v e n t u a l l y l a n d i n g s o m e sixty m e t e r s b e hind him. Despite t h e i r p o t e n t i a l for d a m a g e , r e t u r n i n g b o o m e r a n g s , as mentioned, are seldom used as h u n t i n g w e a p o n s because it is m u c h easier to hit a target s u c h as an a n i m a l or an e n e m y w i t h a direct t h r o w of a s p e a r or a s t o n e , r a t h e r t h a n w i t h s o m e t h i n g t h a t n o t o n l y follows a w i d e l y c u r v i n g p a t h , b u t w h i c h also rises as it flies. W h e n A u s t r a l i a n A b o r i g i n e s u s e b o o m e r a n g - s h a p e d sticks a s w e a p o n s for w a r o r h u n t i n g , t h e sticks (called kylies in s o m e Aboriginal l a n g u a g e s ) a r e deliberately c h o s e n not t o r e t u r n . T h e a r m s a r e s h a p e d t o h a v e a e r o d y n a m i c "lift" s o t h a t w h e n t h e stick i s t h r o w n horizontally, s p i n n i n g at a r o u n d t e n r e v o l u t i o n s p e r s e c o n d , it s k i m s a m e ter or so a b o v e t h e g r o u n d in a straight p a t h u n t i l it hits w h a t ever is u n f o r t u n a t e e n o u g h to be in the way. Some 95 percent of t h e b o o m e r a n g - s h a p e d objects t h a t h a v e b e e n collected fall i n t o this category. B o o m e r a n g s t h e m s e l v e s a r e different. T h e i r a r m s a r e also s h a p e d to give a e r o d y n a m i c "lift," b u t t h e lift o p e r a t e s in s u c h a w a y t h a t w h e n t h e b o o m e r a n g i s t h r o w n i n a n initially n e a r vertical o r i e n t a t i o n , it g r a d u a l l y t u r n s o v e r as it t r a v e l s in a circle u n t i l , by t h e t i m e it r e t u r n s to t h e t h r o w e r , it is s p i n n i n g in a h o r i z o n t a l p l a n e a n d h o v e r i n g , j u s t w a i t i n g to be c a u g h t . As 1 l o o k e d at S e a n ' s large b o o m e r a n g , a n d e v e n t h o s e ol more modest proportions, I thought with some trepidation t h a t t h e y w o u l d b e p r e t t y lethal e v e n w h e n h o v e r i n g , a n d could easily t a k e a c o u p l e of fingers off. He d e m o n s t r a t e d t h e

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w a y t o avoid this, w h i c h w a s t o catch t h e b o o m e r a n g b e t w e e n the p a l m s o f t h e h a n d s b y c l a p p i n g t h e m t o g e t h e r . This t u r n e d out to be easier t h a n it l o o k e d , a n d w a s t h e start of my love affair w i t h b o o m e r a n g s . Records are plentiful in b o o m e r a n g t h r o w i n g , w h i c h is n o w an o r g a n i z e d sport, w i t h c o m p e t i t i o n s lor "fast c a t c h , " "dist a n c e t h r o w n " (this w a s also a c o m p e t i t i o n a m o n g t h e Aborigines), " m a x i m u m t i m e aloft," a n d n u m e r o u s o t h e r c a t e g o r i e s . The g r a n d prize for " m a x i m u m t i m e aloft" m u s t s u r e l y go to Bob Reid, a British u n i v e r s i t y physicist w h o m a n a g e d to k e e p a b o o m e r a n g in t h e air for t w e n t y - f o u r h o u r s a n d e l e v e n seco n d s . I m p o s s i b l e ? Not if y o u a r e e n t h u s i a s t i c , a n d eccentric, e n o u g h t o t a k e a b o o m e r a n g t o t h e S o u t h Pole a n d t h r o w i t t h r o u g h all t h e t i m e z o n e s , t h u s a d d i n g t w e n t y - f o u r h o u r s t o t h e actual t i m e of flight (Figure 5.1).

F i g u r e 5 . 1 : Dr. B o b R e i d i n t h e P r o c e s s o f T h r o w i n g a B o o m e r a n g Around the South Pole.

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W i t h p e o p l e s u c h as S e a n a n d Bob for s u p p o r t , I felt that I w a s i n m y e l e m e n t a s I settled d o w n t o a d d r e s s t h e q u e s t i o n "What m a k e s a b o o m e r a n g come back?" The short a n s w e r is spin, t o g e t h e r w i t h t h e fact t h a t t h e t w o b l a d e s ol a s t a n d a r d b o o m e r a n g a r e o r i e n t e d differently (Figure 5.2).

Figure 5.2: W i n g S h a p e s in a Traditional B o o m e r a n g .

E a c h b l a d e i s s h a p e d like a n a i r p l a n e w i n g , b u t t h e t w o blades a r e j o i n e d t o g e t h e r i n s u c h a w a y t h a t t h e r o u n d e d e d g e of b o t h w i n g s a l w a y s leads as t h e b o o m e r a n g spins after it is t h r o w n . B o t h w i n g s t h u s p r o v i d e "lift" hut, b e c a u s e t h e b o o m e r a n g is s p i n n i n g in a vertical p l a n e , t h e "lift" p u s h e s t h e b o o m e r a n g sideways, ultimately returning it to the thrower. I h o p e t h a t t h e a b o v e e x p l a n a t i o n d o e s n o t satisfy y o u . It is t h e o n e t h a t I p u t t o g e t h e r for t h e TV p r o d u c e r in r e s p o n s e to n a g g i n g d e m a n d s lor a t e n - s e c o n d " s o u n d b i t e " o n h o w b o o m e r a n g s w o r k . Scientists a r e f r e q u e n t l y a s k e d for s u c h s o u n d bites, t h e p r e s u m p t i o n b e i n g t h a t t h e a u d i e n c e could n o t possibly r e m a i n i n t e r e s t e d for a n y longer, o r u n d e r s t a n d a n y t h i n g m o r e c o m p l i c a t e d . I d o n ' t b e l i e v e it, a n d I t h i n k that a u d i e n c e s a r e b e i n g p a t r o n i z e d b y s u c h practices. T h e real r e a s o n s for t h e r e t u r n of t h e b o o m e r a n g a r e easier

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t o u n d e r s t a n d t h a n t h e simplified e x p l a n a t i o n , w h i c h raises m o r e q u e s t i o n s t h a n it a n s w e r s , a n d a r e also a lot m o r e i n t e r esting a n d a e s t h e t i c a l l y p l e a s i n g . In science, as in art, t h e b e a u t y is in t h e detail. Not t h a t visual b e a u t y is missing. Boomerangs themselves have a pleasing symmetry, and are usually p a i n t e d , a l t h o u g h t h e p a i n t i n g s o n p r e - E u r o p e a n A b o riginal b o o m e r a n g s w e r e s e l d o m i n t e n d e d for d e c o r a t i v e p u r poses. T h e y w e r e used i n t h e s a m e w a y a s o t h e r Aboriginal art is used — as a r e f e r e n c e to a n c e s t o r s a n d to t h e D r e a m t i m e w h e n t h e E a r t h w a s f o r m e d (Figure 5.3). M o s t s u r v i v i n g e x a m p l e s h a v e long since b e e n s n a p p e d u p b y collectors, a n d m o d e r n Aboriginal d e c o r a t i o n is exclusively for t h e t o u r i s t market. f c a m e across o n e c u r i o u s e x a m p l e w h e n I w a s p u r c h a s i n g b o o m e r a n g s from D u n c a n M a c L e n n a n , a n o l d - t i m e A u s tralian w h o h a s r u n a b o o m e r a n g school in S y d n e y for n e a r l y sixty years. W h e n h e started, h e w a n t e d Aboriginal motifs for

Figure 5.3: Australian Aboriginal D e c o r a t e d B o o m e r a n g s . a Kimberley Region of Western Australia. b. Diamantina River Region. Picture provided by Philip Jones, Senior Curator, South Australian M u s e u m .

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t h e p l y w o o d b o o m e r a n g s that h e w a s m a n u f a c t u r i n g , a n d a p p r o a c h e d t h e m e m b e r s of a local tribe to do t h e p a i n t i n g . T h e y w e r e v e r y i n t e r e s t e d , n o t o n l y i n d o i n g t h e p a i n t i n g , b u t also in the b o o m e r a n g s themselves. It turned out that they had never seen one, and Duncan had the unique pleasure of t e a c h i n g a n Aboriginal tribe h o w t o t h r o w b o o m e r a n g s . T h e science o f w h a t h a p p e n s w h e n a b o o m e r a n g leaves t h e h a n d of t h e t h r o w e r is as aesthetically pleasing as t h e b o o m e r a n g itself. T h e simple k e y n o t i o n is that t h e t w o a r m s , e v e n t h o u g h t h e y a r e identical a n d s y m m e t r i c a l l y d i s p o s e d a b o u t t h e axis of spin, e x p e r i e n c e different a e r o d y n a m i c forces b e c a u s e t h e b o o m e r a n g i s m o v i n g f o r w a r d a s well a s s p i n n i n g . T h e n e t result is t h a t t h e u p p e r a r m is m o v i n g faster t h r o u g h t h e air t h a n t h e l o w e r a r m , s o t h a t t h e s i d e w a y s "lift" i s g r e a t e r on the upper a r m than it is on the lower arm, and the boomera n g tilts (Figure 5.4).

Figure 5.4: Flying B o o m e r a n g V i e w e d Along Flight Path (Central Circle) from Behind. (The magnitude of the aerodynamic force on each boomerang arm is proportional to the length of the arrow.)

W h a t h a p p e n s n e x t is t h a t t h e b o o m e r a n g ' s {light d i r e c t i o n c h a n g e s to follow t h e direction of t h e tilt. This p h e n o m e n o n , called precession, is o n e t h a t we often e x p e r i e n c e , e v e n if we c a n ' t p u t a n a m e to it. W h e n we lean s i d e w a y s w h i l e riding a bicycle, for e x a m p l e , t h e s p i n n i n g front w h e e l a u t o m a t i c a l l y t u r n s t o follow t h e d i r e c t i o n i n w h i c h w e l e a n (the back w h e e l

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w o u l d do likewise if it c o u l d ) . T h e p h e n o m e n o n also w o r k s in r e v e r s e . If we t u r n t h e front w h e e l of a bicycle, we a u t o m a t i cally l e a n in t h e d i r e c t i o n of t h e t u r n . This is n o t v o l u n t a r y — it's physics. Precession c a n t u r n u p i n u n e x p e c t e d places. Hospital MRI ( m a g n e t i c r e s o n a n c e i m a g i n g ) s c a n n e r s u s e it, for e x a m p l e , in i m a g i n g soft tissues s u c h a s t h e b r a i n . T h e t h i n g s t h a t are spinning are not the patients but the atoms in the patients' brains. A n M R i s c a n n e r subjects t h e s e a t o m s t o a w e a k r a d i o signal t h a t tilts t h e m over. T h e s p i n n i n g a t o m s r e s p o n d j u s t as a tilted bicycle w h e e l w o u l d , by t r y i n g to r e c o v e r t h e d i r e c t i o n of t h e i r spins. T h e s p e e d a t w h i c h t h e y can d o this d e p e n d s o n h o w "sticky" t h e local b r a i n e n v i r o n m e n t is, w h i c h c a n b e different i n sickness a n d i n h e a l t h , s o t h a t t h e s p e e d a t w h i c h t h e s p i n n i n g a t o m s r e c o v e r after b e i n g s u b j e c t e d to a r a d i o p u l s e c a n give v a l u a b l e clues a b o u t w h e t h e r t h e p a r t o f t h e b r a i n t h a t t h e y i n h a b i t is h e a l t h y or ailing. Precession in b o o m e r a n g s , bicycles, a n d b r a i n s w o r k s i n t h e s a m e w a y i n e a c h case, a n d is u l t i m a t e l y describable by a v e r y s i m p l e a n d b e a u t i f u l r u l e , called t h e gyro rule, w h i c h says t h a t the spin axis chases the torque axis. It is easiest to e x p l a i n this r u l e w i t h a d i a g r a m , as in Figure 5.5.

Figure 5.5: T h e Gyro Rule A p p l i e d to B o o m e r a n g s .

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T h e spin axis is t h e line a b o u t w h i c h t h e spin is t a k i n g place (e.g., t h e axle of a bicycle w h e e l ) . Similarly, t h e t o r q u e axis is t h e o n e a b o u t w h i c h t h e tilt i s t a k i n g place. For t h e b o o m e r a n g s h o w n in t h e d i a g r a m , t h e t o r q u e axis is t h e line of flight, w i t h its direction specified by t h e right-hand screw rule. B e n d t h e fingers of y o u r right h a n d in t h e direction of r o t a t i o n or t o r q u e . T h e t h u m b will n o w b e p o i n t i n g i n t h e direction o f t h e a p p r o priate axis. T h e r i g h t - h a n d s c r e w rule also applies to t h e spin ol t h e b o o m e r a n g itself. T h e directions of t h e spin a n d t o r q u e axes, t o g e t h e r w i t h t h e g y r o rule, tell us t h a t b o o m e r a n g s s w i n g to t h e left if t h e y tilt to t h e left, e v e n t u a l l y s w i n g i n g right a r o u n d a n d c o m i n g back t o w a r d s t h e t h r o w e r . It is also possible to d e sign a b o o m e r a n g t h a t tilts to t h e right w h e n t h r o w n , a n d t h e r e f o r e t u r n s a r o u n d i n t h e o p p o s i t e d i r e c t i o n . T h e first t y p e is u s u a l l y used by r i g h t - h a n d e d t h r o w e r s , a n d t h e s e c o n d t y p e b y l e f t - h a n d e d t h r o w e r s . S o t h e r e a r e r i g h t - h a n d e d a n d lefth a n d e d b o o m e r a n g s , j u s t a s t h e r e a r e r i g h t - h a n d e d a n d lefthanded corkscrews. T h e g y r o r u l e follows from o n e of t h e g r e a t c o n s e r v a t i o n laws of classical p h y s i c s . T h e r e a r e j u s t four of t h e s e , all e n u n ciated in t h e n i n e t e e n t h c e n t u r y , a n d all describing a f u n d a m e n t a l q u a n t i t y w h o s e total t h r o u g h o u t t h e u n i v e r s e r e m a i n s forever u n c h a n g e d . O n e of t h o s e q u a n t i t i e s is e n e r g y (see c h a p t e r t w o ) . T h e o t h e r t h r e e a r e electrical c h a r g e , linear m o m e n t u m , and angular m o m e n t u m . ' Precession e x p l a i n s v e r y elegantly why b o o m e r a n g s c o m e back, b u t t h a t is o n l y a start, as Figure 5.6 reveals. T h e path s h o w n is t h e simplest, a n d typical of m a n y b o o m e r a n g s . Viewed from a b o v e , it is a circle. V i e w e d from t h e side (as in t h e p h o t o g r a p h ) , t h e b o o m e r a n g rises e v e r m o r e rapidly as it leaves ' Linear m o m e n t u m is just mass x linear velocity (i.e., speed in a given direction). m o m e n t u m is mass x angular velocity (i.e., rotational speed). Linear m o mentum is conserved unless a force is applied, and the direction ol the lorce determines the direction of the n e w m o m e n t u m . Angular m o m e n t u m is conserved unless a tilting force (a torque) is applied, and the direction ol the torque determines the n e w direction of the angular m o m e n t u m . The spin axis defines the direction of angular m o m e n t u m . W h e n the torque axis is at right angles to the spin axis, then the latter is forever chasing the former.

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Figure 5.6: T i m e - L a p s e P h o t o g r a p h of a B o o m e r a n g in Flight. The boomerang, thrown by Michael Hanson and photographed by Christian Taylor, was lit by a small battery-powered bulb at the tip.

t h e t h r o w e r , t h e n slowly settles as it r e t u r n s , l o o p i n g a n d spinn i n g as it d o e s so. This p h o t o g r a p h is t h e latest ( a n d best) in a long line that s t r e t c h e s back to a t i m e - l a p s e p h o t o g r a p h t a k e n in front oi t h e old A u s t r a l i a n P a r l i a m e n t H o u s e by Lorin Hawes, an e c c e n t r i c A m e r i c a n physicist w h o g a v e up a j o b as a n u c l e a r w e a p o n s i n s t r u c t o r a n d m o v e d t o Australia, w h e r e he set up as a b o o m e r a n g d e s i g n e r a n d f o u n d e r oi t h e w o n derful Fvludgeeraba Creek E m u Racing a n d B o o m e r a n g T h r o w ing Association. It s e e m s impossible that s u c h a (light p a t h could be acc o u n t e d lor by s i m p l e physical rules. People before C o p e r n i c u s had a similar p r o b l e m w i t h t h e p l a n e t s . Viewed from Earth, t h e y can a p p e a r t o speed u p , slow d o w n , a n d e v e n o c c a s i o n ally do b a c k w a r d s s o m e r s a u l t s . If we c o u l d p u t a large e n o u g h sparkler on M a r s a n d t a k e a t i m e - l a p s e p h o t o g r a p h of its m o v e m e n t s , t h e y w o u l d a p p e a r r e m a r k a b l y similar t o t h o s e o i a b o o m e r a n g . The Greek a s t r o n o m e r Ptolemy explained such complicated p l a n e t a r y m o v e m e n t s in t e r m s oi small-scale circular m o v e m e n t s (called epicycles) s u p e r i m p o s e d o n t h e m a i n

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orbit, a n d e v e n smaller-scale circular m o v e m e n t s s u p e r i m p o s e d on t h e s e . It t o o k t h e g e n i u s of C o p e r n i c u s to realize that all of P t o l e m y ' s p r o b l e m s s t e m m e d from t a k i n g t h e E a r t h as t h e p o i n t o f o b s e r v a t i o n . V i e w e d from t h e S u n i n s t e a d , p l a n e tary m o v e m e n t s b e c a m e e x t r a o r d i n a r i l y s i m p l e , w i t h all p l a n ets following s m o o t h elliptical orbits. B o o m e r a n g m o v e m e n t s b e c o m e e q u a l l y simple w h e n v i e w e d from t h e p o i n t of v i e w of t h e b o o m e r a n g . T h e first step is to e x p l a i n w h y t h e b o o m e r a n g flies in a circle. A circular orbit r e q u i r e s a force t h a t is a l w a y s directed t o w a r d s t h e c e n t e r a n d w h i c h d o e s n o t c h a n g e i n m a g n i t u d e . This force i s p r o v i d e d b y t h e a e r o d y n a m i c lift. For it to stay c o n s t a n t , t h e a n g l e of attack of t h e airfoil (i.e., t h e a n g l e of t h e b o o m e r a n g w i n g to t h e o n r u s h i n g air) m u s t be c o n s t a n t . This will o n l y h a p p e n if t h e rate at w h i c h t h e b o o m e r a n g tilts is e x a c t l y t h e s a m e as t h e r a t e at w h i c h it flies a r o u n d t h e circle. It t a k e s o n l y t h r e e lines of ( a d m i t t e d l y c o m p l e x ) algebra to s h o w t h a t a simple, ideal b o o m e r a n g w i t h w i n g s of a u n i f o r m cross-sectional s h a p e o b e y s this c o n d i t i o n . T h e m a t h e m a t i c s , s u m m a r i z e d i n t w o excellent articles by t h e irrepressible B o b Reid, leads to a " b o o m e r a n g e q u a t i o n " t h a t tells u s a lot a b o u t b o o m e r a n g s a n d h o w t h e y w o r k . H e r e I h a v e w r i t t e n t h e b o o m e r a n g e q u a t i o n using w o r d s instead of algebraic s y m b o l s :

In o t h e r w o r d s , t h e flight circle will be bigger if t h e m a t e r i a l from w h i c h t h e b o o m e r a n g is c o n s t r u c t e d is d e n s e r a n d if t h e a r m s a r e thicker. T h e flight circle will also be bigger if t h e lift coefficient (i.e., t h e a e r o d y n a m i c effectiveness of t h e w i n g s ) is smaller, if t h e a r m s a r e n a r r o w e r , a n d if t h e d e n s i t y of t h e air is lower. So if y o u w a n t d i s t a n c e , go to a h i g h place, as t h e Swiss t h r o w e r M a n u e l Schiitz did i n 1 9 9 9 w h e n h e e s t a b lished a n e w w o r l d d i s t a n c e r e c o r d o f 2 3 8 m e t e r s ( m o r e t h a n a q u a r t e r of a m i l e , t h e r e a n d b a c k ! ) . T h e r e c o r d w a s e s t a b -

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lished at Kloten, n e a r Zurich, 4 0 9 m e t e r s a b o v e sea level, a n d with an air d e n s i t y four p e r c e n t less t h a n t h a t at sea level. E v e n m o r e i n t e r e s t i n g t h a n t h e factors t h a t a r e i n t h e e q u a tion a r e t h e factors t h a t a r e n ' t . T h e r a d i u s of t h e flight p a t h is i n d e p e n d e n t o f b o t h t h e f o r w a r d velocity a n d t h e a n g u l a r spin velocity. It is also i n d e p e n d e n t of t h e l e n g t h of t h e a r m s , e x cept insofar as this l e n g t h affects t h e lift coefficient, a n d is Cven i n d e p e n d e n t of t h e n u m b e r of a r m s . S o m e of t h e factors in t h e b o o m e r a n g e q u a t i o n fight w i t h each o t h e r . A l o w lift coefficient, for e x a m p l e , u s u a l l y n e e d s a thin, flat a r m , r a t h e r t h a n a thick o n e . Practical b o o m e r a n g design, t h e n , is m o r e t h a n a m a t t e r of fitting an e q u a t i o n , e v e n t h o u g h t h e e q u a t i o n p r o v i d e s a useful g u i d e . C o m p r o m i s e , based o n e x p e r i e n c e , can c o n s i d e r a b l y i m p r o v e t h e performance. W h a t e v e r t h e design o f t h e b o o m e r a n g , t h e r a d i u s o f t h e flight circle is built in, a l t h o u g h factors s u c h as t h e a n g l e of tilt a n d speed of r o t a t i o n at t h e t h r o w can s o m e t i m e s h a v e a s u b stantial effect. T h e m a i n result of t h r o w i n g a b o o m e r a n g harder, t h o u g h , is to m a k e it travel a r o u n d its flight p a t h faster, a n d c o m e back s o o n e r . L a w r e n c e West, t h e c u r r e n t world record h o l d e r for i n d o o r b o o m e r a n g flying, took a d v a n t a g e of this fact in t h e c o m p e t i t i o n that I organized for t h e British TV s h o w Tomorrow's World. T h e competition w a s for t h e m a x i m u m n u m b e r of t i m e s t h a t a cardboard b o o m e r a n g could be t h r o w n a n d c a u g h t in o n e m i n u t e after passing a r o u n d a pole t h r e e m e t e r s a w a y . L a w r e n c e designed a b o o m e r a n g w h e r e t h e b a l a n c e of factors in t h e b o o m e r a n g e q u a t i o n provided a built-in flying radius of just o v e r f .5 m e t e r s , w h i p p i n g it a r o u n d t h e pole t w e n t y - f o u r times in practice, a n d t w e n t y t i m e s in t h e actual c o m p e t i t i o n (Figure 5.7). T h e science i n v o l v e d s o m e i n t e r e s t i n g subtleties t h a t 1 i n t r o duced to the participants in my course w h e n they w e r e designing t h e i r o w n b o o m e r a n g s . T h e f i r s t c o n c e r n e d t h e stability of t h e b o o m e r a n g , a n d t h e a n g l e b e t w e e n t h e a r m s . It m i g h t s e e m from t h e b o o m e r a n g e q u a t i o n t h a t t h e a n g l e b e t w e e n t h e a r m s d o e s n ' t m a t t e r , since it isn't m e n t i o n e d . It

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Figure 5.7: Design of Lawrence West's "World Record" C a r d b o a r d Boomerang, Made from

1.5 m m - t h i c k M o u n t B o a r d .

d o c s m a t t e r , t h o u g h , for a r e a s o n t h a t is easy to u n d e r s t a n d intuitively a l t h o u g h r a t h e r c o m p l e x to e x p l a i n scientifically. If y o u i m a g i n e m a k i n g a straight b o o m e r a n g , w i t h t h e t w o a r m s in t h e s a m e line, it is easy to see t h a t this w o u l d be v e r y difficult to t h r o w so t h a t it k e p t s p i n n i n g in t h e s a m e p l a n e , ft is all too likely also to start r o t a t i n g a b o u t t h e l o n g i t u d i n a l axis, e v e n t u a l l y r e s u l t i n g in a crazy t u m b l i n g . Stability a n d r o t a t i o n a r e favorite subjects of my Bristol University c o l l e a g u e Professor M i k e Berry, w h o h a s e s t a b l i s h e d a w o r l d w i d e r e p u t a t i o n lor d e m o l i s h i n g l o n g - h e l d beliefs in this a r e a . His latest t r i u m p h e a r n e d h i m t h e spoof fgNobel Prize from H a r v a r d U n i v e r s i t y b e c a u s e of its e y e - c a t c h i n g d e s c r i p tion — "Of Flying Frogs a n d L e v i t r o n s . " T h e science, t h o u g h ,

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w a s very real. T h e frog w a s a toy t h a t s e e m e d to d i s o b e y a fund a m e n t a l physical l a w b y r e m a i n i n g s u s p e n d e d i n space. T h e p r o b l e m w a s n o t t h e d e f i a n c e of gravity — this w a s a c h i e v e d by p u t t i n g a set of m a g n e t s in t h e frog, w i t h t h e i r n o r t h p o l e s p o i n t i n g d o w n w a r d s , a n d placing t h e frog o v e r a base c o n t a i n i n g a set of m a g n e t s w i t h t h e i r n o r t h p o l e s p o i n t i n g u p w a r d s . T h e real p r o b l e m w a s t h a t s u c h a n a r r a n g e m e n t h a s b e e n k n o w n for a t least o n e h u n d r e d y e a r s t o b e u n s t a b l e . T h e slightest t o u c h , or puff of b r e e z e , a n d t h e frog s h o u l d flip o v e r a n d fall to t h e g r o u n d . Yet h e r e w a s t h e frog, displayed in a s h o p w i n d o w , lazily s p i n n i n g for h o u r s o n e n d . T h e spin w a s t h e key, a s M i k e d i s c o v e r e d w h e n h e sat d o w n to do t h e m a t h e m a t i c s of t h e p r o b l e m . It t r a n s p i r e d t h a t t h e a r r a n g e m e n t is u n s t a b l e unless t h e frog is s p i n n i n g , in w h i c h case t h e r e is a v e r y n a r r o w r a n g e of p a r a m e t e r s w i t h i n w h i c h t h e a r r a n g e m e n t r e m a i n s stable. T h e i n v e n t o r o f t h e levitating frog, n o t k n o w i n g that it w a s i m p o s s i b l e to levitate a frog by m e a n s of m a g n e t s , h a d s t u m b l e d on t h e precise set of c o n d i tions n e e d e d . B o o m e r a n g designers h a v e a similar p r o b l e m . T h e physicist's "ideal" b o o m e r a n g , w i t h w i n g s of u n i f o r m cross-section, m a k e s the j o b of calculation easier, but isn't particularly ideal w h e n it c o m e s t o c o m p e t i t i o n t h r o w i n g . With a n y o t h e r design, t h o u g h , the t h r o w e r faces t h e i m m e d i a t e p r o b l e m of m a k i n g t h e rate of tilt equal to t h e rate of rotation, w h i c h is m a t h e m a t i c a l l y e q u i v alent to saying that t h e angle of attack h a s to stay c o n s t a n t . This m e a n s t h a t t h e rate of tilt (i.e., t h e precession rate) m u s t be just right. Too slow, a n d t h e angle of attack gradually decreases so that, after a p r o m i s i n g start, t h e b o o m e r a n g w o n ' t c o m e back. Too rapid, a n d t h e angle of attack increases, t h e lift increases, and e v e n t u a l l y t h e b o o m e r a n g stalls. W h a t c a n b e d o n e w i t h a b o o m e r a n g t h a t w o n ' t c o m e back, e i t h e r d i s a p p e a r i n g i n t o t h e d i s t a n c e o r stalling a n d c r a s h i n g ? Some of the students in my course t h o u g h t that the answer w o u l d b e t o c h a n g e t h e s h a p e o f t h e b o o m e r a n g b y s a n d i n g it. The real a n s w e r is m u c h s i m p l e r t h a n t h a t — just t a p e small coins to t h e wings. For a b o o m e r a n g t h a t stalls, t h e m a t h e m a t i c s

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u n d e r l y i n g t h e b o o m e r a n g e q u a t i o n s h o w t h a t t h e coins s h o u l d b e t a p e d n e a r t h e tip, s l o w i n g t h e b o o m e r a n g d o w n . T o speed u p t h e b o o m e r a n g , t h e coins s h o u l d b e t a p e d n e a r t h e center. T h e effect in t h e latter case is t h e s a m e as w h e n a spinn i n g s k a t e r w i t h a r m s o u t s t r e t c h e d pulls his o r h e r a r m s in, s p e e d i n g up as a result b e c a u s e a n g u l a r m o m e n t u m is t h e r e lore c o n s e r v e d . B o o m e r a n g d e s i g n e r s r e g u l a r l y u s e t h e coin trick, o n l y c h a n g i n g t h e basic design o n c e t h e coins h a v e shown w h e r e weight needs to be added and w h e r e it needs to be subtracted. T h e o t h e r m a i n design p r o b l e m w i t h b o o m e r a n g s i s c o n s t r u c t i n g t h e m s o t h a t t h e y "lie d o w n " a t j u s t t h e right stage i n t h e flying circle. But w h y d o e s a b o o m e r a n g "lie d o w n " at all? T h e a n s w e r c o n c e r n s yet a n o t h e r s u b t l e t y o f t h e b o o m e r a n g , w h i c h is t h a t o n e of t h e a r m s is a l w a y s flying in "dirty air," a p h e n o m e n o n t h a t will b e familiar t o y a c h t s m e n , a n d i n d e e d t o a n y o n e w h o h a s b e e n passed b y a f a s t - m o v i n g t r u c k o n a h i g h w a y . This p h e n o m e n o n h a p p e n s b e c a u s e t h e t w o a r m s o f a traditionally shaped b o o m e r a n g , apparently symmetrically disposed, a r e in fact q u i t e different. T h e a r m w i t h t h e s h a r p e d g e o n t h e " i n s i d e " i s called t h e l e a d i n g a r m . T h e o t h e r (with t h e s h a r p e d g e o n t h e " o u t s i d e " ) w a s c h r i s t e n e d b y Lorin H a w e s t h e dingle, o r d a n g l i n g , a r m . T h e p o o r dingle a r m i s forever flying t h r o u g h t h e d i s t u r b e d air c r e a t e d b y t h e leading a r m . This m e a n s that i i t h e t w o a r m s a r e identical, t h e dingle a r m will p r o v i d e less lift t h a n t h e l e a d i n g a r m . "Averaged o v e r a c o m p l e t e r o t a t i o n , " says Bob Reid, " t h e r e is a n e t t o r q u e a b o u t t h e vertical axis, w h i c h in t u r n leads to a p r e c e s s i o n a b o u t t h e d i r e c t i o n of flight, i.e., t h e b o o m e r a n g lies d o w n . " Alter half an h o u r w i t h Bob's d i a g r a m s , f believed h i m . O t h ers will h a v e t o h a v e faith, a s m y s t u d e n t s did w h e n t h e y m a d e t h e i r o w n b o o m e r a n g s , o r read t h e original article t h e m selves. T h e m a i n practical p o i n t i s t h a t t h e b o o m e r a n g ' s p r o p e n s i t y t o lie d o w n can b e c o n t r o l l e d b y s h a p i n g t h e dingle a r m so as to give it slightly m o r e lift t h a n t h e l e a d i n g a r m . This is easily d o n e w i t h a t o u c h of s a n d i n g , w h i c h f i n e - t u n e s t h e b o o m e r a n g so t h a t it will lie d o w n at j u s t t h e right p o i n t , as

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L a w r e n c e West's did, e n a b l i n g h i m t o c a t c h a n d t h r o w i t w i t h machine-like precision. Most of this I l e a r n e d w h e n I w a s p l a n n i n g my o n e - d a y c o u r s e , b u t all of t h e t h e o r e t i c a l k n o w l e d g e in t h e w o r l d w a s n ' t g e t t i n g m y b o o m e r a n g t o c o m e back, a n d , a s t h e t i m e d r e w near, I w a s b e c o m i n g increasingly frustrated. T h e n I found o u t w h a t t h e p r o b l e m w a s : air r e s i s t a n c e . A b o o m e r a n g transfers s o m e of its m o m e n t u m to t h e surr o u n d i n g air m o l e c u l e s a s i t travels, s p e e d i n g t h e m u p (so t h e air b e c o m e s h o t t e r ) but s l o w i n g d o w n itself. T h e d r a g can b e sufficient t o s l o w b o t h t h e forward m o t i o n a n d t h e spin t o t h e point w h e r e t h e b o o m e r a n g s i m p l y gives u p a n d flops t o t h e g r o u n d . T h e a n s w e r is to get t h e b o o m e r a n g s p i n n i n g as fast as possible at t h e start, so t h a t it still r e t a i n s a r e a s o n a b l e p r o p o r tion of its a n g u l a r m o m e n t u m by t h e t i m e it r e t u r n s . T h e secret, as Sean s h o w e d me just in t i m e , is to tilt t h e b o o m e r a n g right back a n d t h e n to release it w i t h a w h i p p i n g action, l a u n c h i n g it at a few d e g r e e s a b o v e t h e h o r i z o n t a l to c o u n t e r act t h e effects of gravity on t h e flight. W h e n t h e t i m e c a m e for t h e c o u r s e itself, I w a s t h r o w i n g like the e x p e r t I w a s n ' t , a n d t h e s t u d e n t s w e r e following m y advice to p r o d u c e s o m e w o n d e r f u l b o o m e r a n g s . I forbore to tell t h e m that A u s t r a l i a n Aborigines m o s t l y use t h e i r b o o m e r a n g s as knives, digging tools, musical i n s t r u m e n t s , a n d for c l e a n i n g t h e i r t e e t h . It w o u l d h a v e b e e n a pity to spoil t h e i r p l e a s u r e as, o n e a n d all, t h e i r b o o m e r a n g s c a m e flying back.

6 catch as catch can

Until recently, c a t c h i n g a ball w a s o n e of t h e few a r e a s of sports t h a t science h a d n o t t o u c h e d . Rackets, bats, a n d t h e o t h e r tools of sports h a v e long b e e n d e s i g n e d a l o n g scientific principles, as h a v e a t h l e t e s ' diets a n d , t o s o m e e x t e n t , a t h l e t e s t h e m s e l v e s . M a n y s p o r t i n g t e c h n i q u e s h a v e also b e e n subject t o scientific r e f i n e m e n t — j a v e l i n s , for e x a m p l e , are n o w l a u n c h e d at a precisely calculated a n g l e , w i t h t h e t h r o w e r m o v i n g in a scientifically g u i d e d w a y . Ball catching, t h o u g h , h a s r e m a i n e d t h e p r o v i n c e of n a t u r a l skill. T h e closest t h a t science h a s c o m e to it is r e c o u n t e d in A. G. M a c d o n e l l ' s classic 1933 a c c o u n t of an English village cricket m a t c h , w h i c h r e m a i n s t h e funniest acc o u n t of a n y s p o r t i n g m o m e n t t h a t I h a v e read. T h e g a m e (in baseball t e r m s ) is all tied up before t h e final o u t , a n d t h e " b o w l e r " is e q u i v a l e n t to a pitcher, w h i l e t h e " w i c k e t - k e e p e r " is t h e e q u i v a l e n t of a catcher. N o w r e a d a n d enjoy! T h e scores w e r e level a n d t h e r e w a s o n e w i c k e t t o fall. T h e last m a n in was the blacksmith. . . . He took guard a n d looked r o u n d savagely. He w a s clearly still in a g r e a t r a g e . T h e first ball h e r e c e i v e d h e l a s h e d a t wildly a n d hit straight u p i n t h e air t o a n e n o r m o u s h e i g h t . I t w e n t u p a n d u p a n d u p , u n til it b e c a m e difficult to focus it p r o p e r l y a g a i n s t t h e d e e p , c l o u d less b l u e of t h e sky, a n d it c a r r i e d w i t h it t h e h o p e s a n d fears of a n E n g l i s h village. U p a n d u p i t w e n t a n d t h e n i t s e e m e d t o h a n g m o t i o n l e s s in t h e air, p o i s e d like a h a w k , fighting, as it w e r e , a h e r o i c b u t f o r l o r n b a t t l e a g a i n s t t h e chief i n v e n t i o n of Sir Isaac N e w t o n , a n d t h e n i t b e g a n its s l o w d e s c e n t . In t h e m e a n w h i l e t h i n g s w e r e h a p p e n i n g b e l o w . . . . T h e titanic B o o n e h a d n o t m o v e d b e c a u s e h e w a s m o r e o r less i n t h e right place, b u t t h e n B o o n e w a s n o t likely t o b r i n g off t h e catch, e s p e -

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daily after the episode of the last ball. Major Hawker, shouting "Mine, mine!" in a magnificently self-confident voice, was coming up from the bowler's end like a battle-cruiser. Mr. Harcourt, the poet, had obviously lost sight of the ball altogether, if indeed he had ever seen it, for he was running round and round Boone and giggling foolishly. Livingstone and Southcott, the two cracks, were approaching competently, their eyes fixed on the ball. . . . In the meantime, the professor of ballistics had made a lightning calculation of angles, velocities, density of the air, barometerreadings and temperature, and had arrived at the conclusion that the critical point, the spot which ought to be marked in the photographs with an X, was one yard to the northeast of Boone, and he proceeded to take up his station there, colliding on the way with Donald and knocking him over. A moment later Bobby Southcott came racing up and tripped over the recumbent Donald and was shot head first into the Abraham-like bosom of Boone. Boone stepped back a yard under the impact and came down with his spiked boot, surmounted by a good eighteen stone of flesh and blood, upon the professor's toe. Almost simultaneously the portly wicket-keeper, whose movements were a positive triumph of the spirit over the body, bumped the professor from behind . . . and all the time the visiting American journalist Mr. Shakespeare Pollock hovered alertly upon the outskirts. . . screaming American university cries in a piercingly high tenor voice. At last the ball came down. . . . it was a striking testimony to the mathematical and ballistical skill of the professor that the ball landed with a sharp report upon the top of his head. Thence it leapt up into the air a foot or so, cannoned on to Boone's head, and then trickled slowly down the colossal expanse of the wicket-keeper's back, bouncing slightly as it reached the massive lower portions. It was only a foot from the ground when Mr. Shakespeare Pollock sprang into the vortex with a last earsplitting howl of victory and grabbed it off the seat of the wicketkeeper's trousers. The match was a tie. I can v o u c h for t h e essential t r u t h of t h e a b o v e d e s c r i p t i o n , since f still play cricket for t h e English village w h e r e 1 live.

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Surprisingly, s c i e n c e n o w s e e m s t o h a v e s h o w n t h a t t h e p r o fessor's ability to rapidly c a l c u l a t e trajectories is s o m e t h i n g thai w e all h a v e , a n d w h i c h w e use w h e n w e r u n t o catch a ball. S u p p o r t for this idea c a m e in a p a p e r p u b l i s h e d in 1993 in t h e p r e s t i g i o u s j o u r n a l Nature, w h e r e t w o psychologists a n a lyzed v i d e o - r e c o r d s of e x p e r t c a t c h e r s r u n n i n g to catch a ball. T h e a u t h o r s f o u n d t h a t t h e c a t c h e r s varied t h e i r r u n n i n g s p e e d s s o t h a t t h e r a t e a t w h i c h t h e y w e r e tilting t h e i r h e a d s to follow t h e flight of t h e ball c o n f o r m e d to a specific e q u a t i o n . T h e y b e l i e v e d t h a t t h e c a t c h e r s c o u l d o n l y a c h i e v e this feat by solving t h e e q u a t i o n in t h e i r h e a d s as t h e y r a n , a n d c o n c l u d e d t h a t this " d e m o n s t r a t e s t h e p o w e r o f t h e b r a i n ' s u n c o n s c i o u s p r o b l e m - s o l v i n g abilities." I w a s initially c o n v i n c e d by t h e i r a r g u m e n t , as w e r e t h e n e w s p a p e r s of t h e day, o n e of w h i c h e v e n r a n t h e story on its front p a g e . W h e n I l o o k e d a t w h a t t h e e q u a t i o n really m e a n t , t h o u g h , I f o u n d t h a t it c o n v e y s an a b s u r d l y s i m p l e physical m e s s a g e a b o u t w h a t w e h a v e t o d o t o catch a ball. T h a t m e s sage i s o n e t h a t w e l e a r n a s c h i l d r e n , a n d w h a t t h e p s y c h o l o gists' w o r k really tells us p r o v i d e s a fascinating insight into h o w we adapt t h e simple techniques that we learn as children to t h e m o r e c o m p l e x s i t u a t i o n s of later life. C h i l d r e n begin l e a r n i n g t o catch b y s t a n d i n g w i t h t h e i r a r m s o u t s t r e t c h e d , w a i t i n g for an a d o r i n g a d u l t to lob a ball into t h e i r h a n d s . T h e success of this e n t e r p r i s e is n o t i n f r e q u e n t l y spoiled b y t h e fact t h a t m o s t y o u n g c h i l d r e n t e n d t o s h u t t h e i r eyes a n d t u r n t h e i r h e a d s a w a y a s s o o n a s t h e ball i s t h r o w n . With t i m e , c h i l d r e n l e a r n t h a t this is n o t a p a r t i c u l a r l y efficient t e c h n i q u e , a n d begin (after s o m e e n c o u r a g e m e n t ) t o w a t c h t h e ball, e v e n t u a l l y l e a r n i n g t o m o v e t h e i r h e a d s s o a s t o follow its flight. W i t h r e p e a t e d practice, c h i l d r e n l e a r n t o u s e t h e rate o i h e a d - t i l t i n g as a c u e to tell t h e m w h e t h e r t h e y a r e s t a n d i n g in t h e right place to m a k e t h e c a t c h . If t h e y a r e , t h e n t h e c u e is a v e r y s i m p l e o n e , a n d c a n b e described b y a n e q u a t i o n t h a t w a s w o r k e d o u t b y t w o g r o u p s o f physicists s o m e t h i r t y years a g o .

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The a u t h o r s of t h e Nature p a p e r s h o w e d t h a t we c o n t i n u e to use this s a m e c u e a s a d u l t s , e v e n w h e n w e h a v e t o r u n t o m a k e a c a t c h . H o w d o w e use it, t h o u g h ? D o w e solve t h e e q u a t i o n i n o u r h e a d s , o r d o e s t h e e q u a t i o n m e r e l y describe s o m e simple physical action t h a t w e l e a r n b y r e p e t i t i o n , i n t h e s a m e w a y t h a t a m u s i c a l score m i g h t tell us to m o v e o u r fingers in a certain w a y on a k e y b o a r d , a w a y t h a t we l e a r n w i t h practice so that we do not therefore need the music to guide us? To find t h e a n s w e r , I decided to r e p e a t t h e earlier c a l c u l a t i o n for myself. I h a d to u s e differential calculus, a m e t h o d t h a t scientists use lor t r a c k i n g rates of c h a n g e . Its principles a r e simple — far s i m p l e r t h a n t h o s e i n v o l v e d in r e a d i n g m u s i c . They w e r e s p l e n d i d l y r e v e a l e d to me as a child in a w o n d e r f u l little b o o k (still available) w r i t t e n b y t h e i m p r e s s i v e l y n a m e d Silvanus P. T h o m p s o n , a C a m b r i d g e professor of e n g i n e e r i n g w h o h a d a s his m o t t o : " W h a t o n e fool c a n u n d e r s t a n d , a n o t h e r c a n . " T h a t w a s g o o d e n o u g h for m y father, w h o o w n e d t h e b o o k , a n d it w a s g o o d e n o u g h for m e . This fool s o o n u n d e r s t o o d t h a t t h e c a l c u l u s tracks c h a n g e b y dividing t h e c h a n g e i n t o small steps. W h e n a ball is t h r o w n , for e x a m p l e , its flight p a t h can be w o r k e d o u t by dividing t h e h o r i z o n t a l m o v e m e n t i n t o small steps, a n d w o r k i n g out t h e effect of gravity on t h e h e i g h t after e a c h s t e p . T h e principle is illustrated in Figure 6 . 1 , w h e r e t h e s m o o t h trajectory of a t h r o w n ball is a p p r o x i m a t e d by eight discrete steps. In this dia g r a m t h e t h r o w e r h a s l a u n c h e d t h e ball at an a n g l e ol 4 5 ° to the h o r i z o n t a l . T h e ball's u p w a r d s p e e d g r a d u a l l y d e c r e a s e s u n d e r t h e r e t a r d i n g i n f l u e n c e o f gravity, a n d t h e u p w a r d m o v e m e n t e v e n t u a l l y stops. T h e ball d o e s n o t d i s o b e y " t h e chief i n v e n t i o n of Isaac N e w t o n " b e c a u s e t h e direction ol its m o t i o n is i m m e d i a t e l y r e v e r s e d , a n d t h e ball starts to fall w i t h e v e r - i n c r e a s i n g s p e e d u n d e r t h e i n f l u e n c e of gravity. T h e s e c h a n g e s i n vertical s p e e d h a v e n o effect o n t h e h o r i z o n t a l speed of t h e ball. It can be q u i t e difficult to see this, as I f o u n d w h e n I w a s called u p o n to settle an a r g u m e n t on t h e subject i n m y village p u b . The discussion that night had t o u c h e d on t h e w e a t h e r , politics,

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h o w to d u n k a

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Figure 6 . 1 : Trajectory of a Ball L a u n c h e d at an A n g l e of 45°, A p p r o x i m a t e d by Eight Equal Horizontal S t e p s . The vertical movement after each horizontal step is calculated from Newton's Law of Gravity, which says that the force of gravity changes the vertical speed by 9.8 meters per second every second (i.e., the acceleration, or rate of change of downward speed, is 9.8 m/s ). 2

a n d t h e state o f t h e t h a t c h e d b u s s h e l t e r i n t h e village s q u a r e , b u t h a d e v e n t u a l l y settled i n s o m e i n s c r u t a b l e w a y o n t h e q u e s t i o n of w b a t h a p p e n s if s o m e o n e riding a bicycle t h r o w s a ball straight up in t h e air. O p i n i o n s w e r e d i v i d e d . S o m e claimed t h a t w h e n t h e ball c a m e d o w n i t w o u l d land beside t h e rider. T h e m a j o r i t y view, t h o u g h , w a s t h a t t h e ball w o u l d l a n d s o m e w a y b e h i n d . T h o s e w h o s u p p o r t e d t h e latter v i e w w e r e q u i t e d i s a p p o i n t e d w h e n I sided w i t h t h e m i n o r i t y , giving a s m y r e a s o n t h a t t h e ball w o u l d k e e p m o v i n g f o r w a r d a t t h e s a m e s p e e d as t h e cyclist. Since several pints of b e e r w e r e riding on t h e o u t c o m e , I w a s c h a l l e n g e d to letch a bicycle a n d prove my point experimentally. I p r o v e d it o n l y t o o w e l l w h e n I f r e e w h e e l e d d o w n t h e hill past t h e c h e e r i n g c r o w d a t t h e p u b d o o r a n d l a u n c h e d a small s t o n e t h a t I h a d p i c k e d up from t h e r o a d vertically i n t o t h e air. T h e s t o n e k e p t p a c e w i t h m e a n d , a few m e t e r s f u r t h e r on, l a n d e d directly on t h e t o p of my h e a d . I w a s glad t h a t it h a d n ' t b e e n a cricket ball or a baseball. An e v e n m o r e d r a m a t i c illustration of t h e i n d e p e n d e n c e of h o r i z o n t a l a n d vertical m o t i o n s is given by Lewis W o l p e r t in his b o o k The Unnatural Nature of Science. S u p p o s e a m a r k s m a n fires a rifle bullet horizontally, a n d s i m u l t a n e o u s l y d r o p s a sec-

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ond bullet from t h e h a n d that is s u p p o r t i n g t h e rifle. B o t h b u l lets will hit t h e g r o u n d a t t h e s a m e t i m e . T h e h o r i z o n t a l s p e e d of t h e first b u l l e t m a k e s no difference at all to its vertical movement. T h e i n d e p e n d e n c e o f h o r i z o n t a l a n d vertical s p e e d s h a s b e e n proved repeatedly u n d e r controlled laboratory conditions, but this i s o n l y half t h e story w h e n i t c o m e s t o u n d e r s t a n d i n g w h y t h e s t o n e l a n d e d o n m y h e a d . T h e o t h e r half c o n c e r n s w h y t h e stone k e p t m o v i n g f o r w a r d at t h e s a m e s p e e d o n c e I h a d let it go. It's n o t o b v i o u s t h a t i t s h o u l d . C o m m o n s e n s e suggests t h a t things o n l y m o v e if t h e y a r e p u s h e d or pulled — in o t h e r w o r d s , if a force is a p p l i e d to t h e m . This w a s t h e v i e w t a k e n by Aristotle t w o a n d a half t h o u s a n d y e a r s ago, a n d it is t h e v i e w t a k e n by m a n y p e o p l e today. A c c o r d i n g to a r e c e n t survey, s o m e 30 p e r c e n t of p e o p l e still s h a r e Aristotle's c o m m o n s e n s e notion that things stop moving once there is n o t h i n g to push o r pull o n t h e m . It took t w o t h o u s a n d years, a n d t h e g e n i u s of N e w t o n , to discover t h a t t h i n g s a c t u a l l y stay still or keep moving at constant speed in a straight line u n l e s s a force is a p p l i e d to t h e m ( N e w ton's First L a w of M o t i o n ) . My s t o n e w a s t h e r e f o r e o b e y i n g N e w t o n ' s First L a w w h e n i t k e p t m o v i n g f o r w a r d a t t h e s a m e speed after it h a d left my h a n d , ff I h a d l o o k e d up at it, it would not h a v e appeared to me to be moving in a horizontal direction, since w e w e r e b o t h t r a v e l i n g w i t h t h e s a m e h o r i zontal s p e e d . F r o m t h e p o i n t of v i e w of t h e o b s e r v e r s at t h e p u b door, t h o u g h , its m o v e m e n t w o u l d h a v e a p p e a r e d t o b e v e r y different. T h e y also w o u l d h a v e o b s e r v e d t h e s t o n e t r a v e l i n g forw a r d at a c o n s t a n t s p e e d (i.e., t r a v e l i n g t w i c e as far in t w o s e c o n d s as it h a d in o n e s e c o n d ) . In t h e vertical d i r e c t i o n , though, the stone was being accelerated d o w n w a r d u n d e r the force of gravity. T h e l a w of a c c e l e r a t i o n , d i s c o v e r e d by Galileo, says t h a t if t h e t i m e of travel is d o u b l e d , t h e s t o n e will t r a v e l four t i m e s as far. C o m b i n a t i o n of this vertical a c c e l e r a t e d m o tion w i t h u n i f o r m h o r i z o n t a l m o t i o n p r o d u c e s a p a r a b o l i c p a t h w h e n v i e w e d from t h e side.

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A c a t c h e r s t a n d i n g in t h e right p o s i t i o n to m a k e a c a t c h h a s a different p o i n t of v i e w a g a i n . He or s h e is not v i e w i n g t h e flight p a t h from t h e side, b u t sees it " e n d - o n , " a n d h a s to u s e t h e a n g l e o f gaze a s t h e m a i n c u e t o j u d g e t h e p o s i t i o n o f t h e ball. H o w d o e s this a n g l e of gaze c h a n g e w i t h t i m e as t h e ball a p p r o a c h e s ? W e c a n m a k e a n intelligent g u e s s b y d r a w i n g a d i a g r a m of t h e p o s i t i o n of t h e ball in its p a r a b o l i c flight at e q u a l t i m e i n t e r v a l s , c o r r e s p o n d i n g t o e q u a l h o r i z o n t a l steps in t h e d i a g r a m b e c a u s e t h e ball is t r a v e l i n g at a c o n s t a n t h o r i z o n t a l speed (Figure 6.2).

Figure 6.2: A n g l e of G a z e at S u c c e s s i v e Equal T i m e Intervals for a C a t c h e r W a t c h i n g a Ball A p p r o a c h A l o n g a P a r a b o l i c P a t h .

It a p p e a r s from this d i a g r a m t h a t t h e c h a n g e s in a n g l e o v e r successive t i m e i n t e r v a l s a r e p r e t t y m u c h t h e s a m e u p t o a n a n g l e of 30° or so (line from p o i n t A to c a t c h e r ) . In o t h e r w o r d s , a c a t c h e r s t a n d i n g in t h e right p o s i t i o n tilts his or h e r h e a d at a c o n s t a n t r a t e to follow t h e flight of t h e ball, so long a s t h e trajectory d o e s n ' t g o t o o h i g h . Conversely, tilting t h e h e a d at a c o n s t a n t r a t e p r o v i d e s a c u e w h i c h tells t h e c a t c h e r t h a t he or s h e is s t a n d i n g in t h e right p o s i t i o n . It s e e m s t h a t this i s t h e c u e t h a t c h i l d r e n l e a r n , a n d w h i c h t h e y c o n t i n u e t o use i n t o later life. It is n o t a c u e t h a t is a l w a y s reliable. W h e n t h e a n g l e b e c o m e s t o o h i g h (e.g., line from p o i n t B to c a t c h e r ) its r a t e of

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c h a n g e slows d o w n . I f t h e c a t c h e r c o n t i n u e s t o u s e t h e s a m e cue, h e o r s h e will i n t e r p r e t this s l o w i n g d o w n t o i n d i c a t e t h a t t h e ball is a p p r o a c h i n g m o r e slowly t h a n it is, a n d will miss t h e catch. This m a y b e t h e r e a s o n w h y h i g h c a t c h e s a r e s o often missed. T h e d i a g r a m a b o v e p r o v i d e s a good g u i d e t o h o w t h e a n g l e of a c a t c h e r ' s gaze c h a n g e s w h e n t h e c a t c h e r is in t h e right p o sition, a n d m a y b e a s far a s s o m e p e o p l e w o u l d w a n t t o go. T o m e , t h e lull a n d satisfying a n s w e r s w o u l d o n l y c o m e w h e n I had w o r k e d o u t a n e q u a t i o n t o describe h o w t h e a n g l e c h a n g e s w i t h t i m e , a n d w h e n 1 could u n d e r s t a n d from t h a t equation w h e t h e r catchers might need to adapt their techn i q u e for different s i t u a t i o n s , i set to w o r k w i t h a light h e a r t o n e S a t u r d a y m o r n i n g b e f o r e a village cricket m a t c h , s t i m u lated by a glass of A u s t r a l i a n c h a r d o n n a y a n d by t h e t h o u g h t that I could c h e c k o u t t h e a n s w e r s a g a i n s t r o u g h e x p e r i m e n tal o b s e r v a t i o n s in t h e a f t e r n o o n . As piles of p a p e r g r e w around me, each sheet containing one or more mistakes in the horribly c o m p l i c a t e d algebra, 1 b e g a n to w o n d e r w h a t f h a d let myself in lor. N e v e r t h e l e s s , 1 pressed o n , a n d w a s r e w a r d e d w h e n m o s t of t h e t e r m s in half a p a g e of algebra c a n c e l e d e a c h o t h e r o u t , l e a v i n g a beautifully s i m p l e s o l u t i o n . M y feeling o n finding a n e l e g a n t m a t h e m a t i c a l s o l u t i o n w a s akin to t h a t of an A u s t r a l i a n t r a v e l e r d i s c o v e r i n g an u n e x pected c o u n t r y p u b . T h e fact t h a t s o m e o n e else h a d f o u n d t h e s a m e s o l u t i o n (albeit e x p r e s s e d in a different form) s o m e thirty y e a r s earlier did n o t d e t r a c t from m y feeling, w h i c h w a s a m i x t u r e of t r i u m p h a n d relief — relief at h a v i n g g o t t e n t h e a n s w e r , t r i u m p h t h a t i t told m e s o m e t h i n g n e w a b o u t t h e scie n c e of c a t c h i n g a ball. T h o s e r e a d e r s w h o prefer t o avoid m a t h e m a t i c a l s y m b o l s entirely can safely skip t h e n e x t t h r e e p a r a g r a p h s . T h e s y m bols tell t h e s t o r y so beautifully, t h o u g h , t h a t 1 i n c l u d e t h e m h e r e for t h o s e w h o w o u l d like to see w h a t I saw, a n d in t h e w a y in w h i c h I first s a w it. W h e n 1 b e g a n t h e c a l c u l a t i o n s , I e x p r e s s e d t h e a n g l e of gaze m t e r m s of its g r a d i e n t , called a " t a n g e n t " in m a t h e m a t i c a l

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l a n g u a g e , a n d a b b r e v i a t e d t o " t a n . " T h e t e r m " g r a d i e n t " has exactly t h e s a m e m e a n i n g t h a t it h a s on a r o a d sign — in o t h e r w o r d s , t h e vertical d i s t a n c e c l i m b e d o r d e s c e n d e d divided b y t h e h o r i z o n t a l d i s t a n c e n e c e s s a r y t o a c h i e v e t h e climb o r d e scent. In F i g u r e 6 . 3 , for e x a m p l e , t h e g r a d i e n t of t h e hill is 1 in 4, e x p r e s s e d by s a y i n g t h a t t a n a = 'A.

F i g u r e 6 . 3 : A Hill w i t h a G r a d i e n t of 1

in 4.

I w a n t e d to find o u t h o w t a n a c h a n g e d w i t h t i m e — in this case, t h e r a t e at w h i c h a c a t c h e r ' s a n g l e of gaze c h a n g e s . N e w t o n e x p r e s s e d r a t e s of c h a n g e by p u t t i n g a d o t o v e r t h e t o p — I did t h e s a m e , so t h a t w h a t I w a s after w a s t a n a . W h a t might t a n a d e p e n d o n ? I put in everything that seemed to be relevant, including the angle of launch, the time for t h e ball t o travel from t h r o w e r t o hitter, a n d t h e d i s t a n c e of t h e c a t c h e r from t h e ball from t h e t h r o w e r or hitter. In t h e e n d , all of t h e s e c a n c e l e d o u t . All t h a t I w a s left w i t h w a s t h e a c c e l e r a t i o n d u e t o gravity (g) a n d t h e h o r i z o n t a l speed of t h e ball (v). T h e gloriously s i m p l e a n s w e r w a s : tana

= gllv

W h a t d o e s this e q u a t i o n tell u s ? For a start, it tells us t h a t if a c a t c h e r is s t a n d i n g in t h e right place to m a k e a catch, t h e g r a d i e n t of t h e a n g l e of gaze will c h a n g e at a c o n s t a n t rate as he or s h e follows t h e flight of t h e ball. C o n v e r s e l y , a c o n s t a n t r a t e of c h a n g e in t h e g r a d i e n t is a c u e t h a t tells us we are s t a n d i n g i n t h e right place. For a n g l e s b e l o w a b o u t 30°, t h e g r a d i e n t of an a n g l e is p r o p o r t i o n a l to t h e a n g l e , so t h e a n g l e of gaze itself c h a n g e s at a c o n s t a n t rate, just as t h e earlier d i a g r a m s u g g e s t e d . For h i g h e r

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angles, t h e g r a d i e n t c h a n g e s m o r e rapidly t h a n t h e a n g l e , s o we h a v e to tilt o u r h e a d s at a progressively s l o w e r p a c e to k e e p the g r a d i e n t c h a n g i n g at a c o n s t a n t r a t e . If we k e e p tilting t h e m a t t h e s a m e rate, o b e y i n g t h e lessons o f o u r c h i l d h o o d , w e will miss t h e c a t c h . T h e e q u a t i o n also predicts t h e actual r a t e at w h i c h a catcher's head n e e d s to tilt, w h i c h d e p e n d s on t h e h o r i z o n t a l speed of t h e ball. If a ball is a p p r o a c h i n g t h e c a t c h e r w i t h a h o r i z o n t a l speed of f o u r t e e n m e t e r s p e r s e c o n d (50 k m / h r ) , for e x a m p l e , the c a t c h e r n e e d s to tilt his or h e r head at a r o u n d 17° p e r seco n d to follow its trajectory, no m a t t e r w h a t t h e a n g l e of l a u n c h . If t h e h o r i z o n t a l speed d o u b l e s , t h e rate at w h i c h t h e c a t c h e r has to tilt his or h e r h e a d halves, m a k i n g it easier to j u d g e whereto place t h e h a n d s for t h e catch, e v e n if t h e catcher's reaction time isn't last e n o u g h to a c h i e v e this in practice. Finally, t h e e q u a t i o n says t h a t t h e h e a d has t o k e e p tilting i n t h e s a m e d i r e c t i o n u n t i l t h e catch is m a d e . If t h e d i r e c t i o n r e verses at a n y stage, t h a t is a s u r e clue t h a t t h e catch is going to be missed, u n l e s s it is m a d e b e l o w e y e level. T h e real lessons o f t h e e q u a t i o n , t h o u g h , c o m e w h e n w e consider h o w we u s e it as a c u e in t h e process of m a k i n g a r u n ning catch. T h e a u t h o r s of t h e Nature p a p e r s h o w e d t h a t g o o d c a t c h e r s c o n t r o l t h e i r r u n n i n g speed i n this s i t u a t i o n s o t h a t the s i m p l e c u e p r o v i d e d b y t h e e q u a t i o n c o n t i n u e s t o b e o b e y e d . W h a t r u n n i n g strategy, t h o u g h , m u s t a c a t c h e r a d o p t to do this? I tried to w o r k it o u t m a t h e m a t i c a l l y , a n d t h e result w a s d e pressing i n d e e d — a h o r r e n d o u s l y c o m p l i c a t e d e x p r e s s i o n for the w a y in w h i c h a c a t c h e r ' s r u n n i n g speed c h a n g e s w i t h t i m e . O n e t h i n g w a s clear, t h o u g h — a c a t c h e r c a n n o t r u n at a c o n s t a n t s p e e d a n d still k e e p tilting his or h e r h e a d at a c o n stant rate to follow t h e ball. To k e e p t h e h e a d tilting at a c o n stant rate, t h e c a t c h e r ' s r u n n i n g speed m u s t c h a n g e w i t h t i m e in a c o m p l i c a t e d w a y t h a t d e p e n d s on t h e a n g l e of l a u n c h , t h e speed of t h e ball, a n d t h e d i s t a n c e of t h e r u n n e r from t h e correct spot. In all cases, t h e r u n n e r is a c c e l e r a t i n g or d e c e l e r a t i n g a s h e o r s h e m a k e s t h e catch.

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W h e n I l o o k e d at t h e physics of t h e s i t u a t i o n , it t u r n e d out t h a t this a c c e l e r a t i o n o r d e c e l e r a t i o n gives t h e r u n n i n g c a t c h e r a clear a d v a n t a g e o v e r s o m e o n e w h o i s a l r e a d y o n t h e right spot a n d d o e s n o t h a v e to m o v e . R u n n i n g is o n e of t h e k e y s to c a t c h i n g a ball, b e c a u s e a p e r s o n w h o is r u n n i n g finds it easier t o m a k e small a d j u s t m e n t s o f p o s i t i o n t h a n o n e w h o i s s t a n d ing still. T h e difference lies in t h e b a l a n c e of forces t h a t t h e people experience. A p e r s o n w h o is s t a n d i n g still e x p e r i e n c e s t w o m a j o r forces: t h e force of gravity, acting d o w n w a r d s , a n d t h e force of t h e g r o u n d ' s r e a c t i o n o n t h e feet, a c t i n g u p w a r d s . S o long a s t h e s e forces stay in line, e v e r y t h i n g is fine. T h e b a l a n c e is p r e c a r i o u s , t h o u g h , b e c a u s e h u m a n b e i n g s a r e relatively long a n d t h i n , w i t h a h i g h c e n t e r of gravity, so that b a l a n c i n g a h u m a n b o d y is r a t h e r like t r y i n g to b a l a n c e a pencil on its e n d . A tilt of no m o r e t h a n 6° is sufficient to t r a n s f o r m t h e g r a v i t a t i o n a l a n d r e a c t i o n a l forces i n t o a c o u p l e t h a t tilts t h e p e r s o n f u r t h e r until, like an o v e r l o a d e d w h e e l b a r r o w , he or s h e falls over, u n l e s s t h e p e r s o n i s q u i c k e n o u g h t o m o v e t h e feet w i d e r a p a r t or m o v e t h e a r m s , like a t i g h t r o p e walker, to shift t h e c e n t e r of gravity. S o m e a n i m a l s , s u c h as tortoises, lizards, frogs, a n d toads, o v e r c o m e t h e b a l a n c e p r o b l e m b y h a v i n g w i d e l y spaced feet a n d a l o w c e n t e r of gravity. S u c h a n i m a l s a r e n o t n o t a b l e hallcatchers, and o n e m a y w o n d e r w h y h u m a n s , with their more u n s t a b l e c o n f i g u r a t i o n , a r e s o m u c h m o r e successful a t this a n d o t h e r tasks t h a t r e q u i r e c o o r d i n a t e d m o v e m e n t . The a n s w e r is that our m o r e unstable configuration makes us m u c h m o r e m a n e u v e r a b l e , since a relatively small force c a n shift o u r position rapidly a n d substantially. T h a t force c o m e s from p u s h i n g d o w n a n d back w i t h o u r feet w h e n w e r u n . This e x t r a force c h a n g e s t h e b a l a n c e s i t u a t i o n s o t h a t w e can tilt b u t still r e m a i n stable, b e c a u s e t h e n e t t h r u s t is a diago n a l o n e , s o t h e r e a c t i o n lorce passes t h r o u g h o u r c e n t e r o i gravity e v e n t h o u g h w e a r e tilted f o r w a r d (Figure 6.4). T h e e x t r a force o n l y cuts i n w h e n w e a r e a c c e l e r a t i n g , w h i c h scientists define a s c h a n g i n g s p e e d a n d / o r c h a n g i n g direction-

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Figure 6.4: F o r c e s W h e n S t a n d i n g or M o v i n g at a C o n s t a n t S p e e d (Left) a n d W h e n A c c e l e r a t i n g (Right). The black arrows represent the force of our bodies on the ground. The white arrows are the reaction force (equal and opposite) of the ground on our feet. Balance is maintained if the net reaction force passes through our center of gravity.

R u n n i n g at a c o n s t a n t speed r e q u i r e s surprisingly little force — just e n o u g h t o o v e r c o m e w i n d resistance, friction i n t h e j o i n t s , a n d w a s t e d e n e r g y i n t h e m u s c l e s . W i t h o u t t h e e x t r a force r e q u i r e d for a c c e l e r a t i o n , r u n n e r s h a v e to a d o p t a virtually u p right position for b a l a n c e . T h e e x c e p t i o n o c c u r s at t h e start of a race, w h e n t h e a t h l e t e is a c c e l e r a t i n g (i.e., c h a n g i n g s p e e d ) a n d can h e n c e lean forward a n d use t h e a d d i t i o n a l force t o maintain balance. A c c o r d i n g to N e w t o n ' s First Law, a p e r s o n w h o is s t a n d i n g still or r u n n i n g at a c o n s t a n t velocity d o e s n o t g e n e r a t e t h e e x tra force r e q u i r e d for b a l a n c e a n d m a n e u v e r a b i l i t y p r o d u c e d by s o m e o n e w h o is a c c e l e r a t i n g . F r o m this p o i n t of view, t h e best w a y to catch a ball is not to r u n at a c o n s t a n t s p e e d to i n tercept it as it falls, b u t to be a c c e l e r a t i n g or d e c e l e r a t i n g w h e n t h e catch is m a d e . This is e x a c t l y w h a t t h e " b a l l - c a t c h i n g " e q u a t i o n predicts, w h e n modified for t h e case of a r u n n i n g catcher, a n d is also w h a t t h e a u t h o r s of t h e Nature p a p e r f o u n d from their e x p e r i m e n t s . It is also w h a t I f o u n d from w a t c h i n g my fellow village cricketers, a n d w h a t I o b s e r v e d from w a t c h i n g cricket a n d baseball on television. T h e r e w a s o n e e x c e p t i o n — professional baseball

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players a p p e a r t o r u n t o t h e correct position a n d t h e n wait w h e n c a t c h i n g a h i g h fly ball. T h e practical r e a s o n tor this is t h a t t h e final vertical s p e e d of t h e ball is m u c h g r e a t e r for a h i g h catch, s o t h a t t h e c a t c h e r h a s t o b e close t o t h e o p t i m u m spot to h a v e a n y c h a n c e of m a k i n g t h e catch at all. T h e r e is also a m o r e subtle r e a s o n , w h i c h is t h a t t h e t a n g e n t of an a n g l e b e gins to i n c r e a s e m u c h m o r e rapidly for a n g l e s o v e r 30° (as in baseball), so t h a t s o m e o n e tilting t h e i r h e a d at a c o n s t a n t rate at t h e start of a ball's flight will be left far b e h i n d t o w a r d s t h e e n d of t h e flight. By g e t t i n g close to t h e o p t i m u m spot, t h e r e is less r o o m for error, w h i c h m o r e t h a n c o m p e n s a t e s i n this case for t h e loss of m a n e u v e r a b i l i t y t h a t c o m e s from s t a n d i n g still. My c o n c l u s i o n , t h e n , is t h a t t h e r u n n i n g catch is t h e b e t t e r t e c h n i q u e for balls l a u n c h e d at a n g l e s b e l o w 45°, w h i l e t h e "get t h e r e a n d w a i t " t e c h n i q u e is b e t t e r for h i g h fly balls. In b o t h cases, t h e successful c a t c h e r i s t h e o n e w h o j u d g e s t h e c a t c h ( u n c o n s c i o u s l y ) t h r o u g h t h e c u e of tilting t h e h e a d at a c o n s t a n t rate, or b e t t e r still at a r a t e t h a t k e e p s t h e g r a d i e n t of t h e v i e w i n g a n g l e c h a n g i n g at a c o n s t a n t r a t e . Rapid m e n t a l c a l c u l a t i o n h a s little to do w i t h it — we a c t u a l l y use v e r y s i m p l e c u e s i n d e e d a s w e k e e p o u r e y e o n t h e ball.

7

bath f o a m , beer f o a m , a n d the m e a n i n g of life

T h e story of science is n o t simply a m a t t e r of h i g h p o i n t s a n d great p e a k s o f discovery. T h e scientists w h o r e a c h e d t h o s e p e a k s g e n e r a l l y did so by dogged p e r s e v e r a n c e a n d by focusing on t h e detail e a c h s t e p of t h e w a y . Stories of t h e p u r s u i t of this detail can be j u s t as fascinating as stories of t h e g r e a t a c h i e v e ments themselves, although they undoubtedly make more demands on the reader because of the a m o u n t of background e x p l a n a t i o n n e c e s s a r y t o u n d e r s t a n d w h a t t h a t detail m e a n s . The following c h a p t e r tells o n e s u c h story. It is t h e story of a relatively m i n o r a d v a n c e i n science, c o n c e r n i n g h o w m o l e cules "self-assemble" to form c o m p l i c a t e d s t r u c t u r e s s u c h as foams. T h e results n o w p e r m e a t e e v e r y c o r n e r o f o u r lives, from t h e w a y w e w a s h o u r h a i r t o t h e w a y w e a d m i n i s t e r d r u g s . O u r u n d e r s t a n d i n g o f t h e processes i n v o l v e d h a s e v e n i n f l u e n c e d o u r v i e w of h o w life itself w a s o r i g i n a t e d a n d evolved o n E a r t h . T h e story is told from my perspective as a privileged inside o b server. By talking a b o u t it in m o r e detail t h a n is u s u a l in a p o p ular science b o o k , I h o p e to c o n v e y s o m e t h i n g of w h a t it feels like to be a real scientist d o i n g real science, w h e r e t h e b e a u t y resides m u c h m o r e often i n t h e d a y - t o - d a y detail t h a n i n t h e grand c o n c e p t i o n s t h a t t h e public h e a r s m u c h m o r e a b o u t . According to t h e American scientist Sidney Perkowitz, the t w e n t y first c e n t u r y will be r e m e m b e r e d as t h e " F o a m Age." A l u m i n u m foams will be used to m a k e cars w i t h light, s t r o n g bodies. Concrete foams t h a t s u p p o r t n o r m a l loads b u t c r u m p l e u n d e r h e a v y w e i g h t s h a v e already b e e n m a d e , a n d will form t h e e n d s of airport r u n w a y s to safely slow d o w n airplanes t h a t h a v e overshot on takeoff or l a n d i n g . NASA, P e r k o w i t z said, h a s e v e n

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l a u n c h e d a rocket w i t h an ultra-lightweight l o a m section designed to c a p t u r e particles from t h e tail of a c o m e t . P e r k o w i t z ' s f o a m s h a v e b u b b l e s w i t h solid walls t h a t give t h e m t h e i r s t r e n g t h . T h e l o a m s t h a t I discuss in this c h a p t e r , s u c h a s b e e r foam a n d b a t h foam, h a v e liquid walls. H o w t h o s e walls form, a n d h o w t h e y m a i n t a i n t h e i r s t r e n g t h , has b e e n a p e r e n n i a l p u z z l e t h a t goes right back to N e w t o n a n d his e x p e r i m e n t s w i t h s o a p h u b b i e s . I like t o t h i n k t h a t h e e x p e r i m e n t e d w i t h t h e m i n his b a t h , b u t t h e t r u t h i s t h a t h e p r o b a bly b l e w t h e m in a glass b o w l of s o a p y w a t e r placed on a table. W h a t h e s a w w a s w h a t w e h a v e all s e e n b u t , b e i n g N e w t o n , h e w a s able t o t a k e his o b s e r v a t i o n s o f a c o m m o n p h e n o m e n o n j u s t t h a t o n e step further, as he later r e p o r t e d in his 1704 b o o k on Opticks: If a Bubble be blown with Water first made tenacious by dissolving a little Soap in it, it will appear tinged with a great variety of Colours. To defend these Bubbles from being agitated by the external Air (whereby their Colours are irregularly moved one among another, so that no accurate Observation can IK- made of them,) as soon as I had blown any of them I cover'd it with a clear Glass, and by that means its Colours emerged in a very regular order, like so many concentrick Rings encompassing the top of the Bubble. And as the Bubble grew thinner by the continual subsiding of the Water, these Rings dilated slowly and overspread the whole Bubble, descending in order to the bottom of it, where they vanish'd successively. N e w t o n k n e w t h a t t h e colors d e p e n d e d o n t h e t h i c k n e s s o i t h e s o a p h i m , w h i c h varied from top to b o t t o m . He also n o t e d t h a t " S o m e t i m e s t h e B u b b l e w o u l d b e c o m e of a u n i f o r m t h i c k n e s s all o v e r . . ." By c o m p a r i n g t h e b u b b l e color at this stage w i t h t h e colors p r o d u c e d b y gaps o f k n o w n t h i c k n e s s b e t w e e n t w o pieces of glass, he w a s able to c a l c u l a t e t h e thickness of a s o a p film t h a t h a d d r a i n e d to a u n i f o r m silvery color as " 3 / s t e n h u n d r e d t h o u s a n d t h s " of an inch — in m o d e r n units, 80 n a n o m e t e r s (80 billionths of a m e t e r ) , w h i c h m e a n s

b a t h f o a m , b e e r f o a m , a n d t h e m e a n i n g o f life

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that his s o a p film w a s a r o u n d five h u n d r e d w a t e r m o l e c u l e s thick. That's a b o u t t e n t i m e s t h i n n e r t h a n can b e o b s e r v e d with the naked eye. H o w does such a gossamer-thin film rem a i n s o stable? N e w t o n t h o u g h t t h a t i t w a s b e c a u s e t h e s o a p dissolved i n t h e w a t e r a n d m a d e i t " t e n a c i o u s . " I t w a s a n o t h e r t w o h u n d r e d y e a r s before i t w a s r e c o g n i z e d t h a t s o a p m o l e cules prefer to i n h a b i t t h e surface of w a t e r , a n d e x e r t t h e i r magical effects m a i n l y at t h a t surface. The person w h o first recognized w h y detergent molecules b e h a v e in this w a y w a s Irving L a n g m u i r , a scientist at t h e G e n e r a l Electric C o m p a n y i n S c h e n e c t a d y , N e w York, w h o h a d t h e e n v i a b l e brief of s t u d y i n g a n y t h i n g t h a t he m i g h t find i n t e r e s t i n g . At v a r i o u s stages in his c a r e e r he d i s c o v e r e d a w a y to greatly e x t e n d t h e life of t h e t u n g s t e n filament l a m p , d e v e l oped n e w v a c u u m t u b e s for u s e i n radio b r o a d c a s t i n g , a n d w a s a w a r d e d a Nobel Prize for his ideas on h o w a t o m s b i n d t o g e t h e r t o m a k e m o l e c u l e s . D u r i n g t h e S e c o n d World War h e became involved in rain-making e x p e r i m e n t s that had the u n e x p e c t e d c o n s e q u e n c e o f o n e A m e r i c a n state t h r e a t e n i n g t o sue a n o t h e r for t h e theft of its r a i n . U n d e r p i n n i n g it all w a s L a n g m u i r ' s i n t e r e s t i n h o w m o l e c u l e s b e h a v e a t surfaces ( o n e m o d e r n j o u r n a l d e v o t e d to this topic is n o w called Langmuir). He b e g a n by s t u d y i n g m o l e c u l e s on solid surfaces, b u t e v e n t u ally t u r n e d his a t t e n t i o n to liquid surfaces, w h e r e , in t h e e a r l y 1930s, h e q u i c k l y realized t h a t d e t e r g e n t - t y p e m a t e r i a l s prefer to reside at t h e surface of w a t e r b e c a u s e t h e i r m o l e c u l e s h a v e chemically different e n d s . O n e e n d , called t h e hydrophilic ( w a t e r - l o v i n g ) e n d , is c h e m i c a l l y similar to w a t e r , a n d h a s a p r e f e r e n c e for b e i n g in w a t e r . T h e o t h e r e n d , called t h e lipophilic (oil-loving) e n d , is chemically similar to oil, a n d prefers an oily e n v i r o n m e n t . If t h e r e is no oil a r o u n d , air will do almost a s well. Scientists w h o h a v e b e c o m e b o r e d w i t h l o n g G r e e k w o r d s simply call t h e h y d r o p h i l i c a n d lipophilic e n d s heads and tails respectively. The peculiar structure of detergent molecules makes t h e m surface active — if s h a k e n up in w a t e r , t h e y will m o v e to t h e s u r face, w h e r e t h e y sit like feeding d u c k s w i t h t h e i r h y d r o p h i l i c

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h e a d s i n t h e w a t e r a n d t h e i r oily tails sticking u p i n t h e air (Figure 7.1). As m a n y d e t e r g e n t m o l e c u l e s as possible will seek t o o c c u p y t h e surface, jostling for p o s i t i o n a n d e v e n t u a l l y b e c o m i n g p a c k e d t o g e t h e r a s closely a s t h e y c a n m a n a g e . T h o s e left u n d e r t h e w a t e r ( t h e majority) will still seek to a r r a n g e t h e m s e l v e s s o t h e i r tails a r e h i d d e n from t h e w a t e r w h i l e t h e i r h e a d s a r e i m m e r s e d in it.

Figure 7 . 1 : Monolayer of Detergent Molecules (Represented as " D u c k s " w i t h Hydrophilic H e a d s a n d H y d r o p h o b i c Tails) o n t h e Surface of Water.

T h e r e a r e t w o basic w a y s t h a t t h e y can d o t h i s . T h e first i s t o a r r a n g e t h e m s e l v e s in a ball (called a micelle), w i t h t h e tails in t h e m i d d l e a n d t h e h e a d s a t t h e surface (Figure 7.2). Micelles c a n t a k e g r e a s e i n t o t h e i r oily c e n t e r s , a n d d o m o s t o f t h e work in washing up. The other type of structure that detergent m o l e c u l e s can a r r a n g e t h e m s e l v e s i n t o u n d e r w a t e r consists of a pair of flat s h e e t s (called a bilayer), aligned so t h e h e a d s point

Figure 7.2: D e t e r g e n t M o l e c u l e s P a c k e d in a Ball (a "Micelle") Underwater.

b a t h

f o a m ,

b e e r f o a m ,

a n d

t h e

m e a n i n g

o f

life

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o u t w a r d s w i t h tails o n t h e inside, a g a i n h i d d e n from t h e w a ter (Figure 7.3).

Figure 7.3: "Bilayer" of Detergent Molecules Underwater.

T h e p r o b l e m w i t h s u c h a bilayer is t h a t t h e m o l e c u l e s at t h e edges still h a v e t h e i r tails e x p o s e d . This p r o b l e m is o v e r c o m e w h e n t h e bilayer s p o n t a n e o u s l y c u r v e s a r o u n d o n itself t o form a closed s p h e r e called a liposome (Figure 7.4). These, like

Figure 7.4: " L i p o s o m e " of Detergent M o l e c u l e s Underwater. Liposomes are often encapsulated by concentric shells of bilayers. Technically, a liposome consisting of just one bilayer is called a vesicle, but I have avoided using the term in this chapter in favor of the more familiar generic term liposome to cover all types.

micelles, can carry m a t e r i a l s i n t h e i r c e n t e r s , h i d d e n from t h e w a t e r o u t s i d e . T h e difference is t h a t micelles c a r r y oil-soluble

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m a t e r i a l s s u c h a s g r e a s e , w h e r e a s l i p o s o m e s can carry m a t e r i als t h a t a r e s o l u b l e in w a t e r . T h e m e m b r a n e s t h a t e n c a p s u l a t e d t h e f i r s t living cells w e r e p r o b a b l y l i p o s o m e s f o r m e d s p o n t a n e o u s l y from lecithins manufactured naturally u n d e r the conditions that then prevailed on E a r t h . T h e r e is great i n t e r e s t in u s i n g s u c h l i p o s o m e s to carry d r u g s to t h e i r site of a c t i o n in t h e b o d y w h i l e k e e p i n g t h e m h i d d e n from d e s t r u c t i v e e n z y m e s e n r o u t e . T h e targeting i s a c h i e v e d b y i n c o r p o r a t i n g m a r k e r m o l e c u l e s i n t o t h e o u t e r w a l l of t h e l i p o s o m e . T h e c h a l l e n g e is to do this in s u c h a w a y t h a t t h e l i p o s o m e bilayer s t r u c t u r e is n o t d i s r u p t e d . This m e a n s u n d e r s t a n d i n g t h e forces t h a t hold t h e l i p o s o m e together, a n d h o w t h e s e forces m i g h t b e affected b y t h e i n t r o d u c t i o n of foreign m o l e c u l e s i n t o t h e b i l a y e r s t r u c t u r e . It also m e a n s u n d e r s t a n d i n g h o w the shapes of detergent molecules affect t h e w a y t h e y pack t o g e t h e r t o form different s t r u c t u r e s . T h e s e t w o lines of t h o u g h t w e r e b r o u g h t t o g e t h e r in a g r a n d s y n t h e s i s in t h e late 1970s. Up until t h e n , t h o u g h , t h e y had d e v e l o p e d as a l m o s t s e p a r a t e lines of inquiry.

How Do Detergent Molecules Stick Together?

T h e first line of i n q u i r y c o n c e r n e d t h e forces b e t w e e n d e t e r g e n t m o l e c u l e s , a n d h o w t h e s e forces c o n v e y stability — not just to s o a p films, b u t to a m u c h w i d e r class of m a t e r i a l s called colloids. I w a s i n t r o d u c e d to colloids in t h e early 1960s by Professor A l e x a n d e r E. A l e x a n d e r (invariably k n o w n as Alex), my fav o r i t e u n i v e r s i t y l e c t u r e r a n d a t h o r n in t h e side of t h e A u s tralian e d u c a t i o n a u t h o r i t i e s . Scarcely a w e e k passed w i t h o u t a s t r o n g l y w o r d e d letter from Alex a p p e a r i n g in at least o n e S y d n e y n e w s p a p e r , u s u a l l y a b o u t t h e lack of state s u p p o r t for scientific e d u c a t i o n o r t h e i n i q u i t o u s b e h a v i o r o f s o m e m e m b e r of t h e e d u c a t i o n b u r e a u c r a c y . Alex's fellow professors f r o w n e d on his practice of o p e n i n g up t h e closed a c a d e m i c w o r l d o f t h e t i m e t o p u b l i c scrutiny, b u t Alex c o u l d n ' t h a v e


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cared less. H e w a s h a v i n g t o o m u c h fun i n his o w n w o r l d , p o p u l a t e d b y scientists w h o w e r e a l m o s t a s g r e g a r i o u s a s h e w a s . W h e n I e v e n t u a l l y m e t a n d w o r k e d w i t h s o m e of t h e m , I a l r e a d y k n e w q u i t e a bit a b o u t t h e i r p e r s o n a l foibles t h r o u g h the a n e c d o t e s that p e p p e r e d Alex's l e c t u r e s . Alex w a s t h e c o a u t h o r o f a n a u t h o r i t a t i v e t e x t b o o k o n colloids, a n d w o n t h e h e a r t s o f his u n d e r g r a d u a t e a u d i e n c e b y declaring t h a t this m a s s i v e t o m e w a s a b o o k t h a t " n e e d n e v e r have been written." Nevertheless, it was loaded with interesting, if n o t a l w a y s r e l e v a n t , i n f o r m a t i o n , s u c h as t h e fact t h a t kolloid w a s t h e a n c i e n t G r e e k w o r d for g l u e . In m o d e r n t e r m i nology, a colloid is simply a s u s p e n s i o n of small particles in a m e d i u m . Milk is a colloid, b e c a u s e it is a s u s p e n s i o n of milk fat globules in w a t e r , a n d so is p a i n t , a s u s p e n s i o n of solid pigm e n t g r a n u l e s in oil or w a t e r . C i g a r e t t e s m o k e is a colloid, b e c a u s e it is a s u s p e n s i o n of ash particles in air ( s m o k e will a p p e a r w h i t e if t h e particles a r e large e n o u g h to reflect light from t h e i r surfaces, a n d bluish if t h e particles a r e so small t h a t all t h e y can do is scatter t h e light). Blood, a s u s p e n s i o n of living cells in s e r u m , is also a colloid, t o g e t h e r w i t h a h o s t of o t h e r m a t e r i a l s vital to life. T h e d e f i n i n g f e a t u r e of colloids is t h a t t h e particles a r e small a n d c o n s e q u e n t l y t h e total surface a r e a i s h u g e . T h e surface area of t h e milk fat globules in a pint of h o m o g e n i z e d milk, for example, is a r o u n d t w o h u n d r e d square meters — about the floor area of an a v e r a g e h o u s e . Forces b e t w e e n t h e surfaces of t h e particles t h u s d o m i n a t e t h e b e h a v i o r of a colloidal s u s p e n sion. T h e s e forces (called surface forces) arise largely from t h e single layer of m o l e c u l e s at t h e surface of e a c h particle. Norm a l red cells, for e x a m p l e , repel a n d slide past t h e i r n e i g h b o r s b e c a u s e t h e i r surfaces a r e c o a t e d w i t h a layer of n e g a t i v e l y c h a r g e d s u g a r m o l e c u l e s . Milk fat g l o b u l e s stay a p a r t for a similar r e a s o n , except that in this case t h e p r o t e c t i v e m o l e c u l e s a r e n a t u r a l milk p r o t e i n s . In t h e a b s e n c e of t h e r e p u l s i v e forces p r o v i d e d by p r o t e c t i v e layers, similar particles will stick t o g e t h e r b e c a u s e t h e y are pulled t o w a r d s e a c h o t h e r by a u n i v e r s a l a t t r a c t i v e force ol

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electrical origin called t h e Van der Waals force, w h i c h increases rapidly in s t r e n g t h as t h e particles get closer to o n e a n o t h e r . This c a n c a u s e p r o b l e m s . If milk fat g l o b u l e s stick t o g e t h e r , for e x a m p l e , t h e milk s e p a r a t e s i n t o a layer of c r e a m a b o v e a n d a layer of w a t e r b e l o w , ff red b l o o d cells stick t o g e t h e r , t h e y can n o l o n g e r s q u e e z e t h r o u g h tiny capillaries, a n d t h e capillaries b e c o m e b l o c k e d . This h a p p e n s t o p e o p l e suffering from sicklecell a n e m i a , o n e o f t h e " m o l e c u l a r " diseases i n w h i c h t h e a l t e r a t i o n of o n e small g r o u p of a t o m s in t h e h e m o g l o b i n m o l e c u l e c a u s e s t h a t m o l e c u l e to a d o p t a different s h a p e , l e a d i n g in t u r n to t h e d e f o r m a t i o n of t h e w h o l e red cell. T h e m o l e c u l a r c h a n g e s also m a k e t h e o u t s i d e of t h e cell slightly sticky, so t h a t i n s t e a d of r e p e l l i n g a n d sliding past its n e i g h bors, it a d h e r e s to t h e m , especially in tight c o r n e r s s u c h as t h o s e i n j o i n t s , w h e r e t h e cells c l u m p t o g e t h e r , b l o c k i n g blood flow a n d c a u s i n g e x c r u c i a t i n g p a i n . Particles s u c h as m i l k fat g l o b u l e s or red b l o o d cells will o n l y stay a p a r t if t h e r e p u l s i v e force is sufficient to o v e r c o m e t h e a t t r a c t i v e Van d e r Waals force at s o m e stage in t h e a p p r o a c h . If t h e r e p u l s i v e force is n o t p r e s e n t n a t u r a l l y , it can be a d d e d . O n e of t h e p r i n c i p a l w a y s of d o i n g this for s u s p e n s i o n s of h y d r o p h o b i c particles in w a t e r (e.g., g r i m e in b a t h w a t e r ) is to add d e t e r g e n t m o l e c u l e s . T h e h y d r o p h o b i c tails of t h e d e t e r g e n t m o l e c u l e s a n c h o r t h e m s e l v e s t o t h e particle surfaces, t h u s h i d i n g b o t h from t h e s u r r o u n d i n g w a t e r , w h i l e t h e electrically c h a r g e d h e a d s of t h e d e t e r g e n t m o l e c u l e s form a p r o t e c t i v e o u t e r layer t h a t repels o t h e r , similarly c o a t e d particles a n d k e e p s t h e m in a loose s u s p e n s i o n t h a t can easily be rinsed a w a y i n s t e a d of collecting as a sticky layer on t h e sides of t h e b a t h . T h e idea t h a t a b a l a n c e of a t t r a c t i v e a n d r e p u l s i v e forces c o n t r o l s colloid stability w a s d e v e l o p e d i n d e p e n d e n t l y i n t h e early 1940s by t w o g r o u p s of scientists, Boris D e r y a g i n a n d Lev L a n d a u i n Russia a n d E v e r t V e r w e y a n d T h e o O v e r b e e k i n Holland. B o t h g r o u p s p u b l i s h e d t h e i r ideas after t h e S e c o n d World W a r a n d , after a brief b a t t l e o v e r priority, t h e t h e o r y b e came democratically k n o w n as the Deryagin-Landau-VerweyO v e r b e e k t h e o r y , u n i v e r s a l l y a b b r e v i a t e d t o "DLVO."


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Deryagin d o m i n a t e d Russian surface science for s o m e seve n t y years, a n d m a d e m a n y i m p o r t a n t discoveries s o m e t i m e s w r o n g l y a t t r i b u t e d t o W e s t e r n scientists, o w i n g t o t h e s l o w ness w i t h w h i c h Russian p u b l i c a t i o n s w e r e d i s s e m i n a t e d a n d accepted in t h e West. He also m a d e m o r e c o n t r o v e r s i a l claims. W h e n l h e a r d h i m give his last m a j o r c o n f e r e n c e talk in M o s c o w in 1992, he laid claim to t h e d e b a t a b l e p h e n o m e n o n of "cold fusion," w h i c h he h a d a t t e m p t e d to initiate in a typically i n g e n i o u s m a n n e r by h a v i n g his s t u d e n t s fire a K a l a s h n i k o v rifle at t h e e x p e r i m e n t a l a p p a r a t u s from close q u a r t e r s . Deryagin s e l d o m left Russia, b u t he did m a k e o n e visit to A u s tralia w h e n he w a s in his eighties, a l t h o u g h he w a s still active — active e n o u g h , in fact, to be d r o p p e d off in t h e red light district of S y d n e y at t e n o'clock at night, not to r e a p p e a r until t h r e e t h e following m o r n i n g , b y w h i c h l i m e his h o s t s w e r e b e s i d e themselves with anxiety. T h e D u t c h scientists Verwey a n d O v e r b e e k w e r e m u c h mores e d a t e w h e n 1 first m e t t h e m i n 1976, a n d v e r y g e n e r o u s w i t h their time a n d expertise to a junior, rather brash researcher from A u s t r a l i a . T h e o O v e r b e e k e v e n offered to give his lect u r e s in English r a t h e r t h a n D u t c h for my benefit. I w a s impressed, but d e c l i n e d . 1 w o u l d h a v e b e e n e v e n m o r e i m p r e s s e d if I h a d k n o w n t h a t he s p o k e live o t h e r l a n g u a g e s as well. DLVO t h e o r y w a s j u s t t h a t — a t h e o r y . It n e e d e d testing, a n d s o a p films s e e m e d to be an ideal vehicle, since t h e r e p u l s i v e f o r c e s d u e t o t h e c h a r g e d h e a d - g r o u p s limited h o w t h i n t h e w a t e r could get. T h e D u t c h g r o u p i n p a r t i c u l a r p e r f o r m e d m a n y e x p e r i m e n t s w i t h s o a p films, v a r y i n g t h e u l t i m a t e film t h i c k n e s s by a d d i n g different a m o u n t s of salt to t h e w a t e r . DLVO t h e o r y p r e d i c t e d t h a t t h e salt w o u l d r e d u c e t h e r e p u l sive force b e t w e e n t h e c h a r g e d h e a d - g r o u p s o n o p p o s i t e sides of t h e s o a p film, a n d so a l l o w t h e film to b e c o m e t h i n n e r . M e a s u r e m e n t s of t h e film t h i c k n e s s u s i n g reflected light p r o d u c e d n u m e r i c a l v a l u e s t h a t w e r e v e r y close t o t h o s e p r e dicted (Figure 7.5). Studies of soap films e v e n t u a l l y yielded a great deal of inform a t i o n a b o u t t h e repulsive forces b e t w e e n d e t e r g e n t h e a d -

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Figure 7.5: M o l e c u l a r Detail of Draining S o a p Film Being E x a m i n e d by Reflected Light.

groups, but did not c o n t r i b u t e directly to solving t h e p r o b l e m of w h y s o m e d e t e r g e n t m o l e c u l e s s p o n t a n e o u s l y form flat films while o t h e r s form s t r u c t u r e s like micelles. Nevertheless, w h e n t h e a n s w e r did c o m e , it t u r n e d o u t t h a t t h e repulsive forces m e a s u r e d by t h e soap Him e n t h u s i a s t s w e r e a key c o m p o n e n t . O n e of t h e p r o b l e m s w i t h soap films is t h a t t h e force t e n d i n g t o t h i n t h e f i l m c o m e s from hydrostatic p r e s s u r e r a t h e r t h a n from Van der Waals forces, w h i c h b e c o m e i m p o r t a n t o n l y w h e n t h e gap b e t w e e n t h e t w o surfaces i s less t h a n t e n n a n o m e t e r s o r so (a g a p t h a t c o u l d be s p a n n e d by a c h a i n of a b o u t sixty w a ter m o l e c u l e s ) . S o a p films a r e u s u a l l y c o n s i d e r a b l y t h i c k e r t h a n this, a n d n e w t e c h n i q u e s h a d t o b e d e v e l o p e d t o m e a s u r e forces at s m a l l e r d i s t a n c e s . All of t h e s e t e c h n i q u e s m a d e u s e of u l t r a - s m o o t h solid surfaces m o u n t e d o n springs stiff e n o u g h t o k e e p t h e m a p a r t u n d e r t h e large close-range attractive forces predicted. T h e Russian school m e a s u r e d t h e forces b e t w e e n crossed wires, w h i l e t h e D u t c h school used polished glass lenses. T h e a d v a n t a g e of glass w a s t h a t t h e e x p e r i m e n t e r could see t h r o u g h it, a n d could use reflected light to m e a s u r e t h e distance b e t w e e n t h e surfaces. Its


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d i s a d v a n t a g e w a s that glass surfaces are relatively b u m p y at an atomic level. Wire is s m o o t h e r , b u t it is impossible to m e a s u r e t h e s e p a r a t i o n distance directly. T h e stage w a s set for a fiery confrontation, w h i c h d u l y o c c u r r e d at a c o n f e r e n c e that I u n fortunately missed, a l t h o u g h t h e r e v e r b e r a t i o n s w e r e still being felt w h e n I e n t e r e d t h e field s o m e ten years later. By that t i m e a n e w t e c h n i q u e h a d b e e n d e v e l o p e d by David Tabor in C a m b r i d g e , England, w h o used mica, w h i c h w a s t r a n s p a r e n t a n d w h i c h could also b e cleaved t o a t o m i c s m o o t h n e s s . A succession of Ph.D s t u d e n t s refined t h e t e c h n i q u e , with t h e final, crucial step being t a k e n by J a c o b Israelachvili, w h o performed t h e a s t o n i s h i n g feat of c o n t r o l l i n g a n d m e a s u r i n g t h e d i s t a n c e b e t w e e n t h e mica surfaces t o w i t h i n o n e a t o m . H e later told m e w i t h s o m e relish t h a t w h e n h e h a d r e p o r t e d his results at a scientific m e e t i n g in A m e r i c a o n e of t h e o l d e r - s t y l e scientists i n t h e a u d i e n c e h a d sat stolidly t h r o u g h his p r e s e n t a t i o n , a n d t h e n told h i m t h a t i t w a s physically impossible t o do such m e a s u r e m e n t s . J a c o b ' s original m e a s u r e m e n t s w e r e m a d e in air. I m e t h i m w h e n h e h a d m o v e d t o Australia a n d h a d b e g u n t o refine his t e c h n i q u e t o m a k e similar m e a s u r e m e n t s w i t h w a t e r b e t w e e n t h e surfaces, w h i c h h e w a s e v e n t u a l l y t o coat w i t h d e t e r g e n t and other molecules. O u r meeting was p u r e serendipity. I h a p p e n e d to d r o p in on a talk t h a t J a c o b w a s giving a b o u t his n e w t e c h n i q u e , a n d rapidly realized t h a t it w o u l d be ideal for t h e totally different p r o b l e m on w h i c h I w a s t h e n w o r k i n g . I o u t lined my idea o v e r coffee after t h e talk. T h e result w a s a coll a b o r a t i o n t h a i lasted several y e a r s a n d totally c h a n g e d t h e direction of my r e s e a r c h . Every few m o n t h s o v e r t h o s e y e a r s I w o u l d d r i v e or fly t h e t h r e e h u n d r e d k i l o m e t e r s from S y d n e y t o J a c o b ' s l a b o r a t o r y in C a n b e r r a to i n d u l g e in an i n t e n s e w e e k of e x p e r i m e n t a t i o n , often w o r k i n g t h r o u g h until t w o o r t h r e e i n t h e m o r n i n g . Situ a t e d in an old w o o d e n c o t t a g e on t h e s h o r e s of Lake B u r l e y Griffin, t h e D e p a r t m e n t o f Applied M a t h e m a t i c s w h e r e J a c o b t h e n w o r k e d w a s rapidly b e c o m i n g o n e o f t h e g r e a t w o r l d c e n t e r s of surface s c i e n c e . C o f f e e - r o o m c o n v e r s a t i o n s s e e m e d

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to c o v e r a l m o s t e v e r y aspect of t h e field, q u e s t i o n i n g old s h i b b o l e t h s a n d p r o d u c i n g n e w ideas i n p r o f u s i o n . T h e d e p a r t m e n t w a s f o u n d e d a n d r u n b y Barry N i n h a m , a m a t h e m a t i c i a n o f e x t r a o r d i n a r y versatility w h o h a d c h o s e n surface science as his held, a n d w h o h a d a l r e a d y w r i t t e n a b o o k on t h e t h e o r y of Van d e r Waals forces, so c o m p l e t e t h a t t h e t h e ory n e e d n e v e r b e t o u c h e d a g a i n . N o w Barry w a s l o o k i n g for n e w f i e l d s t o c o n q u e r . J a c o b p r o v i d e d a n ideal o p p o r t u n i t y w h e n h e b e g a n t o talk a b o u t his ideas o f h o w d e t e r g e n t - t y p e m o l e c u l e s pack t o g e t h e r in different w a y s to form micelles, liposomes, a n d o t h e r s t r u c t u r e s . T h e secret, h e believed, lay n o t j u s t i n t h e forces b e t w e e n t h e m o l e c u l e s , b u t also i n t h e s h a p e of t h e m o l e c u l e s w i t h i n t h e s e s t r u c t u r e s . T h o s e t h a t p a c k e d in layers, h e t h o u g h t , w o u l d n e e d t o h a v e h e a d s w i t h a p p r o x i m a t e l y t h e s a m e cross-sectional area a s t h e tails s o t h a t t h e y could fit easily i n t o a p l a n a r s t r u c t u r e . T h o s e t h a t p a c k e d m o r e easily i n t o micelles, t h o u g h , w o u l d h a v e larger h e a d s , a n d s o w o u l d pack m o r e n a t u r a l l y i n t o s p h e r e s , w i t h t h e h e a d s o n t h e o u s i d e w h e r e t h e r e i s m o r e r o o m (Figure 7.6).

Figure 7.6: P a c k i n g S t r a t e g i e s for S u r f a c e - A c t i v e M o l e c u l e s w i t h Different S h a p e s .


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How Do Molecules Shape Up?

T h e idea t h a t m o l e c u l e s h a v e t h r e e - d i m e n s i o n a l s h a p e s g o e s back t o Louis Pasteur, w h o s e d e d u c t i o n i n 1 8 4 4 a r o s e from t h e fact t h a t s o l u t i o n s of t w o c h e m i c a l c o m p o u n d s w i t h a p p a r e n t l y identical c o m p o s i t i o n c o u l d n e v e r t h e l e s s twist a b e a m of light i n o p p o s i t e d i r e c t i o n s . T h e difference, h e t h o u g h t , m u s t b e b e c a u s e t h e m o l e c u l e s o f t h e c o m p o u n d s h a v e different three-dimensional shapes. P a s t e u r w a s right, a n d his o b s e r v a t i o n s led t o t h e m o d e r n subject of stereochemistry, t h e science of m o l e c u l a r s h a p e s a n d h o w t h e s e s h a p e s affect m o l e c u l a r b e h a v i o r . I t w a s t h e subject of my very first research project, a n d n e a r l y my last. T h e project w a s t o m e a s u r e t h e s h a p e s o f s o m e small m o l e c u l e s called sulfoxides dissolved in b e n z e n e , a h i g h l y i n f l a m m a b l e s o l v e n t . T h e t e c h n i q u e , called t h e K e r r effect, followed P a s t e u r in u s ing t h e t w i s t i n g of a light b e a m to p r o v i d e i n f o r m a t i o n a b o u t t h e m o l e c u l e s t h a t c o u l d b e u s e d t o d e d u c e details o f t h e i r s h a p e s . T o m a k e t h e light r o t a t e sufficiently, t h o u g h , t h e m o l ecules h a d to be aligned in a s t r o n g electric field, w h i c h m e a n s p u t t i n g t e n t h o u s a n d volts across t h e s o l u t i o n . In s u c h a situation, a spark w o u l d h a v e c a u s e d a c a t a s t r o p h i c explosion j u s t a c o u p l e of c e n t i m e t e r s a w a y from my eye, a n d t h e b e n z e n e h a d t o b e t h o r o u g h l y dried t o p r e v e n t this from h a p p e n i n g . I did this by t h e a p p r o v e d t e c h n i q u e of a d d i n g fresh s o d i u m metal to t a k e up t h e residual w a t e r . U n f o r t u n a t e l y , I failed to notice t h a t a speck of s o d i u m w a s still p r e s e n t w h e n I disposed of s o m e residual b e n z e n e d o w n t h e sink (a p r o c e d u r e that w o u l d n e v e r b e a l l o w e d t h e s e d a y s ) . T h e s o d i u m reacted vigorously w i t h t h e w a t e r in t h e pipes, p r o d u c i n g a jet of flaming h y d r o g e n t h a t in t u r n set fire to t h e b e n z e n e , s e n d i n g a scorching flame u p t h e l a b o r a t o r y wall a n d n e a r l y p u t t i n g paid to my scientific c a r e e r before it h a d fairly started. Indirect a p p r o a c h e s like t h e K e r r effect h a v e b e e n largely r e placed by direct t e c h n i q u e s , s u c h as X-ray crystallography, t h a t p e r m i t t h e e x p e r i m e n t e r t o m e a s u r e t h e p o s i t i o n s i n space o f all of t h e individual a t o m s in a m o l e c u l e . X-ray crystallography,

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w h i c h w o r k s w i t h a n y m a t e r i a l t h a t c a n b e p e r s u a d e d t o form a solid crystal, h o w e v e r tiny, w a s t h e t e c h n i q u e t h a t p e r m i t t e d t h e helical s t r u c t u r e of DNA to be w o r k e d o u t in t h e early 1950s. T h e t e c h n i q u e h a s n o w p r o g r e s s e d s o far t h a t scientists can e v e n use i t t o w a t c h e n z y m e s s w a l l o w t h e i r m o l e c u l a r p r e y a n d r e g u r g i t a t e it in a different form in real t i m e . Even m o r e exciting t h a n X-ray crystallography is t h e n e w t e c h n i q u e of scanning probe microscopy, w h i c h p e r m i t s scientists to see individual m o l e c u l e s — or, at least, to feel t h e m . T h e t e c h n i q u e is similar to t h a t used by a blind p e r s o n w h o w a v e s a w h i t e c a n e back a n d forth o n t h e p a v e m e n t a s h e o r s h e walks. T h e c a n e senses b u m p s a n d dips in t h e p a t h , a n d could in principle be used to m a p its c o n t o u r s . S c a n n i n g p r o b e microscopy does t h e s a m e t h i n g at an a t o m i c level, w i t h t h e " c a n e " b e i n g a m i n i a t u r e p o i n t e d tip a t t a c h e d to a tiny spring, w h o s e deflections m a p t h e surface t o a t o m i c resolution. T h e m o d e r n scanning p r o b e m i c r o s c o p e is a lovely little i n s t r u m e n t , a b o u t t h e size of an electric toaster, a n d can be used to v i e w just a b o u t a n y m o l e c u l e , from relatively small d e t e r g e n t m o l e c u l e s to h u g e biological m o l e c u l e s such as DNA (Figure 7.7).

Figure 7.7: S c a n n i n g Probe M i c r o s c o p e Picture of D N A Molecule.


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Early w o r k e r s s t u d y i n g t h e s h a p e a n d size o f d e t e r g e n t m o l e c u l e s did n o t h a v e t h e a d v a n t a g e o f s u c h t e c h n i q u e s , a n d h a d to develop other approaches. These usually involved spreading t h e m o l e c u l e s as a single layer on t h e surface of w a t e r . T h e v e r y first m e a s u r e m e n t of t h e size of a m o l e c u l e w o r k e d in this w a y a n d w a s d e v e l o p e d f o r t u i t o u s l y b y t h e A m e r i c a n scientist a n d s t a t e s m a n B e n j a m i n F r a n k l i n . T h e story b e g a n on a sea j o u r n e y in 1757, w h e n F r a n k l i n noticed t h a t t h e w a k e s b e h i n d t w o o f t h e a c c o m p a n y i n g ships w e r e s m o o t h , w h i l e t h o s e b e h i n d his o w n a n d t h e rest o f t h e ships w e r e r o u g h . He called t h e a t t e n t i o n of t h e ship's c a p t a i n t o this r e m a r k a b l e p h e n o m e n o n , a n d later r e p o r t e d t h e c a p tain's c o n t e m p t u o u s reply in a letter to a friend: "The C o o k s , says h e , h a v e I s u p p o s e , b e e n j u s t e m p t y i n g t h e i r greasy Water t h r o ' t h e S c u p p e r s , w h i c h h a s g r e a s e d t h e Sides o f t h o s e Ships a Little." F r a n k l i n t h o u g h t t h a t i t w a s m u c h m o r e likely t h a t t h e oil w a s h a v i n g a n effect o n t h e w a v e s r a t h e r t h a n t h e ships, b u t wisely k e p t his t h o u g h t s to himself. He tested this idea on a n d off o v e r t h e n e x t s e v e n t e e n y e a r s , c u l m i n a t i n g w i t h t h e e x periment he performed on a pond in London's C l a p h a m Comm o n . T h e w i n d w a s ruffling t h e w a t e r w h e n h e tried p o u r i n g a t e a s p o o n of olive oil o n t o t h e surface. He later w r o t e to his friend William B r o w n r i g g : the Oil tho' not more than a TeaSpoonful produced an instant calm, over a Space of several yards square, which spread amazingly, and extended itself gradually, until it reached the Lee Side, making all of that Quarter of the Pond, perhaps half an Acre, as Smooth as a Looking Glass. Franklin t h o u g h t t h a t he h a d d i s c o v e r e d a m e t h o d for c a l m ing r o u g h seas, a n d kept p r o p o s i n g t h e m e t h o d thereafter, e v e n t h o u g h his later large-scale e x p e r i m e n t s at S p i t h e a d in northwest England produced nothing m o r e than the world's first oil slick. W h a t he h a d in fact d o n e w a s d e v e l o p t h e first m e t h o d for m e a s u r i n g t h e size of a m o l e c u l e .

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F r a n k l i n d i d n ' t realize w h a t he h a d really d o n e — he d i d n ' t e v e n k n o w t h a t m o l e c u l e s existed. N e v e r t h e l e s s , his e x p e r i ment keeps turning up in m o d e r n - d a y examination papers, u s u a l l y w i t h t h e v o l u m e of t h e t e a s p o o n c h o s e n so as to give t h e right a n s w e r . T h e p l a i n fact i s t h a t w e d o n ' t k n o w exactly h o w big F r a n k l i n ' s t e a s p o o n w a s . W h a t w e d o k n o w i s t h a t a film of oil s u c h as t h a t w h i c h he described k e e p s on s p r e a d i n g until it is just o n e m o l e c u l e thick, but d o e s n o t s p r e a d f u r t h e r b e c a u s e t h e m o l e c u l e s in t h e film a r e held t o g e t h e r by Van d e r Waals forces. If t h e v o l u m e a n d t h e a r e a of t h e film are k n o w n , t h e t h i c k n e s s can b e c a l c u l a t e d . A h u n d r e d a n d sixt e e n y e a r s later, Lord Rayleigb r e p e a t e d F r a n k l i n ' s e x p e r i m e n t "in a s p o n g e b a t h of e x t r a size," u s i n g a carefully m e a s u r e d v o l u m e of oil a n d Moating pieces of c a m p h o r to m a r k t h e b o u n d a r y of t h e film. He c o n c l u d e d t h a t t h e t h i c k n e s s of t h e film w a s 1.6 " m i c r o - m i l l i m e t e r s " — in m o d e r n u n i t s , 1.6 n a n o m e t e r s . This m e a n s t h a t F r a n k l i n ' s t e a s p o o n m u s t h a v e h a d a v o l u m e of a b o u t 3 ml, w h i c h is a p p r o x i m a t e l y t h a t of a G e o r g i a n t e a s p o o n i n m y possession. T h e k e y step i n t u r n i n g F r a n k l i n ' s a n d Rayleigh's e x p e r i m e n t s i n t o a p r o p e r , scientific tool for s t u d y i n g t h e s h a p e a n d size of s u r f a c e - a c t i v e m o l e c u l e s w a s t a k e n in 1 8 9 1 , t h e v e r y n e x t year, by o n e of t h e few w o m e n scientists of t h e t i m e , t h e G e r m a n Miss A g n e s Pockels, w h o d i s c o v e r e d t h a t a surface film of s u c h m o l e c u l e s could be c o m p r e s s e d by a sliding barrier. It w a s n o t u n t i l 1935, t h o u g h , t h a t a w o r k i n g scientific ins t r u m e n t b a s e d o n this principle w a s built b y t h e A m e r i c a n scientist Irving L a n g m u i r . This w a s d e v e l o p e d in c o l l a b o r a t i o n w i t h a n o t h e r w o m a n scientist, Dr. K a t h e r i n e Blodgett, b u t n e i t h e r Blodgett's n o r Pockels' c o n t r i b u t i o n is a c k n o w l e d g e d i n t h e m o d e r n n a m e for t h e i n s t r u m e n t , w h i c h i s s i m p l y called a L a n g m u i r t r o u g h . T h e n o m e n c l a t u r e is n o t L a n g m u i r ' s fault — he w a s o n e of t h e few scientists of his t i m e w h o a p p a r e n t l y s h o w e d n o regard for s t a t u s o r g e n d e r , b u t t r e a t e d e v e r y o n e o n a n e q u a l footing. T h e L a n g m u i r t r o u g h (not e v e n m e n t i o n e d a m o n g L a n g m u i r ' s scientific a c h i e v e m e n t s i n his e n t r y in t h e Encyclopaedia Britannica) is s i m p l y a flat s h a l l o w


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t r o u g h filled to t h e b r i m w i t h w a t e r , a n d w i t h a d i l u t e layer of t h e surface-active m o l e c u l e s s p r e a d o n t h e surface. T h e layer is c o m p r e s s e d by a sliding barrier, w i t h t h e e x p e r i m e n t e r using a s p r i n g - m o u n t e d h a n g i n g p l a t e to m o n i t o r t h e r e s p o n s e of t h e layer t o c o m p r e s s i o n (Figure 7.8).

Figure 7.8: S c h e m a t i c Side View of Langmuir Trough Before a n d After C o m p r e s s i o n o f M o l e c u l a r S u r f a c e Layer.

T h e L a n g m u i r t r o u g h p r o v i d e d t w o vital pieces of i n f o r m a tion. T h e f i r s t c a m e from t h e c h a n g e i n a r e a a s t h e b a r r i e r w a s m o v e d , w h i c h told t h e e x p e r i m e n t e r h o w closely t h e m o l e cules w e r e p a c k e d . E v e n t u a l l y t h e p a c k i n g d e n s i t y r e a c h e d a limit t h a t d e p e n d e d o n t h e s h a p e a n d size o f t h e i n d i v i d u a l m o l e c u l e s . A "typical" d e t e r g e n t m o l e c u l e h a s a cross-sectional area of a b o u t 0.25 s q u a r e n a n o m e t e r s . T h e s e c o n d piece of i n f o r m a t i o n c a m e from t h e c h a n g e in surface t e n s i o n (registered b y h o w far t h e s p r i n g - m o u n t e d hanging plate was pulled d o w n ) as the film was compressed, w h i c h g a v e a m e a s u r e of t h e w o r k n e e d e d to p u s h t h e surface

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molecules together, and hence gave information about the forces b e t w e e n t h o s e m o l e c u l e s . For c h a r g e d surface-active m o l e c u l e s , t h e n e t force i s r e p u l s i v e . Given e n o u g h r o o m , t h e m o l e c u l e s will get as far a w a y from e a c h o t h e r as possible, like relatives at a w e d d i n g . I w a s i n t r o d u c e d t o t h e L a n g m u i r t r o u g h t e c h n i q u e b y Alex, w h o w a s a n a u t h o r i t y o n its use, a n d w h o t a u g h t u s t h a t t h e trough and t h e water in it must be scrupulously clean. Mode r n t r o u g h s a r e m a d e from Teflon, t h e p o l y m e r m a t e r i a l that is u s e d to coat n o n s t i c k p a n s . Teflon is relatively easy to k e e p clean, b u t earlier m e t a l o r plastic t r o u g h s h a d t o b e coated w i t h a p r o t e c t i v e m a t e r i a l as a b a r r i e r a g a i n s t c o n t a m i n a t i o n . Alex a n d his C a m b r i d g e - t r a i n e d c o n t e m p o r a r i e s used c h e a p paraffin w a x for this p u r p o s e , b u t s o m e o t h e r e x p e r i m e n t e r s really w e n t t o e x t r e m e s . Alex w a s p a r t i c u l a r l y s c a t h i n g a b o u t a n A m e r i c a n c o l l e a g u e n a m e d J a m e s William M c B a i n , w h o h a d c o a t e d his e n t i r e a p p a r a t u s w i t h gold. T h e t r o u g h s o u n d s v e r y s i m p l e , b u t w a s q u i t e tricky t o use, b e c a u s e t h e a m o u n t o f m a t e r i a l r e q u i r e d t o c o v e r t h e surface c o m p l e t e l y is invisible to t h e n a k e d e y e — a visible speck w o u l d h a v e b e e n far t o o m u c h . T h e trick lay n o t i n w e a r i n g t h e s t r o n g m a g n i f y i n g spectacles t h a t g o w i t h t h e t r a d i t i o n a l i m a g e of a scientist, b u t in dissolving t h e m a t e r i a l in a relatively large v o l u m e of a volatile solvent, s u c h as e t h e r , a n d t h e n p u t t i n g a small m e a s u r e d d r o p of t h e s o l u t i o n on t h e t r o u g h ' s surface. T h e e t h e r e v a p o r a t e d , l e a v i n g t h e m a t e r i a l b e h i n d as a single layer of m o l e c u l e s (a m o n o l a y e r ) c o v e r i n g t h e surface of t h e t r o u g h . T h e L a n g m u i r t r o u g h h a d b y n o w b e e n u s e d t o settle m a n y outstanding questions about the shapes and packing of molecules at surfaces. O n e of t h e earliest of t h e s e c o n c e r n e d t h e s h a p e of t h e c h o l e s t e r o l m o l e c u l e , w h i c h is o n e of t h e basic m o l e c u l e s of life. C h o l e s t e r o l receives bad p r e s s t h e s e d a y s hec a u s e of its role in f o r m i n g p l a q u e s t h a t c a n block b l o o d vessels a n d c a u s e h e a r t a t t a c k s or s t r o k e s , b u t it c a u s e s h a r m f u l effects o n l y w h e n p r e s e n t i n excess. T h e effects w o u l d b e e v e n m o r e h a r m f u l if y o u d i d n ' t h a v e e n o u g h of it — y o u w o u l d be


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dead. T h e s h a p e of t h e c h o l e s t e r o l m o l e c u l e dictates h o w it b e h a v e s c h e m i c a l l y i n o u r b o d i e s . A t t h e t i m e w h e n t h e Langmuir trough was invented, the atomic composition of the cholesterol m o l e c u l e w a s k n o w n , b u t t h e a t o m s could h a v e been a r r a n g e d i n t w o q u i t e different w a y s , w i t h e a c h s t r u c t u r e c o r r e s p o n d i n g to a different m o l e c u l a r s h a p e . E a c h s h a p e h a d its p r o p o n e n t s , w h o w e r e h a p p i l y a r g u i n g i n t h e k n o w l e d g e thai t h e r e w a s n o e x p e r i m e n t a l m e t h o d available t o settle t h e a r g u m e n t . T h e t w o p r o p o s e d s t r u c t u r e s p r e d i c t e d q u i t e different cross-sectional a r e a s for t h e c h o l e s t e r o l m o l e c u l e , a n d t h e f a m o u s surface scientist N. K. A d a m realized t h a t t h e differe n c e w o u l d h e s h o w n u p clearly b y t h e n e w l y i n v e n t e d Langm u i r t e c h n i q u e , b e c a u s e o n e s t r u c t u r e w a s flat, s o t h a t t h e m o l e c u l e s w o u l d stack like plates a r r a n g e d vertically, side by side o n t h e w a t e r surface, w h i l e t h e o t h e r s t r u c t u r e p r e d i c t e d a m o r e "three-dimensional" shape, so that t h e area per molecule w o u l d b e m u c h greater. I t t o o k j u s t o n e e x p e r i m e n t t o r e solve t h e a r g u m e n t in favor of t h e first a l t e r n a t i v e . M a n y similar a r g u m e n t s a b o u t m o l e c u l a r s h a p e , m o l e c u l a r size, a n d h o w closely m o l e c u l e s could pack t o g e t h e r a t s u r faces w e r e settled b y t h e L a n g m u i r t e c h n i q u e . Scientists, h o w ever, w e r e still no closer to u n d e r s t a n d i n g w h a t it w a s a b o u t detergent molecules that m a d e t h e m pack spontaneously into different s t r u c t u r e s . T h e q u e s t i o n w a s especially i m p o r t a n t i n t h e case of lecithin ( t h e m a t e r i a l t h a t is sold in h e a l t h food s h o p s ) , since lecithin is a m a j o r c o m p o n e n t of biological cell m e m b r a n e s , a n d i t h a d b e e n f o u n d t h a t lecithin s p o n t a n e ously forms l i p o s o m e s w h e n s h a k e n u p i n w a t e r . T h e exciting possibility w a s t h a t t h e first cell m e m b r a n e s e v e r t o o c c u r o n Earth m i g h t h a v e b e e n f o r m e d in this way, especially since it had b e e n s h o w n that lecithin m o l e c u l e s w e r e p r o b a b l y p r e s ent in t h e prebiotic s o u p . S u d d e n l y e v e r y o n e , i n c l u d i n g myself, w a s t r y i n g t o w o r k out h o w lecithin m o l e c u l e s get t o g e t h e r . M y a p p r o a c h h a d t o be indirect b e c a u s e by n o w I w a s w o r k i n g in a g o v e r n m e n t food r e s e a r c h l a b o r a t o r y a n d e x p e r i m e n t s on t h e origin of life w e r e r a t h e r o u t s i d e my r e m i t . Lecithin w a s a food m a t e r i a l ,

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often u s e d to h o l d w a t e r in place in t h e oily m a t r i x of foods like m a r g a r i n e , so I t a c k l e d t h e q u e s t i o n of h o w m u c h w a t e r t h e lecithin c o u l d carry, a l t h o u g h this w a s m o s t l y a p r e t e x t for k e e p i n g i n c o n t a c t w i t h w h a t o t h e r s w e r e finding out a b o u t t h e a g g r e g a t i o n of lecithin m o l e c u l e s to form c o m p l e x s t r u c tures. T h e y w e r e finding o u t a lot, t h o u g h n o t m u c h t h a t w a s of lasting v a l u e , p a r t l y b e c a u s e it w a s difficult to o b t a i n p u r e lecithin. It w a s for this r e a s o n t h a t s o m e scientists d e c i d e d to try m a t e r i a l s t h a t could b e o b t a i n e d i n p u r e form a n d w h i c h w o u l d also form bilayers. O n e of t h o s e p e o p l e w a s a C a m bridge scientist n a m e d Denis H a y d o n . T h e m a t e r i a l s t h a t h e tried w e r e t h e monoglycerides, w h i c h a r e m o l e c u l e s f o r m e d b y t h e b r e a k d o w n of oils a n d fats as p a r t of o u r n a t u r a l digestive processes. I n e v e r got a r o u n d t o a s k i n g Denis j u s t w h y h e c h o s e t h e s e m a t e r i a l s , but it s e e m s in r e t r o s p e c t t h a t he h a d a glimmering of the revolution that was to come, and sought to use s u r f a c e - a c t i v e m o l e c u l e s w h o s e s h a p e s e n s u r e d t h a t t h e y w o u l d pack n e a t l y i n t o flat s h e e t s . H e k n e w t h a t o n e m o n o glyceride in particular, called glycerol monooleate, or G M O , h a d t h e right d i m e n s i o n s to fit t h e bill, partly o w i n g to s o m e earlier w o r k on m o n o g l y c e r i d e s by a g r o u p w h o s e star s t u d e n t in t h e u s e o f t h e L a n g m u i r t r o u g h w a s a y o u n g grocer's d a u g h t e r called M a r g a r e t Roberts, w h o w a s t h e n e m b a r k i n g o n a c a r e e r as a food scientist. As it t u r n e d o u t , M a r g a r e t R o b e r t s ' hrst piece of scientific w o r k w a s also h e r last. S h e m a r r i e d a m a n n a m e d Denis T h a t c h e r , d e c i d e d t h a t politics w a s a far m o r e e x citing a n d r e w a r d i n g o c c u p a t i o n , a n d b e c a m e Britain's first w o m a n prime minister. I t t u r n e d o u t t h a t G M O w a s a n ideal m a t e r i a l for m a k i n g artificial bilayers. Denis H a y d o n m a d e t h e m b y dissolving t h e G M O in oil a n d p a i n t i n g t h e s o l u t i o n o v e r a h o l e in a piece ol Teflon s e p a r a t i n g t w o h a l v e s of a small t a n k full of w a t e r . T h e oil d r a i n e d a w a y to t h e b o u n d a r y , leaving a film w h o s e struct u r e w a s basically similar to t h a t w h i c h o c c u r s in n a t u r a l m e m b r a n e s (Figure 7.9). S u c h films b e c a m e k n o w n as black lipid membranes, or BLMs,

bath foam,

b e e r f o a m , a n d t h e m e a n i n g o f life

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Figure 7.9: S c h e m a t i c Representation of Glycerol M o n o o l e a t e Bilayer.

b e c a u s e t h e y w e r e s o t h i n t h a t t h e y reflected v e r y little light. The b o u n d a r y , w h i c h is t h e r e s e r v o i r to w h i c h all of t h e excess solvent d r a i n s , is k n o w n as t h e P l a t e a u b o r d e r in h o n o r of t h e Belgian Josef Plateau, w h o s e f a m e a m o n g surface scientists c o m e s p a r t l y from t h e fact t h a t h e w o r k e d o u t e x p e r i m e n t a l l y the e l e g a n t rules g o v e r n i n g t h e a n g l e s b e t w e e n t h e c o r n e r s a n d edges in a l o a m ( w h i c h a r e also called P l a t e a u b o r d e r s ) , but still m o r e from t h e fact t h a t he did all of this after he h a d b e e n blinded d u r i n g e x p e r i m e n t s i n w h i c h h e h a d l o o k e d for too long at t h e s u n . Despite this, his p u b l i s h e d p a p e r s a r e full of t h e most beautiful a n d a c c u r a t e d i a g r a m s , p r o d u c e d w i t h the aid of a sighted assistant. Denis's w o r k on black lipid m e m b r a n e s u l t i m a t e l y g a v e a good deal of i n f o r m a t i o n on t h e p r o c e s s e s t h a t g u i d e selfassembly, a n d i n p a r t i c u l a r o n h o w o t h e r m o l e c u l e s c a n w o r m their w a y i n t o bilayers w i t h o u t d i s r u p t i n g t h e w h o l e s t r u c t u r e . M a n y o f t h e m o l e c u l e s t h a t h e s t u d i e d w e r e local a n e s thetics, a n d h e d i s c o v e r e d t h a t t h e s e w o r k b y f a t t e n i n g t h e bilayer s t r u c t u r e so t h a t m e m b r a n e m o l e c u l e s w h o s e j o b it is

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how to d u n k a d o u g h n u t

t o pass m a t e r i a l from o n e side t o t h e o t h e r can n o l o n g e r s p a n t h e full d i s t a n c e . A m o n g t h e o t h e r q u e s t i o n s t h a t Denis t a c k l e d w a s t h e v e x e d p h e n o m e n o n of w h y t h e tails of d e t e r g e n t m o l e c u l e s prefer t h e i r o w n c o m p a n y to t h a t of w a t e r . It w a s a case of "oil a n d w a t e r d o n ' t m i x " — b u t why? H e w a s u n a b l e t o c o m e u p w i t h a n a n s w e r — i n fact, n o o n e w a s . E v e n n o w , w e d o n ' t really k n o w w h a t it is t h a t m a k e s oil virtually i n s o l u b l e in w a t e r . It's not t h e lack of a t t r a c t i o n b e t w e e n t h e m o l e c u l e s — i n d i v i d u a l oil a n d w a t e r m o l e c u l e s c a n c o h a b i t q u i t e happily. It is m o r e that w a t e r m o l e c u l e s p r e f e r to a r r a n g e t h e m s e l v e s in a flickering, e v a n e s c e n t array. An i n d i v i d u a l oil m o l e c u l e p e n e t r a t i n g this a r r a y forces t h e n e a r b y w a t e r m o l e c u l e s t o a d o p t a m o r e p e r m a n e n t a r r a n g e m e n t , a n d is a b o u t as w e l c o m e as a m a r riage c e l e b r a n t in a menage a trois. At least D e n i s w a s able to m e a s u r e t h e d r i v i n g force t h a t p u s h e s oil a n d w a t e r a p a r t , b y m e a s u r i n g t h e w o r k r e q u i r e d t o i n c r e a s e t h e a r e a of c o n t a c t b e t w e e n oil a n d w a t e r surfaces — in o t h e r w o r d s , t h e interfacial t e n s i o n , ft w a s d a t a s u c h as t h e s e , t o g e t h e r w i t h i n f o r m a t i o n o n t h e r e p u l s i v e forces bet w e e n t h e h e a d - g r o u p s , t h e s h a p e s of different sorts of d e t e r g e n t m o l e c u l e , a n d t h e u l t i m a t e p a c k i n g d e n s i t y of different t y p e s of h y d r o p h o b i c tail, t h a t J a c o b , Barry, a n d t h e i r coll e a g u e J o h n Mitchell b r o u g h t t o g e t h e r i n o n e b e a u t i f u l synthesis t h a t e n a b l e d t h e m t o predict j u s t w h a t sort o f d e t e r g e n t m o l e c u l e s w o u l d form w h a t sort of s t r u c t u r e s .

A Grand Synthesis

I was particularly interested in w h a t they w e r e doing because I h a d just w r i t t e n a r e v i e w s u m m a r i z i n g w h a t w a s k n o w n a b o u t h o w m o l e c u l e s pack to form micelles. It h a d b e c o m e a b u n d a n t l y clear t h a t t h e r e w a s n o w a y t h a t m o s t d e t e r g e n t m o l e c u l e s c o u l d p a c k to form a spherical micelle: t h e r e w a s simply no r o o m in t h e m i d d l e for t h e e n d s of all t h e tails. T h e r e w e r e p l e n t y o f s u g g e s t i o n s a b o u t h o w this p r o b l e m


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might be o v e r c o m e , s o m e involving very weird micelle s h a p e s . My c o a u t h o r , David Oakenfull, a n d I favored t h e simplest, w h i c h w a s t h a t micelles m u s t h a v e t h e s h a p e o f e i t h e r a p r o late or an o b l a t e ellipsoid — in o t h e r w o r d s , t h e y w e r e e i t h e r e g g - s h a p e d or d i s c u s - s h a p e d — to a l l o w r o o m for t h e tails in the middle. Even before o u r r e v i e w a p p e a r e d i n p r i n t , J a c o b , Barry, a n d J o h n w e r e a t w o r k o n a n idea t h a t w o u l d leave o u r s i m p l e m i n d e d a r g u m e n t s far b e h i n d . T h e y a r g u e d t h a t t h e o n l y m o l ecules c a p a b l e of f o r m i n g micelles w o u l d be t h o s e t h a t could pack to form essentially spherical s t r u c t u r e s . As p o i n t e d o u t earlier b y t h e A m e r i c a n scientist C h a r l e s Tanford, m o l e c u l e s w i t h o t h e r s h a p e s w o u l d simply pack t o form o t h e r s t r u c t u r e s . J a c o b , Barry, a n d J o h n refined this idea i n t o a q u a n t i t a t i v e m o d e l that w a s c o m p l i c a t e d m a t h e m a t i c a l l y , b u t w h i c h led t o o n e e x t r a o r d i n a r i l y s i m p l e result. It t u r n e d o u t t h a t t h e sort of s t r u c t u r e i n t o w h i c h d e t e r g e n t m o l e c u l e s pack d e p e n d s o n o n l y t h r e e t h i n g s : t h e l e n g t h of t h e tail "L," t h e v o l u m e of t h e m o l e c u l e "V," a n d t h e " o p t i m a l " cross-sectional a r e a of t h e h e a d - g r o u p "A" — in o t h e r w o r d s , t h e a m o u n t of space t h a t the h e a d - g r o u p prefers t o h a v e w h e n i n c o m p a n y w i t h o t h e r s ol its kind. If (V/(A X L)) is less t h a n o n e - t h i r d , t h e m o l e c u l e s pack as spherical micelles. II it is b e t w e e n o n e - t h i r d a n d o n e hall, the micelles b e c o m e ellipsoidal, li it is b e t w e e n a half a n d one, t h e m o l e c u l e s pack as bilayers or liposomes. If it is g r e a t e r t h a n o n e , inverted micelles are formed. T h e m o d e l w a s a n i m m e d i a t e success, a n d a profusion of p a p e r s followed in w h i c h scientists a r o u n d t h e world explained t h e i r results in t e r m s of it. O n e t h i n g t h a t t h e t h e o r y could e x p l a i n w a s t r a n s p a r e n t microemulsions w h i c h , u n l i k e n o r m a l e m u l s i o n s s u c h as milk and m a y o n n a i s e , w e r e indefinitely stable. This w a s a difficult pill to s w a l l o w for scientists like myself, w h o h a d b e e n b r o u g h t up with t h e idea t h a t e m u l s i o n s , w h i c h are s u s p e n s i o n s of droplets of o n e liquid in a n o t h e r (e.g., oil in w a t e r ) , w o u l d e v e n t u a l l y " b r e a k " as t h e d r o p l e t s floated to t h e surface a n d coalesced. W e k n e w that w e could slow t h e process d o w n b y coating t h e d r o p l e t s w i t h a p r o t e c t i v e layer of surface-active

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m a t e r i a l s u c h a s glycerol m o n o o l e a t e o r t h e lactoglobulin p r o tein w i t h w h i c h milk fat globules a r e coated, but we also k n e w that this w a s a h o l d i n g m e a s u r e at best, a n d that t h e oil a n d w a t e r w o u l d e v e n t u a l l y s e p a r a t e a s t h e d r o p l e t s coalesced. Here, t h o u g h , w e r e n e w e m u l s i o n s that s e e m e d t o b e indefinitely stable. Their e x i s t e n c e h a d b e e n k n o w n for s o m e forty years, b u t t h e w a y i n w h i c h t h e y w e r e stabilized w a s not u n derstood until t h e "packing" t h e o r y w a s d e v e l o p e d , w h e n Barry a n d o t h e r s quickly realized t h a t t h e secret lay in t h e s h a p e oi the detergent molecules that formed t h e m . Two sorts of molecule with c o m p l e m e n t a r y s h a p e s w e r e used, so t h a t t h e voids bet w e e n o n e g r o u p w e r e f i l l e d b y t h e other. T h e result w a s a n e m u l s i o n c o n t a i n i n g extraordinarily tiny droplets — so small that t h e e m u l s i o n a p p e a r e d t r a n s p a r e n t . S o m e m i c r o e m u l s i o n s c o n t a i n e d no droplets at all. The oil a n d w a t e r phases simply w o u n d in a n d o u t of e a c h o t h e r in a series of intricate curves, g e n e r a t i n g w h a t c a m e to be called a bicontinuous p h a s e . T h e m a t h e m a t i c a l t h e o r y of s u c h systems p e r m i t t e d Barry a n d o t h ers to design n e w m i c r o e m u l s i o n s . O n e of t h e c o n s e q u e n c e s of this w a s that Barry b e c a m e a n e x p e r i m e n t a l i s t , r a t h e r t o Jacob's disapproval. A n o t h e r w a s that a r a n g e of n e w d e t e r g e n t products hit t h e m a r k e t , w i t h an attractive t r a n s p a r e n c y of a p p e a r a n c e a n d flow p r o p e r t i e s t h a t let t h e m sit as a gel until s h a k e n , w h e n t h e y p r o m p t l y flowed at t h e user's c o m m a n d . A m a r k e t niche lor t h e s e p r o d u c t s w a s f o u n d in hair s h a m p o o s , for w h i c h t h e d e t e r g e n t s in m i c r o e m u l s i o n s arc ideal. By this t i m e I w a s 12,000 miles a w a y , s p e n d i n g a sabbatical y e a r w i t h Denis H a y d o n in C a m b r i d g e , p u r s u i n g an idea t h a t I h a d a b o u t black lipid m e m b r a n e s . M y p r o p o s a l w a s t o use w a ter p r e s s u r e t o b u l g e t h e m u p like b a l l o o n s , s o t h a t t h e y could be pushed together in the same way that Jacob had pushed mica surfaces t o g e t h e r , b u t h e r e m o d e l i n g w h a t h a p p e n s w h e n t w o cell m e m b r a n e s c o m e i n t o c o n t a c t . A s i t t u r n e d out, I got no results for t h e w h o l e year. In fact, it took a f u r t h e r t h r e e y e a r s b e f o r e I w a s able to b u l g e black lipid m e m b r a n e s successfully a n d p u s h t h e m t o g e t h e r , a n d a f u r t h e r t w o years before I p u b l i s h e d t h e results of t h e s e e x p e r i m e n t s w i t h Denis.


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T h e results s h o w e d t h a t t h e black lipid m e m b r a n e s j u m p e d t o g e t h e r from a d i s t a n c e of s o m e t h i r t y n a n o m e t e r s , i m m e d i ately losing t o p r o d u c e a n u n u s u a l s t r u c t u r e n o t n o r m a l l y s e e n w h e n t w o real biological m e m b r a n e s fuse. For this a n d several o t h e r t e c h n i c a l r e a s o n s t h e black lipid m e m b r a n e s w e r e not good m o d e l s , a n d I a b a n d o n e d this line of i n q u i r y in favor of w o r k i n g w i t h real biological cells, w h i c h o t h e r s w e r e finding c o n t a i n e d a small p r o p o r t i o n of m o l e c u l e s called lysophosplwlipids t h a t h a d relatively large h e a d s a n d w h i c h w o u l d n o r m a l l y be e x p e c t e d to o c c u r as micelles. It is n o w b e lieved t h a t l y s o p h o s p h o l i p i d s a r e n o r m a l l y dispersed w i t h i n t h e m e m b r a n e , b u t c a n get t o g e t h e r w h e n r e q u i r e d t o o p e n up a h o l e — t h e first step t o w a r d s t w o m e m b r a n e s fusing to b e c o m e o n e i n s u c h processes a s fertilization. Was t h e w o r k t h a t I started w i t h D e n i s w a s t e d ? In o n e s e n s e , yes, a l t h o u g h it did lead to t h e d e v e l o p m e n t of a n e w e x p e r i m e n t a l t e c h n i q u e t h a t i s n o w f i n d i n g a p p l i c a t i o n i n s u c h diverse (ields as oil r e c o v e r y a n d t h e m a n u f a c t u r e of ice c r e a m . In a n o t h e r s e n s e , no scientific effort is t r u l y w a s t e d , so l o n g as t h e q u e s t i o n b e i n g a s k e d is a s e r i o u s o n e . T h e a n s w e r s m a y n o t p r o v e r e l e v a n t t o t h e original q u e s t i o n , b u t t h e i r c o n s e q u e n c e s are largely u n p r e d i c t a b l e , as Pasteur, F r a n k l i n , a n d a host of o t h e r s h a v e f o u n d by p e r s i s t e n t l y p u r s u i n g p a r t i c u l a r lines of inquiry. Persistence is o n e of t h e m o s t v a l u a b l e a t t r i b utes that a scientist can h a v e . W i t h o u t t h e p e r s i s t e n c e of m a n y scientists, s o m e g o i n g i n t h e right d i r e c t i o n , s o m e c o n c e r n e d with w h a t m a y h a v e a p p e a r e d t o b e lost causes, w e w o u l d n e v e r h a v e realized t h a t t h e m e m b r a n e s t h a t e n v e l o p living cells a r e f o r m e d s p o n t a n e o u s l y by t h e " s e l l - a s s e m b l y " of m a n y small m o l e c u l e s , a n d t h a t t h e v e r y e x i s t e n c e o f living m e m b r a n e s d e p e n d s critically o n t h e s h a p e s o f t h o s e m o l e c u l e s . This k n o w l e d g e , applied in o t h e r areas, has led to t h e d e v e l o p m e n t of b e t t e r h a i r s h a m p o o s , n e w foams for fire e x t i n g u i s h ers, a n d o t h e r practical applications. Applied to m e d i c i n e , a n d to t h e b e t t e r u n d e r s t a n d i n g of o u r s e l v e s a n d o u r e v o l u t i o n , it is possible t h a t it m a y e v e n be t h e s a v i n g of t h e h u m a n r a c e .

8

a q u e s t i o n of t a s t e

I w a s o n c e a s k e d to give an a f t e r - d i n n e r s p e e c h at an i m p o r t a n t c o n f e r e n c e i n P h i l a d e l p h i a o n food tastes a n d a r o m a s . O n t h e night of t h e d i n n e r I discovered that t h e a f t e r - d i n n e r s p e e c h given t h e p r e v i o u s y e a r w a s m a d e by a Nobel Prize w i n n e r a n d t h a t , o n a n o t h e r occasion, t h e e n t e r t a i n m e n t had b e e n p r o v i d e d by a full d a n c i n g t r o u p e from India. A n y confid e n c e t h a t 1 m i g h t h a v e h a d r a t h e r e v a p o r a t e d a l t e r I received this i n f o r m a t i o n , b u t at least I k n e w t h a t I w a s g o i n g to he w a y a h e a d of t h e I n d i a n d a n c i n g t r o u p e in t h e p o p u l a r i t y stakes. T h e y h a d p o s i t i o n e d t h e m s e l v e s s o a s t o block t h e p a t h t o t h e toilets, a n d t h e n d a n c e d for half a n h o u r l o n g e r t h a n e x p e c t e d , j u s t w h e n t h e b l a d d e r - e x p a n d i n g effects of a p a r t i c u l a r l y good c h a r d o n n a y w e r e b e i n g felt by t h e m a j o r i t y of t h o s e p r e s e n t . M y host, t h e c h a i r m a n o f t h e c o n f e r e n c e , h a d asked m e t o give a s p e e c h t h a t w a s " i n f o r m a t i v e b u t a m u s i n g . " It w a s difficult to see w h a t I could o i l e r to an a u d i e n c e of w o r l d e x p e r t s at a c o n f e r e n c e w h e r e e v e n t h e d i n n e r m e n u c o n t a i n e d a detailed analysis of t h e flavor c o m b i n a t i o n in e a c h dish. If I tried to talk a b o u t flavor from t h e d i n e r ' s point of view, t h e n t h e a m u s e m e n t , I t h o u g h t , w o u l d m o s t l y he at my i g n o r a n c e . I t h o u g h t t h a t I could see a way, h o w e v e r , in l o o k i n g at eating from t h e p o i n t of v i e w of a physical scientist, a n d to conc e n t r a t e o n h o w foods release t h e i r tastes a n d a r o m a s . I w a s r e a s o n a b l y well qualified lor t h e task, h a v i n g s p e n t t w e n t y y e a r s w o r k i n g as a physical scientist in a g o v e r n m e n t research laboratory, a n d h a v i n g s p e n t q u i t e a bit of t i m e since w o r k i n g w i t h chefs a n d food scientists. E v e n so, I f o u n d t h a t t h e r e w a s a lot t h a t 1 d i d n ' t k n o w a n d , as 1 s o o n d i s c o v e r e d , t h a t no oneelse k n e w either, a n d I w a s forced to d e v e l o p s o m e n e w ideas t h a t t u r n e d o u t t o b e n o v e l t o m a n y p r e s e n t a s well. O t h e r sci-


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enlists h a v e since p i c k e d u p o n t h e s e ideas, o r d e v e l o p e d t h e m i n d e p e n d e n t l y , a g a i n s h o w i n g h o w science is a c o m m u n i t y affair, a n d h o w y o u c a n n e v e r tell w h e r e s o m e t h i n g m i g h t lead. I h a v e l o o k e d at e a t i n g from t h e p o i n t of v i e w of t h e s p e e c h m a n y t i m e s since — s o m e t i m e s as s e r i o u s science, s o m e t i m e s u s i n g food as a h o o k to e x e m p l i f y h o w scientists look at t h e w o r l d . S o m e of t h o s e stories a r e given in t h e following c h a p ter, w h e r e I e x a m i n e t h e science of e a t i n g a m e a l . All of t h e science is serious, e v e n if n o t all of t h e stories a r e .

Introduction

A friend of t h e great n i n e t e e n t h - c e n t u r y F r e n c h g a s t r o n o m e J e a n A n t h e l m e Brillat-Savarin told t h e story o f h o w h e h a d visited t h e f a m o u s m a n i n m i d a f t e r n o o n , o n l y t o b e k e p t w a i t ing for s o m e t i m e . E v e n t u a l l y Brillat-Savarin a p p e a r e d , full of apologies: "I w a s in t h e d r a w i n g r o o m , e n j o y i n g my d i n n e r . " " W h a t ? " said his guest, w h o k n e w t h a t Brillat-Savarin always h a d his d i n n e r s e r v e d formally at t h e d i n i n g - r o o m t a b l e . "Eating y o u r d i n n e r i n t h e d r a w i n g r o o m ? " "I m u s t b e g y o u to o b s e r v e , M o n s i e u r , " replied BrillatSavarin, " t h a t I did n o t say t h a t I w a s e a t i n g my d i n n e r , b u t enjoying it. I h a d d i n e d an h o u r b e f o r e . " Brillat-Savarin w a s o n e of t h e first p e o p l e to a n a l y z e t h e art of g a s t r o n o m y . He s u m m a r i z e d a lifetime s p e n t largely at t h e m e a l table in a t w o - v o l u m e c o m p e n d i u m p u b l i s h e d in 1826 w i t h an u n w i e l d l y title t h a t b e g i n s Physiologie du gout, ou Meditations de gastronomie transcendante, ouvrage theorique, historique et a Vordre du jour (The P h y s i o l o g y of Taste, or M e d i t a t i o n s on T r a n s c e n d e n t G a s t r o n o m y , a W o r k T h e o r e t i c a l , Historical, a n d P r o g r a m m e d ) , w h i c h lists p r e c e p t s , a n e c d o t e s , a n d o b s e r v a tions o n h o w t o e n h a n c e t h e p l e a s u r e s o f t h e t a b l e . W e still follow m a n y of Brillat-Savarin's p r e c e p t s , in p r i n c i p l e if n o t alw a y s i n practice. T h e science u n d e r l y i n g t h o s e p r e c e p t s , h o w ever, i s o n l y j u s t n o w b e g i n n i n g t o b e u n d e r s t o o d , a n d m a n y

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basic q u e s t i o n s r e m a i n u n a n s w e r e d . W h y , for e x a m p l e , does t h e visual a p p e a r a n c e of a m e a l affect o u r p e r c e p t i o n of its flav o r ? H o w d o taste, a r o m a , a n d o t h e r factors interact t o p r o d u c e t h e s e n s a t i o n t h a t t h e F r e n c h ca\\ gout, a n d for w h i c h t h e closest English w o r d is flavor? H o w do foods release taste a n d a r o m a m o l e c u l e s t h a t affect r e c e p t o r s i n t h e t o n g u e a n d t h e n o s e respectively t o p r o d u c e this s e n s a t i o n ? In this c h a p t e r I follow t h e science of e a t i n g a m e a l from start t o f i n i s h , t o e x a m i n e t h e progress t h a t scientists h a v e m a d e i n u n d e r s t a n d i n g w h a t h a p p e n s a s w e look, c h e w , a n d swallow.

Perception

A g o o d m e a l b e g i n s w i t h e x p e c t a t i o n , c o n t i n u e s w i t h gratification, a n d e n d s w i t h satisfaction. Brillat-Savarin w a s o n e o f t h e first to r e c o g n i z e t h a t t h e first of t h e s e , e x p e c t a t i o n , is an i m p o r t a n t p a r t of t h e e n j o y m e n t of a m e a l . He believed t h a t t h e e x p e c t a t i o n p r o d u c e d b y a n a p p r o p r i a t e a m b i e n c e w a s especially i m p o r t a n t , a n d t h a t t h e e n j o y m e n t of a m e a l w h e n d i n i n g o u t w a s e n h a n c e d b y " a n e l e g a n t r o o m [ a n d | smart w a i t e r s , " as well as "a c h o i c e cellar, a n d s u p e r i o r c o o k i n g . " M o d e r n psychologists w o u l d a g r e e w i t h Brillat-Savarin. T h e y h a v e s h o w n that e x p e c t a t i o n s based o n a m b i e n c e , lighting, t h e c o m p a n y p r e s e n t , t h e food's a p p e a r a n c e , a r o m a , a n d t e x t u r e , a n d e v e n t h e q u a l i t y of t h e table n a p k i n s , can all affect t h e w a y t h a t food actually tastes to t h e diner. T h e s e effects are not confined to gourmets, or to those w h o imagine t h e m selves to be g o u r m e t s . A c o m m e r c i a l h a m b u r g e r t h a t tastes great to a t e e n a g e r w h e n e a t e n in t h e c o m p a n y of a g r o u p oi friends m a y t a s t e terrible t o t h e s a m e t e e n a g e r w h e n e a t e n i n t h e c o m p a n y of his or h e r p a r e n t s . A r e s t a u r a n t m e a l that m e l t s i n t h e m o u t h w h e n s h a r e d w i t h a lover will not taste quite the same to s o m e o n e having a domestic a r g u m e n t with his or h e r s p o u s e . T h e e x p r e s s i o n " t h e food t u r n e d to a s h e s in


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m y m o u t h " h a s real m e a n i n g w h e n i t c o m e s t o t h e p e r c e p t i o n of flavor. We taste w i t h o u r b r a i n s . All t h a t o u r t o n g u e s a n d noses do is send sensory information to the brain about t h e taste a n d a r o m a m o l e c u l e s r e a c h i n g t h e m . T h e b r a i n p r o c e s s e s the information, together with w h a t e v e r other information it perceives to be r e l e v a n t , a n d p r o d u c e s a r e s p o n s e . T h e " o t h e r i n f o r m a t i o n " can c o m e from s o m e c u r i o u s s o u r c e s . T h e Italian Filippo T o m m a s o M a r i n e t t i r e p o r t e d in his Futurist Cookbook of 1932 t h e e x p e r i m e n t of e a t i n g t h e s a m e food w h i l e r e s t i n g his fingers lightly on e i t h e r velvet or s a n d paper. T h e p e r c e i v e d t e x t u r e o f t h e food, h e r e p o r t e d , w a s q u i t e different i n t h e t w o cases. M a r i n e t t i d i n e d his w a y from Milan to Paris to B u d a p e s t , staging e y e - c a t c h i n g d e m o n s t r a tions w i t h his talks a s h e ate m e a l s t h a t i n c l u d e d " R a w M e a t Torn A p a r t by T r u m p e t Blasts," a n d a recipe t h a t i n c l u d e d chickpeas, capers, l i q u e u r c h e r r i e s , a n d fried p o t a t o chips, all e a t e n i n d i v i d u a l l y b e t w e e n carefully clocked s t r e t c h e s of silence. T h e F u t u r i s t m o v e m e n t " d i s d a i n [ e d ] t h e e x a m p l e a n d a d m o n i t i o n of t r a d i t i o n in o r d e r to i n v e n t at a n y cost s o m e t h i n g n e w w h i c h e v e r y o n e c o n s i d e r s crazy." T h e i r a i m w a s t o shock. Their m o d e r n successors a r e chefs s u c h as Ffeston Blum e n t h a l , c h e f - p r o p r i e t o r of t h e Fat D u c k r e s t a u r a n t at B r a y beside t h e River T h a m e s n e a r L o n d o n , w h o a i m s t o use t h e b r a i n ' s r e s p o n s e s t o c r e a t e n e w flavor e x p e r i e n c e s t h a t m i g h t n o t shock, b u t certainly s u r p r i s e . A r o m a s , for e x a m p l e , u s u a l l y c o n t a i n h u n d r e d s , o r e v e n t h o u s a n d s , o f different c h e m i c a l c o m p o u n d s , a n d s o m e a r o mas, s u c h as garlic a n d coffee, h a v e m a j o r c o m p o n e n t s in c o m m o n . H e s t o n h a s tried m i x i n g t h e t w o m a t e r i a l s in a creme brulee. The mixture sounds horrible, but it seems to fool t h e b r a i n , w h i c h c a n ' t d e c i d e w h e t h e r it is e x p e r i e n c i n g garlic o r coffee, a n d oscillates b e t w e e n t h e t w o , e n j o y i n g e a c h o n e s e p a r a t e l y b u t n e v e r b e i n g able t o " m i x " t h e m . A r o m a i s n o t t h e o n l y t h i n g t h a t a p p e a r s t o trick t h e b r a i n . H e s t o n also m a k e s a b e e t jelly, to w h i c h he a d d s tartaric acid, t h e m a i n c o m p o n e n t i n t h e "crust" t h r o w n b y a g o o d w i n e . Tartaric acid, as its n a m e suggests, m a k e s t h e jelly taste "tart,"

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h o w to dunk a

doughnut

a n d this, c o m b i n e d w i t h t h e visual a p p e a r a n c e , gives t h e taster the impression that he or she is eating blackcurrant rather t h a n b e e t . O n e taster, w h e n told t h a t t h e jelly w a s beet, said t h a t it tasted d i s g u s t i n g . W h e n told it w a s really b l a c k c u r r a n t , h o w e v e r , s h e d e c i d e d t h a t it w a s a c t u a l l y delicious. But it w a s really beet. H e s t o n bases m u c h of his c u l i n a r y art on t h e p r e m i s e that t h e h u m a n b r a i n loves surprises, a p r e m i s e t h a t h a s n o w b e e n s u p p o r t e d by scientific e x p e r i m e n t s . S u r p r i s e s arise from a contrast between expectation and experience, but expectation can p r o v e d o m i n a n t i n m a n y cases. I t starts w i t h t h e a p p e a r a n c e o f t h e food o n t h e plate, w h i c h can e v e n affect w h e t h e r t h e d i n e r i s p r e p a r e d t o p u t t h e food i n t o his o r h e r m o u t h . Most p e o p l e h a v e h e a r d o f e x p e r i m e n t s w h e r e m e a t i s served u n d e r g r e e n o r y e l l o w lighting, w i t h t h e result t h a t d i n e r s c a n n o t face e a t i n g t h e food. So far as I k n o w , t h e e x p e r i m e n t s h a v e n o t b e e n e x t e n d e d to t h e effects of flickering TV light on t h e p e r c e p t i o n of a m e a l — it w o u l d be an i n t e r e s t i n g study. E v e n if t h e lighting is n o r m a l , a p p e a r a n c e can still h a v e a d r a m a t i c effect on t h e acceptability of a food. W h e n I w a s w o r k i n g i n a n A u s t r a l i a n g o v e r n m e n t food r e s e a r c h laboratory, I w a s a m e m b e r of a tasting p a n e l w h o s e job w a s to evalu a t e t h e flavor of v e g e t a r i a n s a u s a g e s , p r o d u c e d from s o y b e a n p r o t e i n by a local a g r i c u l t u r a l college. T h e s a u s a g e s w e r e perfectly n o r m a l in a p p e a r a n c e , a g o o d crisp b r o w n , a n d neatly p r e s e n t e d on a w h i t e c h i n a plate w i t h stainless steel cutlery. All w a s well u n t i l w e applied o u r k n i v e s a n d forks t o o n e e n d o f t h e sausages, w h e n t h e c o n t e n t s p r o m p t l y r a n u p t o t h e o t h e r e n d in a liquid m e s s . T h e r e w a s no w a y t h a t I, or a n y o t h e r m e m b e r of t h e taste p a n e l , could p u t t h o s e s a u s a g e s in our mouths. T h e a p p e a r a n c e a n d t e x t u r e o f food o n t h e plate give i m p o r tant, t h o u g h s o m e t i m e s m i s l e a d i n g , c u e s a s t o w h a t w e m i g h t e x p e c t w h e n w e p u t t h e food i n o u r m o u t h s . That w e r e s p o n d to t h e s e c u e s so strongly suggests t h a t t h e r e s p o n s e is d e e p l y e m b e d d e d i n o u r p s y c h e , p e r h a p s from p r e h i s t o r i c t i m e s


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w h e r e crucial distinctions h a d t o b e m a d e b e t w e e n foods a n d t h e positively d a n g e r o u s . T h e really s t r o n g cue, t h o u g h , is t h e o n e t h a t is used by m o s t a n i m a l s , including ourselves — a r o m a . T h e r e is n o t h i n g like t h e a r o m a of a fresh m e a l , a n d so far t h e r e is n o t h i n g to r e p l a c e it. At a m e e t i n g 1 a t t e n d e d in Sicily, t h e F r e n c h chef A n n e - M a r i e D e G e n n e s p r o d u c e d t w o r a t a touilles, o n e w h i c h h a d b e e n flavored b y fresh t h y m e a n d b a y leaf, a n d t h e o t h e r by e x t r a c t s from t h e s e s a m e p l a n t s . T h e first w a s u n d o u b t e d l y preferable, e v e n t h o u g h n o a r o m a c o m p o u n d s h a d b e e n lost i n t h e e x t r a c t i o n p r o c e s s . T h e difference w a s p r o b a b l y d u e t o t h e fact t h a t t h e e x t r a c t i o n p r o c e d u r e w a s m o r e efficient for s o m e a r o m a c o m p o u n d s t h a n o t h e r s , s o t h a t t h e b a l a n c e i n t h e c o m p l e x m i x t u r e o f a r o m a s w a s subtly changed. Even so, flavor scientists a r e m a k i n g progress. A d r o p of t h e c o m p o u n d h e x a n a l , w h i c h p r o d u c e s t h e "green n o t e " c h a r a c teristic of fresh fruit a n d vegetables, c a n restore t h a t n o t e of freshness to a cooked dish. S o m e m a y balk at a d d i n g a " c h e m i cal," b u t t h e w o r l d is m a d e of chemicals, a n d h e x a n a l is o n e that plants p r o d u c e for t h e m s e l v e s a n d w h i c h we eat all t h e t i m e . W h y not a d d it in p u r e form, r a t h e r t h a n following t h e chef's p r o c e d u r e of t h r o w i n g in a handful of fresh material, as t h e y do w h e n t h e y add a p u r e e of fresh a s p a r a g u s tips to e n h a n c e t h e a r o m a of a s p a r a g u s s o u p ? Chefs often " c h e a t " in this way, if you can call it c h e a t i n g . So do h o m e cooks. W h o h a s n o t h e a r d of, a n d probably used, t h e trick of p u t t i n g a few coffee b e a n s u n d e r t h e grill so t h a t t h e a r o m a will e n h a n c e t h e a p p e a l of i n s t a n t coffee? This trick has b e e n t h e subject of psychological tests, w h e r e blindfolded subjects w e r e given h o t w a t e r t o drink w h i l e being a l l o w e d to smell t h e a r o m a of fresh coffee. All of t h e m w e r e c o n v i n c e d t h a t t h e y w e r e d r i n k i n g t h e real t h i n g . W e often e n h a n c e t h e a r o m a t i c a p p e a l o f o u r m e a l s p r i o r t o ingestion b y c o a t i n g t h e m w i t h g r a v y a n d s a u c e s . B e c a u s e o f t h e i r liquid c o n s t i t u t i o n , t h e s e m a t e r i a l s r e l e a s e t h e i r a r o m a s m o r e readily t h a n d o t h e foods t h a t t h e y coat, a n d p r o v i d e a n e n h a n c e d a r o m a e x p e r i e n c e a n d flavor e x p e c t a t i o n e v e n before t h e food r e a c h e s t h e m o u t h . P e o p l e q u i c k l y c o m e t o

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associate a p p e a r a n c e a n d a r o m a , w h i c h is o n e of t h e r e a s o n s a rich b r o w n g r a v y is so favored on roast m e a l s , especially in E n gland, t h e h o m e of t h e roast d i n n e r . T h e use of g r a v y is so c o m m o n t h a t o n e w o u l d t h i n k it h a d few surprises left to offer, b u t o n e w o u l d be w r o n g , as I f o u n d w h e n I w a s a s k e d by an a d v e r t i s i n g firm to i n v e s t i g a t e t h e science of gravy. I o n l y u n d e r t a k e s u c h projects on r a r e occasions, if I c a n see t h e m as a w a y of d r a w i n g p u b l i c a t t e n t i o n to t h e fact t h a t scie n c e i s e v e r y w h e r e a r o u n d us, a n d n o t j u s t c o n f i n e d t o m e d ical a d v a n c e s , t h e d e s t r u c t i o n of n a t i o n s , or t h e fate of t h e u n i v e r s e . This project c e r t a i n l y d r e w p u b l i c a t t e n t i o n , t o t h e e x t e n t t h a t I r e c e i v e d a d e l i g h t e d e - m a i l from M a r c A b r a h a m s , o r g a n i z e r of t h e IgNobel Prizes, s a y i n g t h a t I m i g h t be in line for a s e c o n d a w a r d . In t h e b e g i n n i n g , all I could t h i n k of d o i n g w a s t o look a t h o w m u c h g r a v y w o u l d b e t a k e n u p b y t h e various c o m p o n e n t s of a t r a d i t i o n a l roast d i n n e r . M e a t , I t h o u g h t , w o u l d o b v i o u s l y t a k e u p q u i t e a bit, a s w o u l d m a s h e d p o t a toes, w h i l e roast p o t a t o e s , p e a s , a n d b e a n s w o u l d a b s o r b v e r y little. As it t u r n e d o u t , I w a s a l m o s t 100 p e r c e n t w r o n g . I p e r f o r m e d t h e e x p e r i m e n t s w i t h t h e h e l p of my c o l l e a g u e , Peter B a r h a m , w h o did t h e n e c e s s a r y c o o k i n g i n his h o m e kitchen. My wile, Wendy, kept the experimental records and acted as u m p i r e in cases of d i s p u t e . O u r p r o c e d u r e w a s s i m p l e . We d r e w up a list of t h e m o s t c o m m o n i n g r e d i e n t s in a traditional roast d i n n e r , w e i g h e d t h e m , c o o k e d t h e m separately, w e i g h e d t h e m again, s o a k e d t h e m i n t h e g r a v y specified b y t h e a d v e r t i s e r s , w i p e d off t h e excess gravy, a n d w e i g h e d t h e m yet a g a i n . For g o o d luck, w e m e a s u r e d t h e d i m e n s i o n s o f t h e food pieces b e f o r e a n d after c o o k i n g , following t h e basic scientist's principle of m e a s u r i n g e v e r y t h i n g t h a t m i g h t c o n c e i v a b l y be relevant. S o m e of t h e w e i g h t c h a n g e s w e r e o n l y a fraction of a g r a m . I t s o o n b e c a m e a p p a r e n t t h a t Peter's k i t c h e n scales w e r e n o t sufficiently a c c u r a t e , so we b o r r o w e d a t o p - l o a d i n g b a l a n c e t h a t w a s n o r m a l l y used to w e i g h o u t small q u a n t i t i e s of fine c h e m i c a l s , c l e a n e d off t h e m o r e p o i s o n o u s of t h e r e s i d u e s , a n d started again.


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O u r first surprise w a s that roast m e a t d o e s not t a k e up a n y gravy at all — n o n e . T h e s e c o n d w a s t h a t m a s h e d p o t a t o d o e s not t a k e up gravy e i t h e r — in fact, m a s h e d p o t a t o loses w e i g h t w h e n d i p p e d i n gravy. T h e r e w e r e m o r e s u r p r i s e s t o follow. Peas a n d b e a n s , it t u r n e d o u t , t a k e up q u i t e a lot of gravy. So do roast v e g e t a b l e s ( u p to 30 p e r c e n t in t h e case oi roast p o t a t o e s ) . For s o m e v e g e t a b l e s , s u c h as p a r s n i p s , t h e a m o u n t of gravy a b s o r b e d t u r n e d o u t t o d e p e n d o n h o w t h e v e g e t a b l e w a s cut b e f o r e c o o k i n g . T h e a m o u n t o i g r a v y t a k e n u p also seemed to depend on which end of the cooked vegetable was d i p p e d in t h e gravy. We p u t o u r results t o g e t h e r in a table, w h e r e we i n c l u d e d t h e t r a d i t i o n a l English Yorkshire p u d d i n g , a p o r o u s d o u g h that t a k e s u p a n i n c r e d i b l e a m o u n t o f gravy, a n d b r e a d , w h i c h m a n y p e o p l e use t o m o p u p excess gravy. T h e results a r e s h o w n in Figure 8 . 1 .

W h a t w e r e w e t o m a k e o i all this? T h e simplest p i c t u r e t h a t we could t h i n k of w a s t h a t t h e m o i s t u r e lost in c o o k i n g leaves a void v o l u m e that can be refilled w i t h gravy (Figure 8.2). Was t h e r e s o m e w a y t h a t w e could test this p i c t u r e ? T h e r e w a s . W e h a d w e i g h e d t h e m a t e r i a l s b e f o r e a n d after cooking, s o w e could w o r k o u t t h e p e r c e n t a g e m o i s t u r e loss d u r i n g c o o k i n g . If this w a s t h e s a m e as t h e p e r c e n t a g e w e i g h t

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gain w h e n t h e c o o k e d food w a s d i p p e d i n gravy, o u r m o d e l w a s p r o v e d , o r a t least e x t r e m e l y well s u p p o r t e d . A s e v e r y cook k n o w s , t h o u g h , s o m e foods s h r i n k w h e n t h e y a r e c o o k e d , r e d u c i n g t h e space available for refilling by gravy. So we h a d to i n c l u d e a c o r r e c t i o n factor, c a l c u l a t e d from t h e c h a n g e in t h e physical d i m e n s i o n s of t h e food, to a l l o w for this s h r i n k a g e effect. I t w a s j u s t a s well t h a t w e h a d t a k e n t h e a p p r o p r i a t e m e a s u r e m e n t s . T h e s h r i n k a g e factor w a s small for m o s t foods, b u t for m e a t i t t u r n e d o u t t o a c c o u n t c o m p l e t e l y for t h e w a t e r loss, a n d t h e r e w a s n o void v o l u m e left for t h e gravy t o e n t e r . T h a t w a s o n e p u z z l e e x p l a i n e d . A n o t h e r p u z z l e concerned the peas and beans, which do not shrink w h e n c o o k e d — if a n y t h i n g , t h e y swell. A closer look s o o n r e v e a l e d t h e a n s w e r — t h e o u t e r casing of p e a s b e c o m e s loose, a n d t h e seeds d r o p o u t o f m a n y b e a n s , i n b o t h cases l e a v i n g void volu m e s t h a t f i l l u p w h e n t h e v e g e t a b l e i s d i p p e d i n gravy. That was a n o t h e r puzzle explained. The third query concerned the m a s h e d p o t a t o e s . This t i m e w e u s e d t h e H e r c u l e Poirot a p p r o a c h , a n d o u r little gray cells, fed by s u i t a b l e w i n e , s o o n rem i n d e d us t h a t p o t a t o m a s h e d w i t h a little milk is a l r e a d y totally s a t u r a t e d w i t h liquid, a n d h a s n o r o o m for m o r e . With t h e s e p r o b l e m s o u t o f t h e w a y , w e sat d o w n t o c o m p a r e t h e p e r c e n t a g e m o i s t u r e loss (corrected lor s h r i n k a g e ) w i t h t h e p e r c e n t a g e g r a v y u p t a k e for t h e v a r i o u s foods t h a t w e h a d c o o k e d . I f o u r h y p o t h e s i s w a s right, t h e n t h e t w o q u a n t i t i e s s h o u l d h a v e b e e n t h e s a m e for e a c h food. T h e y w e r e , w i t h a c l o s e n e s s of fit t h a t w o u l d h a v e pleased a n y e x p e r i m e n t a l scientist, as F i g u r e 8.2 s h o w s . O u r m o d e l s e e m e d p r e t t y good, a l t h o u g h t h e r e w a s still p l e n t y left to c h e w over. W h y , for e x a m p l e , did b a k e d p o t a t o e s take up to ten minutes to absorb the m a x i m u m a m o u n t of gravy, w h i l e b a k e d p a r s n i p s t o o k less t h a n a m i n u t e ? W h y did p a r s n i p s cut "across t h e g r a i n " a b s o r b no gravy at all after roasting, w h i l e t h o s e cut l e n g t h w i s e a b s o r b e d up to 10 perc e n t ? W h y did r o a s t e d v e g e t a b l e s t a k e u p m o r e gravy t h r o u g h t h e side t h a t h a d b e e n i n c o n t a c t w i t h t h e r o a s t i n g p a n ? T h e s e q u e s t i o n s d i d n ' t b o t h e r t h e m e d i a , w h o w e r e in-


1 55

Figure 8.2: Gravy U p t a k e Ratings (Percentage of Dry Weight).

trigued b y t h e idea t h a t science h a d s o m e t h i n g t o say a b o u t s o m e t h i n g a s h o m e l y a s gravy, a n d t h a t a scientist h a d c o m e up with a "Gravy Equation." They bothered me, though, because u n a n s w e r e d q u e s t i o n s a r e a l w a y s a b o t h e r to a scientist. T h e a n s w e r s w e r e u n l i k e l y t o b e useful t o m a i n s t r e a m science, like R o m f o r d ' s o b s e r v a t i o n s o n a p p l e pies, o r B e n j a m i n F r a n k lin's insight after s e e i n g ship's cooks toss t h e i r greasy w a t e r o v e r b o a r d . T h e best I could h o p e for w a s t h a t s o m e of t h e a n swers m i g h t b e r e l e v a n t t o r e s t a u r a n t a n d c o o k i n g practice — in o t h e r w o r d s , t h e science of e a t i n g .

Chewing

T h e science of e a t i n g w a s defined by t h e satirist A m b r o s e Bierce in his Devil's Dictionary as " p e r f o r m i n g successively ( a n d successfully) t h e acts of mastication, h u m e c t a t i o n a n d deglutition" — in o t h e r w o r d s , biting a n d c h e w i n g , m i x i n g t h e c h e w e d food w i t h saliva, a n d s w a l l o w i n g t h e result, f o n c e a t t e n d e d a

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h o w to d u n k a

doughnut

m e e t i n g o n t h e science o f g a s t r o n o m y w h e r e this w h o l e process w a s d i s p l a y e d in a s t o m a c h - t u r n i n g X-ray v i d e o t h a t s h o w e d a s h a d o w y skull, c o m p l e t e w i t h spectacles, r h y t h m i cally c h e w i n g a n d e v e n t u a l l y s w a l l o w i n g a b o l u s of food (Figu r e 8.3). F o r t u n a t e l y , n o t m a n y of us get to v i e w e a t i n g in this way, u n l e s s o u r e a t i n g p a r t n e r s a r e particularly o p e n - m o u t h e d . O n c e t h e food d i s a p p e a r s i n t o o u r o w n m o u t h s , all t h a t m a t ters is t h e ff avor, or gout.

Figure 8.3: X-Ray Video of C h e w i n g H e a d .

T h e p e r s o n w h o s h o w e d t h e film w a s c o n c e r n e d w i t h w h a t h a p p e n s w h e n people experience problems in eating, and was u s i n g t h e film t o s h o w w h a t " n o r m a l " e a t i n g l o o k s like. O n e o f his c o n c l u s i o n s w a s t h a t w e t e n d t o o r i e n t a s y m m e t r i c pieces of food w i t h t h e l o n g e d g e parallel to t h e line of o u r t e e t h , a n d t h a t t h e pieces o f c h e w e d m a t e r i a l from t h e t w o e n d s d o n o t m i x . If t h e tastes at t h e t w o e n d s a r e different, as t h e y will be on a slice of t o a s t w i t h , say, p a t e on o n e e n d t h e y will n o t mix initially as we c h e w . O n e will stay on t h e right side of t h e m o u t h , a n d t h e o t h e r will stay o n t h e left. Clearly, t h e w a y i n w h i c h w e cut a n d p r e s e n t o u r food can affect t h e t a s t e o u t -


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c o m e , a l t h o u g h as far as f k n o w this aspect of food p r e s e n t a t i o n h a s received little o r n o a t t e n t i o n . T h e r e are t w o m a i n p o i n t s t o c h e w i n g . O n e i s t o b r e a k t h e food i n t o pieces small e n o u g h to swallow. T h e o t h e r is to r e lease tastes ( e x p e r i e n c e d b y t h e t o n g u e ) a n d a r o m a s ( e x p e r i e n c e d by t h e back of t h e n o s e ) , b o t h of w h i c h c o n t r i b u t e to t h e final flavor e x p e r i e n c e . T h e tastes a n d a r o m a s , i n t u r n , p r o m o t e t h e flow of saliva, m a k i n g t h e food easier to s w a l l o w . T h e forces t h a t g o i n t o b r e a k i n g u p t h e food a r e t r a n s m i t t e d b o t h b y t h e t e e t h a n d t h e t o n g u e , a n d a r e e x t r a o r d i n a r i l y difficult to m o d e l satisfactorily; far m o r e difficult t h a n t h o s e involved i n s e n d i n g a r o c k e t t o t h e M o o n , w h i c h h a s b e e n m o d e l e d successfully on a n u m b e r of o c c a s i o n s . By " m o d e l " I m e a n w r i t i n g d o w n e q u a t i o n s ( w h i c h m a y b e fed i n t o a c o m p u t e r ) that will predict t h e c o u r s e of e v e n t s . T h e w o r d can also h a v e a practical m e a n i n g : t h e food i n d u s t r y is full of i n s t r u m e n t s t h a t " m o d e l " h o w w e eat o u r food. M o s t o f t h e s e a r e ins t r u m e n t s d e s i g n e d t o m e a s u r e t e x t u r e . T h e y r a n g e from t h e simple pea m a t u r o m e t e r , w h i c h is n o t h i n g m o r e t h a n a s p r i n g - l o a d e d pin t h a t i s s t u c k i n t o p e a s t o m e a s u r e h o w h a r d they are, to complicated i n s t r u m e n t s that mimic the action of a c h e w i n g j a w . All of t h e s e i n s t r u m e n t s , w i t h o u t e x c e p t i o n , are close to useless w h e n it c o m e s to p r e d i c t i n g t h e t e x t u r e , or " m o u t h - f e e l , " of a food w h e n it is a c t u a l l y e a t e n . T h e p r o b l e m , in physical t e r m s , is t h a t c h e w i n g is a h i g h l y " n o n l i n e a r " process: in o t h e r w o r d s , t h e effect is n o t p r o p o r tional to t h e a c t i o n . In t h e case of c h e w i n g , a v e r y small c h a n g e i n t h e w a y w e c h e w can h a v e a h u g e effect o n t h e o u t c o m e . A bite on a g i n g e r s n a p w i t h a force of 4 . 9 9 k i l o g r a m s , for e x a m p l e , m i g h t fail to b r e a k t h e c o o k i e , w h e r e a s a force of 5.00 k i l o g r a m s m a y s h a t t e r it. ft is difficult to s t u d y n o n l i n e a r processes, e v e n in a laboratory, a n d still m o r e difficult to t r a n s late t h e results i n t o practical s i t u a t i o n s . This applies especially w h e n t h e effects p r o g r e s s all t h e w a y d o w n t h e line, a s t h e y d o in c h e w i n g , w h e r e b r e a k i n g up food particles is o n l y t h e first step. As t h e y are b r o k e n u p , t h e particles g a t h e r t o g e t h e r in a l u m p called a bolus, w h o s e r e s p o n s e to t h e forces e x e r t e d by

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t h e t e e t h a n d t o n g u e i s also likely t o b e n o n l i n e a r . T h e b o l u s may, for e x a m p l e , be " s h e a r - t h i c k e n i n g , " b e c o m i n g stiffer as it is c h e w e d on, or " s h e a r - t h i n n i n g , " w h e r e t h e m o r e it is c h e w e d , t h e m o r e liquid-like i t b e c o m e s . T h e n o r m a l b o l u s can s h o w b o t h b e h a v i o r s , a fact t h a t s e e m s t o h a v e b e e n k n o w n t o t h e n i n e t e e n t h - c e n t u r y British p r i m e minister Sir William G l a d s t o n e . Gladstone, a careful a n d patient m a n , r e c o m m e n d e d c h e w i n g e a c h m o u t h f u l of food thirty times. As it t u r n s out, t h e bolus is n o r m a l l y s h e a r - t h i c k e n i n g o v e r this r a n g e , r e a c h i n g its m a x i m u m c o h e s i o n after t h i r t y o r so c h e w s , a p o i n t w h i c h t h e b o d y t a k e s as a signal to swallow. With m o r e chewing, t h e bolus becomes shear-thinning and e v e n t u a l l y b r e a k s u p . A f u r t h e r c o m p l i c a t i o n in t h e analysis of t h e b o l u s is t h e p r e s e n c e of saliva, w h i c h m a k e s solid pieces of food easier to b r e a k u p . Gravy a n d sauces h a v e a similar effect, w h i c h arises b e c a u s e t h e p r e s e n c e of a liquid m a k e s it easier to stretch, b e n d , a n d o p e n cracks in a solid surface. Overall, w e k n o w a lot less a b o u t w h a t h a p p e n s d u r i n g chewing t h a n we do about w h a t h a p p e n s in the interiors oi stars. O n e t h i n g t h a t w e d o k n o w , t h o u g h , i s t h a t c h e w i n g w o r k s , n o t j u s t t o b r e a k food i n t o m a n a g e a b l e bits, b u t also t o release its flavors. This is an a r e a we are n o w l e a r n i n g q u i t e a lot a b o u t , especially w h e n i t c o m e s t o u n d e r s t a n d i n g w h a t h a p p e n s w h e n taste a n d a r o m a m o l e c u l e s r e a c h t h e t o n g u e a n d t h e n o s e respectively.

F l a v o r — A Mixture of T a s t e , A r o m a , a n d P a i n

T h e m o l e c u l e s t h a t a r e released from t h e food b o l u s in t h e process of c h e w i n g i n d u c e t h r e e m a i n s e n s a t i o n s — taste, smell, a n d , surprisingly, p a i n . Taste h a p p e n s , o b v i o u s l y e n o u g h , o n t h e t o n g u e a n d palate, w h i c h can distinguish five basic taste s e n s a t i o n s — hitter, s w e e t , salt, sour, a n d " u m a m i , " described as " m e a t y , brothy, full-flavored." Bitter tastes are e x p e r i e n c e d b e c a u s e t h e m o l e -

a

q u e s t i o n of t a s t e

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culcs t h a t i n d u c e t h e m b i n d t o p a r t i c u l a r p r o t e i n m o l e c u l e s (called r e c e p t o r s ) in a s e n s o r y cell's m e m b r a n e . T h e s e n s o r y cells are g a t h e r e d t o g e t h e r in taste b u d s , w h i c h a r e h o u s e d in g r o u p s o f t h r e e t o f i f t e e n i n t h e tiny b u t visible b u m p s o n t h e t o n g u e called papillae. W h e n a m o l e c u l e b i n d s to a r e c e p t o r (often b e c a u s e t h e m o l e c u l e h a s a s h a p e t h a t a l l o w s it to fit as a " k e y " i n t o t h e r e c e p t o r ' s "lock"), t h e r e c e p t o r p r o t e i n passes a c h e m i c a l m e s s a g e to t h e inside of t h e cell to say that b i n d i n g has o c c u r r e d . T h e cell's r e s p o n s e is to e m i t an electrical signal that is sent to t h e b r a i n , w h i c h registers, "Ah, bitter!" Bitter tastes a r e t h e r e for a r e a s o n : to w a r n us a g a i n s t e a t i n g a p a r ticular food, often b e c a u s e it is p o i s o n o u s ("bitter a l m o n d s , " for e x a m p l e , c o n t a i n traces of c y a n i d e ) . It is surprising, t h e n , that s o m e of o u r foods of c h o i c e (such as b e e r a n d d a r k c h o c o late) o w e m u c h o f t h e i r a p p e a l t o b i t t e r n e s s , a n d t h e r e i s n o real e x p l a n a t i o n w h y this s h o u l d be so, a l t h o u g h it is n o t e w o r t h y t h a t t h e m a j o r i t y o f " p r e f e r r e d " bitter foods a r e p h a r macologically active. W e h a v e s o m e sixty different r e c e p t o r s for c o m p o u n d s t h a t taste bitter; w h e n a p e r s o n is missing o n e of these receptors, they b e c o m e "bitter-blind" to the comp o u n d s t h a t it r e s p o n d s to. A r o u n d a q u a r t e r of t h e p o p u l a tion, for e x a m p l e , is genetically b i t t e r - b l i n d to t h e c o m p o u n d p h e n y l t h i o c a r b a m i d e , w h i c h is d e t e c t e d as incredibly bitter by the remaining 75 percent. Another quarter of the population (mostly w o m e n ) s e e m to be b i t t e r n e s s supertasters, able to d e tect bitter c o m p o u n d s at a b n o r m a l l y l o w levels. In t h e s e p e o p l e t h e papillae a r e tightly c l u s t e r e d a n d s u r r o u n d e d by a u n i q u e ring s t r u c t u r e , w h o s e f u n c t i o n i s n o t yet k n o w n . T h e r e a r e t a s t e b u d s t h a t r e s p o n d t o b i t t e r n e s s all o v e r t h e tongue, a l t h o u g h most are concentrated towards the back. Taste b u d s t h a t r e s p o n d t o s w e e t n e s s a r e c o n c e n t r a t e d t o w a r d s t h e front, w h i c h is h a r d l y s u r p r i s i n g as it is this part of t h e t o n g u e t h a t first e n c o u n t e r s t h e lactose ( o n e of t h e s w e e t e s t of sugars) in m o t h e r ' s milk. Curiously, " s w e e t - b l i n d n e s s " is p r a c tically u n k n o w n , p e r h a p s b e c a u s e a taste for s w e e t n e s s is a survival trait. T h e o t h e r taste t h a t uses a r e c e p t o r is t h e c o n t r o v e r s i a l

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" u m a m i , " a taste described v a r i o u s l y as " b r o t h y " or " m e a t y , " a n d w h i c h I h a v e n a m e d t h e " W o w ! " factor in a n e w s p a p e r c o l u m n . It is i n d u c e d by m o n o s o d i u m g l u t a m a t e , t h e wellk n o w n MSG t h a t is f r e q u e n t l y a d d e d to C h i n e s e food in p a r ticular as a flavor e n h a n c e r . M S G o c c u r s n a t u r a l l y in m a n y foods, i n c l u d i n g t o m a t o e s a n d P a r m e s a n c h e e s e . It exists in t h e c h e e s e as visible w h i t e crystals t h a t can be dissolved in w a ter, l e a v i n g a c h e e s e distinctly lacking in flavor. U m a m i h a s b e e n claimed to be a s e p a r a t e t a s t e b e c a u s e a rec e p t o r for g l u t a m a t e h a s b e e n d i s c o v e r e d o n t h e t o n g u e , but t h e r e i s still s o m e a r g u m e n t w h e t h e r MSG (and s o m e o t h e r c o m p o u n d s t h a t also b i n d to t h e r e c e p t o r ) itself h a s a s e p a r a t e taste or n o t . P e r h a p s t h e c h o i c e itself is a m a t t e r of t a s t e . T h e t w o o t h e r tastes — saltiness a n d s o u r n e s s — use different t y p e s of r e c e p t o r a n d a r e g e n e r a l effects of acid (for s o u r n e s s ) or salt on t h e t o n g u e as a w h o l e . Tastes can affect e a c h o t h e r in s u r p r i s i n g w a y s . O n e is t h e w e l l - k n o w n e n h a n c i n g effect of a small a m o u n t of salt on t h e p e r c e p t i o n of s w e e t n e s s , w h i c h is w h y recipes for s w e e t s c o n e s often specify t h e a d d i t i o n of a p i n c h of salt. Salt can also affect t h e p e r c e p t i o n of b i t t e r n e s s . I o n c e p a r t i c i p a t e d in a tasting of red w i n e w h e r e w e w e r e a s k e d t o assess t h e b i t t e r n e s s c a u s e d by the presence of tannins, which are universal c o m p o n e n t s of red w i n e . We w e r e t h e n given s o m e salty c r a c k e r s to eat, a n d a s k e d t o r e p e a t t h e test. T h e b i t t e r n e s s o f t h e w i n e w a s definitely d i m i n i s h e d , w h i c h i s p e r h a p s o n e r e a s o n w h y red w i n e goes well w i t h s a v o r y food. Bitter foods can s a t u r a t e t h e b i t t e r n e s s r e c e p t o r s a n d t h u s w i p e o u t t h e b i t t e r n e s s of a s u b s e q u e n t l y e a t e n food, w h i c h is w h y chefs avoid s u c h c o m b i n a t i o n s o r p r o g r e s s i o n s . Try d r i n k ing s o m e t o n i c w a t e r b e f o r e e a t i n g y o u r n e x t piece of dark c h o c o l a t e . T h e b i t t e r n e s s of t h e c h o c o l a t e will be e l i m i n a t e d , leaving o n l y t h e taste a n d t h e m o u t h - f e e l o f w a x . T h e r e is also a w e l l - e s t a b l i s h e d r e l a t i o n s h i p b e t w e e n a liking for s w e e t t h i n g s a n d a liking lor a l c o h o l . B o t h of t h e s e m a t e r i als s e e m t o a c t i v a t e t h e s a m e n e r v e signals t o t h e b r a i n . Conversely, a n i n d u c e d a v e r s i o n t o s w e e t t h i n g s can i n d u c e a n


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a v e r s i o n to alcohol, a l t h o u g h so far as I k n o w this effect h a s so far o n l y b e e n o b s e r v e d in m i c e . Taste is c o m p l i c a t e d e n o u g h , b u t t h e c o m p l i c a t i o n s m u l t i p l y w h e n i t c o m e s t o a r o m a , w h e r e t h e r e a r e o v e r 3,000 t y p e s o f r e c e p t o r to be c o n s i d e r e d , 2 , 0 0 0 of w h i c h are active in h u m a n s . We have most of these receptors in c o m m o n , but hardly a n y o f u s h a s e x a c t l y t h e s a m e set. E v e n for t h e limited r a n g e of o d o r s so far s t u d i e d , t h e r e a r e s o m e for w h i c h o n l y 10 p e r c e n t of t h e p o p u l a t i o n h a v e a receptor, o t h e r s for w h i c h a r o u n d f p e r c e n t of t h e p o p u l a t i o n a r e missing a receptor, a n d some twenty or thirty odors in b e t w e e n these t w o extremes. It is likely, t h e n , t h a t e a c h of us h a s an e x p e r i e n c e t h a t is a little, or e v e n a lot, different w h e n it c o m e s to picking up t h e a r o m a of a m e a l . A case in p o i n t is t h e f a m o u s truffle, described by Rossini as t h e M o z a r t of fungi, w h e r e s o m e 40 p e r c e n t of t h e p o p u l a t i o n a r e "tone-deaf" t o t h e c e n t r a l a r o m a t h a t g o u r m e t s rave a b o u t . E v e n a m o n g t h o s e w h o can detect this a r o m a , t h e effect r a n g e s from s e n s u a l a r o u s a l t o o u t r i g h t r e p u l s i o n . A r o m a is g e n e r a l l y m o r e i m p o r t a n t t h a n taste w h e n it c o m e s t o Ilavor p e r c e p t i o n . This p o i n t c a n b e s h o w n very clearly b y c u t t i n g a n a p p l e a n d a n o n i o n i n t o e q u a l - s i z e c u b e s , ami h a v i n g a friend feed t h e m to y o u in r a n d o m o r d e r w h i l e you p i n c h y o u r n o s e s h u t a n d close y o u r e y e s . W i t h o u t t h e a r o m a a n d visual cues, m o s t p e o p l e find it impossible to distinguish b e t w e e n t h e t w o foods, e v e n t h o u g h t h e i r flavors a r e very different. E v e n w i t h a r o m a cues, p e o p l e c a n n o t a l w a y s distinguish b e t w e e n a p p a r e n t l y dissimilar foods. G r u y e r e c h e e s e a n d h o n e y , for e x a m p l e , are v e r y difficult to distinguish b y a r o m a a l o n e . A r o m a r e a c h e s us in o n e of t w o w a y s . T h e first is from t h e outside, as w h e n we initially d e t e c t t h e smell of a m e a l . T h e second i s from t h e inside, w h e n t h e a r o m a r e a c h e s t h e b a c k o f t h e n o s e retronasally — t h a t is, via t h e b a c k of t h e m o u t h a n d n o s e after w e h a v e t a k e n t h e food i n t o o u r m o u t h s . A r o m a s that r e a c h u s from t h e o u t s i d e s e e m m u c h m o r e p o w e r f u l w h e n we sniff, b u t it is o n l y r e c e n t l y t h a t a g r o u p of scientists, led by A n d y Taylor at t h e U n i v e r s i t y of N o t t i n g h a m , h a v e

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found out why. The a n s w e r is not that we take in m o r e of the a r o m a , b u t t h a t we t a k e it in at a m o r e rapidly v a r y i n g rate. It is t h e r a t e at w h i c h a r o m a c o n c e n t r a t i o n c h a n g e s in t h e n o s e , r a t h e r t h a n t h e c o n c e n t r a t i o n itself, t h a t d e t e r m i n e s h o w strong we perceive the aroma to be. T h e s a m e effect h a p p e n s from t h e inside. This w a s o n l y disc o v e r e d t h r o u g h t h e u s e of a clever piece of t e c h n o l o g y d e v e l o p e d by A n d y a n d his t e a m called "MSMose," a l t h o u g h I prefer t h e slightly m o r e s u r r e a l n a m e o f " N o s e S p a c e . " T h e t e c h n i q u e a n a l y z e s food a r o m a s r e l e a s e d t o t h e b a c k o f t h e n o s e d u r i n g c h e w i n g a n d m e a s u r e s t h e i r c o n c e n t r a t i o n i n t h e n o s e i n real t i m e (Figure 8.4).

Figure 8.4: M S N o s e . Aroma molecules from chewed food reach the olfactory bulb (where smelling takes place) retronasally, i.e., from the back of the mouth. M S N o s e takes samples of each breath to analyze the aroma molecules that have reached the back of the nose at that time.

It d o e s this by t a k i n g a s a m p l e of e a c h b r e a t h as t h e subject c h e w s . T h e s a m p l e is t a k e n via a t u b e i n s e r t e d ( q u i t e p a i n lessly) i n t o t h e subject's n o s e . This h a r d l y c r e a t e s ideal c o n d i t i o n s for g o u r m e t e n j o y m e n t , b u t it is all w o r t h w h i l e in t h e c a u s e of science, as I d i s c o v e r e d w h e n I used it to s t u d y t h e el-


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feet of d u n k i n g a c o o k i e on flavor r e l e a s e . This project w a s a f o l l o w - u p t o t h e original " c o o k i e - d u n k i n g " e x e r c i s e . T h e p r e m i s e , o r h y p o t h e s i s , t h a t w e w e r e testing w a s t h a t d u n k i n g i m p r o v e s c o o k i e flavor, a n d t h a t it d o e s so b e c a u s e t h e d r i n k helps to release a r o m a m o l e c u l e s from t h e solid m a t r i x of t h e cookie. Hot tea, w e e x p e c t e d , w o u l d give t h e m o s t release b y w a r m i n g u p t h e volatile a r o m a t i c m a t e r i a l s . For c o m p l e t e n e s s , t h o u g h , w e tried cold tea, h o t a n d cold c h o c o l a t e , h o t a n d cold milk, a n d e v e n o r a n g e j u i c e . A s t h i n g s t u r n e d o u t , i t w a s j u s t a s well t h a t w e did. My g u i d e in t h e use of M S N o s e for t h e s e e x p e r i m e n t s w a s Rob Linforth, w h o b a d b e e n h a p p i l y u n e m p l o y e d u n t i l h e j o i n e d A n d y ' s g r o u p as a result of a c a s u a l c h a t o u t s i d e t h e local n e w s d e a l e r , a n d w h o n o w d i r e c t e d t h e u s e o f t h e t e c h n i q u e . R o b sports a m a g n i f i c e n t , f o o t - l o n g red b e a r d , s y m m e t rically divided to reveal t h e fact t h a t he s e i d o m w e a r s a tie, a n d w a s ideal p h o t o g e n i c m a t e r i a l for t h e a d v e r t i s e r s w h o w e r e s u p p o r t i n g t h e project. T h e o n l y p e r s o n w h o d i d n ' t t h i n k so w a s Rob, w h o s e e x c e l l e n c e as a scientist is m a t c h e d o n l y by his dislike o f c a m e r a s , especially w h e n t h e y i n t e r f e r e w i t h t h e s m o o t h r u n n i n g of his l a b o r a t o r y . T h e r e w a s v e r y little t i m e t o u s e t h e M S N o s e i n b e t w e e n m o r e s e r i o u s r e s e a r c h a p p l i c a t i o n s , b u t t h a n k s t o Rob's e x p e r tise w e m a n a g e d it, a n d a n e x p e r i m e n t t h a t s h o u l d h a v e t a k e n w e e k s w a s c o m p l e t e d i n j u s t o n e day, albeit w i t h t h e o d d s h o r t c u t . R o b k i n d l y sacrificed t h a t day, a l t h o u g h 1 felt at t h e t i m e t h a t m y o w n sacrifice w a s j u s t a s great, since I h a d t o d u n k a n d eat 140 c o o k i e s w i t h a stainless steel t u b e t h r u s t u p my n o s e , c h e w i n g for a p r e s c r i b e d c o u n t w h i l e R o b pressed b u t t o n s a n d r e c o r d e d a n d a n a l y z e d t h e results. T h e o u t c o m e w a s v e r y s u r p r i s i n g . Hot tea, i t t u r n e d o u t , h a d no effect w h a t s o e v e r on t h e c o n c e n t r a t i o n of a r o m a m o l e c u l e s released from t h e c o o k i e a n d r e a c h i n g t h e b a c k o f t h e n o s e . W e later w o r k e d o u t t h a t this w a s b e c a u s e t h e a r o m a m o l e cules w e r e w a s h e d d o w n t h e t h r o a t before t h e y h a d a c h a n c e t o r e a c h t h e n o s e . T h e d r i n k s t h a t w o r k e d really well w e r e cold milk a n d , b e t t e r again, cold c h o c o l a t e , ft w a s easier to find

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a r e t r o s p e c t i v e e x p l a n a t i o n t h a n it h a d b e e n to p r e d i c t this r e sult. T h e e x p l a n a t i o n I e v e n t u a l l y c a m e u p w i t h w a s b a s e d o n t h e fact t h a t m o s t a r o m a m o l e c u l e s dissolve easily in fats a n d oils, b u t n o t i n w a t e r ( w h i c h i s o n e r e a s o n w h y "fat-free" foods t e n d to be so dull to e a t ) . Milk c o n t a i n s fatty globules, w h i c h a b s o r b a r o m a s from t h e d u n k e d c o o k i e a n d w h i c h coat t h e t o n g u e a n d t e n d t o linger i n t h e m o u t h w h e n t h e d u n k e d c o o k i e is e a t e n . T h e s e g l o b u l e s will g r a d u a l l y r e l e a s e a r o m a s t h a t t h e y h a v e a b s o r b e d from t h e cookie, e v e n t h o u g h t h e c o o k i e itself h a s l o n g since d i s a p p e a r e d d o w n t h e t h r o a t . C h o c o l a t e milk, o n this h y p o t h e s i s , s h o u l d b e e v e n m o r e effective, b e c a u s e it c o n t a i n s cocoa solids, w h i c h a r e fatty a n d w h i c h will also a b s o r b a r o m a m o l e c u l e s from t h e c o o k i e . S u c h solids also h a n g a r o u n d in t h e m o u t h (just look in a child's m o u t h after h e o r s h e h a s h a d a c h o c o l a t e d r i n k ) , a n d will g r a d u a l l y r e l e a s e a r o m a s a b s o r b e d from a d u n k e d c o o k i e . T h a t w a s t h e h y p o t h e s i s , w h i c h w e w e r e u n a b l e t o test furt h e r b e c a u s e t h e m a c h i n e h a d t o b e r e t u r n e d t o o t h e r activities. N e v e r t h e l e s s , it m a d e s e n s e , a n d t u r n e d o u t to be a great hit w i t h t h e m e d i a , w h o t u r n e d up in d r o v e s for a series of p h o t o sessions, m u c h to Rob's d i s m a y . O n e of t h o s e sessions, a live b r o a d c a s t on CBS television's Early Show, p r o v i d e d incid e n t a l e v i d e n c e of t h e e x t e n t to w h i c h scientists t r a v e l w h e n a friend from t h e n e x t - d o o r l a b o r a t o r y b a c k h o m e r a n g t o say t h a t h e h a d s e e n m e o n T V i n his N e w York h o t e l r o o m t h e previous morning. M S N o s e h a s r e v e a l e d u n e x p e c t e d facets o f t h e w a y t h a t w e d e t e c t a n d i n t e r p r e t a r o m a s , ft h a s s h o w n , for e x a m p l e , that m a n y o f t h e a r o m a s r e l e a s e d b y a t o m a t o w h e n w e eat i t a r e n o t p r e s e n t i n t h e original t o m a t o . T h e a r o m a s t h a t o u r b r a i n s i n t e r p r e t a s flavor a r e p r o d u c e d m a i n l y o n c e t h e t o m a t o i s d a m a g e d b y c u t t i n g o r biting, p r o c e s s e s t h a t b u r s t t h e cells w i t h i n t h e t o m a t o , p e r m i t t i n g t h e c o n t e n t s t o m i x a n d react chemically. A n o t h e r success of M S N o s e c o n c e r n s t h e effect of s w e e t n e s s o n t h e p e r c e p t i o n o f m i n t flavor. M o s t p e o p l e will h a v e n o ticed t h a t a m i n t y c h e w i n g g u m slowly loses its flavor as it is


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c h e w e d . G u m c h e w e r s find t h a t t h e flavor c a n b e refreshed b y t a k i n g a sip of a s w e e t d r i n k . E x p e r i m e n t s w i t h M S N o s e h a v e shown that the concentration of minty a r o m a molecules in the nose is u n c h a n g e d t h r o u g h o u t the w h o l e process. It seems that the nose gradually becomes accustomed to the presence of a m i n t y a r o m a , a n d its r e s p o n s e b e c o m e s d u l l e d . Sugar, w h i c h has n o direct effect o n t h e n o s e , n e v e r t h e l e s s s t i m u l a t e s t h e b r a i n to " n o t i c e " t h a t t h e r e a r e still signals c o m i n g in w h i c h say t h a t t h e r e is a m i n t y a r o m a p r e s e n t . This is an e x t r a o r d i n a r i l y clear case of h o w o n e s e n s e c a n affect a n o t h e r . T h e r e a r e m a n y o t h e r s . M e n t h o l , for e x a m p l e , t h e active c o m p o n e n t of m i n t y s w e e t s , can m o d u l a t e o u r p e r c e p t i o n s of h o t or cold. A m e n t h o l s o l u t i o n in w a r m w a t e r will feel h o t t e r in the m o u t h t h a n water at the s a m e t e m p e r a t u r e . Conversely, a m e n t h o l s o l u t i o n in cold w a t e r will feel colder t h a n w a t e r at the s a m e t e m p e r a t u r e . S o m e " p u r e " o d o r s , s u c h a s p i n e n e (pine o d o r ) a n d c a d i n e n e (juniper, an i m p o r t a n t c o m p o n e n t of gin), can e v e n p r o d u c e a sense of p a i n . T h e n e r v e s c o n c e r n e d a r e called t h e trigeminal n e r v e s . It is t h r o u g h t h e s e t h a t we feel t h e a c u t e p a i n of a blocked s i n u s . W h e n we sniff p i n e n e , c a d i n e n e , or a small range of other odors, the trigeminal nerves are stimulated. An oddity of this effect, as carefully c o n t r o l l e d e x p e r i m e n t s h a v e revealed, is t h a t we c a n ' t locate w h i c h nostril t h e o d o r is c o m ing from. That's not so m u c h of a p r o b l e m w h e n we eat food c o n t a i n ing hot chili p e p p e r s , w h e r e t h e pain c o m e s i n s t e a d from t h e t o n g u e . T h e h o t n e s s of chili p e p p e r s is d u e to a family of t a s t e less, o d o r l e s s c h e m i c a l c o m p o u n d s called capsaicinoids, w h i c h are m a n u f a c t u r e d a n d s t o r e d i n t h e s e e d - p r o d u c i n g g l a n d s along t h e ribs of t h e fruit. T h e capsaicinoid m o l e c u l e s b i n d tightly to t h e surfaces of t r i g e m i n a l cells in t h e m o u t h , n o s e , throat, a n d s t o m a c h , w h o s e n o r m a l j o b i s t o w a r n t h e b r a i n o f p a i n - c a u s i n g d a m a g e . Capsaicinoid b i n d i n g c a u s e s t h e cells t o send t h e s a m e m e s s a g e , e v e n t h o u g h t h e r e i s n o a c t u a l d a m age. This is w h a t t h e chili p e p p e r addict h a s b e e n w a i t i n g lor. A c c o r d i n g t o o n e u n p r o v e n t h e o r y , t h e b r a i n r e s p o n d s b y

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h o w to dunk

a doughnut

releasing e n d o r p h i n s , n a t u r a l painkillers t h a t c r e a t e a feeling of e u p h o r i a in t h e a b s e n c e of p a i n ( t h e s o u r c e of " r u n n e r ' s h i g h " ) . An a l t e r n a t i v e theory, also u n p r o v e n , ascribes t h e att r a c t i o n of chili p e p p e r s to " b e n i g n m a s o c h i s m , " like t h e thrill of riding on a roller-coaster, w h e r e t h e rider can e x p e r i e n c e feelings of fear in safety, k n o w i n g t h a t all will be OK in t h e e n d .

How D o e s C h e w i n g R e l e a s e the F l a v o r ?

T h e effect t h a t a m o l e c u l e p r o d u c e s , w h e t h e r it is p a i n , a r o m a , or taste, can o n l y o c c u r if t h e m o l e c u l e is released from t h e food a n d can r e a c h r e c e p t o r s o r o t h e r sites i n t h e m o u t h a n d n o s e . H o w d o e s this h a p p e n ? This q u e s t i o n , o b v i o u s l y a n i m p o r t a n t o n e for g a s t r o n o m y , w a s t h e c e n t r a l t h e m e o f m y s p e e c h in P h i l a d e l p h i a , b u t it is n o t a q u e s t i o n t h a t is often a s k e d . W h e n I b e g a n h u n t i n g a r o u n d i n t h e r e l e v a n t literat u r e , I f o u n d t h a t t h e few a n s w e r s p o s i t e d h a d n o t stood u p t o e x p e r i m e n t a l test. T h e c o m m o n p i c t u r e s e e m e d t o b e t h a t a r o m a m o l e c u l e s diffuse o u t of t h e food b o l u s a n d a r e t h e n s w e p t b y air c u r r e n t s (caused b y b r e a t h i n g ) t o t h e b a c k o f t h e n o s e . T h e p r o b l e m w i t h this p i c t u r e , it s e e m e d to m e , is t h a t t h e b o l u s is g e n e r a l l y a p r e t t y w a t e r y m i x , w h e r e a s most a r o m a m o l e c u l e s dissolve in oils or fats, w h i c h are likely to be dispersed as droplets or particles in t h e b o l u s . I p o i n t e d o u t to m y a u d i e n c e t h a t this leaves t h e a r o m a m o l e c u l e s w i t h t w o p r o b l e m s . T h e first is to get to t h e surface of t h e droplet. T h e seco n d is to get across t h e w a t e r barrier into t h e air space a b o v e . I already had some information about the first problem t h r o u g h e x p e r i m e n t s t h a t I h a d d o n e w i t h chef Fritz Blank in Erice. W e h a d m a d e a flavored m a y o n n a i s e i n t w o w a y s : o n e w a s g e n t l y stirred a n d t h e o t h e r w a s b e a t e n v i g o r o u s l y i n ord e r to m a k e t h e oil d r o p l e t s smaller. T h e flavor of t h e s e c o n d m a y o n n a i s e c a m e t h r o u g h m u c h m o r e strongly t o tasters, partly b e c a u s e t h e d r o p l e t s w e r e s m a l l e r a n d s o t h e flavor m o l e c u l e s took less t i m e to r e a c h t h e surface by diffusion, and


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partly b e c a u s e t h e r e w a s a m u c h larger surface a r e a for t h e m o l e c u l e s t o escape t h r o u g h . W h e n William G l a d s t o n e c l a i m e d t h a t b e c h e w e d e v e r y m o u t h f u l t h i r t y times, h e w a s p r o b a b l y d o i n g t h e right t h i n g a c c o r d i n g t o this e x p e r i m e n t , since c h e w i n g will t e n d t o b r e a k t h e oily c o n s t i t u e n t s i n t h e food i n t o s m a l l e r a n d s m a l l e r droplets, m a k i n g it easier for a r o m a m o l e c u l e s to e s c a p e . T h e y still h a v e t o m a k e t h e i r w a y across a w i d e w a t e r y e x p a n s e , h o w e v e r . It w a s not clear to me h o w this could h a p p e n u n t i l I remembered some experiments that I had d o n e years previously in c o n n e c t i o n with an entirely different p r o b l e m , t h a t of m i n e r a l flotation in m i n i n g . In this t e c h n i q u e t h e o r e is c r u s h e d , placed in a vat of w a t e r a n d d e t e r g e n t , a n d b u b b l e s are b l o w n u p t h r o u g h it. T h e b u b b l e s c a p t u r e t h e desirable m i n e r a l particles in t h e o r e a n d carry t h e m to t h e t o p of t h e t a n k , leaving u n w a n t e d materials s u c h a s q u a r t z b e h i n d . M y task w a s t o investigate h o w t h e particles are selectively c a p t u r e d . It t u r n e d o u t t h a t t h e surfaces of t h e m i n e r a l particles a r e oil-like (the t e c h n i c a l t e r m is hydrophobic), a n d w h e n an air b u b b l e a p p r o a c h e s t h e m t h e film o f w a t e r i n b e t w e e n t h e p a r ticles s u d d e n l y collapses at a t h i c k n e s s of a m i c r o m e t e r or so, a l l o w i n g t h e air b u b b l e to stick to t h e solid surface. " C o u l d t h e a q u e o u s film s e p a r a t i n g an oil d r o p from t h e air in a food b o lus collapse in t h e s a m e w a y w h e n an oil d r o p gets w i t h i n a micrometer or so of t h e surface?" I w o n d e r e d out loud to my a u d i e n c e . "Could t h e t h i n film of w a t e r b e t w e e n t h e droplet a n d t h e air s u d d e n l y b u r s t to let t h e d r o p l e t a n d its c a r g o of a r o m a m o l e c u l e s o u t i n t o t h e air space a b o v e ? " T h e a q u e o u s film c o n t a i n s m o r e t h a n just w a t e r , of c o u r s e — it is full of salts, p r o t e i n s from t h e food, a n d c a r b o h y d r a t e s b o t h from t h e food a n d t h e saliva. T h e p r e s e n c e of t h e s e m a t e r i a l s m a y affect t h e c h a n c e of a w a t e r film b u r s t i n g ; but n o b o d y k n o w s , b e c a u s e n o b o d y , t o m y k n o w l e d g e , h a s looked. I s p e c u l a t e d to my a u d i e n c e , s o m e of w h o m w e r e still eating, t h a t food a r o m a s a r e released in l u m p s , a droplet-full at a t i m e as e a c h d r o p l e t gets close e n o u g h to t h e surface of t h e bolus for t h e w a t e r film b e t w e e n it a n d t h e air to b u r s t (Figure

168


8.5). A r o m a m o l e c u l e s could t h e n diffuse rapidly o u t of t h e d r o p l e t s , p r o v i d i n g a r o m a bursts to t h e n o s e , w h i c h is just w h a t it n e e d s to get t h e full effect, as A n d y Taylor a n d his g r o u p d i s c o v e r e d . As 1 m a d e this s u g g e s t i o n , I noticed t h a i the t a r d y d i n e r s h a d b e g u n t o c h e w t h e i r lood m o r e vigorously. My host, Gary B e a u c h a m p , d i r e c t o r of t h e M o n e l l C h e m i c a l S e n s e s I n s t i t u t e i n P h i l a d e l p h i a , p o i n t e d o u t after t h e talk t h a t t h e m e c h a n i s m t h a t I h a d suggested also a l l o w s for a n e w possibility, w h i c h is t h a t t h e d r o p l e t s t h e m s e l v e s , a n d n o t just m o l e c u l e s diffusing o u t of t h e m , m i g h t be carried on air currents and reach t h e nose as an aerosol, bringing with t h e m not o n l y volatile a r o m a c o m p o u n d s b u t also involatile c o m p o u n d s t h a t could n o t r e a c h t h e n o s e b y a n y o t h e r r o u t e , but w h i c h m i g h t in this w a y play a part in o u r a r o m a e x p e r i e n c e .

Figure 8.5: Taste a n d A r o m a Release from a Food Bolus.

A m o d e l s u c h as t h e o n e a b o v e is o n l y t h e first step in t h e scientific p r o c e s s . T h e p i c t u r e that it p o r t r a y s m a y s o u n d convincing, but t h e r e h a v e b e e n p l e n t y o f m o d e l s t h a t h a v e


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sounded oven more convincing which have turned out to be w r o n g . T h e s e r a n g e from Aristotle's n o t i o n that objects o n l y m o v e if t h e y a r e b e i n g p u s h e d or p u l l e d , to T h o m p s o n ' s " p l u m p u d d i n g " m o d e l of t h e a t o m . E a c h of t h e s e w a s b e l i e v e d in its day, b e c a u s e t h e m o d e l m a d e s e n s e of so m a n y o b s e r v a t i o n s . But testing e v e n t u a l l y p r o v e d t h a t e a c h m o d e l w a s w r o n g . M u c h of t h e s p e c u l a t i v e " s c i e n c e " t h a t a p p e a r s in t h e m e d i a t h e s e days is no m o r e t h a n t h e p r e s e n t a t i o n of a m o d e l d e v e l oped to a c c o u n t for s o m e set of k n o w n facts. No r e p u t a b l e scientific j o u r n a l w o u l d accept s u c h a m o d e l u n l e s s t h e a u t h o r h a d m a d e an effort to check it o u t in s o m e way, u s u a l l y by testing its p r e d i c t i o n s against reality. I could test o u t my m o d e l for a r o m a release, for e x a m p l e , by stirring a food b o l u s a n d m o n i t o r i n g t h e space a b o v e for a s p r a y of oil d r o p l e t s . I could also pass a c u r r e n t of air o v e r a stirred food b o l u s , pass t h e air directly into M S N o s e , a n d w a t c h to see if t h e a r o m a s arrive in b u r s t s . I h a v e n o t yet d o n e e i t h e r of t h e s e t h i n g s , a n d w i t h o u t such testing my m o d e l r e m a i n s j u s t t h a t — a m o d e l . People o u t s i d e science often t h i n k t h a t m o d e l s , s u c h a s t h a t for t h e b e h a v i o r of light w h i c h Einstein p r o p o s e d in his Special T h e o r y ol Relativity, are the sine qua non of science, t h e ultim a t e o u t p u t of t h e scientific m i n d , ft d o e s n o t t a k e an act of g e n i u s , t h o u g h , to devise most scientific m o d e l s — j u s t a little i m a g i n a t i o n . That i m a g i n a t i o n m a y b e fed b y p r i o r k n o w l edge, insight, or e v e n t h e m e m o r y of a d r e a m . In a few cases, the m o d e l s m a y e v e n b e a g e n u i n e p r o d u c t o f g e n i u s . T h e t r u e w o r t h of a n y m o d e l , t h o u g h , is that it is able to pass r i g o r o u s testing. W i t h o u t this, t h e m o d e l i s w o r t h l e s s , n o m a t t e r h o w c o n v i n c i n g it m a y a p p e a r to its c r e a t o r or to o t h e r s . T h e t h e o r y of relativity, h o w e v e r inspired, w o u l d be v a l u e l e s s if it w e r e not for t h e fact t h a t its p r e d i c t i o n s h a v e t u r n e d o u t to be t r u e . On a r a t h e r l o w e r p l a n e , my p i c t u r e of h o w food a r o m a s a r e released will o n l y h a v e v a l u e if it t u r n s o u t to be t r u e . N o r did it need me to d e v e l o p it, a l t h o u g h as far as I k n o w I w a s t h e first to e n u n c i a t e it in public. Six m o n t h s later, I m e n t i o n e d its o u t l i n e s informally at a n o t h e r food c o n f e r e n c e , a n d w a s p r o m p t l y a c c u s e d ( t o n g u e - i n - c h e e k ) of i n d u s t r i a l spying by

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o n e o f t h e o t h e r p a r t i c i p a n t s , w h o h a d , a s i t t u r n e d out, dev e l o p e d a v e r y similar p i c t u r e q u i t e i n d e p e n d e n t l y . It often h a p p e n s t h a t w a y in science, w h i c h is w h y l i n e a r " h i s t o r i e s " of h o w o n e d i s c o v e r y led to a n o t h e r are so m i s l e a d i n g . T h e r e is a c o m m u n i t y of p e o p l e i n v o l v e d in a n y discovery, a n d m o s t of t h e m e m b e r s of t h a t c o m m u n i t y will be well a w a r e , at least at a s u b l i m i n a l level, of w h a t t h e m a j o r u n a n s w e r e d q u e s t i o n s a r e , a n d will h a v e p u t s o m e t h o u g h t i n t o w h a t t h e a n s w e r s might b e . My p i c t u r e of a r o m a release is n o w out in t h e o p e n , as a n y piece of science s h o u l d b e , to be t h o u g h t a b o u t , tested, dissected, a n d used if o t h e r s so w i s h as a starting point for f u r t h e r w o r k . I m a y or m a y n o t do s o m e of t h a t w o r k myself — that d e p e n d s , a s d e t e c t i v e - s t o r y w r i t e r s say, o n m o t i v e a n d o p p o r t u n i t y . E v e n if t h e p i c t u r e t u r n s o u t to be t r u e , it m a y or m a y n o t b e i m p o r t a n t i n t h e overall s c h e m e o f t h i n g s g a s t r o n o m i cal. Like t h e p r e s e n t a t i o n of food on a plate, it is o n l y a first step, a n d is yet to be c h e w e d over, s w a l l o w e d , a n d digested.

9

the physics of sex

I w a s o n c e a s k e d to give a talk to a s c h o o l science club on a n y subject t h a t I c h o s e . I suggested " T h e Physics of Sex," a topic on w h i c h I h a d r e c e n t l y w r i t t e n an article, a n d w a s a little t a k e n a b a c k w h e n t h e o r g a n i z e r a g r e e d . I w a s told later t h a t t h e a u d i e n c e h a d b e e n r a t h e r larger t h a n m o s t m e e t i n g s o f t h e science club, a n d w a s also u n i q u e i n t h a t t h e r e w e r e moreteachers than students present. Even t h e s e n i o r s t u d e n t s w e r e surprisingly v a g u e i n t h e i r k n o w l e d g e of t h e physical aspects of sex. T h e h i g h l i g h t for me c a m e a t t h e e n d o f t h e talk, w h e n a n e a r n e s t a d o l e s c e n t w a n t e d to ask a private q u e s t i o n . "Is it t r u e , " he a s k e d in a c o n spiratorial w h i s p e r , " t h a t if t h e girl is a virgin it goes b a n g ? " I d o n ' t k n o w h o w h e c a m e b y this c u r i o u s belief; b u t a t least it w a s a relatively h a r m l e s s o n e . O t h e r t e e n a g e beliefs m a y h a v e m o r e s e r i o u s c o n s e q u e n c e s . A s u r v e y of British g e n e r a l p r a c t i t i o n e r s in April 2 0 0 1 r e v e a l e d t h a t c u r r e n t a d o l e s c e n t t h i n k i n g m a i n t a i n e d that " P u t t i n g a w a t c h a r o u n d y o u r p e n i s before sex m e a n s t h e radioactivity of t h e dial kills off s p e r m . " Other teenagers believe that standing on a t e l e p h o n e book d u r i n g sex p r e v e n t s c o n c e p t i o n , p r e s u m a b l y b e c a u s e o f s o m e i m a g i n e d effect of gravity on t h e s p e r m . This is a belief t h a t goes back t o Aristotle, w h o t h o u g h t t h a t m a l e s w e r e c o n c e i v e d on t h e right side of t h e w o m b , a n d females on t h e left. He t h e r e f o r e r e c o m m e n d e d t h a t a w o m a n s h o u l d lie o n h e r right side after i n t e r c o u r s e if s h e w a n t e d a m a l e baby, so t h a t t h e sperm w o u l d d r a i n i n this d i r e c t i o n . Aristotle's beliefs w e r e t r a n s m i t t e d in a c u r i o u s h o t c h p o t c h of information a n d m i s i n f o r m a t i o n for m i d w i v e s called Aristotle's Complete Masterpiece, w h i c h a p p e a r e d d u r i n g t h e s e v e n t e e n t h c e n t u r y a n d w a s t h e m o s t w i d e l y used s o u r c e o f i n f o r m a t i o n

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a b o u t sex in t h e E n g l i s h - s p e a k i n g w o r l d up until t h e e n d of t h e n i n e t e e n t h c e n t u r y . Its origin is u n k n o w n — o n l y a little of t h e i n f o r m a t i o n in it c a n be traced back to Aristotle. It w a s b a n n e d in E n g l a n d lor a long t i m e on a c c o u n t of t h e explicit n a t u r e of its illustrations. W h e n I b o u g h t my o w n copy, I f o u n d a n e w s p a p e r c u t t i n g from t h e 1930s inside it w i t h a reader's q u e s t i o n , " W h e r e m a y I b u y a copy of Aristotle's Complete Masterpiece, a n d h o w m u c h m a y I expect to p a y ? " T h e a n s w e r w a s a m o d e l of p r a g m a t i s m : "You m a y n o t b u y a copy of Aristotle's Complete Masterpiece. You m a y e x p e c t to p a y t h r e e - a n d - s i x p e n c e . " Sex is e v e n n o w r e g a r d e d as a s o m e w h a t d u b i o u s t o p i c for a scientist to be discussing o u t s i d e a m e d i c a l setting. I f o u n d this o u t w h e n I w a s a s k e d to give a p r e d i n n e r talk lor a scientific society, a n d c h o s e , o n c e again, "The Physics of S e x " as my t h e m e . Most p e o p l e s e e m e d t o e n j o y t h e talk, b u t o n e m e m b e r of t h e society's e x e c u t i v e sat t h r o u g h it w i t h an air of o b v i o u s a n d d e e p e n i n g d i s a p p r o v a l . I t t u r n e d o u t t h a t h e had b e e n led by my title to t h i n k that I w a s g o i n g to talk a b o u t t h e role of w o m e n in physics. W h a t I did talk a b o u t w a s t h e physical p r o b l e m s t h a t a s p e r m h a s to o v e r c o m e in t h e race to t h e egg, w h i c h i n v o l v e diving, t u n n e l i n g , surfing, a n d e v e n s y n c h r o n i z e d s w i m m i n g . A t every stage, from t h e r o c k e t - p r o p e l l e d l a u n c h to t h e final c o n s t r u c tion of an electrically g u a r d e d r a m p a r t , t h e s p e r m cell's j o u r n e y is a m o d e l of t h e realpolitik of physics, a n d t h e w i n n i n g s p e r m is t h e o n e w i t h t h e greatest m a s t e r y of physics. T h e o d d s for a n y p a r t i c u l a r s p e r m ' s success a r e a b o u t t h e s a m e a s w i n n i n g t h e lottery, b u t t h e r e w a r d is incalculable — life itself.

S t e p 1: P r e p a r i n g for the L a u n c h

M a m m a l i a n species s u c h a s m a n u s e t h e r o c k e t l a u n c h e r t o p r o p e l s p e r m a t o z o a on t h e first stage of t h e i r j o u r n e y . C o n v e n t i o n a l w i s d o m d e c r e e s t h a t t h e l a u n c h e r m u s t b e erect a n d rigid to p e r f o r m its f u n c t i o n , b u t t h e r e is a l w a y s s o m e o n e w h o

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has to be different. O n e rebel, a f o r e r u n n e r of t o d a y ' s sensitive n e w - a g e guys, was an eccentric Australian w h o decided in t h e 1930s t h a t e r e c t i o n s w e r e an u n n e c e s s a r i l y forceful w a y of inserting s p e r m i n t o a f e m a l e p a r t n e r , a n d t h a t m e n of refinement ought to be content to permit the female partner to d r a w t h e flaccid p e n i s in. Not c o n t e n t w i t h m a i n t a i n i n g this w o r t h y policy as a p r i v a t e i n d i v i d u a l , he insisted on p r o c l a i m i n g it publicly e v e r y S u n d a y i n t h e S y d n e y D o m a i n ( a p u b l i c space r e s e r v e d for s o a p b o x d e c l a m a t i o n s ) . In t h e c l i m a t e of t h e d a y this w a s n o t h i n g less t h a n p o r n o g r a p h i c , a n d t h e p o o r m a n w a s d u l y h a u l e d off t o t h e l o c k u p e a c h w e e k , t o b e f i n e d o n t h e M o n d a y a n d r e l e a s e d t o try a g a i n t h e following S u n d a y . Possibly t h e p o l i c e m e n w h o a r r e s t e d h i m w e r e a g h a s t a t w h a t m i g h t h a p p e n if t h e i r w i v e s h e a r d of his a r g u m e n t s a n d t o o k t h e m seriously. A t a n y rate, his a r g u m e n t s h a v e d i s a p p e a r e d i n t o oblivion, a n d t h e r o c k e t l a u n c h e r c o n t i n u e s t o b e u s e d i n t h e erect p o s i t i o n . T h e e r e c t i o n is a m a t t e r of hydrostatics, t h e b r a n c h of physics c o n c e r n e d w i t h fluid p r e s s u r e a n d t h e a p p l i c a t i o n o f t h a t p r e s s u r e in t h e right place. T h e p r e s s u r e in this case is b l o o d p r e s sure, g e n e r a t e d b y t h e p u m p i n g o f t h e h e a r t t o p u s h blood o u t through the arteries and have it return t h r o u g h t h e veins. In t h e p e n i s , t h e a r t e r i e s lie across t h e v e i n s . H o r m o n e s released d u r i n g s e x u a l e x c i t e m e n t relax t h e s m o o t h m u s c l e i n t h e a r t e r y walls. T h e d i s t e n d e d a r t e r i e s press d o w n o n t h e v e i n s a n d stop t h e b l o o d t h a t i s e n t e r i n g t h e p e n i s from e s c a p i n g . T h e result i s a n e r e c t i o n , m a i n t a i n e d b y h y d r o s t a t i c p r e s s u r e . You can get t h e s a m e effect by t u r n i n g on a h o s e after p u t t i n g a c r i m p in it or b l o c k i n g off t h e n o z z l e . W h e n t h e p r e s s u r e c a n n o t b e m a i n t a i n e d , t h e result i s i m p o t e n c e , a c o n d i t i o n t h a t is r u m o r e d to h a v e b e e n suffered by H e n r y VIII in his r e l a t i o n s h i p w i t h A n n e of Cleves. It is a c o n dition t h a t I a m a s s u r e d b y m y m e d i c a l friends c a n n o w a d a y s almost always be cured. O n e n i n e t e e n t h - c e n t u r y "cure" w a s a splint m a d e from b a m b o o a n d fitted o v e r t h e p e n i s , a p r o c e d u r e t h a t m u s t h a v e b e e n i n c r e d i b l y u n c o m f o r t a b l e for b o t h parties. N o w a d a y s a s i m p l e r a n d m o r e c o m f o r t a b l e f i r s t

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h o w to d u n k a

doughnut

a p p r o a c h is t h e brief a p p l i c a t i o n of a small v a c u u m device to i n d u c e a "passive e r e c t i o n . " For m o s t m e n , t h e libido is a sufficient d r i v i n g force to p r o d u c e a n e r e c t i o n . S o m e p e o p l e a r e n e v e r satisfied, t h o u g h , a n d h a v e s o u g h t w a y s t o e n h a n c e t h e libido b y t h e u s e o f a p h r o d i s i a c s . U n l u c k i l y for t h e s e p e o p l e , t h e r e i s n o s u c h t h i n g as an a p h r o d i s i a c s u b s t a n c e — t h e o n l y real a p h r o d i s i a c is in t h e m i n d . T h a t h a s n ' t s t o p p e d p e o p l e o f b o t h s e x e s from trying s u c h t h i n g s as tripe, r h u b a r b , a n d t h e n e c k s of snails in t h e s e a r c h for e n h a n c e d s e x u a l gratification. T h e s e a n d o t h e r equally odd materials c o m e u n d e r the heading of "sympat h e t i c m e d i c i n e " — in o t h e r w o r d s , t h e y b e a r a fancied r e s e m b l a n c e e i t h e r to a p e n i s (e.g., a s p a r a g u s , g i n s e n g ) or to a vulva (e.g., o y s t e r s ) . S o m e so-called a p h r o d i s i a c m a t e r i a l s act a s i r r i t a n t s t o t h e sensitive m u c o u s m e m b r a n e s . O n e s u c h e x a m p l e i s t h e n e t t l e , w h i c h t h e R o m a n a u t h o r Pliny suggested r u b b i n g o n t h e p e n i s e s o f u n d e r p e r f o r m i n g bulls. This m a y e x p l a i n w h y t h e a n c i e n t R o m a n s w e r e s u c h fast r u n n e r s . T h e b e s t - k n o w n m a terial in t h e i r r i t a n t class, t h o u g h , is cantharidin, t h e active p r i n c i p l e in S p a n i s h fly, i.e., blister beetles of t h e Cantharis or Mylabris g e n u s . C a n t h a r i d i n , f o r m e r l y listed as an a p h r o d i s i a c by s o m e c o m m e r c i a l d r u g c o m p a n i e s , w a s classified as a S c h e d u l e I p o i s o n on its last a p p e a r a n c e in t h e British P h a r m a c o p o e i a of 1 9 5 3 . It is a v e r y d a n g e r o u s m a t e r i a l , w i t h a toxic d o s e of t h r e e milligrams a n d a fatal d o s e of t h i r t y milligrams. Its effects i n c l u d e dry m o u t h , gastric p a i n , blood in t h e u r i n e , a n d , e v e n t u a l l y , d e a t h following k i d n e y failure. T h e irritant effect o f c a n t h a r i d i n m a y n o t e n h a n c e t h e libido, b u t at j u s t t h e right d o s e it c a n p r o d u c e e r e c t i o n s . In a f a m o u s case in 1869, several battalions of F r e n c h t r o o p s in N o r t h Africa rep o r t e d t o t h e i r m e d i c a l officer w i t h gastric p a i n s a n d p e r m a nent erections. It transpired that they had been eating the legs of t h e local frogs, w h i c h h a d b e e n feeding on t h e blister beetles prevalent in t h e area. T h e British a n s w e r t o c a n t h a r i d i n w a s cocoa. I n t h e early 1950s sales o f cocoa s h o t u p w h e n a r u m o r w e n t a r o u n d t h a t

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it h a d l i b i d o - e n h a n c i n g p r o p e r t i e s . T h e New Statesman m a g a zine r a n a c o m p e t i t i o n in 1953 for t h e best p o e m c e l e b r a t i n g this m y t h . T h e w i n n i n g entry, "Cupid's N i g h t c a p , " w a s w r i t t e n by t h e appropriately n a m e d Stanley J. Sharpless: Half-past n i n e — h i g h t i m e for s u p p e r ; " C o c o a , l o v e ? , " "Of c o u r s e , m y d e a r . " H e l e n t h i n k s it q u i t e delicious, J o h n prefers i t n o w t o b e e r . K n o c k i n g back t h e sepia p o t i o n , H u b b y w i n k s , says, " W h o ' s for b e d ? " " S h a n ' t b e l o n g , " says H e l e n softly, C h e e k s a faintly f l u s h i n g r e d . For t h e y ' v e s t u m b l e d o n t h e secret Of a l o v e t h a t n e v e r w a n e s . Rapt b e n e a t h t h e t u m b l e d b e d c l o t h e s , Cocoa coursing t h r o u g h their veins.

Cocoa, like m a n y " a p h r o d i s i a c s , " w a s t h o u g h t t o h a v e a n e q u a l effect o n b o t h sexes. O n e s u b s t a n c e w h i c h d o e s a c t u a l l y h a v e a n effect o n b o t h m e n a n d w o m e n , albeit i n a n e g a t i v e s e n s e , is alcohol, a v a s o d i l a t o r t h a t m a y relax t h e i n h i b i t i o n s , b u t w h i c h u n f o r t u n a t e l y r e l a x e s o t h e r t h i n g s a s well o n t h e m a l e side of t h e e q u a t i o n — h e n c e t h e e x p r e s s i o n " b r e w e r ' s d r o o p . " On t h e f e m a l e side, it h a s b e e n f o u n d by a s u b s t a n t i a l p r o p o r t i o n o f w o m e n t o p r o d u c e d r y n e s s a n d discomfort. N o d r u g i s y e t k n o w n that c a n excite t h e libido, b u t t h e r e a r e quite a lew that can help to produce and maintain an erection t h a t t h e libido h a s failed to s t i m u l a t e . O n e of t h e earliest w a s papavarin, w h o s e effects w e r e s p e c t a c u l a r l y d e m o n s t r a t e d by t h e psychiatrist C h a r l e s B r i n d l e y at a m e e t i n g of t h e British A n d r o l o g y Society. Brindley, a b o r n s h o w m a n , b e g a n his talk by l o w e r i n g his t r o u s e r s , injecting a s o l u t i o n of t h e d r u g i n t o his t h i g h , a n d "displaying t h e results t h r o u g h o u t t h e d u r a t i o n of his h o u r - l o n g talk." T h e e x a c t d o s e of p a p a v a r i n is critical, a n d cases h a v e b e e n r e c o r d e d o f p e o p l e h a v i n g t o cut s h o r t holidays and return in pain with the same erection that they

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started w i t h four d a y s earlier. T h e idea of h a v i n g an injection as a p r e l u d e to sex is also n o t o n e t h a t m a n y p e o p l e w o u l d e n joy. Most p e o p l e w o u l d prefer a s t i m u l a n t t h a t could be t a k e n orally. It is this, r a t h e r t h a n a n y a p h r o d i s i a c effect, t h a t is t h e m a i n a d v a n t a g e of Viagra (sildenafil citrate), a s u b s t a n c e t h a t can m a k e e v e n wilting flowers s t a n d u p straight. Viagra w a s originally d e v e l o p e d by Pfizer P h a r m a c e u t i c a l s as a d r u g for t r e a t i n g a n g i n a . A c c o r d i n g to o n e r e p o r t , its d r a m a t i c effects o n t h e rigidity o f t h e m a l e p e n i s w e r e o n l y d i s c o v e r e d after s o m e o n e w o n d e r e d w h y all o f t h e m a l e p a r ticipants i n t h e e x p e r i m e n t h a d failed t o r e t u r n leftover pills o n c e t h e trial finished. Viagra received t h e a p p r o v a l of t h e U.S. F o o d a n d D r u g A d m i n i s t r a t i o n as a t r e a t m e n t for i m p o t e n c e early in 1998, a n d h a s a l r e a d y built up a c o n s i d e r a b l e folklore. O n e F r e n c h r e s t a u r a t e u r e v e n d e v e l o p e d a beef piccata in Viagra s a u c e , infused w i t h fig v i n e g a r a n d h e r b s . T h e c r e a t o r of this dish, J e a n - L o u i s Galland, said t h a t he w a n t e d to m a k e his c u s t o m e r s h a p p y , p a r t i c u l a r l y g r a n d f a t h e r s a n d t h e i r w i v e s . U n f o r t u n a t e l y for Galland a n d his c u s t o m e r s , t h e French authorities decided that he was dispensing drugs witho u t a license.

Step 2: The R a c e Begins

Muscle spasms within t h e erect penis eventually launch the s p e r m o n its j o u r n e y . T h e e j a c u l a t e h a s b e e n t h r o u g h a similar process to t h a t of g a s o l i n e in a m o d e r n gas p u m p , w h e r e vario u s additives a r e i n c o r p o r a t e d a s t h e gas p r o c e e d s t h r o u g h t h e p u m p , u n t i l t h e final m i x t u r e t h a t e m e r g e s i s r e a d y for a c t i o n . T h e m a n u f a c t u r e of s p e r m cells ( s p e r m a t o g e n e s i s ) o c c u r s in t h e testes, w i t h i n t h e s e m i n i f e r o u s t u b u l e s . T h e cells a r e t r a n s ported t h r o u g h t h e epididymus, w h e r e they b e c o m e motile, a n d t h e n t h r o u g h t h e vas d e f e r e n s in a s o l u t i o n of salts a n d p r o t e i n s to t h e i r p o i n t of p r o j e c t i o n . T h e s o l u t i o n in w h i c h t h e y a r e carried is e n r i c h e d from t h e s e m i n a l vesicles by an al-

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kaline y e l l o w fluid called t h e s e m i n a l p l a s m a . This s o l u t i o n contains hormones, enzymes, and metabolites, m a n y of which have an u n k n o w n function. T h e s e m i n a l p l a s m a t h a t i s e v e n t u a l l y ejected c o n t a i n s s o m e 2 0 0 - 4 0 0 million wriggling s p e r m a t o z o a . T h e o d d s that o n e o f t h e s e will r e a c h a n d fertilize t h e egg i n a n y p a r t i c u l a r m o n t h a r e r o u g h l y 3:1 against, w h i c h m e a n s t h a t a n o r m a l c o u p l e h a v e a 90 p e r c e n t c h a n c e of success in t w e l v e m o n t h s of t r y ing. T h e o d d s o f o n e p a r t i c u l a r s p e r m w i n n i n g t h e race, t h o u g h , are r a t h e r w o r s e t h a n t h e o d d s of a p a r t i c u l a r p e r s o n w i n n i n g the lottery w i t h o n e ticket a t t h e f i r s t a t t e m p t . H u m a n s p e r m a t o z o a a r e a b o u t sixty m i c r o m e t e r s long, w i t h a flattish w e d g e - s h a p e d h e a d like a m i n i - s u r f b o a r d . T h e y m u s t s w i m a t h o u s a n d t i m e s t h e i r o w n b o d y l e n g t h t o reach t h e egg — e q u i v a l e n t to a h u m a n s w i m m i n g 1500 m e t e r s . For at least hall of t h a t d i s t a n c e , t h e s p e r m m u s t s w i m t h r o u g h a m a terial w i t h t h e c o n s i s t e n c y of a t h i n jelly. First, t h o u g h , it m u s t escape from t h e s e m i n a l p l a s m a t h a t h a s carried it to t h e starting p o i n t of t h e r a c e . T h e n , it m u s t b r e a k i n t o t h e jelly-like m a t e r i a l , w h i c h is called cervical mucus. N a t u r e h a s c o n s p i r e d to m a k e s u r e t h a t n e i t h e r j o b is at all easy.

Figure 9 . 1 : A Physicist's View of the Vagina, Cervix, Uterus, and Fallopian T u b e s — An O b s t a c l e C o u r s e for S p e r m a t o z o a .

T h e (irst obstacle is t h e s e m i n a l p l a s m a itself, w h i c h is i n i m ical to t h e h e a l t h of t h e s p e r m a t o z o a t r a p p e d in it, a n d will kill t h e m unless they escape within t w e n t y m i n u t e s . The s e m e n settles as a pool n e a r t h e e n t r a n c e to t h e cervix, w i t h t h e volu m e o f t h e s e m e n pool a v e r a g i n g t h r e e milliliters. S i m p l e g e o m e t r y says t h a t t h e furthest d i s t a n c e t h a t a s p e r m a t o z o o n n e e d s to s w i m to get to t h e surface of s u c h a p o o l is a r o u n d

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nine millimeters. Most spermatozoa can swim at a r o u n d three m i l l i m e t e r s p e r m i n u t e in w a t e r y fluids, a n d so s h o u l d m a k e it t o t h e surface i n t h r e e m i n u t e s o r so. U n f o r t u n a t e l y for t h o s e o p t i m i s t i c s p e r m a t o z o a , t h e s e m i n a l p l a s m a , w h i c h travels t h r o u g h t h e p e n i s in liquid form, sets i n s t a n t l y to a jelly on e m e r g e n c e . O n l y t h e luckiest o r m o s t v i g o r o u s s p e r m a t o z o a m a k e it o u t of this jelly. If t h e s p e r m a t o z o a a r e sufficiently close t o e a c h o t h e r , t h e y m a y display " s y n c h r o n i z e d s w i m m i n g " — a h y d r o d y n a m i c effect w h e r e t h e " w a v e s " c r e a t e d by o n e s p e r m a t o z o o n affect t h e m o t i o n of closely a d j a c e n t sperm a t o z o a , s o t h a t t h e y e n d u p s w i m m i n g i n u n i s o n . This p h e n o m e n o n is used to assess t h e q u a l i t y of bull s e m e n . T h o s e s p e r m a t o z o a t h a t e s c a p e from t h e s e m i n a l fluid are immediately confronted with a n o t h e r barrier — the column o f m u c u s t h a t f i l l s t h e cervical canal linking t h e v a g i n a a n d t h e u t e r u s (Figure 9 . 1 ) . This e x t e n d s b e t w e e n t h e i n t e r n a l a n d e x t e r n a l os — a w o r d of e q u a l use to gynecologists a n d Scrabble p l a y e r s alike. T h e c o n s i s t e n c y o f t h e m u c u s varies u n d e r t h e influence of the t w o h o r m o n e s progesterone a n d estrogen. P r o g e s t e r o n e m a k e s t h e m u c u s m o r e viscous, w h i l e e s t r o g e n i n d u c e s i t t o t a k e u p w a t e r a n d b e c o m e less viscous. T h e balance between these two h o r m o n e s changes throughout the m o n t h l y cycle, a n d t h e c o n s i s t e n c y o f t h e cervical m u c u s c h a n g e s w i t h it, b e c o m i n g m o s t easily p e n e t r a b l e n e a r m i d cycle, a l t h o u g h t h e r e is a l w a y s a c h a n c e of s o m e s p e r m finding t h e i r w a y in at a n y stage of t h e cycle. T h e r e a r e v a r i o u s tests for t h e " g o o d n e s s " of cervical m u c u s , i.e., t h e e a s e w i t h w h i c h s p e r m a t o z o a can p e n e t r a t e a n d s w i m t h r o u g h it. T h e simplest, called t h e Billings test, is t h e o n e u s e d in " n a t u r a l " family p l a n n i n g , w h e r e a w o m a n t a k e s a small a m o u n t o f h e r o w n cervical m u c u s b e t w e e n t h u m b a n d forefinger a n d m e a s u r e s h o w far i t c a n b e e x t e n d e d w i t h o u t b r e a k i n g . T h e f u r t h e r it s t r e t c h e s , t h e b e t t e r it is, from t h e p o i n t of v i e w of t h e c h a n c e of c o n c e p t i o n . T h e d e g r e e of s t r e t c h i n g s e e m s t o c o r r e l a t e q u i t e well w i t h t h e c o n c e n t r a t i o n of w a t e r in t h e m u c u s , a n d is easy to m e a s u r e w i t h o u t r e c o u r s e to c o m p l i c a t e d e q u i p m e n t . It is t e c h n i c a l l y k n o w n as

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spinnbarkeit, for w h i c h t h e W o r l d H e a l t h O r g a n i z a t i o n gives t h e following ratings: Table 9 . 1 : S t r e t c h R a t i n g s for C e r v i c a l M u c u s . Stretching length (cm)

Rating

1

0 (worst)

1 - 4

1

5-8

2

> 9

3 (best)

If a m i c r o s c o p e is available, it is also possible to m e a s u r e "ferning," w h e r e s o m e m u c u s is placed on a m i c r o s c o p e slide, a l l o w e d t o dry, a n d t h e r e s u l t i n g crystalline deposit i s e x a m ined u n d e r a m i c r o s c o p e . T h e m o r e " b r a n c h e s " t h a t t h e f e a t h ery crystals h a v e , t h e b e t t e r t h e m u c u s . T h e m o s t c o m p l e t e test r e p r o d u c e s t h e initial stages o f t h e fertilization p r o c e s s in vitro — literally "in glass." S e m e n a n d cervical m u c u s a r e i n t r o d u c e d t o e a c h o t h e r a s t h i n f i l m s t r a p p e d b e t w e e n a glass m i c r o s c o p e slide a n d a glass coverslip. Sufficient cervical m u c u s is p l a c e d in t h e g a p to c o v e r a b o u t hall t h e a r e a , a n d a d r o p of freshly collected s e m e n is t h e n int r o d u c e d at t h e far side, w h e r e it is d r a w n in by capillary action, in v e r y m u c h t h e s a m e w a y t h a t tea is d r a w n i n t o a d u n k e d c o o k i e (Figure 9.2).

Figure 9.2: S e m e n a n d M u c u s Being Introduced to Each Other on a Microscope

Slide.

I w a s i n t r o d u c e d to this p r o c e d u r e by Dr. Eileen M c L a u g h lin a n d h e r staff in t h e fertility u n i t at St. Michael's Hospital in

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Bristol. I w a s surprised to see t h r o u g h t h e m i c r o s c o p e that, w h e n t h e s e m e n a n d m u c u s first c o m e into contact, t h e interface bet w e e n t h e t w o rapidly develops a series ol cusps (Figure 9.3).

Figure 9.3: The Interface B e t w e e n S e m e n a n d M u c u s , S h o w i n g Formation of Cusps.

T h e s p e r m a t o z o a , I w a s told, e n t e r t h e cervical m u c u s t h r o u g h t h e tips of t h e s e c u s p s . It w a s t h e c u s p s t h e m s e l v e s that intrigued me, t h o u g h . How were they formed, and w h y s h o u l d s p e r m a t o z o a e n t e r o n l y t h r o u g h t h e tips? A l t h o u g h l i q u i d / l i q u i d interfaces a r e a speciality of m i n e , I h a d o n l y s e e n c u s p s like this o n o n e p r e v i o u s o c c a s i o n , w h e n I h a d d i p p e d an oil d r o p l e t i n t o a s o l u t i o n of p r o t e i n . As m o r e a n d m o r e p r o t e i n m o l e c u l e s c o m p e t e d for space a t t h e d r o p l e t surface, t h e s i d e w a y s p r e s s u r e that t h e y g e n e r a t e d i n t r y i n g t o p u s h e a c h o t h e r o u t o f t h e w a y w a s sufficient t o collapse t h e surface i n t o a series of folds. This case s e e m e d different. It a p -

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p e a r e d thai s o m e t h i n g i n t h e s e m e n w a s r e a c t i n g c h e m i c a l l y vviih s o m e t h i n g in t h e cervical m u c u s to form a surface film t h a t s p o n t a n e o u s l y folded. T h e surface film is o b v i o u s l y i m p o r t a n t , since it could form a b a r r i e r to s p e r m p e n e t r a t i o n . To find o u t m o r e a b o u t it, I d e cided t o c h e c k o u t w h a t w o u l d h a p p e n i f t h e s e m e n w a s r e placed by w a t e r . To my i n t e n s e s u r p r i s e , t h e s a m e t y p e of c u s p appeared. W h a t e v e r was going on, it didn't involve chemicals i n t h e s e m e n . M y g u e s s w a s t h a t p r o t e i n from t h e m u c u s w a s a c c u m u l a t i n g a t t h e m u c u s / w a t e r interface i n t h e s a m e w a y t h a t p r o t e i n h a d a c c u m u l a t e d at t h e surface of my oil d r o p . This m a d e s o m e physical s e n s e from t h e p o i n t o f v i e w t h a t t h e tips of t h e c u s p s a r e likely to be t h e w e a k e s t p o i n t s in s u c h a s t r u c t u r e , a n d h e n c e t h e m o s t easily p e n e t r a t e d b y a wriggling spermatozoon. My e x p e r i e n c e of surface c h e m i s t r y told me t h a t if p r o t e i n w a s g o i n g to a c c u m u l a t e at t h e m u c u s / w a t e r interface, it s h o u l d also a c c u m u l a t e at a m u c u s / a i r interface. If this w e r e t h e case, t h e rigid p r o t e i n lilm s h o u l d collapse i n t o folds as soon as w a t e r t o u c h e d a n y part of it. W h e n 1 l o o k e d m o r e closely, I w a s gratilied to find t h a t my scientific instinct h a d , for o n c e , b e e n right (Figure 9.4).

Figure 9.4: C u s p s F o r m e d at Air/Water Interface W h e n S e m e n or W a t e r C o m e s into C o n t a c t with Cervical M u c u s .

T h e folds, w h i c h will e v e n t u a l l y b e c o v e r e d w i t h w a t e r (or s e m e n ) , a r e likely t o crack a t t h e tips, e x p o s i n g t h e u n d e r l y i n g m u c u s . For a s p e r m a t o z o o n to be able to p u s h its w a y in to this m u c u s , it n e e d s to e x e r t a p r e s s u r e g r e a t e r t h a n t h e yield stress of t h e m u c u s , w h i c h is ( r o u g h l y ) t h e p r e s s u r e at w h i c h t h e

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m u c u s gives w a y . T h e yield stresses of jelly-like m a t e r i a l s a r e m e a s u r e d in u n i t s of p r e s s u r e called Pascals (Pa). F o r t h e p u r p o s e s of r e f e r e n c e , a t h i n p a p e r b a c k b o o k lying on a desk e x erts a p r e s s u r e of a r o u n d f 00 Pa. T h e p r e s s u r e in a car tire is a r o u n d 2 0 0 , 0 0 0 Pa. T h e yield stress of cervical m u c u s at m i d c y c l e is a r o u n d sixty Pascals, a c h a r a c t e r i s t i c figure for jelly-like m a t e r i a l s t h a t can hold t h e i r o w n s h a p e b u t a r e still fairly e a s y t o w o r k (like a n i n d u s t r i a l b a n d - c l e a n i n g gel, for e x a m p l e ) . For cervical m u cus, N a t u r e h a s w o r k e d t h i n g s o u t p r e t t y well. A yield stress of 60 Pa m e a n s that any spermatozoon capable of s w i m m i n g faster t h a n 2 m m / m i n c a n p u s h its w a y t h r o u g h t h e surface. On e i t h e r side of m i d c y c l e , t h e yield stress rises rapidly, so that t h e m u c u s p r o v i d e s a n efficient, t h o u g h n o t g u a r a n t e e d , barrier to c o n c e p t i o n . T h e final w o r d o n w h e t h e r s p e r m a t o z o a can p e n e t r a t e t h e cervical m u c u s m a y c o m e from t h e f e m a l e p a r t n e r i n a c o u p l e , since a link h a s b e e n d i s c o v e r e d b e t w e e n h e r e n j o y m e n t of a particular sexual e n c o u n t e r and the quantity of sperm in the cervical m u c u s a f t e r w a r d s . This m a y partly be a m a t t e r of orgasm (there is s o m e evidence that spermatozoa are sucked in d u r i n g o r g a s m ) , b u t s e e m s t o e m b r a c e m a n y o t h e r factors, including the moistness a n d receptiveness of t h e vagina. These a r e , of c o u r s e , physical factors, so p e r h a p s physics h a s t h e last w o r d a l t e r all.

Step 3: The R a c e Is On

O n c e o n e s p e r m a t o z o o n h a s p e n e t r a t e d , o t h e r s follow. T h e y d o n ' t s w i m off in a n y old d i r e c t i o n , b u t play f o l l o w - t h e - l e a d e r . If several s p e r m a t o z o a h a v e initially p e n e t r a t e d at different places, t h e result is lines of s p e r m a t o z o a t r a v e l i n g in l a n e s , oft e n at different s p e e d s . T h e t y p e of m u c u s in w h i c h this h a p p e n s is e v o c a t i v e l y called motorway mucus. This is t h e "best" m u c u s , w i t h p r o p e r t i e s t h a t give a s m a n y s p e r m a t o z o a a s p o s -

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siblc a c h a n c e of m a k i n g it to t h e u t e r u s after a s w i m of s o m e t h i r t y m i l l i m e t e r s . How, t h o u g h , c a n s p e r m a t o z o a s w i m a t all in this jelly-like m a t e r i a l ? It w o u l d be impossible if t h e s w i m m i n g m o v e m e n t s of a s p e r m a t o z o o n w e r e reversible (like t h e o a r m o v e m e n t s of a r o w i n g boat, or t h e m o v e m e n t s of a s w i m m e r w h o i s s w i m m i n g "stiff-armed") b e c a u s e a n y m o v e m e n t that would drive t h e spermatozoon forward in the glutinous m e d i u m would be canceled out by an opposite m o v e m e n t that w o u l d d r i v e it right b a c k a g a i n (Figure 9.5).

Figure 9.5: The P r o b l e m of S w i m m i n g in a Viscous M e d i u m Using Reversible M o v e m e n t of the Arms. (Left) starting position; (center) body moves forward as arms move back; (right) body returns to starting position as arms move forward. In a medium of low viscosity, the problem can be overcome in part by making the driving movement faster in one direction than the other, e.g., pulling the arms back rapidly, then moving them forward slowly If viscosity dominates, this tactic fails.

W h e n I a s k e d Eileen h o w s p e r m w e r e t h o u g h t t o m a n a g e it, s h e told me t h a t it w a s still v e r y m u c h a m a t t e r of o p i n i o n . S o m e w o r k e r s b e l i e v e t h a t t h e a n s w e r lies i n t h e fine s t r u c t u r e o f t h e m u c u s , w h i c h c o n t a i n s long string-like m o l e c u l e s called mucopolysaccharides. T h e s e w o r k e r s claim t h a t t h e m u c o p o l y s a c c h a r i d e s form b u n d l e s a b o u t 0.5 u,m in d i a m e t e r ( o n e - t e n t h of t h e d i a m e t e r of a s p e r m h e a d ) , w i t h a q u e o u s c h a n n e l s in b e t w e e n t h a t t h e s p e r m can s q u e e z e a l o n g . O t h e r a u t h o r s

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believe t h a t t h e m u c u s itself m o v e s . S o m e b e l i e v e t h a t t h e b e a t i n g of t h e s p e r m tails sets up a r e s o n a n c e w i t h t h e n a t u r a l f r e q u e n c y of t h e m u c o p o l y s a c c h a r i d e s , like w a l k e r s crossing a bridge in step a n d setting it s w a y i n g , a n d t h a t t h e r e s u l t i n g r h y t h m i c w a v e s i n t h e m u c u s carry t h e s p e r m a l o n g . Still o t h ers claim t h a t t h e r h y t h m i c b e a t i n g of t h e kinocilia (tiny hairs t h a t line t h e cervix) p r o d u c e s w a v e s t h a t e n h a n c e s p e r m m i gration. There m a y be s o m e m e a s u r e of t r u t h in each of these explan a t i o n s , b u t t o m e n o n e w a s c o m p l e t e l y satisfactory, b e c a u s e n o n e t o o k i n t o a c c o u n t h o w large, string-like m o l e c u l e s a c t u ally b e h a v e in s o l u t i o n . I h a d h a d s o m e e x p e r i e n c e of this b e h a v i o r as a food scientist w h e n s t u d y i n g t h e w a y t h a t jellies set. Most food jellies a r e based on gelatin, a long thin m o l e c u l e t h a t wriggles a r o u n d freely in h o t w a t e r . As t h e w a t e r cools, t h e gelatin m o l e c u l e s begin to form a t h r e e - d i m e n s i o n a l net, held t o g e t h e r b y w e a k links a t t h e p o i n t s w h e r e t h e m o l e c u l e s r a n d o m l y cross o v e r e a c h o t h e r . If t h e w e a k jelly is stirred at this stage, it rapidly b e c o m e s m o r e liquid; in o t h e r w o r d s , it is shear-thinning. Stirring d i s r u p t s t h e w e a k l i n k a g e s a n d lines up t h e l o n g m o l e c u l e s a l o n g t h e flow lines, s o t h e y can slide past e a c h o t h e r m o r e readily. I k n e w t h a t cervical m u c u s , like edible jelly, is a s o l u t i o n of long m o l e c u l e s that has s h e a r - t h i n n i n g p r o p e r t i e s , s o t h a t m u cus stirred by t h e l a s h i n g tail of t h e s p e r m a t o z o o n w o u l d form a trail of l o w e r viscosity t h a n t h e s u r r o u n d i n g m u c u s , a line of least r e s i s t a n c e for s u b s e q u e n t s p e r m a t o z o a to follow. This explained t h e " m o t o r w a y m u c u s " effect, b u t still did n o t e x p l a i n t h e ability o f s p e r m a t o z o a t o s w i m t h r o u g h cervical m u c u s i n t h e f i r s t place. I w a s p u z z l i n g o u t l o u d o v e r this q u e s t i o n o n e m o r n i n g i n t h e d e p a r t m e n t a l coffee r o o m . M y n e w P h . D stud e n t R a c h e l w a s b u s y r e a d i n g h e r e-mails, a n d o v e r h e a r d m y q u e s t i o n . Later t h a t d a y s h e silently h a n d e d me a r e p r i n t of a 1976 article t h a t told m e e v e r y t h i n g I w a n t e d t o k n o w . T h e article w a s t h e t r a n s c r i p t of a talk by E. M. Purcell called "Life at L o w R e y n o l d s N u m b e r s " — in o t h e r w o r d s , life u n d e r c i r c u m s t a n c e s w h e r e viscous drag d o m i n a t e s e v e r y a t t e m p t t o

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m o v e . O r g a n i s m s like s p e r m a t o z o a m a n a g e t o s w i m u n d e r s u c h c i r c u m s t a n c e s by u s i n g t h e tail (or flagellum) as a flexible oar, o r w h i p . This d o d g e s t h e p r o b l e m t h a t a h u m a n s w i m m e r w i t h rigid a r m s or a r o w e r w i t h rigid o a r s w o u l d e x p e r i e n c e , because a flexible a r m or oar can bend o n e way during the f i r s t hall o f a s t r o k e a n d t h e n c h a n g e s h a p e t o b e n d t h e o t h e r w a y d u r i n g t h e s e c o n d half. S o m e small o r g a n i s m s , s u c h as t h e biflagellate alga Chlamydomonas, use t h e i r flexible flagellae in this w a y to do t h e b r e a s t s t r o k e (Figure 9.6). H u m a n s p e r m do it in a different way, l a s h i n g t h e i r single flagellum from side t o side u n d e r t h e drive of a m o l e c u l a r m o t o r . T h e tail l a s h i n g d o e s t h e trick b e -

F i g u r e 9 . 6 : S w i m m i n g M o t i o n o f Chlamydomonas.

c a u s e it flexes so t h a t a t w o - d i m e n s i o n a l w a v e a p p e a r s to be c o n t i n u a l l y t r a v e l i n g a l o n g it. E v e n t h o u g h viscous drag alw a y s o p p o s e s t h e d i r e c t i o n of m o t i o n , Purcell s h o w e d t h a t a tail m o v i n g in this w a y can, incredibly, use viscous drag to p r o pel itself f o r w a r d . A fuller e x p l a n a t i o n is given in F i g u r e 9.7. T h e d i a g r a m m a y look c o m p l i c a t e d b u t , like m a n y scientific d i a g r a m s , it is relatively s i m p l e to follow if t a k e n step by s t e p . f t t a k e s 1 0 - 1 5 m i n u t e s for t h e fastest h u m a n s p e r m t o s w i m t h e l e n g t h of t h e cervical c a n a l . A few s p e r m a t o z o a m a k e it m u c h m o r e q u i c k l y by a p r o c e s s called rapid transport, w h i c h can carry i n e r t particles t h r o u g h w i t h i n t w o m i n u t e s . N o o n e k n o w s h o w this p r o c e s s w o r k s , b u t t h e s p e r m t h a t t a k e a d v a n t a g e of it a r e n o t as lucky as t h e y a p p e a r , b e c a u s e t h e t i m e


186

Net horizontal force F,

Figure 9.7: Viscous Drag on a Flagellum. The flagellum is the wavy line. The segment portion shown as a filled rectangular box is moving upward with velocity V; the open box portion is moving downward with velocity V. Each velocity can be broken into two separate velocities — one parallel to the segment, and one perpendicular to it. The principle is the s a m e as that of the knight's move in chess, which is a steep diagonal move that can also be thought of as two steps parallel to one side of the board, followed by one step parallel to the other side. For the filled rectangular segment, the two separate velocities are marked V and V (with similar nomenclature for the clear rectangular segment). The forces F of the viscous drags that oppose these velocities are labeled F and F respectively. p a r

p e r p

p a r

Now for the clever bit. We recombine F and F to give an overall drag force F, and then break this down again, but this time into a force parallel to the horizontal axis ( F ) and one perpendicular to the axis ( F ) . The perpendicular one acts downwards, and the parallel one acts forwards. W h e n we go through the same procedure for the open segment, the final perpendicular component F of the viscous drag acts upward, canceling the effect of that on the filled segment. The parallel component F , however, acts forward, adding to the parallel component acting on the filled segment. The overall viscous drag, then, acts to push the spermatozoon forward. p a r

horlz

p e r p

vert

v e r t

h o n z

t h a t t h e i r c o m p a n i o n s s p e n d in t h e cervix is n e e d e d for c h e m ical c h a n g e s t h a t a l l o w t h e m t o p e n e t r a t e a n d fertilize t h e egg. T h o s e s p e r m a t o z o a t h a t m a k e i t t o t h e u t e r u s h a v e yet m o r e p r o b l e m s to o v e r c o m e . T h e first is similar to t h a t e x p e r i e n c e d by surfers on s o m e S y d n e y b e a c h e s — t h e w a t e r is full of s h a r k s . T h e " s h a r k s " a r e w h i t e cells p r o d u c e d b y t h e i m m u n e s y s t e m , a n d w h o s e j o b it is to s c a v e n g e foreign cells a n d o t h e r m a t e r i a l s n o t r e c o g n i z e d as "self." N o t h i n g could be m o r e foreign t h a n a s p e r m a t o z o o n in a u t e r u s , a n d l u c k y i n d e e d is t h e s p e r m a t o z o o n t h a t m a k e s i t t o t h e n e c k o f o n e o r o t h e r Fallopian t u b e . Of t h e original few h u n d r e d million, o n l y a few

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h u n d r e d a r e n o w left. M o s t o f t h e s e h a v e m a d e i t t h r o u g h t h e u t e r u s b y surfing o n u t e r i n e w a v e s , i n d u c e d b y p r o s t a g l a n d i n s in the seminal plasma. The waves seem to go towards the o v i d u c t and t h e cervix, s o t h e s p e r m a t o z o o n h a s t o catch t h e right o n e . O n c e i n t h e F a l l o p i a n t u b e , t h e s p e r m a t o z o a b e g i n jostling for p o s i t i o n like a d o l e s c e n t y o u t h s at a street c o r n e r , w a i t i n g for t h e egg to a r r i v e . W h e n it d o e s , it is p l a s t e r e d in m a k e u p — a layer of jelly so thick t h a t it t a k e s all of t h e efforts of t h e s p e r m a t o z o a to p e n e t r a t e it (Figure 9.8).

Figure 9.8: Fertilization of the Egg. This is a very simplified picture, giving the main outlines only. Even the picture of the egg itself is simplified. In real life, it is surrounded by a cloud of cells that includes cumulus cells, which secrete a matrix of hyaluronic acid, similar to the lubricating material in the joints.

T h e process is a c o m p l i c a t e d o n e , i n v o l v i n g e n z y m e a c t i o n and biochemical and structural changes. In outline, t h e sperm first h a s to drill t h r o u g h t h e s u r r o u n d i n g cell l a y e r (called t h e cumulus oophorus) u s i n g a c o m b i n a t i o n of m e c h a n i c a l m o v e m e n t and chemical dissolution. Once through, t h e sperm enc o u n t e r s a rigid layer, t h e zona pellucida, w h e r e t h e cap of t h e s p e r m t h a t w a s t h e drill bit is lost in a c o m p l i c a t e d p r o c e s s called t h e acrosome reaction. T h e s p e r m n o w h a s to w o r k

188


t h r o u g h t h e zona in its m o r e - o r - l e s s n a k e d c o n d i t i o n . It d o e s this b y u s i n g its a s y m m e t r i c tail m o t i o n t o rock t h e b l a d e s h a p e d h e a d b a c k a n d forth, g e n e r a t i n g sufficient force t o b r e a k i n d i v i d u a l m o l e c u l a r b o n d s a s t h e h e a d levers a n d cuts its w a y t h r o u g h . T h e s p e r m e v e n t u a l l y r e a c h e s a g a p called t h e perivitelline space, w h e r e t h e t h i n m e m b r a n e s u r r o u n d i n g i t m a k e s c o n t a c t w i t h t h e m e m b r a n e s u r r o u n d i n g t h e egg (oolemma). T h e t w o m e m b r a n e s fuse, a n d t h e w h o l e s p e r m , w i t h its D N A - c a r r y i n g h e a d , is e n g u l f e d by t h e egg. T h e w i n n i n g s p e r m a t o z o o n is like a k n i g h t of old, scaling t h e d e f e n d e d r a m p a r t s a n d e v e n t u a l l y b r e a k i n g t h r o u g h t o t h e m a i d e n w i t h i n . Like a n y c a u t i o u s k n i g h t , i t t a k e s t h e p r e c a u t i o n o f t u r n i n g t h e k e y o n t h e inside of t h e d o o r as s o o n as it is t h r o u g h , by r e l e a s i n g a b u r s t of calc i u m t h a t irreversibly alters t h e egg m e m b r a n e s o t h a t o t h e r s p e r m c a n n o t e n t e r w h i l e t h e w i n n e r i s c o m b i n i n g its DNA w i t h t h a t of t h e egg n u c l e u s . A n e w life h a s n o w b e g u n . P e r h a p s i t i s n o m o r e t h a n Darw i n i a n e v o l u t i o n a t w o r k w h i c h dictates t h a t t h e s p e r m w i t h t h e g r e a t e s t m a s t e r y o f physics i s t h e o n e w h i c h h a s t h e best c h a n c e of i n i t i a t i n g t h a t life.

coda

I h a v e a t t e m p t e d to c o n v e y s o m e t h i n g of w h a t it feels like to be a scientist, w i t h t h e daily task of w o r k i n g o u t h o w s o m e small part of t h e w o r l d f u n c t i o n s . We e n j o y o u r s e l v e s , j u s t as a n y o n e i n a satisfying a n d r e w a r d i n g o c c u p a t i o n d o e s , b u t u n d e r n e a t h t h e p l e a s u r e a n d e x c i t e m e n t t h e r e is a real s e n s e of p u r p o s e . As t h e stories in this b o o k h a v e s h o w n , t h e r e is alw a y s t h e possibility t h a t a n a n s w e r t o e v e n t h e m o s t trivials o u n d i n g q u e s t i o n m i g h t h e l p t o p r o d u c e a n e w insight i n t o t h e n a t u r e of t h e w o r l d in w h i c h we live. Scientists live for these m o m e n t s . P e o p l e o u t s i d e science often p i c t u r e scientists as solitary gen i u s e s , o c c u p y i n g p i n n a c l e s far a b o v e t h e rest of us. T h a t m a y be t r u e for a few, j u s t as it is t r u e for a few m u s i c i a n s or artists or w r i t e r s . F o r t u n a t e l y for m o s t w o r k i n g scientists, i n c l u d i n g myself, it is perfectly possible to m a k e useful c o n t r i b u t i o n s to science w i t h o u t b e i n g a g e n i u s . This is b e c a u s e science is largely a c o m m u n a l activity, to w h i c h p e o p l e w i t h m a n y different skills c o n t r i b u t e . T h e s e i n c l u d e s o m e w h o a r e good w i t h their h a n d s , c o m p u l s i v e g a t h e r e r s a n d a r r a n g e r s of facts, p e r sistent s e e k e r s of a n s w e r s to niggling q u e s t i o n s , t h o s e w i t h a "feel" for a n i m a l s or rocks or p l a n t s , a n d m a n y o t h e r s . All h a v e t h e i r p a r t s t o play. O u r m a i n c o m m o n c h a r a c t e r i s t i c i s a n o p e n n e s s t o criticism, albeit s o m e t i m e s w i t h gritted t e e t h . W e s h a r e results a n d ideas t h r o u g h o p e n p u b l i c a t i o n , w h i c h s o m e t i m e s leads t o m o r e criticism, b u t p r o d u c e s a n a w a r e n e s s of i m p o r t a n t q u e s t i o n s , a n d acts as a r e s o u r c e of i n f o r m a t i o n t h a t h a s p a s s e d t h e critical test a n d w h i c h can lead t o fresh insights. W i t h o u t this c o m m u n a l s h a r i n g , t h e r e w o u l d b e n o such r e s o u r c e , a n d u l t i m a t e l y n o science. W o u l d it m a t t e r if t h e r e w e r e no s c i e n c e ? It w o u l d to me a n d


my fellow scientists, of c o u r s e , b e c a u s e science p r o v i d e s o u r livelihood, f t w o u l d also h a v e m a t t e r e d t o m e p e r s o n a l l y b e c a u s e I w o u l d be d e a d by n o w b u t for t h e i n v e n t i o n of m o d e r n antibiotics. This a n d o t h e r practical benefits for o u r lives a n d lifestyles a r e often a d v a n c e d as m a j o r r e a s o n s for s u p p o r t ing a n d i n v e s t i n g i n science, a n d i t c a n n o t b e d e n i e d t h a t w e are i m m e a s u r a b l y b e t t e r off, in this s e n s e , as a result of scientific discoveries. T h e practical results of science e x t e n d well b e y o n d t h e b i o m e d i c a l a n d c o m m u n i c a t i o n fields t h a t t e n d t o d o m i n a t e the headlines. Even the shelves in o u r supermarkets w o u l d be relatively e m p t y if scientific a d v a n c e s h a d n o t let us understand and control decay processes in plant and animal products. Practical benefits, t h o u g h , a r e o u t w e i g h e d i n m a n y p e o p l e ' s m i n d s by practical p r o b l e m s . Of w h a t u s e is a l o n g e r life, or e v e n a l o a d e d s u p e r m a r k e t shelf, w h e n t h a t life a n d lifestyle a r e t h r e a t e n e d b y a n a t o m i c b o m b o r a genetically e n g i n e e r e d virus? S o m e p e o p l e , w h e n faced w i t h s u c h p r o b l e m s , t a k e t h e e x t r e m e v i e w t h a t this science s h o u l d h a v e b e e n s t o p p e d earlier, a n d s h o u l d b e s t o p p e d n o w , b e f o r e w e get i n t o e v e n d e e p e r w a t e r s . O t h e r s believe t h a t m a n ' s best ( a n d possibly only) c h a n c e is to press o n , s e e k i n g f u r t h e r u n d e r s t a n d i n g of o u r w o r l d o u r s e l v e s a n d t h e w a y s i n w h i c h w e m i g h t u s e science for g o o d r a t h e r t h a n ill. A c o m p r o m i s e , s u p p o r t e d by t h e m a j o r i t y of p e o p l e , is to e n c o u r a g e t h e p u r s u i t of science, b u t to direct scientific r e s e a r c h t o w a r d s peaceful a p p l i c a t i o n s only. G i v e n t h a t it is impossible t o q u e l l o u r n a t u r a l h u m a n curiosity, t h e y ask, s u r e l y i t m u s t a t least b e possible t o direct t h a t curiosity t o w a r d s p e a c e l u l e n d s ? U n i o r t u n a t e l y for t h o s e of us w h o w i s h o n l y for p e a c e a n d c o o p e r a t i o n , t h e a n s w e r is " n o . " E v e n if all direct military r e s e a r c h could b e s t o p p e d , w e w o u l d b e little f u r t h e r forward, b e c a u s e it is simply n o t possible to predict w h e r e an a d v a n c e in scientific u n d e r s t a n d i n g m i g h t lead. A p r i m e e x a m p l e occ u r r e d in 1939, j u s t before t h e o u t b r e a k of t h e S e c o n d World War, w h e n t w o G e r m a n scientists p u b l i s h e d t h e key t h e o r y

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w h i c h m a d e t h e a t o m b o m b possible, i n t h e British j o u r n a l Nature. O n l y w h e n A m e r i c a n a n d British scientists b e g a n to c o n s i d e r w h e t h e r a n a t o m b o m b could b e built did this f i n d i n g a s s u m e significance. If its c o n s e q u e n c e s h a d b e e n o b v i o u s , t h e G e r m a n g r o u p w o u l d n o t h a v e r e v e a l e d t h e i r discovery s o openly. T h e c o n s e q u e n c e s of a n y p a r t i c u l a r scientific discovery a r e often n o t o b v i o u s , e v e n t o t h e discoverer. R u t h e r f o r d , c o m m e n t i n g o n t h e p o s s i b i l i t y o f splitting t h e a t o m ( t h e f i r s t step a l o n g t h e r o a d t o t h e a t o m b o m b ) , w a s q u o t e d a s saying, " A n y o n e w h o t h i n k s t h a t a n y practical benefit c a n b e g a i n e d from splitting t h e a t o m i s t a l k i n g m o o n s h i n e . " Nor w a s h e looking for practical benefit. T h e p r i m e r e a s o n for a t t e m p t i n g t o split t h e a t o m w a s t o find o u t w h a t w a s inside, a n d t h e n c e t o u n d e r s t a n d a little m o r e a b o u t t h e m a t e r i a l from w h i c h w e a n d t h e w h o l e u n i v e r s e a r e built. T h e t e c h n o l o g i c a l c o n s e q u e n c e s (so far) h a v e i n c l u d e d , not o n l y t h e a t o m i c b o m b , b u t n u c l e a r p o w e r s t a t i o n s ( w h o s e utility s o m e will d e b a t e ) , n e w m e t h o d s o f r e v e a l i n g a n d h e a l i n g diseased a n d a b n o r m a l tissue, a n d a t r u e r p i c t u r e of t h e n a t u r e a n d origin of t h e u n i verse. I n t h e f u t u r e t h e y m a y i n c l u d e " c l e a n " a t o m i c p o w e r t h r o u g h n u c l e a r fusion, a n d e v e n w a y s o f r e a c h i n g distant stars a n d s a v i n g t h e h u m a n race from e x t i n c t i o n a s t h e S u n ' s o w n n u c l e a r p o w e r p l a n t s r u n d o w n . W h o i s t o say, t h e n , w h e t h e r t h e c o n s e q u e n c e s of R u t h e r f o r d ' s d i s c o v e r y will ultimately be "good" or "bad"? I myself b e l i e v e t h a t c u r i o s i t y - d r i v e n scientific r e s e a r c h is n o t intrinsically " g o o d " or " b a d . " T h e m o t i v a t i o n s of individual scientists m a y s o m e t i m e s be classified in this way, b u t in g e n e r a l it is so difficult to predict t h e a n s w e r to a n y seriously asked q u e s t i o n , let a l o n e a n y a p p l i c a t i o n s of t h a t a n s w e r , t h a t ethical j u d g m e n t s o n t h e q u e s t i o n o r q u e s t i o n e r a r e s i m p l y ina p p r o p r i a t e . S u c h j u d g m e n t s o n l y c o m e i n w h e n w e begin t o think of h o w we might use the answers, and they involve not only scientists, b u t t h e w h o l e c o m m u n i t y . It is t h e a p p l i c a t i o n s that we n e e d to c o n t r o l , n o t t h e p r o c e s s of discovery. This is not to say t h a t scientists s h o u l d abdicate responsibility,

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b u t t h e responsibility s h o u l d b e placed s q u a r e l y w h e r e i t b e l o n g s — in sharing their knowledge with the wider c o m m u nity, s o t h a t t h e c o m m u n i t y a n d its political l e a d e r s c a n m a k e i n f o r m e d j u d g m e n t s . Scientists c a n d o n o m o r e t h a n t h a t , b u t t h e y s h o u l d d o n o less. One of the prime things that we need to share, and which I h o p e t h a t this b o o k h a s g o n e s o m e w a y t o w a r d s s h a r i n g , i s h o w science a c t u a l l y w o r k s . T h e fact t h a t w e c a n n o t predict w h i c h q u e s t i o n s will p r o d u c e trivial a n s w e r s (or n o a n s w e r s a t all) a n d w h i c h q u e s t i o n s will p r o d u c e significant a n s w e r s m e a n s t h a t w e n e e d p e o p l e w i t h m a n y different a p p r o a c h e s t o p r o v i d e t h e v a r i e t y from w h i c h a few m a j o r results will e m e r g e . T h e p r o b l e m is a k i n to t h a t of g e n e t i c diversity in t h e wild. If we e n d up w i t h a scientific m o n o c u l t u r e , w i t h e v e r y o n e w o r k i n g o n t h e s a m e few q u e s t i o n s ( t h o s e p e r c e i v e d t o b e i m p o r t a n t b y politicians, b u s i n e s s m e n , o r t e c h n o c r a t s ) , t h e result will be no science at all. Unfortunately, that is the w a y that things seem to be heading. T h e d i r e c t i o n of science is largely in t h e c o n t r o l of c o m m i t t e e s w h o d o l e o u t m o n e y for specific projects. P r e s s u r e from t h e m o n e y p r o v i d e r s (mostly g o v e r n m e n t a n d i n d u s t r y ) increasingly m e a n s that support is not forthcoming unless the a p p l i c a n t c a n s h o w a r e a s o n a b l e p r o s p e c t of g e t t i n g a "useful" result. T h e i n e v i t a b l e c o n s e q u e n c e is a focus on p r o b l e m s w h e r e the a n s w e r is either k n o w n or is predictable with such assurance that it is hardly w o r t h checking. Genuinely important questions are pushed to the margins, eventually to b e c o m e extinct, a n d , c o n s e q u e n t l y , t h e diversity of science d e c r e a s e s daily. The above process might have s o m e merit if the answers to p a r t i c u l a r scientific q u e s t i o n s c o u l d lead to p r e d i c t a b l e adv a n c e s in t e c h n o l o g i c a l a p p l i c a t i o n . As m a n y of t h e e x a m p l e s i n this b o o k h a v e s h o w n , t h o u g h , t h e m o s t i m p o r t a n t applications of scientific a d v a n c e s are s e l d o m r e l a t e d to t h e original scientific m o t i v a t i o n . T h e A m e r i c a n b i o c h e m i s t H a n s R o m berg o n c e d r e w up a list of t h e t e n m o s t significant m e d i c a l adv a n c e s of t h e t w e n t i e t h c e n t u r y . S e v e n o u t of t h e ten arose

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from research t h a t h a d n o t h i n g t o d o w i t h t h e e v e n t u a l application. T h e driving force for g e n u i n e r e s e a r c h c o m e s from e a c h individual scientist's p e r c e p t i o n t h a t a q u e s t i o n is important, a n d w o r t h investigating. M a n y q u e s t i o n s t u r n o u t t o b e u n i m p o r tant, but w e c a n n o t a l w a y s tell i n a d v a n c e w h i c h i s w h i c h . T h e very best that we can do is to e n c o u r a g e scientific diversity. All a t t e m p t s t o pick o u t i n a d v a n c e w h i c h q u e s t i o n s a r e w o r t h p u r s u i n g , a n d to focus o n l y on t h o s e , will p r o d u c e a lesser r e sult. With diversity c o m e s responsibility, w h i c h is n o t t h a t of t h e scientist a l o n e , b u t also t h a t of t h e c o m m u n i t y of w h i c h t h e scientist is a part. At t h e m o m e n t , scientists a r e t o o often a p a r t rather than a part, and other m e m b e r s of t h e c o m m u n i t y can c o n s e q u e n t l y feel s u s p i c i o u s a n d d i s e m p o w e r e d . It is up to us, as scientists, to s h a r e w h a t science is a b o u t , a n d w h a t it can a n d c a n n o t d o , w i t h t h e rest of o u r c o m m u n i t y . I h o p e t h a t this hook has a t least t a k e n o n e small step a l o n g t h e way.

appendix 1 : mayer, joule, and the concept of energy

M a y e r ' s u n l i k e l y i n s p i r a t i o n for t h e c o n c e p t of " e n e r g y " w a s t h e sight of a h o r s e s w e a t i n g as it p u l l e d a load up a hill. His key idea w a s t h a t t h e h o r s e w a s g e t t i n g h o t , n o t b e c a u s e i t w a s m o v i n g , b u t b e c a u s e of t h e physical w o r k t h a t it h a d to do to generate the m o v e m e n t . He thus turned the question of the r e l a t i o n s h i p b e t w e e n heat a n d movement i n t o a q u e s t i o n of t h e r e l a t i o n s h i p b e t w e e n heat a n d t h e physical work n e e d e d to p r o duce m o v e m e n t . Having reframed the question, he d r e w three f a r - r e a c h i n g c o n c l u s i o n s . T h e f i r s t w a s t h a t w h e n w e use h e a t to do w o r k (e.g., to d r i v e a s t e a m e n g i n e ) or p e r f o r m physical w o r k t o g e n e r a t e h e a t (e.g., w h e n w e r u b o u r h a n d s t o g e t h e r ) , t h e t w o a r e literally t r a n s f o r m e d i n t o e a c h o t h e r . Heat b e c o m e s w o r k , a n d w o r k s b e c o m e s h e a t . T h a t idea w a s r e m a r k able e n o u g h , b u t h e w e n t f u r t h e r t o d e d u c e t h a t h e a t a n d w o r k m u s t be i n t e r - c o n v e r t i b l e in a c o n s t a n t ratio. O t h e r w i s e , h e a r g u e d , w e could use a n initial small a m o u n t o f h e a t t o d o a s m u c h w o r k a s w e w a n t , simply b y u s i n g t h e w o r k p r o d u c e d initially t o g e n e r a t e m o r e h e a t t h a n w e started w i t h , a n d s o o n . S u c h p r o c e s s e s d o n ' t w o r k , or else we could fly a B o e i n g 7 4 7 by striking a m a t c h . T h e r e is no s u c h t h i n g as a free l u n c h . M a y e r tried t o p r o v e his t h e s i s b y a r r a n g i n g a n e x p e r i m e n t at a p a p e r factory w h e r e t h e p u l p in a large c a u l d r o n w a s stirred by a h o r s e g o i n g a r o u n d a n d a r o u n d in a circle. M e a s u r i n g t h e rise in t h e p u l p t e m p e r a t u r e , he o b t a i n e d a figure for t h e a m o u n t of h e a t p r o d u c e d by a g i v e n a m o u n t of m e chanical w o r k d o n e b y t h e h o r s e . Mayer's e x p e r i m e n t s w e r e crude, a n d he does not receive a n y credit for t h e m i n m o d e r n t e x t b o o k s , d e s p i t e h a v i n g b e e n t h e f i r s t t o c o n c e i v e o r a t t e m p t t h e m . T h e credit goes i n s t e a d t o a n English b r e w e r n a m e d J a m e s Prescott J o u l e , w h o u s e d a

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p a d d l e w h e e l d r i v e n by a falling w e i g h t to stir a b u c k e t of w a ter, finding t h a t t h e t e m p e r a t u r e of t h e w a t e r rose by twice as m u c h w h e n t h e w e i g h t d r o p p e d twice a s far, s o t h a t twice a s m u c h physical w o r k w a s g e n e r a t i n g t w i c e a s m u c h h e a t . J o u l e d e s e r v e s his credit, since h e w a s t h e f i r s t t o p e r f o r m e x p e r i m e n t s w h o s e results w e r e sufficiently a c c u r a t e a n d rep r o d u c i b l e to be c o n v i n c i n g , ft is m o r e difficult, t h o u g h , to reject M a y e r ' s claim to p r i o r i t y for his t h i r d a n d m o s t i m p o r t a n t insight, w h i c h w a s t h a t h e a t a n d physical w o r k a r e n o t o n l y t r a n s f o r m a b l e i n t o e a c h o t h e r , b u t a r e a c t u a l l y different forms o f t h e s a m e t h i n g . W e n o w call t h a t t h i n g e n e r g y . What Mayer had enunciated became what we k n o w now as t h e p r i n c i p l e of conservation of energy, t h e c o r n e r s t o n e of m o d e r n science. Yet his n a m e is h a r d l y e v e r associated w i t h it. M a y e r c o m m i t t e d t h e c a r d i n a l sin — h e w a s a n o u t s i d e r . S o m e e s t a b l i s h m e n t scientists of t h e t i m e d e f e n d e d his priority, b u t o t h e r s , especially t h e British scientist P e t e r G u t h r i e Tait, p o u r e d x e n o p h o b i c s c o r n o n his r a t h e r m e t a p h y s i c a l style of a r g u m e n t as " s u b v e r s i v e of t h e m e t h o d of e x p e r i m e n t a l scie n c e . " E v e n his fellow G e r m a n , H e r m a n n H e l m h o l t z , initially a d e f e n d e r of M a y e r ' s i n n o v a t i v e n e s s , s u b s e q e n t l y d e r i d e d his " p s e u d o - p r o o f . " U n d e r t h e s e criticisms, M a y e r a t t e m p t e d suicide by j u m p i n g o u t of a w i n d o w t h i r t y feet a b o v e t h e street. Luckily, his lack of e x p e r i m e n t a l ability w a s o n c e again p r o v e n and he survived the attempt. He was eventually h o n o r e d as a g e n u i n e i n n o v a t o r , a l t h o u g h his m e t h o d s lacked t h e rigor n e e d e d to c o n v i n c e o t h e r s of t h e c o r r e c t n e s s of his r e m a r k a b l e insights. M a y e r w a s a m a n of ideas. J o u l e w a s a m a n of a c t i o n , eager to c o n f r o n t ideas w i t h h a r d facts. If J o u l e ' s e x p e r i m e n t s to p r o v e t h a t t h e h e a t g e n e r a t e d b y physical w o r k i s i n direct p r o p o r t i o n t o t h e a m o u n t o f w o r k d o n e w e r e truly correct, t h e n t h e rest of M a y e r ' s logic follows. First, t h o u g h , J o u l e h a d t o d e c i d e w h a t "physical w o r k " m e a n t . M a y e r h a d b e e n q u i t e v a g u e a b o u t it. Obviously, "physical w o r k " i s s o m e t h i n g t h a t w e d o w h e n w e m o v e a n object by p u s h i n g or pulling — in o t h e r w o r d s , by a p p l y i n g a

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force. J o u l e decided, a p p a r e n t l y intuitively ( a n d following Carnot's earlier ideas, p u b l i s h e d in 1824 u n d e r t h e title "Reflections o n t h e M o t i v e P o w e r o f Fire"), t h a t t h e a m o u n t o f w o r k t h a t w e d o i n m o v i n g a n object d e p e n d s o n l y o n t h e force t h a t w e a p p l y a n d o n h o w far t h e object i s m o v e d . T h e further we push, and the harder we have to push, the more work we a r e d o i n g . In s i m p l e m a t h e m a t i c a l t e r m s : w o r k = force X d i s t a n c e . T h e definition m a k e s g o o d i n t u i t i v e s e n s e . W h e n w e h a v e t o p u s h a car w h o s e e n g i n e h a s failed, for e x a m p l e , t h e w o r k t h a t w e feel w e a r e d o i n g surely d e p e n d s o n h o w h a r d w e h a v e t o p u s h a n d h o w far w e h a v e t o p u s h t h e car. T h e furt h e r w e p u s h , o r t h e h a r d e r w e p u s h , t h e m o r e w o r k w e feel we are doing. T h e i n t u i t i v e idea of " w o r k " u n d e r l i e s a l m o s t t h e w h o l e of m o d e r n p h y s i c s . All of o u r m e a s u r e m e n t s of " e n e r g y , " for e x a m p l e , rely e v e n t u a l l y o n m e a s u r i n g h o w m u c h w o r k t h e e n ergy c a n b e m a d e t o d o . Since e n e r g y i s n o w b e l i e v e d t o b e t h e stuff of t h e u n i v e r s e , t h e c o r r e c t definition of " w o r k " is crucial. J o u l e ' s i n t u i t i v e g u e s s a t t h e definition, a p p a r e n t l y s o simple, has t u r n e d o u t to be t h e o n e t h a t p r o v i d e s a totally selfconsistent p i c t u r e , a n d is t h e o n e t h a t we still u s e . It is r e m a r k able t h a t t h e w h o l e of m o d e r n physics, r i g o r o u s as it is, h a s as its f o u n d a t i o n a totally i n t u i t i v e g u e s s . J o u l e w a s able t o d e m o n s t r a t e his g u e s s practically b y c o n s t r u c t i n g his f a m o u s p a d d l e - w h e e l e x p e r i m e n t . S h o r t l y after h e h a d c o m p l e t e d it, J o u l e m a r r i e d , a n d t o o k his n e w b r i d e for a h o n e y m o o n at t h e f a m o u s C h a m o n i x falls in t h e Swiss Alps. O n e can i m a g i n e his wife's c h a g r i n w h e n s h e f o u n d t h a t J o u l e h a d secreted a t h e r m o m e t e r i n t h e b a g g a g e , i n t e n d i n g t o m e a sure t h e t e m p e r a t u r e of t h e falls as t h e w a t e r fell t h r o u g h different d i s t a n c e s . I t can o n l y h a v e b e e n m a t c h e d b y J o u l e ' s chagrin w h e n he found that a n y increase in t e m p e r a t u r e was offset by t h e effects of t h e cold air as it carried t h e h e a t a w a y . M a y e r ' s insight h a s n o w b e e n e x t e n d e d t o e n c o m p a s s t h e idea t h a t all f o r m s of e n e r g y c a n be t r a n s f o r m e d i n t o e a c h o t h e r . All of t h e m , for e x a m p l e , c a n be t r a n s f o r m e d i n t o h e a t a n d h e n c e u s e d i n c o o k i n g . T h e f i n a l step w a s m a d e b y Einstein

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w h e n h e s h o w e d t h a t m a t t e r itself m a y b e r e g a r d e d a s c o m p r e s s e d energy, t r a n s f o r m a b l e directly i n t o t h e h e a t of a n u clear p o w e r s t a t i o n o r t h e h e a t a n d light o f a n a t o m i c b o m b . M a y e r ' s logic is f o r m a l i z e d t h e s e d a y s i n t o t h e first of t h e t h r e e l a w s of t h e r m o d y n a m i c s . This l a w (well k n o w n , e v e n if its m e a n i n g is n o t a l w a y s fully a p p r e c i a t e d ) states t h a t e n e r g y c a n n o t b e e i t h e r c r e a t e d o r d e s t r o y e d . T h e s e c o n d l a w stales that converting a n y form of energy to w o r k is never o n e h u n d r e d p e r c e n t efficient ( s o m e i s a l w a y s c o n v e r t e d t o h e a t ) , e x cept at a t e m p e r a t u r e of a b s o l u t e z e r o . T h e third l a w states that we can n e v e r reach absolute zero. These laws are equival e n t to t h e l a w s of g a m b l i n g in t h e old Wild West: 1. You c a n ' t w i n . 2. You c a n ' t b r e a k e v e n . 3 . You m a y n o t l e a v e t h e g a m e .

appendix 2: the effect of temperature on food molecules

T h e effect o f t e m p e r a t u r e o n food m o l e c u l e s d e p e n d s o n t h e t y p e of m o l e c u l e . T h e r e a r e four m a i n t y p e s of m o l e c u l e to c o n s i d e r — w a t e r , fats, c a r b o h y d r a t e s , a n d p r o t e i n s . F r o m t h e p o i n t of v i e w of t h e chef, w a t e r w a s an u n f o r t u n a t e c h o i c e by N a t u r e as t h e u n i v e r s a l , dietetically i n n o c u o u s liquid base for o u r e x i s t e n c e . Essential for life it m a y b e , b u t t h e g a s t r o n o m i cally u n f o r t u n a t e fact is t h a t it is not o n l y b o r i n g in its c o n t r i b u t i o n to flavor, b u t also boils at a t e m p e r a t u r e w h e r e h a r d l y a n y of t h e i n t e r e s t i n g processes in c o o k i n g occur. T h e c o n v e n i e n c e of t h e t e m p e r a t u r e is s u c h , n e v e r t h e l e s s , t h a t boiling w a t e r is f r e q u e n t l y u s e d in c o o k i n g as a safe a n d efficient m e t h o d of t r a n s f e r r i n g h e a t . O n l y t h e surface of t h e food initially r e a c h e s t h e boiling t e m p e r a t u r e of 100°C. T h e secret of u s i n g boiling w a t e r is to t i m e t h e c o o k i n g so t h a t t h e inside of t h e food o n l y h e a t s u p t o t h e ideal c o o k e d t e m p e r a t u r e ( u s u ally well b e l o w 100°C). W a t e r in t h e food itself also f r e q u e n t l y c o n t r i b u t e s to o t h e r desirable c h a n g e s . W h e n w e c o o k rice, pasta, o r p o t a t o e s , for e x a m p l e , w a t e r acts n o t j u s t a s a m e d i u m t o t r a n s f e r h e a t b u t also t o h e l p c h a n g e t h e v e r y t e x t u r e a n d palatability o f t h e c o o k e d food. If h i g h e r t e m p e r a t u r e s are desired, fats a n d oils c a n be u s e d as h e a t transfer m e d i a . T h e y also o c c u r as i m p o r t a n t d i e t a r y c o m p o n e n t s of m a n y foods. M o s t of t h e flavors t h a t we p e r ceive are carried by t h e oily c o m p o n e n t of t h e food (this is w h y diet foods, lacking oil, can taste so b l a n d ) , a n d t h e oil w h e n digested releases t w i c e a s m u c h e n e r g y a s a n e q u i v a l e n t q u a n t i t y of c a r b o h y d r a t e . An oil is simply a fat in t h e m e l t e d , liquid state. T h e r e is a big difference, t h o u g h , b e t w e e n t h e oils f o u n d i n foods a n d t h o s e

200

the effect of temperature on food

molecules

Figure A . 1 : C o m p u t e r - G e n e r a t e d Pictures of Different Types of Food Molecule. A Molecule Consists of Atoms (Represented Here as Spherical Balls) Linked Together by C h e m i c a l B o n d s (Represented Here by Sticks Joining the Atoms). These diagrams are intended to show the shapes and relative complexities of the molecules that go to make up our food. a. Water — Here there are just three atoms — an oxygen atom in the center, linked to two hydrogen atoms. b. Fat— Fats contain three long hydrocarbon chains (i.e., chains of linked carbon atoms with hydrogen atoms attached to each carbon atom), with all three chains attached to a c o m m o n glycerol head-group (on the left of the diagram). They typically contain several hundred atoms. The particular fat shown is an unsaturated fat, which means that a bond in at least one of the chains is doubled up. This has the effect that the chain itself doubles up, as if kicked in the stomach. The one shown here has such double bonds in two of its chains. c. Carbohydrate — Carbohydrates are built from small sugar molecules such as glucose, which comprises a ring of five carbon atoms and one oxygen atom, with other oxygen and hydrogen atoms attached to its periphery. It contains 24 atoms. Most carbohydrates (such as the starch in potatoes and cereals) consist of many such rings joined in a line, and can contain tens of thousands of atoms.

the effect of temperature on food molecules

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d. Protein — Proteins, such as the egg albumin shown here, can also contain thousands of atoms, joined together in chains that can fold to form helices, flat sheets, or an apparently random mess. The mess can be resolved by concentrating on the shapes of the chains rather than the positions of the individual atoms. Here are four albumin molecules with the shapes they adopt in space revealed by this technique.

u s e d to l u b r i c a t e car e n g i n e s . It is t h e difference b e t w e e n J a k e the Peg a n d L o n g J o h n Silver. Food oil m o l e c u l e s , like J a k e t h e Peg, h a v e t h r e e legs a t t a c h e d t o a c o m m o n b a c k b o n e . Lubricating oils, like Long J o h n Silver, h a v e o n l y o n e . T h e s h a p e of t h e legs affects t h e t h e r m a l b e h a v i o r of t h e oil or fat. E a c h "leg" consists of a jointed c h a i n of c a r b o n a t o m s . At sufficiently l o w t e m p e r a t u r e s , t h e legs c a n pack side by side to form a solid crystal. Fat m o l e c u l e s w i t h straight legs ("satur a t e d " fats) pack closely, v i b r a t e little, a n d r e q u i r e a relatively high e n e r g y t o s e p a r a t e t h e m . T h o s e w i t h b e n t legs ( " u n s a t u r a t e d " fats) pack less well, a r e easier to s e p a r a t e , a n d m e l t at a l o w e r t e m p e r a t u r e . S o m e , like t h o s e from p e a n u t a n d safflower, m a y e v e n b e oils a t r o o m t e m p e r a t u r e . Fat a n d w a t e r m o l e c u l e s a r e relatively small, a n d t h e effect of t e m p e r a t u r e on their c u l i n a r y b e h a v i o r is relatively simple, consisting largely of freezing or m e l t i n g . Protein a n d c a r b o h y d r a t e m o l e c u l e s a r e usually m u c h larger. A typical fat m o l e c u l e m a y c o n t a i n a c o u p l e of h u n d r e d a t o m s , w h e r e a s p r o t e i n s a n d c a r b o h y d r a t e s m a y c o n t a i n m a n y t h o u s a n d s . T h e smallest carb o h y d r a t e m o l e c u l e , glucose, is actually r a t h e r smaller t h a n a fat m o l e c u l e . Plants store glucose, h o w e v e r , n o t as single m o l ecules, b u t m o s t l y as long c h a i n s of linked m o l e c u l e s in t h e form of starch. T h e s e c h a i n s in t u r n pack i n t o e l a b o r a t e s t r u c t u r e s , w h e r e crystalline layers a l t e r n a t e w i t h a m o r p h o u s layers in a series of c o n c e n t r i c rings, beautiful to o b s e r v e u n d e r t h e microscope. All oi this n a t u r a l b e a u t y is u n d o n e w h e n we cook starchy foods such as rice, pasta, or potatoes. As t h e t e m p e r a t u r e increases, w a t e r m o l e c u l e s gradually i n s i n u a t e t h e m s e l v e s bet w e e n t h e starch c h a i n s . T h e delicate e n e r g e t i c b a l a n c e b e t w e e n t h e a t t r a c t i o n of t h e c h a i n s for w a t e r or for e a c h o t h e r is g r a d ually shifted until, at a p a r t i c u l a r t e m p e r a t u r e (62°C for p o t a t o

202


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starch), the chains suddenly separate hugely to a c c o m m o d a t e a n influx o f w a t e r t h a t t u r n s t h e starch g r a n u l e s from h a r d gritty particles to a soft s w o l l e n jelly. H i g h e r t e m p e r a t u r e s d o n ' t p r o d u c e a n y f u r t h e r effect — p o t a t o e s , for e x a m p l e , c a n be c o o k e d q u i t e c o m f o r t a b l y at 70°C. ft j u s t t a k e s l o n g e r for the heat to reach t h e center. M e a t a n d fish a r e m a j o r s o u r c e s of p r o t e i n s , w h i c h g e n e r a l l y r e q u i r e l o w e r t e m p e r a t u r e s t h a n c a r b o h y d r a t e s for t h e d i s r u p tion o f t h e i r s t r u c t u r e . T h e e n e r g y n e e d e d t o d i s r u p t t h e t h r e e d i m e n s i o n a l s t r u c t u r e of m a n y folded p r o t e i n c h a i n s , for e x a m p l e , c o r r e s p o n d s to a t e m p e r a t u r e of a r o u n d 40°C (this is w h y o u r b o d y t e m p e r a t u r e s a r e locked at 37°C). A h i g h - q u a l i t y steak, s u c h as fillet or sirloin, consists principally of t h e m u s c l e p r o t e i n s actin a n d m y o s i n , w h i c h a d o p t a n e x t e n d e d configur a t i o n i n t h e r e l a x e d m u s c l e t h a t i s m a i n t a i n e d b y w e a k crosslinks. T h e m u s c l e p r o t e i n s s h o r t e n w h e n t h e i r cross-links a r e b r o k e n ; a p r o c e s s t h a t m a k e s t h e m e a t t o u g h e r . S u c h steaks should not be heated at the center to t e m p e r a t u r e s m u c h a b o v e 40°C, w h i c h i s w h y w e use s u c h s h o r t c o o k i n g t i m e s for them. T h e p r o t e i n s i n c o n n e c t i v e tissue ( t h e w h i t e s t r a n d s a n d s h e e t s i n m e a t ) r e q u i r e m u c h h i g h e r t e m p e r a t u r e s for d i s r u p t i o n of t h e i r t h r e e - d i m e n s i o n a l s t r u c t u r e . T h e p r i n c i p a l c o m p o n e n t of c o n n e c t i v e tissue is t h e p r o t e i n collagen, w h i c h actually consists o f t h r e e p r o t e i n c h a i n s , w o u n d a r o u n d e a c h o t h e r to give a s t r o n g r o p e - l i k e s t r u c t u r e , w h i c h is w h y m e a t w i t h a lot of c o n n e c t i v e tissue in it is so t o u g h . To d i s r u p t this s t r u c t u r e r e q u i r e s a t e m p e r a t u r e of a r o u n d 60°C, t o g e t h e r w i t h t h e p r e s e n c e of w a t e r . A c o m b i n a t i o n of t h e t w o c o n v e r t s t h e t r i p l e - s t r a n d e d collagen i n t o s i n g l e - s t r a n d e d gelatin, w h i c h is m u c h softer a n d m o r e digestible. Unfortunately, at such a high t e m p e r a t u r e t h e m u s c l e p r o t e i n s will h a v e b e c o m e very t o u g h . T h e s o l u t i o n , s u c h as it is, is e i t h e r to c h o o s e h i g h - q u a l i t y m e a t s or to accept a c o m p r o m i s e in t e x t u r e . At even higher temperatures, t h e kinetic energy of the molecules c a n b e c o m e g r e a t e r t h a n t h e e n e r g y o f t h e b o n d s b e t w e e n individual a t o m s in the chain. The chain m a y break up,


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a n d t h e b o n d s can b e c o m e available t o form n e w links w i t h o t h e r m o l e c u l e s . This is w h a t h a p p e n s in browning, w h e r e t h e k i n e t i c e n e r g y at t e m p e r a t u r e s a b o v e 140°C is so h i g h t h a t p r o t e i n a n d c a r b o h y d r a t e c h a i n s can form c o m p l i c a t e d n e w cross-links w i t h e a c h o t h e r , p r o d u c i n g n e w m a t e r i a l s that a r e b o t h b r o w n a n d tasty. W e start o u r roasts off a t h i g h o v e n t e m peratures to p r o m o t e these browning reactions.

notes and references

c h a p t e r 1 : the art a n d s c i e n c e o f d u n k i n g Page 1 Market research on cookie dunking. Informal survey c o n d u c t e d in London in c o n n e c t i o n with t h e "cookie d u n k i n g " project. 2 . . . ait clastic net of the protein gluten. N e t w o r k was defined t o n g u e in-cheek in J o h n s o n ' s 1755 Dictionary of the English Language as " a n y t h i n g reticulated or decussated at equal intervals, w i t h interslices b e t w e e n t h e intersections." It is t h e interstices, or crosslinks, that c o u n t ; w i t h o u t t h e m t h e r e w o u l d be no net. For t h e last fifty years it has been believed that these cross-links in w h e a t Hour d o u g h are formed by disulphide b o n d s . Only recently has it been discovered (Tilley, K., Journal of Agricultural and Food Chemistry, vol. 4 9 , p. 2627) that they are formed by cross-links b e t w e e n the totally different tyrosine residues, and that t h e disulphide idea was not based on hard evidence. It just goes to s h o w that "folk exp l a n a t i o n s " are as likely to p e n e t r a t e science as a n y w h e r e else. The difference is that, in science, t h e r e is at least a w a y of eliminating t h e m . 3 . . . seven thousand calls in a quarter of an hour. Not all of the calls were about d u n k i n g . M a n y inquirers w a n t e d t o k n o w a b o u t t h e science u n d e r l y i n g o t h e r familiar activities, such as cooking, s u n bathing, and using mobile t e l e p h o n e s . The supposedly abstruse and difficult scientific principles involved in t h e a n s w e r s s e e m e d to pose little difficulty lor t h e questioners, since t h e principles w e r e being related to s o m e t h i n g with w h i c h t h e y w e r e already familiar. 3 Robert Hooke and the Royal Society. "Hooke, Robert," article in Encyclopaedia Britannka, I l i b edition, Cambridge University Press, Cambridge, 1911. The exact terms of Uooke's a p p o i n t m e n t , as recorded in t h e .Journal Book of t h e Royal Society lor 5 N o v e m b e r 1662, w e r e : "Sir Robert Moray proposed a person [Hooke] willing to be e m ployed as a curator by t h e Society, a n d offering to furnish t h e m every day, on w h i c h they met, with t h r e e or four considerable exp e r i m e n t s , a n d expecting no r e c o m p e n c e till t h e Society should gel a stock enabling t h e m to give it."


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"Considerable," it transpired, m e a n t "original." And today's Ph.D s t u d e n t s think t h a t they h a v e it t o u g h ! 4 The structure of DNA. Watson, J a m e s D., The Double Helix, A t h e n e u m , N e w York, 1968. 5 Francis Bacon and the nature of scientific research. Bacon, Francis, The Novum Organon, or, A True Guide to the Interpretation of Nature, Kitchen, G. W. (transl.), Oxford University Press, Oxford, 1855. An a m a z i n g n u m b e r of p e o p l e still t h i n k t h a t science w o r k s in the w a y t h a t Bacon suggested. 5

Paradigm shifts in science. K u h n , Thomas, The Structure of Scientific Revolutions, 2 n d edition, Chicago University Press, Chicago, 1970. 5 Proof in science. Medawar, Peter, The Limits of Science, Oxford University Press, Oxford, 1985. 6 The mathematics of a drunkard's walk. " D r u n k a r d ' s Walk Helps Unfold Secret of Polymers," New Scientist m a g a z i n e (136), 12 D e c e m ber 1992. This article s u m m a r i z e s t h e principles of r a n d o m walks in an accessible way, and s h o w s h o w t h e s q u a r e relationship and t h e factor of four t h a t follows arises. T h e r e are also n u m e r o u s Web sites t h a t cover t h e subject of r a n d o m walks at different levels of sophistication. 7 Washburn's experiments (andequation). W a s h b u r n , E. W., Physics Review (17), 1921, p. 374. 8 Graphs, symbols, and equations. These are an i m m e n s e source of confusion to non-scientists (and to s o m e scientists!), but they n e e d n ' t be. T h e principle is very simple. An equation describes h o w o n e t h i n g d e p e n d s on a n o t h e r . 11 a car is traveling at 60 kilom e t e r s p e r h o u r , for e x a m p l e , t h e n t h e e q u a t i o n (distance in kilometers) = 60 X ( n u m b e r of h o u r s ) s h o w s just h o w t h e distance traveled d e p e n d s o n t h e time spent. To avoid writing e v e r y t h i n g out in full, scientists use abbreviations. D is a c o m m o n abbreviation for distance, and t is t h e universal abbreviation for time. T h e e q u a t i o n a b o v e t h u s b e c o m e s D = 60 X t, w h i c h is m u c h easier to write a n d just as easy to read with a little practice. A graph is simply a n o t h e r w a y of writing an e q u a t i o n to display visually h o w o n e t h i n g d e p e n d s o n a n o t h e r . B y c o n v e n t i o n , the t h i n g t h a t is d e p e n d e d on (in this case, t h e time) is d r a w n along t h e b o t t o m (horizontal) axis, a n d t h e t h i n g that d e p e n d s on it (the distance) occupies t h e vertical axis. It's t h a t simple. 10 Young's version of the Young-Laplace equation. Young, T h o m a s , Philosophical Transactions of the Royal Society of London (95), 1805, p. 65. See also Young, T h o m a s , A Course of Lectures on Natural Philosophy and the Mechanical Arts (2 vols.), J. J o h n s o n , L o n d o n , 1807.


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Young h a t e d m a t h e m a t i c a l symbols a n d w r o t e his e q u a t i o n s o u t entirely in words, w h i c h m a k e s reading his papers incredibly hard going. 11 Laplace's version of the Young-Laplace equation. Laplace, Pierre Simon de (Marquis), Supplement au dixleme llvre du tralte de mecanlque celeste, 1806. Translated a n d a n n o t a t e d by B o w d i t c h , N. (4 vols.), 1 8 2 9 - 1 8 3 9 , Boston. Reprinted by Chelsea Publishing Co., N e w York, 1966. 12 Scientists investigating familiar phenomena. This has frequently led to i m p o r t a n t and f u n d a m e n t a l discoveries. The f a m o u s story t h a t N e w t o n discovered t h e universal law of gravitation after being hit on t h e h e a d by a falling apple u n f o r t u n a t e l y has no f o u n d a t i o n ( a l t h o u g h it is interesting to n o t e t h a t t h e m o d e r n unit of force [the N e w t o n ] is a p p r o x i m a t e l y equal to t h e force of gravity on an average-sized apple). There are, t h o u g h , p l e n t y of real e x a m p l e s of universal laws being derived from t h e observation of c o m m o n place p h e n o m e n a . These include: Galileo's discovery of t h e p e n d u l u m laws after observing t h e swinging of a c h a n d e l i e r in t h e cathedral of Pisa; M e n d e l ' s d e d u c t i o n of t h e laws of genetics from his observations of peas g r o w i n g in a g a r d e n ; Rumford's h y p o t h e sis t h a t h e a t is a form of m o t i o n , a conclusion t h a t he c a m e to alter observing t h e e n o r m o u s a m o u n t s of h e a t g e n e r a t e d d u r i n g t h e boring of brass c a n n o n s ( a n y o n e w h o has ever had occasion to drill a hole in a piece of m e t a l will be a w a r e of this p h e n o m e n o n on a smaller scale). In m o d e r n times, t h e universal t h e o r y of chaos, w h i c h d o m i n a t e s such diverse topics as t h e g r o w t h a n d decline of a n i m a l p o p u l a t i o n s a n d financial m o v e m e n t s in t h e stock m a r ket, originated from Lorenz's efforts to u n d e r s t a n d w e a t h e r patterns. 12 Mean radius of curvature. I h a v e used t h e technical t e r m " m e a n " h e r e so t h a t my fellow specialists in t h e field d o n ' t s h o o t me d o w n . Most menisci are curved differently in different directions, and t h e calculation of a " m e a n " is used to a c c o u n t for this fact. 14

Poiseuille's equation. The e q u a t i o n is simply:

w h e r e L is t h e distance traveled by a liquid of viscosity r\ in t i m e t along a cylindrical t u b e of radius R u n d e r a p r e s s u r e head AP (Poiseuille, J. L. M., Comptes Rendus de I'Academie de Sciences, Paris (11) 9 6 1 , 1041 (1840); (15) 1167 (1844)). Note: A is t h e usual scientific s h o r t h a n d for "a c h a n g e in."


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Experiments on the swelling of individual starch granules. These were reported in Fisher, L. R., Carrington, S. P., a n d Odell, I. A., "Deformation M e c h a n i c s ol Individual Swollen Starch G r a n u l e s , " Starch, Structure and Functionality (P. J. Frazier, P. R i c h m o n d , a n d A. M. Donald, eds.), Royal Society of C h e m i s t r y ( L o n d o n ) , Special Publication, n o . 2 0 5 , 1997, p. 105. 18 Stress. The t e r m has a precise technical definition, w h i c h in this case is just t h e force divided by t h e area over which it is applied. Since t h e area at t h e crack tip is tiny, the stress is h u g e . 18 The science of how cracks form and grow. The p h e n o m e n o n is discussed in an e n t e r t a i n i n g and simple fashion in The New Science of Strong Materials, G o r d o n , .1. E., 2nd edition, Pelican, London, 1976, w h i c h also gives a p h o t o g r a p h of the Majesties near-disaster. A picture of t h e Schenectady actual disaster is given in Structures, Gordon, J. E., Pelican, London, 1978. 20 Media coverage of cookie dunking. The story was featured in all major Britisli n e w s p a p e r s over 2 4 - 2 5 N o v e m b e r 1998, a p p e a r e d on TV and radio n e w s w o r l d w i d e , and e v e n found a place in t h e Wall Street Journal. It also b e c a m e t h e subject of n u m e r o u s features. 21 N a t u r e article on cookie dunking. Fisher, Len, "Physics Takes t h e Biscuit," Nature (397), 4 6 9 , 1999.

c h a p t e r 2 : h o w d o e s a scientist boil a n e g g ? Page 23 James Bond's gourmet pretensions. These are amusingly dealt with l>\ Kingsley Amis in The James Bond Dossier, J o n a t h a n Cape, 1965. 24 Nicholas Kurti. His r e m a r k a b l e life is d o c u m e n t e d in Biographical Memoirs of the Royal Society of London (46), 2000, pp. 2 9 9 - 3 1 5. 24 The Physicist in the Kitchen. This w a s the topic of o n e of t h e famous Friday E v e n i n g Discourses p r e s e n t e d at L o n d o n ' s Royal Institution (founded by R u m f o r d ) . Nicholas broke with tradition in having his lecture televised live, a n d also by refusing to be locked up b e f o r e h a n d , a tradition that developed after a lecturer in t h e last c e n t u r y (Charles W h e a t s t o n e ) took fright a n d ran a w a y before t h e lecture. The actual date of t h e broadcast was Friday, 14 March 1969. Unfortunately, t h e BBC has destroyed t h e only tape ol this historic e v e n t . The only record is t h e script, published in Proceedings of the Royal Institution (42), no. 199. 26 . . . the sensation of heat is caused by particles of caloric passing into our bodies. M a u n d e r , S., Scientific and Literary Treasury, 1841.


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The life of Benjamin Thompson. This has b e e n written up in m a n y plates. A particularly interesting a t c o u n t is given in t h e ineffable 11th edition of t h e Encyclopaedia Britannica (artitle on "Rumford, Benjamin T h o m p s o n , C o u n t , " Encyclopaedia Britannica. 11th edition, Cambridge University Press, Cambridge, 191 1). W h e n R u m ford gained his title, his American origins asserted themselves, and he took t h e title of " C o u n t R u m f o r d " in recognition ol his wife's h o m e t o w n of Rumford, New Hampshire, n o w k n o w n as Concord and t h e state capital. Rumford was an insatiable observer of life's m i n u t i a e , and a prime e x a m p l e of a scientist w h o used observations of c o m m o n place p h e n o m e n a as a basis for a d v a n c i n g o u r scientific understanding. His personal philosophy, very a p p r o p r i a t e to t h e present book, w a s t h a t : " . . . in the o r d i n a r y affairs and o c c u p a t i o n s of life, o p p o r t u n i t i e s [often] present i h e m s e l v e s ol c o n t e m p l a t i n g s o m e of t h e most c u r i o u s o p e r a t i o n s of N a t u r e . . . a habit of keeping the eyes open to e v e r y t h i n g that is going on in d i e o r d i n a r y course ol the business ol life has oftener led . . . to useful d o u b t s , and sensible s c h e m e s ol investigation a n d i m p r o v e m e n t , t h a n all t h e m o r e intense m e d i t a t i o n s of p h i l o s o p h e r s . . ." O n e of the "ordinary affairs" in w h i c h Rumford interested himself was cooking. He wished "to inspire cooks with a just idea of t h e i m p o r t a n c e of their art, a n d of t h e i n t i m a t e c o n n e c tion t h e r e is b e t w e e n the various processes in which they arc daily t o n t e r n e d , a n d m a n y of t h e most beautiful discoveries that have been m a d e by e x p e r i m e n t a l p h i l o s o p h e r s in t h e present age." The story of Rumford and t h e bread oven was brought to my attention by t h e food writer Harold MeGee, w h o reported it in his fascinating book The Curious Cook, North Point Press, New York, 1999, p. 22.

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The history of the demise of caloric. This is fascinating in its o w n right as an e x a m p l e of h o w seienee really w o r k s — not by definitive exp e r i m e n t a n d i m m e d i a t e acceptance of a n e w idea, but by test and countertest, a r g u m e n t and c o u n t e r a r g u m e n t , and a b o v e all by o p e n n e s s , a too frequent casualty in today's world of industrial and military secrecy. The history is discussed in most standard histories of science, and, for t h o s e with a scientific b a t k g r o u n d , H a r m a n , P. M., Energy, Force and Matter, Cambridge University Press, Cambridge, 1982, a n d Brush, S. G., The Kind of Motion We Call Heat. North-Holland, 1976.

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. . . it was considered prudent that he should seek an early opportunity of leaving. See "Rumford, Benjamin T h o m p s o n , C o u n t , " Encyclopae-


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dia Britannica, l l t h edition, Cambridge University Press, C a m bridge, 191 1. Rumford's observations on boring cannons. These are reported in his Collected Works, vol. II, essay IX. Read before Royal Society, 25 J a n u a r y 1798. Mayer's ideas. These w e r e first reported in The Motions of Organisms and their Relation to Metabolism, published in 1824 (reprinted in Lindsay, R. Bruce, Energy: Historical Development of the Concept, D o w d e n , H u t c h i n s o n Ross, Inc., 1975). The notion of heat as motion. This w a s finally codified by J o h n Tyndall in Heat: A Mode of Motion, 6th edition, L o n g m a n s , Green 8- Co., London, 1880, a book in which he also p r e s e n t e d a spirited defense of Mayer's c o n t r i b u t i o n . Einstein on heat and temperature. The q u o t e is from Albert Einstein and Leopold Infeld in The Evolution of Physics, Cambridge University Press, Cambridge, 1938. The presence of Infeld as a c o a u t h o r provides a n o t h e r insight into h o w science really works. W h e n Einstein moved to Princeton, he m a d e it a condition of his e m p l o y m e n t that a second position be created so that he w o u l d h a v e s o m e o n e to talk to. The person w h o gained that position w a s Infeld. The story shows that even scientists such as Einstein do not live in ivory towers. C o m m u n i c a t i o n and exchange of ideas is t h e n a m e of the game, for Einstein and for almost every scientist I have k n o w n .

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Temperature as average kinetic energy. To be precise, the energy of a m o l e c u l e is given by k X T, w h e r e k is a n u m b e r called Boltzm a n n ' s c o n s t a n t . The multiple w e a k i n t r a c h a i n links that m a i n tain t h e t h r e e - d i m e n s i o n a l structures of long c a r b o h y d r a t e and p r o t e i n molecules typically require an e n e r g y of a few £7* to break t h e m . To break a chemical b o n d w i t h i n t h e chain requires an e n ergy of a r o u n d 80 kT.

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Rumford's discovery of convection. This is described in Rumford's Collected Works, vol. II, essay VII. Q u o t e d in Magie, W. F., A Source Book in Physics, Harvard University Press, Cambridge, Mass., 1965, p. 146.

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Chefs and the rules of conduction. I am again indebted to Harold McGee for t h e story of an informal poll by t h e A m e r i c a n food writer E d w a r d Behr w h i c h resulted in a c o n s e n s u s a m o n g the chefs polled that a fish fillet twice as thick as a n o t h e r w o u l d takeless t h a n twice t h e time to cook (see The Curious Cook, N o r t h Point Press, New York, 1999, p. 33). Harold has recently p r o d u c e d a c o m p u t e r m o d e l of t h e t e m p e r a t u r e distribution in a piece ol steak cooked u n d e r various conditions (McGee, H., M c l n e r n e y , J., a n d Harrus, A., Physics Today, N o v e m b e r 1999, p. 30).


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34 Solutions to Fourier equation for objects of different shape. These are discussed in an u n d e r s t a n d a b l e m a n n e r by my colleague a n d freq u e n t c o a u t h o r on food m a t t e r s , Dr. Peter B a r h a m , in his book The Science of Cooking, Springer-Verlag, 2000, p. 4 3 . 35 The "interesting mathematical reason. " In this instance t h e reason for t h e r a n g e of a g r e e m e n t b e t w e e n t h e s q u a r e rule a n d classical rules for cooking times comes from t h e fact that, if t h e cooking time t is p r o p o r t i o n a l to t h e s q u a r e of t h e thickness d for a slab of m e a t , t h e n a small increase Ad in t h e thickness m e a n s t h a t t h e cooking t i m e will increase by a factor (d + Ad) 1 d , w h i c h is e q u a l to (d + 2d + (Ad) ) I d . The point, as t h o s e w h o h a v e l e a r n e d calculus will k n o w , is t h a t if (Ad) is very small c o m p a r e d to t h e o t h e r t w o t e r m s , a n d can b e neglected, t h e n t h e cooking t i m e increases linearly w i t h thickness, just as predicted by Mrs. B e e t o n (and my m o t h e r ) . The p o i n t is m a d e in a different w a y by P. B. Fellgett in Kurti, N. & G. (eds.), But the Crackling Is Superb, A d a m Hilger, 1988, p. 40 (an a n t h o l o g y on food a n d d r i n k by Fellows and Foreign M e m b e r s of t h e Royal Society). 2

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Richard Gardner. His t e m p e r a t u r e m e a s u r e m e n t s on boiling eggs are r e p o r t e d in Kurti, N. & G. (eds.), ibid., p. 53. 39 Charles Williams. His calculations of egg-boiling times, a n d Herve This's c o m m e n t s on t h e relative setting t e m p e r a t u r e s of w h i t e a n d yolk, w e r e r e p o r t e d in New Scientist, 13 J u n e 1998. 40 The effects of temperature on food molecules. For m o r e detail see, for e x a m p l e , McGee, H., On Food and Cooking, Fireside Books, N e w York, 1997, and, B a r h a m , P. J., The Science of Cooking, SpringerVerlag, 2 0 0 0 .

c h a p t e r 3: the t a o of t o o l s

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Woodworking Tools and How to Use Them. This classic book w a s rew o r k e d by Jack Hill (David & Charles, N e w t o n Abbot, 1983). 44 The Greek author called the "pseudo-Aristotle." This a u t h o r derived t h e law of t h e lever a r o u n d a h u n d r e d years before A r c h i m e d e s , b u t t h e derivation only stands up to critical e x a m i n a t i o n if it is ass u m e d t h a t t h e a u t h o r was a w a r e of t h e m o d e r n "principle of virtual velocities," w h i c h he probably w a s n o t (Lindsay, R. B., ed., Energy: Historical Development of the Concept, D o w d e n , Hutchinson & Ross, Inc., 1975, p. 32). 48 Geiger counters. These are designed to register t h e passage of p a r ticles such as alpha-particles t h a t are e m i t t e d d u r i n g radioactive

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decay. A r e a d e r of t h e Australian m a g a z i n e Radio and Hobbies (a m o n t h l y periodical on w h i c h I a n d m a n y o t h e r s cut o u r electronic teeth) did n o t k n o w this, a n d w r o t e t o t h e editor t o ask w h a t Geiger c o u n t e r s c o u n t e d . The editor, straight-faced, replied: "Why, Geigers, of c o u r s e , " and w e n t on to explain t h a t Geigers w e r e w h a t m o d e r n scientists c o u n t e d in o r d e r to get to sleep. He e v e n p r o v i d e d a p i c t u r e of o n e :

48 Geiger and Marsden. Their observations w e r e published in J u n e 1909, a n d t h e w h o l e w o r l d had a c h a n c e to w o r k o u t w h a t t h e y m e a n t . Rutherford got t h e r e first, a l t h o u g h it took h i m e i g h t e e n months. Rutherford tried two pictures of t h e a t o m — o n e w h e r e all the positive charge was in t h e middle, and o n e w h e r e all t h e negative charge was in the middle. In t h e first case, t h e positively charged alpha-particles would be repelled if t h e y c a m e too close. The second case was not ruled out, t h o u g h , because, a l t h o u g h alpha-particles in this instance w o u l d be attracted to the nucleus, they could well swing a r o u n d it and r e t u r n in t h e direction from w h i c h t h e y came, like a c o m e t a r o u n d the sun. W h e n Rutherford did t h e m a t h e m a t ics for t h e t w o cases, t h e answers c a m e o u t t h e same. It needed o t h e r evidence to s h o w that t h e first a n s w e r was the correct one. Rutherford's picture of t h e a t o m was n o t just based on o n e imaginative conceptual leap, i m p o r t a n t t h o u g h that w a s . There h a v e b e e n plenty of equally brilliant conceptual leaps that have landed on t h e w r o n g answer. Rutherford, t h o u g h , used his picture to predict just w h a t fraction of alpha-particles w o u l d be scattered t h r o u g h various angles, a n d found that his q u a n t i t a t i v e predictions agreed with M a r s d e n ' s m e a s u r e m e n t s . This w a s t h e real clincher.


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Rutherford a n n o u n c e d his idea, not in t h e prestigious Proceedings of the Royal Society as Geiger and M a r s d e n had d o n e , but to a m e e t i n g of the M a n c h e s t e r Literary a n d Philosophical Society. This says s o m e t h i n g for t h e status of s u c h societies a n d for public interest in real science at that t i m e . 48 Rutherford and the atom. Rutherford was fond of recounting t h e story of Marsden's e x p e r i m e n t s . The version h e r e is assembled from several sources, t h e principal o n e being David Wilson's Rutherford: Simple Genius, MIT Press, Cambridge, Mass., 1984, p. 2 9 1 . 49 The less likely an experiment is to work, the more significant the result is likely to be. Unfortunately, t h e p o w e r s n o w in charge of providing support for science often v i e w things in the opposite light, a n d pay o u t largely on t h e basis of t h e a priori chances of success. This has led to s o m e interesting g a m e s , w h e r e scientists do experim e n t s first and t h e n apply for t h e m o n e y , using that m o n e y to secretly fund t h e n e x t r o u n d . 49

History of the hammer. See G o o d m a n , W. L., History of Woodworking Tools, Bell, 1964. My grandfather, a carpenter, claimed to have used t h e s a m e h a m m e r t h r o u g h his entire w o r k i n g life, and only had to replace t h e h e a d twice and t h e h a n d l e t h r e e times. 49 Fitting the hammer handle through a hole in the head. Australian Aborigines used rocks with holes in t h e middle as spear straighteners, but a p p a r e n t l y did not take t h e n e x t step of fitting axe h e a d s , etc., in a similar way. 52 Work = force X distance. My search t h r o u g h old scientific articles, books, a n d encyclopedias has revealed that no o n e scientist h a s ever p r o v e d that w o r k = force X distance. All that h a p p e n e d w a s that t h e c o n s e r v e d q u a n t i t y (force X distance), identified as imp o r t a n t by Galileo, gradually b e c a m e identified w i t h t h e w o r d "work," so t h a t by 1855, 150 years after Galileo's d e a t h , scientists had hijacked t h e w o r d from c o m m o n l a n g u a g e for good. Its n e w definition was accepted w i t h o u t q u e s t i o n by scientists such as J o u l e w h e n he established t h e e q u i v a l e n c e of heat a n d w o r k . 53 Conservative forces and friction. Scientists call t h e force used to m o v e a load in t h e a b s e n c e of friction a conservative force, because t h e m o v e d load can in principle s u b s e q u e n t l y be used to t h e n m o v e a n o t h e r o n e , so that t h e effort isn't lost. Frictional forces, t h o u g h , are n o n - c o n s e r v a t i v e , since t h e w o r k t h a t has g o n e i n t o g e n e r a t ing h e a t is usually lost. 54 The force required to remove a nail. This is given in Marks' Standard Handbook for Mechanical Engineers, 8th edition, McGraw-Hill, 1978,


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p p . 1 2 - 2 9 . T h e actual force d e p e n d s on t h e 2.5 p o w e r of t h e d e n sity of t h e w o o d , a n d is also p r o p o r t i o n a l to t h e d i a m e t e r of t h e nail and t h e length of e m b e d m e n t . 56 The length of engagement formula. This, t o g e t h e r w i t h o t h e r formulae too n u m e r o u s a n d exciting to m e n t i o n , a r e given in Ryffel, Henry H. (ed.), Machinery's Handbook, 23rd edition, Industrial Press Inc., N e w York, 1988, p. 1278. 57 Tightening bolts. Stuart Burgess has m a d e s o m e interesting further points, w h i c h I q u o t e h e r e with his permission: 1. A n e a t w a y to tighten a bolt is to h e a t it up first, a n d t h e n do it up to h a n d tightness. W h e n it cools d o w n it s h o r t e n s , and becomes pretensioned. 2. M a n y screws are m a d e of soft metals, a n d a r e easily d a m a g e d by h a r d e n e d screwdrivers, a n d still m o r e by h a r d e n e d misusers of screwdrivers. 3. Spring w a s h e r s are good at indicating t h e correct preload in screws a n d bolts. 4. There is a p p a r e n t l y a special screwdriver available with an offset in t h e middle section of t h e h a n d l e , so t h a t t h e tightening h a n d s w e e p s t h r o u g h a larger circle t h a n just twisting. This does p r o v i d e a t r u e "lever" m e c h a n i c a l a d v a n t a g e . 63 63

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The historic definition of a "barrow." See t h e c o m p l e t e edition of the Oxford English Dictionary. The wheelbarrow in China. This is discussed in N e e d h a m , Joseph, Science and Civilisation in China (abridged by Colin R o n a n ) , Cambridge University Press, Cambridge, 1978, p. 7 5 . Cutting tools . . . are the oldest. S t o n e flakes discovered in t h e Nihew a n Basin of China, for e x a m p l e , h a v e n o w b e e n dated as 1.36 million years old (Nature, vol. 4 1 3 , p. 4 1 3 ) . Formulas for Stress and Strain, Roark, R. J., 3rd edition, McGrawHill, 1954. A screwdriver thus used acts as a rigid extension to the operator's arm. Stuart Burgess claims that "a screwdriver is really a w r e n c h used in-line." I leave it to t h e reader to decide b e t w e e n Stuart a n d Jeff. Engineering reference information. Most of this is t a k e n from Baumeister, T, Avallone, E. A., a n d Baumeister, T., Ill, Marks' Standard Handbook for Mechanical Engineers, 8th edition, McGrawHill, 1978.


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c h a p t e r 4 : h o w t o a d d u p y o u r s u p e r m a r k e t bill Page 79

The principle of concentrating on significant figures. This is a principle that scientists use all t h e t i m e . The trick is to recognize w h i c h figures are significant a n d w h i c h a r e n ' t . Failure to do this can lead to scientific ruin, as h a p p e n e d to t h e congenial Viennese physicist Felix Ehrenhaft, a frequent host to Einstein a n d o t h e r s . Ehrenhaft spent m u c h of his life trying to m e a s u r e the charge on t h e electron, using a t e c h n i q u e w h e r e a cloud of tiny w a t e r droplets was sprayed b e t w e e n t w o horizontal charged m e t a l plates. Most of t h e droplets w o u l d fall slowly u n d e r t h e i n l l u e n c e of gravity. Occasionally, h o w e v e r , a droplet w o u l d pick up a stray electron liberated by a passing cosmic ray. The charged droplet w o u l d t h e n start to m o v e t o w a r d s t h e positively charged u p p e r plate. By m e a s u r i n g t h e rate of m o v e m e n t , t h e e x p e r i m e n t e r could calculate t h e electrical charge. The p r o b l e m w a s t h a t s o m e of t h e droplets, u n a w a r e of t h e e x p e r i m e n t e r ' s i n t e n t i o n s , i n c o n veniently chose t o pick u p m o r e t h a n o n e electron. Ehrenhaft k n e w that this was a possibility, and took m a n y m e a s u r e m e n t s , calculating t h e charge on each drop a n d looking for a c o m m o n factor w h i c h w o u l d be t h e charge c o r r e s p o n d i n g to just o n e electron. He d r e w a frequency distribution of his results, s h o w i n g h o w m a n y times each particular v a l u e of t h e charge occurred. His results for 500 separate e x p e r i m e n t s are r e d r a w n h e r e as faithfully as I can m a n a g e from t h e full set of data r e p r o d u c e d in G. Holton's excellent book, The Scientific Imagination: Case Studies, Cambridge University Press, Cambridge, 1978, p. 74. The charge on an individual electron is n o w k n o w n to be 4.80 X 1 0 ' " electrostatic units, and it seems obvious in retrospect t h a t Ehrenhaft's first (and largest) peak c o r r e s p o n d e d to drops carrying just o n e electron, while t h e s u b s e q u e n t p e a k s ( s o m e w h a t displaced because of an u n k n o w n e x p e r i m e n t a l artifact) corres p o n d e d to droplets carrying t w o , t h r e e , four, etc., electrons. The scatter in the results ( s o m e t h i n g that all scientists h a v e e x p e r i enced) could h a v e b e e n d u e to dust, pairs of droplets sticking t o gether, convection c u r r e n t s in t h e air, or a n y of a n u m b e r of o t h e r reasons. Ehrenhaft didn't see it that way. He believed t h a t all of his results should be given equal weight, since he could see no r e a s o n to believe o n e m o r e t h a n a n o t h e r , a n d t h a t t h e y w e r e all accurate to t h r e e , lour, a n d e v e n five significant figures, so that each tiny horizontal step r e p r e s e n t e d , not e x p e r i m e n t a l error, but t h e

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Figure N.2: R e s u l t s o f E h r e n h a f t ' s First 5 0 0 M e a s u r e m e n t s o f t h e Charges on Water Droplets.

addition of a n o t h e r electron. He t h u s e n d e d up calculating t h e charge on the electron to be a b o u t a h u n d r e d limes smaller t h a n it actually is. He e v e n t u a l l y performed t h o u s a n d s of e x p e r i m e n t s . The m o r e e x p e r i m e n t s he did, t h e smaller t h e e l e m e n t a r y charge on t h e electron a p p e a r e d to b e c o m e . The American Robert Millikan was m e a n w h i l e performing very similar e x p e r i m e n t s to Ehrenhaft, but robustly choosing to lotus only on t h e most significant figures a n d to ignore later figures as being d u e to e x p e r i m e n t a l variation and therefore not significant. Using this a p p r o a c h , he obtained the correcl value lor t h e charge on t h e electron, for w h i c h he w a s a w a r d e d t h e 1923 Nobel Prize for physics. Poor Ehrenhaft, m e a n w h i l e , carried on for a n o t h e r t w e n t y years claiming that t h e r e m u s t be "subelectrons" with m u c h smaller charges — b u t n o b o d y was listening. There are s o m e very d e e p statistical issues here, c o n c e r n i n g the e x t e n t to w h i c h prior expectations should influence statistical analysis, a n d if so just h o w they should be allowed for. M a n y of these issues r e m a i n unresolved to this day.


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Averaging of upper and lower bounds. This is easily s h o w n to be equivalent to adding half the number of items to the total in the "pounds" column. If t h e total of t h e " p o u n d s " c o l u m n is P, a n d t h e total n u m b e r of items is N, t h e n t h e l o w e r b o u n d is £P, and the u p p e r b o u n d is £(P + N). T h e a v e r a g e of t h e t w o is £(P + (P + N)) 12. w h i c h c o m e s to £{P + N/2), w h i c h is t h e s a m e as a d d i n g hall the n u m b e r of items (N/2) to P. 83 Cancellation of errors. A surprising n u m b e r of scientists h a v e c o m e to a correct conclusion alter m a k i n g t w o mistakes that h a v e canceled each o t h e r o u t . O n e famous case w a s w h e n t h e American scientists Gorter and Grendel w e r e trying to m e a s u r e t h e c o m p o sition of t h e t h i n m e m b r a n e that s u r r o u n d s all living cells. They e v e n t u a l l y concluded (correctly) that this m e m b r a n e w a s just t w o molecules thick. This was a major result, a n d set m o d e r n cell biology on its p a t h . It was only thirty years later that s o m e o n e pointed out that t h e Gorter a n d Grendel p a p e r c o n t a i n e d t w o errors, each of a factor of t w o , w h i c h luckily canceled each o t h e r out. See E. Gorter and F. Grendel in Journal of Experimental Medicine, vol. 4 1 , 1925, p. 439. 85

Robert Millikan. His n o t e b o o k s are n o w preserved in n i n e t y - n i n e file boxes in t h e California Institute of Technology Archives. 85 Patterns in supermarket prices. W h e n I s h o w e d t h e s e frequency distrihutions to my colleague Jeff Odell, his i m m e d i a t e suggestion was that I should a t t e m p t a Fourier transform. This is a m a t h e matical t e c h n i q u e , n o w m a d e easier with t h e a d v e n t of powerful c o m p u t e r s , lor revealing u n d e r l y i n g p a t t e r n s , or periodicities. Pictures from space probes are invariably treated in this w a y before being released to t h e public. 1 was very t e m p t e d to try it with s u p e r m a r k e t bills, especially since, as Jeff p o i n t e d out, t h e r e is an e x p e r i m e n t a l l y n e a t w a y to do Fourier transforms, w h i c h is to take a 35 mm slide of t h e object (here, the graph ol t h e s u p e r m a r k e t price distribution) a n d shine a laser t h r o u g h it. The light will he deflected t h r o u g h different angles via a p h e n o m e n o n called interference, with each angle c o r r e s p o n d i n g to a particular periodicity in t h e price distribution. In the end, t h o u g h , it t u r n e d out to be too messy. You can do y o u r o w n Fourier transform simply by looking at the reflection of a light from a CD. Pick o n e color to watch, and look lor the r e a p p e a r a n c e of that color as t h e CD is tilted. Each r e a p p e a r a n c e c o r r e s p o n d s to a different periodicity. Those at t h e shallowest angle represent t h e spacing b e t w e e n adjacent tracks; those farther in c o r r e s p o n d to t h e gaps b e t w e e n every second track, every third track, etc.

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85 The underlying statistics. The statistics of t h e m e t h o d s that I h a v e suggested really deserve an essay in their o w n right, focusing on w h a t w e m e a n w h e n w e speak o f a n "average." The a v e r a g e that most people a r e familiar with is technically called a " m e a n . " If t h e figures in a "cents" c o l u m n are r a n d o m l y distributed, it m a k e s sense to say that t h e " m e a n " v a l u e is app r o x i m a t e l y 50, lor e x a m p l e (49.5, to be exact). It also m a k e s sense to talk a b o u t a " m e a n " if t h e figures are not r a n d o m l y distributed, so long as t h e distribution is s m o o t h . " M e a n s " c o r r e s p o n d to expectations, but are not always a p p r o priate for a situation. The " m e a n " n u m b e r of h u m p s on a camel, for e x a m p l e , is 1.5, but no o n e has ever seen a camel with o n e a n d a half h u m p s — t h e y always h a v e e i t h e r o n e h u m p or t w o humps. I h a v e avoided talking a b o u t " m e a n s " w h e n it c o m e s to overall s u p e r m a r k e t prices, since t h e distribution of t h e s e prices is very spiky. There a r e m a n y m a t h e m a t i c a l tricks for h a n d l i n g such n o n s m o o t h distributions, most of w h i c h are w a y o u t of my league, a n d probably t h e reader's as well. O n e that is w i t h i n e v e r y o n e ' s grasp, t h o u g h , is to locus on t h e median, i.e., t h e value that occurs with t h e highest frequency. This is w h a t I h a v e d o n e in t h e simple m e t h o d s that I h a v e suggested lor c o m p a r i n g prices b e t w e e n different s u p e r m a r k e t s . 89 The use of calculators. A friend to w h o m I w a s explaining s o m e of t h e tricks in this c h a p t e r asked: " W h y not just use a calculator?" My a n s w e r w a s that a calculator is far from a foolproof aid to addition — it is m o r e like a ticking b o m b . The b o m b becomes p r i m e d t h e m o m e n t that a n u m b e r or a symbol is e n t e r e d incorrectly. The s u b s e q u e n t explosion m a y be a personal o n e , after t h e o p e r a t o r has used a calculator to add up t h e s a m e c o l u m n of figures t h r e e times, a n d p r o d u c e d t h r e e different a n s w e r s . It m a y e v e n involve o t h e r p e o p l e if t h e w r o n g figure is used to challenge s o m e o n e else's calculation. No professional scientist w o u l d d r e a m of trusting t h e o u t p u t of a calculator (or a c o m p u t e r , w h i c h for m o s t p u r p o s e s is just a p r o g r a m m a b l e calculator) unless t h e result agreed r e a s o n a b l y w i t h t h a t arrived at by a p p r o x i m a t e calculation. Even t h e n , he or she w o u l d probably repeat t h e calculation, just to m a k e sure. There is just too m u c h c h a n c e of hitting a w r o n g key, resulting in GIGO — garbage in, garbage o u t . S o m e spectacular e x a m p l e s of GIGO have b e e n recorded. On 21 July 1962, a misplaced c o m m a in a c o m p u t e r p r o g r a m was sufficient to cause t h e spacecraft bearing America's first p r o b e to Venus to e x p l o d e shortly after liftoff. In 1988, t h e Soviets' first


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Mars mission, Phobos 1, was lost w h e n Russian controllers sent a long s e q u e n c e of c o m m a n d s with a single error: a plus symbol w h e r e a m i n u s symbol belonged. A single e r r o n e o u s keystroke is not likely to cost t h e average p e r s o n quite as m u c h , b u t if trained space scientists can m a k e such mistakes, t h e n it b e h o o v e s t h e rest of us to be wary. The easiest w a y to be w a r y is to use quick m e n t a l s h o r t c u t s to check t h a t t h e figure calculated by you or s o m e o n e else is at least a p p r o x i m a t e l y correct. It is surprising h o w often s u c h calculations help t o avoid paying o u t o n y o u r o w n o r s o m e o n e else's mistake. F u r t h e r e x a m p l e s of GIGO in t h e space p r o g r a m can be found in an interesting article by Bruce Neufeld called "Software Reliability in I n t e r p l a n e t a r y Probes," published on t h e I n t e r n e t at http://web.tampabay.rr.com/dneufeld/sftrel.html Belief in t h e infallibility of calculators, a n d m o r e so of c o m p u t ers, has r e a c h e d such a level in s o m e q u a r t e r s that t h e m e a n i n g of GIGO has b e e n u p g r a d e d to "garbage in, gospel o u t . "

chapter 5: h o w to throw a b o o m e r a n g Page 93

The oldest wooden boomerang. The oldest w o o d e n b o o m e r a n g discovered in Australia was found by radiocarbon dating to be 10,000 years old. The age record for b o o m e r a n g s , t h o u g h , goes to o n e m a d e from a m a m m o t h tusk in w h a t is n o w Poland, a n d w h i c h w a s dated at 2 3 , 0 0 0 years. B o o m e r a n g s a p p e a r to h a v e b e e n i n v e n t e d i n d e p e n d e n t l y in m a n y places, including Egypt, w h e r e m a n y b o o m e r a n g s w e r e found i n a n a n n e x t o T u t a n k h a m e n ' s t o m b , including s o m e with gold tips.

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Modern boomerang materials. These e v e n include t h e ultra-strong material Kevlar, used in bulletproof vests and to t e t h e r spacecraft, a n d " b o r r o w e d " on this occasion from t h e b r a k e linings of a Russian MIG fighter by t h e Bulgarian b o o m e r a n g enthusiast Georgi D i m a n c h e v .

93 Aboriginal boomerang "sport." The a c c o u n t is from D a w s o n , J., The Australian Aborigines, Facsimile edition, AIATSIS, 1 8 8 1 . 94 The boomerang distance record. The record of 149.12 m e t e r s (long since surpassed) w a s set by Michel Dufayard at S h r e w s b u r y in 1992. 94 Invisible boomerangs. Sean Slade tells t h e story of t h e t i m e t h a t he m a d e a b o o m e r a n g from t r a n s p a r e n t p o l y c a r b o n a t e plastic. He

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p u t s o m e effort into polishing t h e surfaces a n d s h a r p e n i n g t h e edges, a n d it w a s only after he l a u n c h e d it that he realized that he h a d no idea of w h e r e it was going to land w h e n it r e t u r n e d . Passersby w e r e treated to t h e sight of a m a n r u n n i n g frantically from a totally invisible p u r s u e r . 94 Boomerangs as hunting weapons. These a r e occasionally used for catching ducks, w h e r e t h e b o o m e r a n g h o v e r s a b o v e a flock and a p p e a r s to t h e birds as a h a w k , driving t h e m t o w a r d s t h e g r o u n d w h e r e t h e y a r e clubbed. 95 The best time for maximum time aloft. This w a s achieved by J o h n Gorski of t h e United States with a b o o m e r a n g that c a u g h t a thermal over t h e P o t o m a c River, r e t u r n i n g to w i t h i n s e v e n t y meters of t h e t h r o w e r after an incredible s e v e n t e e n m i n u t e s a n d six seco n d s . Unfortunately, t h e t h r o w was a practice shot, a n d so t h e t i m e d o e s n ' t c o u n t as a world record. 96 What makes a boomerang come back. The rationale for this applies with equal validity t o b o o m e r a n g s with m o r e t h a n t w o a r m s . 96 Aerodynamic lift. A complex subject: t h e classical e x p l a n a t i o n is t h a t t h e air flows faster o v e r o n e side of a w i n g (the u p p e r side in t h e case of an aircraft; t h e " i n n e r " side in t h e case of a b o o m e r a n g ) t h a n it does over t h e other, creating a lower pressure on t h e side w h e r e it flows faster (Bernoulli's principle). T h e reader can observe this effect by holding t w o sheets of p a p e r close to each o t h e r a n d b l o w i n g b e t w e e n t h e m . The sheets will b e d r a w n t o w a r d s e a c h other. This classical e x p l a n a t i o n has recently b e e n challenged c o n t r o versially by David A n d e r s o n a n d Scott E b e r h a r d t in a book called Understanding Flight. A n d e r s o n , a Fermilab physicist, claims that lift is very simple — it's just a reaction force, as described by Newt o n ' s Third Law of M o t i o n (for every action t h e r e is an e q u a l and opposite reaction). The wing p u s h e s t h e air d o w n , so in t u r n air pushes the wing up. I haven't been through Anderson's argument in detail, b u t it's likely that he's right. This d o e s n ' t m a k e Bernoulli w r o n g . T h e t w o e x p l a n a t i o n s p r o d u c e t h e s a m e e q u a t i o n s — it's o n l y t h e imagery that is different. 97 Art on boomerangs. T h e decorative imaging has b e e n described by Philip J o n e s , c u r a t o r of t h e collection of over 3,000 Aboriginal b o o m e r a n g s at t h e S o u t h Australian M u s e u m , in t h e lavishly illustrated Boomerang: Behind an Australian Icon. Wakefield Press, S o u t h Australia, 1996. 98 Aboriginal ignorance of boomerangs. W h e n I told t h e story of D u n c a n M a c L e n n a n t e a c h i n g Aborigines t o t h r o w b o o m e r a n g s , Sean Slade p r o m p t l y t o p p e d it with t h e story of A n d y Furniss, a well-


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k n o w n British b o o m e r a n g enthusiast, w h o w a s h i t c h h i k i n g across Australia a n d had b e e n d r o p p e d off in t h e middle of n o w h e r e . While waiting for his n e x t lift, he idly took o u t a b o o m e r a n g a n d began to t h r o w it. A local Aborigine c a m e up a n d asked " w h a t t h e feller t h i n g ? " A n d y told h i m , a n d p r o c e e d e d t o teach h i m h o w t o t h r o w it. Just as t h e m a n was getting t h e h a n g of it, a b u s full of A m e r i c a n tourists d r e w u p a n d p r o c e e d e d t o p h o t o g r a p h w h a t they perceived to be an Aborigine t e a c h i n g a w h i t e m a n h o w to throw a boomerang. 99 Hospital MRI scanners. These used to be called by t h e technically correct title of Nuclear M a g n e t i c R e s o n a n c e s c a n n e r s . "Nuclear" refers to t h e nuclei of t h e h y d r o g e n a t o m s in t h e tissue water, but t h e n a m e w a s c h a n g e d w h e n patients (and t h e m e d i a ) m i s t a k e n l y associated "nuclear" with t h e idea of n u c l e a r w e a p o n s , w h i c h get their e n e r g y from disrupting t h e nuclei of m u c h larger a t o m s , w h e r e a s MRI s c a n n i n g gently tilts t h e single spinning p r o t o n at t h e core of a h y d r o g e n a t o m . 101 The Mudgeeraba Creek Emu Racing and Boomerang Throwing Association. O n e of its rules reads: "The decisions of t h e j u d g e s are final unless s h o u t e d d o w n by a really o v e r w h e l m i n g majority of t h e crowd p r e s e n t . Abusive a n d obscene l a n g u a g e m a y not be used by c o n t e s t a n t s w h e n addressing m e m b e r s of t h e j u d g i n g p a n e l or, conversely, by m e m b e r s of t h e j u d g i n g panel w h e n addressing c o n t e s t a n t s (unless struck by a b o o m e r a n g ) . " 101 Simplification of physical rules by changing viewpoint. The most s t u n ning e x a m p l e of this w a s w h e n G e r m a n female physicist E m m y N o e t h e r p o i n t e d out that t h e law of t h e c o n s e r v a t i o n of linear m o m e n t u m arises directly from t h e fact t h a t t h e laws of physics do not c h a n g e w h e n t h e p o i n t of view is shifted linearly in space, and t h a t t h e l a w of c o n s e r v a t i o n of a n g u l a r m o m e n t u m a m o u n t s to no m o r e t h a n t h e fact t h a t t h e laws of physics do n o t c h a n g e w h e n t h e p o i n t of v i e w is rotated in space. It says s o m e t h i n g for t h e m a s c u l i n e o r i e n t a t i o n t h a t science h a d in t h e early t w e n t i e t h c e n t u r y (and u n f o r t u n a t e l y still has) that E m m y N o e t h e r did n o t receive a Nobel Prize for this incredible insight. 102 The mathematics of boomerang flight. This w a s spelled o u t in a s e m i p o p u l a r article by t h e D u t c h physicist Felix Hess (Scientific American, 2 1 9 , 1968, pp. 1 2 4 - 1 3 6 ) a n d elucidated in excruciating detail by t h e s a m e a u t h o r in a 500-page Ph.D thesis published s o m e seven years later. Bob Reid m a d e t h e physics accessible in "The Physics of B o o m e r a n g s " (Mathematical Spectrum, vol, 17, 1984/5, p. 4 8 , published by t h e University of Sheffield), a n d amplified his a c c o u n t of h o w b o o m e r a n g s lie d o w n in a recent edition of t h e

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British Boomerang Society Journal ( S u m m e r 1998, p. 19). A m o r e detailed, step-by-step a c c o u n t w a s also p r e s e n t e d by E. C. Z e e m a n in t h e splendid Royal Institution M a t h e m a t i c s Masterclass "Gyroscopes a n d B o o m e r a n g s , " w h i c h w a s i n t e n d e d "to provide enrichm e n t material for gifted t h i r t e e n - y e a r - o l d s . " 104 . . . eventually resulting in a crazy tumbling. The m a t h e m a t i c a l reason for this is that t h e m o m e n t of inertia a b o u t t h e spin axis m u s t be at least 30 p e r c e n t g r e a t e r t h a n t h e n e x t largest m o m e n t of inertia a b o u t an axis p e r p e n d i c u l a r to t h e spin axis, o t h e r w i s e t h e spin can transfer from o n e axis to t h e o t h e r w i t h disastrous results. 104 The physics of levitating frogs. This is described by Michael Berry and Andre Geim in European Journal of Physics, vol. 18, 1997, p . 307.

chapter 6: catch as catch can Page 108

The description of an English village cricket match. This is from Macdonell, A. G., England, Their England (MacMillan, 1933; The Reprint Society, L o n d o n , 1941), p p . 1 2 2 - 1 2 4 . Despite t h e interval of time, n o t h i n g has c h a n g e d , t h a n k g o o d n e s s .

I h a v e a d d e d a c o u p l e of e x p l a n a t o r y w o r d s (e.g., "the poet" after Mr. Harcourt) to clarify t h e b a c k g r o u n d w i t h o u t doing violence to t h e flavor: that of a village life w h i c h still exists in spite of everything. 110 "Running to Catch the Ball" is a p a p e r by Peter McLeod a n d Zoltan Dienes, published in Nature, vol. 362, 4 M a r c h 1993, p. 2 3 . 110 The brain's unconscious problem-solving abilities. The psychologist a n d writer Oliver Sacks tells t h e story of identical twins w h o w e r e savants, able to "just see" n u m b e r s a n d h o w t h e y go together. Their ability to visualize n u m b e r s w a s such that, w h e n Sacks accidentally d r o p p e d a box of m a t c h e s , o n e of t h e m glanced at t h e scattered pile a n d said i m m e d i a t e l y : "A h u n d r e d and e l e v e n . " His b r o t h e r p r o m p t l y c o m m e n t e d , "Thirty-seven, t h i r t y - s e v e n , thirtyseven." Sacks c o u n t e d t h e m a t c h e s ; t h e r e w e r e indeed a h u n d r e d and eleven (3 X 37). The t w i n s ' u n c o n s c i o u s calculating abilities w e r e extraordinary. They w e r e , for e x a m p l e , able to w o r k o u t in a few seconds w h e t h e r or n o t a given twelve-digit n u m b e r w a s p r i m e — s o m e t h i n g for w h i c h scientists still do not h a v e an a l g o r i t h m (i.e., a set of rules to guide t h e calculation).


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There is t h u s n o t h i n g intrinsically impossible a b o u t McLeod and D i e n e s ' p o s t u l a t i o n of u n c o n s c i o u s m e n t a l abilities that help us to catch a ball. It is just that t h e scientist's guiding principle ( k n o w n in p h i l o s o p h y as Occam's razor) in choosing b e t w e e n t w o o t h e r w i s e e q u a l e x p l a n a t i o n s is to accept t h e simplest. This d o e s n ' t m e a n that t h e simplest e x p l a n a t i o n is always t h e right o n e ; it is just that Occam's razor has t u r n e d out from e x p e r i e n c e to be t h e p r o c e d u r e that gives us t h e best c h a n c e of selecting t h e right e x p l a n a t i o n . McLeod a n d D i e n e s ' e x p l a n a t i o n uses t h e blunt edge of Occam's razor. 110 Newspaper report of the "ball-catching" equation. The journalist w h o m a n a g e d to get t h e "ball-catching" e q u a t i o n published on t h e front page of his n e w s p a p e r m a d e a b r a v e a t t e m p t to explain w h a t t h e e q u a t i o n m e a n t in lay t e r m s . The result was r a t h e r reminiscent of President K e n n e d y ' s famous a t t e m p t to declare in Germ a n : "Ich bin ein Berliner." Not really u n d e r s t a n d i n g , he used a w o r d that s e e m e d like t h e right o n e , but w h i c h c a m e o u t in t r a n s lation as "I am a d o u g h n u t . " Every G e r m a n in t h e a u d i e n c e caught President K e n n e d y ' s mistake. Only a l e w of my journalist friend's readers picked up on his mistake, b e c a u s e only a few u n derstood t h e l a n g u a g e of m a t h e m a t i c s . That's a pity, because m a t h e m a t i c s gives a picture of h o w things h a p p e n , a picture well w o r t h t h e t h o u s a n d or so w o r d s that a verbal description w o u l d take. The description in this case w a s of h o w o u r angle of gaze changes w h e n we r u n to catch a ball. The e q u a t i o n w a s described by my journalist as:

rfmanO) = 0, where 6 is the angle of gaze, t is the time, and d is the distance di-

ll he had k n o w n h o w to read t h e l a n g u a g e in w h i c h the e q u a tion was written, he w o u l d h a v e realized that distance d o e s n ' t c o m e into it at all; d isn't a symbol in a c o n v e n t i o n a l sense, a n d 2

2

t h e expression (d I dt ) only has m e a n i n g if t a k e n as a w h o l e . It m e a n s "acceleration" (Newton w o u l d h a v e w r i t t e n it by p u t t i n g t w o dots a b o v e t h e 9). All that t h e e q u a t i o n is saying is that, w h e n we run to catch a ball, we j u d g e t h e catch by r u n n i n g in s u c h a way that o u r rate of h e a d tilting does n o t accelerate or decelerate (i.e., it equals zero). 111 Silvanus P. Thompson, "Calculus Made Easy." This book has recently b e e n u p d a t e d and reprinted — see T h o m p s o n , S. P., a n d Gardner, M., Calculus Made Easy, St. Martin's Press, N e w York, 1999.

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112 From the point of view of the observers at the pub door. The s a m e principle applies to t h e m a n y satellites that are n o w in geostationary orbit, and w h i c h a p p e a r to h o v e r a b o v e o n e spot on t h e Earth's surface. Viewed from outside, t h e y are w h i z z i n g a r o u n d t h e Earth o n c e every t w e n t y - f o u r h o u r s . T h e Earth, h o w e v e r , is rotating at t h e s a m e speed, s o t h a t t h e satellite a p p e a r s stationary w h e n v i e w e d from a p o i n t directly b e l o w on t h e Earth's surface. 113 Some 30 percent of people still share Aristotle's . . . notion. Miller, J. D., Daedalus 112(2), 1983, p p . 2 9 - 4 8 ; D u r r a n t , J. R., Evans, G. A., and T h o m a s , G. P., Nature 340, 11, 1989. Aristotle's w a s a r e a s o n a b l e , c o m m o n s e n s e a p p r o a c h to u n d e r s t a n d i n g m o t i o n , but flying a r r o w s a p p e a r e d to c o n s t i t u t e an exception, since t h e r e was n o t h i n g p u s h i n g o n t h e m . Aristotle was so convinced of t h e correctness of his a p p r o a c h , t h o u g h , that he e v e n t u a l l y c o n c l u d e d t h a t t h e b o w s t r i n g m u s t p u s h t h e air, even from afar, w i t h t h e air t h e n p u s h i n g t h e a r r o w . M o d e r n - d a y Aristotelians follow Aristotle in trying, perfectly reasonably, t o apply c o m m o n sense t o situations w h e r e N a t u r e h a s decreed t h a t c o m m o n sense shall not apply. The history of scie n c e is littered with s u c h situations, a n d could, in fact, be said to consist largely of m a n ' s a t t e m p t s to u n d e r s t a n d and resolve such conflicts b e t w e e n c o m m o n sense a n d reality. 113 Galileo's discovery of the law of acceleration. This is discussed in Tricker, R. & B., The Science of Movement, Mills &- Boon, 1968, a book full of absorbing ideas that 1 found very helpful in writing this chapter. It t h r o w s an interesting sidelight on h o w e v e n t h e greatest scientists can m a k e mistakes, a n d also h o w lucky they can be: . . . the h y p o t h e s i s that t h e velocity of a b o d y increased uniformly with the distance t h r o u g h w h i c h it had fallen w a s t h e o n e that w a s generally accepted. Galileo himself a d o p t e d it at first. At the s a m e time he also m a d e a m i s t a k e in his early calculations w h i c h neutralized t h e error in this a s s u m p t i o n , a n d he t h u s arrived at t h e correct result t h a t t h e distance that a body w o u l d fall in a given time w o u l d be p r o p o r t i o n a l to t h e s q u a r e of t h e t i m e . . . (He later saw t h e e r r o r in his earlier calculation, a n d also realized that t h e "uniform velocity" h y p o t h e s i s w a s w r o n g ) . 113 The formula for a parabola. This takes t h e form (vertical distance) = (constant) X (horizontal d i s t a n c e ) . Since a projectile travels horizontally at a c o n s t a n t speed, t h e horizontal distance traveled is p r o p o r t i o n a l to t h e t i m e of flight, so t h a t t h e e q u a t i o n can be writ2


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ten (vertical distance) = (different c o n s t a n t ) X ( t i m e ) , i.e., t h e distance fallen is p r o p o r t i o n a l to t h e s q u a r e of t h e time. A parabola is o n e of the "conic sections" originally described by t h e Greek m a t h e m a t i c i a n Apollonius of Perge. Their shapes can be obtained by slicing a c o n e at different angles. O n e of these sections is t h e circle (obtained by slicing a c o n e parallel to t h e base). A n o t h e r is t h e ellipse (obtained by slicing t h e c o n e at an angle to t h e base). The parabola is a third, obtained by slicing a c o n e parallel to t h e side. 2

114 // is not a cue that is always reliable. As t h e m a t h e m a t i c s eventually s h o w e d , it is t h e t a n g e n t of t h e angle that needs to c h a n g e at a constant rate, r a t h e r t h a n t h e angle itself. O u r c h i l d h o o d c u e of using t h e angle, r a t h e r t h a n its t a n g e n t , w o r k s well because an angle is p r o p o r t i o n a l to its t a n g e n t for small angles, a n d is actually nearly equal to its t a n g e n t if t h e angle is expressed in " n a t u r a l " units, r a t h e r t h a n t h e m o r e familiar degrees, w h i c h arbitrarily divide a circle into 360 equal parts a n d w h i c h derive from a Babylonian c o u n t i n g system based o n the n u m b e r 60. The " n a t u r a l " unit is t h e radian. An angle ol o n e radian corresponds to a w e d g e of a circle w h e r e t h e length of t h e circumferential arc is t h e s a m e as t h e length of t h e radius (Figure N.3).

Figure N.3: An Angle of O n e Radian.

The table b e l o w s h o w s h o w close t h e t a n g e n t of an angle is to t h e angle itself, w h e n t h e angle is expressed in radians:


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The error in t h e a p p r o x i m a t i o n is a r o u n d ten p e r c e n t or less for angles up to 30°, but rapidly w o r s e n s for larger angles, w h i c h m a y partly explain w h y we find it so difficult to j u d g e high catches. 11 5 The "ball-catching " equation for the case of a catcher standing in the right place. The e q u a t i o n ( t a n a = gllv) leads directly to that published by McLeod a n d Dienes (d ( t a n a ) / dt = 0), since t h e expression (gl(2 X v)) has a c o n s t a n t value for a n y particular catch, so that t h e rate at w h i c h d (Xana)ldt) itself c h a n g e s w i t h time (i.e., d (tana)ldt ) is zero. This w a s also t h e form in w h i c h t h e e q u a t i o n w a s originally published by S. C h a p m a n (American Journal of Physics 36, 1968, pp. 8 6 8 - 8 7 0 ) and P. Brancazio (American Journal of Physics 53, 1985, pp. 8 4 8 - 8 5 5 ) . Both of t h e s e references are q u o t e d in t h e subseq u e n t Nature paper. It w a s probably t h e difference in form that led McLeod and Dienes to miss t h e obvious physical interpretation that I h a v e discussed in this chapter. 118 Action and reaction. This is N e w t o n ' s Third Law of M o t i o n ("For every action t h e r e is an e q u a l a n d opposite reaction"). In o t h e r w o r d s , if we p u s h on s o m e t h i n g , it p u s h e s back just as h a r d . From t h e " s o m e t h i n g ' s " p o i n t of view (e.g., t h e g r o u n d ) it is p u s h i n g on us, a n d we are p u s h i n g back just as h a r d . It just d e p e n d s on y o u r point of view. 2

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c h a p t e r 7 : b a t h f o a m , b e e r f o a m , a n d the m e a n i n g of life In this c h a p t e r I h a v e tried to give a picture of h o w science actually works, w h i c h is not usually by p r e p l a n n e d strategies b u t m o r e often by a c o m b i n a t i o n of a w a r e n e s s of w h a t q u e s t i o n s are imp o r t a n t , a readiness to take up n e w ideas t h a t m i g h t be relevant to


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those questions, and sheer, dogged persistence in following up t h e c o n s e q u e n c e s of these ideas. In o r d e r to give t h e detail, I have focused on work w h e r e I have had direct k n o w l e d g e of w h a t was going on, a n d e v e n t h e n I h a v e been able to m e n t i o n only a few of t h e scientists c o n c e r n e d . I have r e p o r t e d most of t h e incidents from t h e point of view of h o w I saw things at t h e time, and I w a s n o t always privy to e v e r y t h i n g that was going o n . O t h e r s m a y well h a v e seen things differently, or with a different e m p h a s i s . In o t h e r words, to q u o t e from Lawrence Bragg's introduction to The Double Helix, "this is not a history, but an autobiographical c o n t r i b u t i o n to t h e history that [may] s o m e d a y be written." (Bragg was the head of t h e Cavendish laboratory d u r i n g t h e period w h e n fames Watson a n d Francis Crick devised their d o u b l e helical s t r u c t u r e for DNA [ 1 9 5 1 - 1 9 5 3 ] . Watson, J. D„ The Double Helix, A t h e n e u m Press, New York, 1968). Page 12 1

How molecules self-assemble. A good starting point for non-specialist scientists w h o wish to follow up is the articles in Current Opinion in Colloid and Interface Science (February 1999). 121 American Scientist Sidney Perkowitz. On t h e BBC radio program Lord Kelvin's Bedspring, Sidney Perkowitz and I discussed t h e science of foams at s o m e length. Those p u n d i t s w h o believe that t h e public is interested only in t h e s h o w i e r aspects ol science might like to n o t e that this p r o g r a m , dealing with such an a p p a r e n t l y m u n d a n e subject, b e c a m e BBC Radio 4's "Pick of t h e Week." 122 Sir Isaac Newton. N e w t o n published his observations of t h e colors of soap bubbles in Opticks (G. Bell & Sons, London, 1730), a w o n derfully readable account ol his i n g e n i o u s ( t h o u g h incorrect) corpuscular t h e o r y ol light.

123 . . . about ten times thinner than can be observed with the naked eye. Even with the aid of a powerful microscope, the h u m a n eye can only resolve objects that are m o r e t h a n a m i c r o m e t e r or so apart. It can detect t h e presence of m u c h smaller objects, t h o u g h , t h r o u g h their ability to scalier light, w h i c h is w h y car headlights stand out so vividly in a fog, e v e n t h o u g h t h e observer can't m a k e out t h e shapes of t h e individual w a t e r droplets. 123 Irving Langmuir. Langmuir's very interesting biography is given in The Selected Papers of Irving Langmuir, vol. 12, Pergamon Press, 1962. 123 Stories surrounding Irving Langmuir. These are m a n y a n d varied. He looked lor science in e v e r y t h i n g about him, and w a s n e v e r w i t h out a n o t e b o o k and m e a s u r i n g tools. On o n e famous occasion he used t h e entire toilet [taper supply of a r e m o t e guest h o u s e w h e r e

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a n d

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he was staying in pursuit of an e x p e r i m e n t . He was also a keen a m a t e u r pilot, and fond of playing a g a m e which involved close e n c o u n t e r s with clouds. On o n e occasion he passed his wheels t h r o u g h t h e top of a cloud, and w a s a s t o n i s h e d to find that t h e w h e e l - t r a c k s r e m a i n e d . In following up this observation he e v e n tually d e v e l o p e d n e w m e t h o d s of w e a t h e r modification, mostly c o n c e r n e d with "cloud seeding" by d r o p p i n g dry ice into the cloud to initiate precipitation. I once m e t a scientist w h o had w o r k e d d o w n t h e corridor from Langmuir, a n d w h o told me that Langmuir's laboratory was a constant source of surprises. On o n e occasion litis scientist walked i n t o it, only to find himself e n v e l o p e d in a s n o w s t o r m , artificially created by L a n g m u i r and his colleague Vincent Schaefer as p a n ol their e x p e r i m e n t s o n w e a t h e r modification. 126 Liposomes formed spontaneously from lecithins manufactured naturally under the conditions that then prevailed on Earth. The destructive oxidizing n a t u r e of t h e a t m o s p h e r e of t h e early Eartli lias led to s o m e speculation thai complex organic molecules could not have been formed t h e r e and w e r e actually "seeded" via c a r b o n a c e o u s c h o n d r i t e s , such as t h e M u r c h i s o n m e t e o r i t e discovered in central Australia. My colleague Professor Richard Pashlcy has found surface-active materials in t h e core of this m e t e o r i t e , w h i c h is dated 2 0 0 million years older t h a n t h e Earth itself (Deamer, D. W., a n d Pashley, R. M., "Surface properties ol a m p h i p h i l i c c o m p o n e n t s of t h e M u r c h i s o n c a r b o n a c e o u s c h o n d r i t e , " Origins of Life and Evolution of the Biosphere. 19, 2 1 - 3 8 (1989). 127 Liposomes as precursors for living cell membranes. This notion was first p r o p o s e d by D e a m e r a n d Ord {Biosystems. vol. 12, 1980, p. 167). 127 Alex's authoritative textbook on colloids. The book was modestly entitled Colloid Science (A. E. A l e x a n d e r a n d P. J o h n s o n , Oxford University Press, 1947). 128 The adhesive properties of sickle cells. These w e r e studied by Evan Evans at t h e University of British Columbia in Vancouver. Evan, a former engineer, t u r n e d his a t t e n t i o n to t h e m e c h a n i c a l properties of living cells, w h e r e he rapidly b e c a m e t h e world authority, a n d m u c h feared at conferences for his devastatingly straightforw a r d q u e s t i o n s and refusal to accept evasive a n s w e r s . In his studies on sickle cells, Evan found that their inability to recover from d e f o r m a t i o n was an i m p o r t a n t factor, p e r h a p s m o r e i m p o r t a n t t h a n their a d h e s i v e n e s s . 128 The DLVO quartet. Then Overbeek is t h e only o n e still alive. He was still scientifically active al the lime ol writing — a r e m a r k a b l e record.


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The repulsive forces between charged head-groups. These actually arise from t h e overlap of t h e clouds of d u n g e d ions thai gather about each h e a d - g r o u p . For this reason, t h e forces a r e technically called "double layer" forces. F o a m stability is not a m a t t e r of DLVO t h e ory a l o n e . O n e Dutch scientist s h o w e d m e this w h e n h e took m e on a t o u r of A m s t e r d a m bars, pointing out that s o m e of t h e beers kept their heads very well, while o t h e r s collapsed m u c h m o r e quickly. T h e difference, he had discovered, was that t h e m o r e rapidly collapsing froths c o n t a i n e d " n a t u r a l " carbon dioxide from the b r e w i n g process, while the longer-lasting ones hail been p r o duced with nitrogen from a gas cylinder. Carbon dioxide, unlike nitrogen, dissolves in water, and can h e n c e escape into the atm o s p h e r e t h r o u g h the w a t e r films s u r r o u n d i n g t h e bubbles, so that t h e bubbles in a " n a t u r a l " froth shrink rapidly with time. I kept m e e t i n g this scientist at conferences o v e r t h e n e x t t w e n t y years. He was often a c c o m p a n i e d by his wife, a lady of rather forbidding a p p e a r a n c e , w h o was n e v e r m o r e so t h a n at a conference in Bulgaria, w h e n t h e local organizers p r o d u c e d a t r o u p e of nubile d a n c i n g girls for o u r e n t e r t a i n m e n t at t h e conference dinner. Her h u s b a n d w a s fascinated, but his wife a p p e a r e d to be r a t h e r less so.

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Jacob Israelachvili. The work of Tabor and his school w a s s u m m a rized by Israelachvili in his excellent hook Intermodular and Surface Forces, Academic Press, 1985. The term "surface forces" simply refers to t h e close-range attractive and repulsive forces b e t w e e n surfaces w h o s e interplay d o m i n a t e s m a n y of t h e processes of life, including sell-assembly. Jacob points out in his i n t r o d u c t i o n that the Creeks needed only t w o such forces to account lor all n a t u r a l p h e n o m e n a . O n e w a s Love, and t h e o t h e r w a s Hate.

132 Barry Ninham. His book (with M a h a n t y ) on Van d e r Waals forces is M a h a n t y , J., a n d N i n h a m , B. W., Dispersion Forces, Academic Press, 1978. 133 Louis Pasteur. As a scientist, Pasteur is mostly famous for h a v i n g discovered the principles of sterilization (which led, a m o n g o t h e r things, to t h e process ol "pasteurization" a n d of vaccination using a t t e n u a t e d (i.e., live, but w e a k e n e d ) vaccines). Going against t h e advice of colleagues, he dramatically tried his u n t e s t e d rabies vaccine in 1885 on a n i n e - y e a r - o l d boy, Josef Meister, w h o had b e e n bitten by a rabid clog. Meister lived to b e c o m e c a r e t a k e r of t h e Pasteur Institute, a n d died fifty-five years later by c o m m i t t i n g suicide rather t h a n o p e n the t o m b ol Pasteur to invading Nazi forces. 133

Pasteur's discovery that molecules have three-dimensional structures. W h e n Pasteur discovered this he w a s n ' t trying to u n d e r s t a n d molecular s h a p e , a n y m o r e t h a n the scientists w h o initiated t h e

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foam revolution w e r e trying to u n d e r s t a n d the origins of life. It w a s an insight that c a m e , as so often in science, from an a t t e m p t to a n s w e r a totally different q u e s t i o n . The q u e s t i o n w a s posed by t h e F r e n c h w i n e industry, w h o s e m e m b e r s w a n t e d t o k n o w w h e t h e r t h e n e w l y discovered racemic acid, a by-product ol s o m e industrial processes in t h e Alsace region of France, was t h e s a m e as tartaric acid (the main c o m p o n e n t in t h e "crust" t h r o w n by a good w i n e ) . 133 Twisting a beam of light. M o r e technically, t h e tartaric acid solutions that Pasteur studied rotated t h e plane ol polarization, while the a p p a r e n t l y identical racemic acid solutions did not. Pasteur traced t h e difference to t h e fact that racemic acid is in fact a m i x t u r e ol t w o acids, o n e of w h i c h is tartaric acid a n d t h e o t h e r of w h i c h has molecules that are m i r r o r images of those of tartaric acid, and w h i c h rotate t h e p l a n e of polarization in t h e opposite direction to t h o s e of tartaric acid, so that in a m i x t u r e t h e r e is no net effect. If Pasteur had been a cuttlefish, he could have seen t h e s e effects directly, since cuttlefish eyes are a d a p t e d to respond to t h e rotation of a b e a m of light that has passed t h r o u g h o t h e r w i s e invisible prey, such as t h e glass s h r i m p . As it was, Pasteur had to use a relatively n e w i n v e n t i o n called a polarimeter. A rough p o l a r i m e t e r can be m a d e by taking t w o pairs ol ( g e n u i n e ) Polaroid sunglass lenses, placing o n e behind t h e other, and looking t h r o u g h both t o g e t h e r at a bright light. If o n e is rotated, a point will be found w h e r e t h e light is practically cut o u t . This is because t h e lirst lens selects light w a v e s vibrating in o n e direction, but the second is set only to pass light w a v e s vibrating at 90° to that direction, a n d to cut out all light w a v e s vibrating in t h e original direction. If a thick piece of clear plastic, or a c o n c e n t r a t e d sugar solution, is placed b e t w e e n t h e t w o lenses, t h e light will r e a p p e a r because both of t h e s e materials rotate t h e plane ol polarized light. 133 My one and only paper on the Kerr effect. This was published in the Journal of the Chemical Society, 1963, p. 4 4 5 0 . 134 The scanning probe microscope picture. This was kindly provided by my Bristol University colleague Professor M e r v y n Miles, a world a u t h o r i t y on t h e imaging of biological molecules by this techn i q u e , a n d a r e m a r k a b l y fine pianist at t h e a n n u a l d e p a r t m e n t a l Christmas s h o w . 135 The Franklin quotes. These are t a k e n from his collected papers. The p o n d w h e r e he did his e x p e r i m e n t s on C l a p h a m C o m m o n was called M o u n t Pond, w h i c h was d u g by his friend (and banker!) Henton Brown. 1 35 Franklin's letter to William Brownrigg. The letter was transmitted by

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his friend to t h e Royal Society, which p r o m p t l y published it (with slight modifications) in Philosophical Transactions of the Royal Society, vol. LXIV, 1774, p. 4 4 7 . Would that it was as easy to get a piece of w o r k published these days. 1 35 Pouring oil on troubled waters. This idea goes back to t h e Venerable Bede, w h o gave this sage advice in his Ecclesiastical History, book 3, c h a p t e r 1 5 ( " R e m e m b e r to t h r o w into t h e sea t h e oil w h i c h 1 gave you, w h e n straightway t h e w i n d s will abate, and a calm and smiling sea will a c c o m p a n y you t h r o u g h o u t y o u r voyage"). Unfortunately, it d o e s n ' t w o r k with waters t h a t are not so m u c h troubled as psychotic. My Australian c o n t e m p o r a r y . Bill Mansfield, found this in t h e 1950s w h e n he repeated Franklin's e x p e r i m e n t with t h e aim of using t h e surface film to reduce t h e rate of evaporation of w a t e r from Australian d a m s . Instead of olive oil, he used a w a x y surface-active material called stearic acid. Stearic acid, u n like olive oil, will spread indefinitely on a w a t e r surface unless confined, but Bill's idea was to p u t e n o u g h stearic acid on t h e d a m surface to form a packed layer of molecules, with t h e walls of t h e d a m limiting t h e spread. It was a clever idea that w o r k e d well in small-scale e x p e r i m e n t s , but which failed on a larger scale b e cause high w i n d s caused ripples large e n o u g h to break up t h e stearic acid layer a n d exposed t h e u n d e r l y i n g water. If t h e idea had succeeded, it would h a v e been a remarkable, almost pollutionfree a c h i e v e m e n t . Stearic acid is a n a t u r a l molecule that degrades fairly easily, a n d in a n y case a layer of stearic acid containing sufficient material to cover a d a m w o u l d still c o n t a i n only a lew grams of material. 136 Lord Rayleigh's bathtub experiments. These w e r e reported in Proceedings of the Royal Society, vol. XLVII, March 1890, p. 364. 136 Agnes Pockets. Her e x p e r i m e n t s w e r e reported in Nature, vol. 4 3 , 1891, p. 4 3 7 . 136 The first description of a Langmuir trough. This appears to h a v e b e e n given by L a n g m u i r in Journal of the American Chemical Society, vol. 39, p. 1848. 138 . . . molecules will get as far away from each other as possible, like relatives at a wedding. The repulsion b e t w e e n t h e electrically charged h e a d - g r o u p s usually o u t w e i g h s t h e Van der Waals attractive forces b e t w e e n t h e tails at all distances. 138 The single layer of molecules on the surface of a Langmuir trough. The molecules can actually be picked up on a glass slide that is lilted up t h r o u g h t h e surface. A second layer can be picked up on t o p of t h e first o n e by passing t h e slide back d o w n t h r o u g h t h e surface, a n d t h e process repeated indefinitely so long as t h e r e a r e

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molecules left to pick u p . This t e c h n i q u e , originated by Irving L a n g m u i r a n d K a t h e r i n e Blodgett, is at least k n o w n by both n a m e s a n d is called t h e Langmuir-Blodgett t e c h n i q u e . It could in t h e o r y be used to m a k e "thin film" electronic devices with u n i q u e characteristics, but despite m a n y efforts, small imperfections in t h e films h a v e p r o v e d to be an almost i n s u p e r a b l e p r o b l e m . 138 Cholesterol. This substance is an ideal c a n d i d a t e for t h e LangmuirBlodgett t e c h n i q u e , w h i c h I used early in my career to m a k e m u l tiple layers of cholesterol that s h o w e d brilliant interference colors in reflected light. 138

The early uses of the Langmuir trough to measure molecular shapes. These w e r e s u m m a r i z e d by Alex in a review (Annual Reports of the Chemical Society, vol. 4 1 , 1944, p. 5). 140 Margaret Thatcher's contribution to science. This is recorded by H. H. G. Jellinek and M. H. Roberts in Journal of the Science of Food and Agriculture, vol. 2, 1951, p. 3 9 1 . Margaret T h a t c h e r ' s political career took h e r to Parliament, w h e r e , as leader of t h e Conservative Party, s h e served as p r i m e minister for a n u m b e r of years, overlapping with Ronald Reagan, for w h o m she had a great (and m u tual) a d m i r a t i o n . 140 Denis Haydon. H a y d o n described his early w o r k on BLMs with his m a n y c o w o r k e r s in a typically t h o r o u g h review in Methods in Membrane Biology, vol. 4, 1975, p. 1. He b e c a m e a father figure, or at least an uncle ligure, to t h e m a n y s t u d e n t s w h o passed t h r o u g h his laboratory, and stories about his n a t u r a l inclination to lake t h e lead w e r e legion. O n e t h a t he used to tell against himself concerned his favorite sport of rock-climbing, in w h i c h he w a s indulging a l o n e on t h e Isle ol Skye. C a m p e d at t h e base of a cliff, he fell into c o n v e r s a t i o n with a fellow camper, a n d offered to lead him on a climb. The fellow camper, it appears, was no climber, but Denis had a very persuasive way with h i m and, as I found w h e n w o r k i n g with h i m , w o u l d not usually take no for an a n s w e r . They set off t h e n e x t m o r n i n g w i t h Denis leading and his reluctant follower roped on b e h i n d . Denis had to do m o s t of t h e w o r k a n d was relieved w h e n he m a d e it to a high ledge w h e r e he sat, waiting for his follower to appear. He w a i t e d for s o m e time, a n d e v e n t u a l l y pulled on t h e slack rope, to discover that it w a s s u p porting a dead w e i g h t . Alarmed, he began to pull on t h e rope, and alter s o m e t i m e t h e o t h e r end a p p e a r e d . It was tied to a h u g e boulder. W h e n Denis p e e r e d over t h e edge of t h e ledge, he saw t h e small figure of his erstwhile follower r u n n i n g off i n t o t h e dist a n c e . I often use this story as a m e t a p h o r for w h a t it feels like to be a scientist.


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Denis died of b o n e cancer s o m e years after t h e publication of otir results. In his Biographical Memoir for the Royal Society (Biographical Memoirs of Fellows of the Royal Society, vol. 36, 1990, pp. 1 9 9 - 2 1 6 ) , he described me as "persistent" — a t r u e c o m p l i m e n t to a scientist. 141 Josef Plateau's original papers are u n f o r t u n a t e l y h a r d to obtain. I e v e n t u a l l y tracked t h e m d o w n in t h e Annual Reports of the Smithsonian Institution for 1 8 6 4 - 1 8 6 6 ! 141 Plateau's results. These, t o g e t h e r with m a n y o t h e r fascinating facts a b o u t t h e science of soap bubbles, w e r e popularized in a series of packed lectures " i n t e n d e d for j u v e n i l e s " by a r e m a r k a b l e Victorian scientist called Charles Vernon Boys, i n v e n t o r of t h e highspeed c a m e r a . Boys, apart from being a top-class e x p e r i m e n t a l scientist, w a s also o n e of t h e first scientific h u m o r i s t s , w h o s e activities included t h e creation of giant s m o k e rings that he d r o p p e d over u n s u s p e c t i n g passersby from t h e w i n d o w of his laboratory on t h e first floor of L o n d o n ' s Royal Institution. He is m o s t f a m o u s a m o n g surface scientists for p e r s u a d i n g t h e Society for t h e Prom o t i o n of Christian K n o w l e d g e that t h e b o o k of his lectures, Soap Bubbles and the Forces that Mold Them, was a suitable subject for their imprint. I am fortunate e n o u g h to possess a first edition of this book, w h i c h w a s published in 1890 (the year that Rayleigh published t h e results of his " b a t h t u b " e x p e r i m e n t s ) , a n d w h i c h is t h e only book I k n o w that is dedicated to a school science master. 141 Denis Haydon's work on anesthetics. See, for e x a m p l e , D. W. R. G r u e n and D. A. Haydon in Pure and Applied Chemistry, vol. 52, 1980. 142 The phenomenon that keeps oil and water molecules apart. This is k n o w n as t h e " h y d r o p h o b i c effect," a n d has b e e n t h e subject of an intense a m o u n t of research. Technically, it occurs b e c a u s e t h e e n try of an oil m o l e c u l e into liquid w a t e r forces t h e w a t e r to a d o p t a m o r e o r d e r e d s t r u c t u r e , decreasing its entropy, a process w h i c h is t h e opposite of s p o n t a n e o u s . H o w this h a p p e n s , t h o u g h , r e m a i n s a mystery. The 1 rouble is that t h e effect on t h e e n e r g y of t h e system is c o m p o s e d of several different c h a n g e s , each of w h i c h is h u g e , b u t w h i c h go in different directions, so that t h e overall effect is tiny. To calculate that tiny effect, t h o u g h , each of the h u g e c h a n g e s m u s t be k n o w n to incredible precision, still w a y b e y o n d t h e p o w e r of t h e present g e n e r a t i o n of c o m p u t e r m o d e l s . 143 The seminal "molecular packing" paper. This w a s published Israelachvili, J o h n Mitchell, and Barry N i n h a m in t h e the Chemical Society, Faraday Transactions, vol. 72, 1976, 144 Barry Ninham's work on microemulsions. See, for e x a m p l e ,

by Jacob Journal of p. 1525. Zemb, T.

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N., Barnes, I. S., Derian, P. J., a n d N i n h a m , B. W., Faraday Transactions of the Royal Society of Chemistry, vol. 8 1 , 1 9 9 0 , p. 20. 144 Commercial dishwashing liquids. Such liquids are formulated to clean well, but also to foam. The foam is stabilized by molecules with a different s h a p e t h a n t h o s e w h i c h c o n t r i b u t e to the cleaning, and is only t h e r e as an optional extra, designed to impress t h e c o n s u m e r w i t h the efficacy oi t h e p r o d u c t , but stabilized by m o l ecules w h o s e s h a p e s m e a n that t h e y do little of t h e actual w o r k . 144 The interaction between two BLMs. This was reported in t h e Royal Society of Chemistry Faraday Discussion, n o . 8 1 , 1986, p. 249. 145 The saving of the human race. For e x a m p l e , it m a y be possible to preserve o u r genetic record tor future r e p r o d u c t i o n by encasing DNA in artificial hi layers p r o d u c e d by self-assembly.

c h a p t e r 8: a q u e s t i o n of taste Page 147 Brillat-Savarin. O n e of t h e b e s t - k n o w n n a m e s in g a s t r o n o m y . His r e m a r k a b l e book, w h o s e title is usually s h o r t e n e d to Physiologic Ju gout, was published shortly before his d e a t h . "Gout" ( p r o n o u n c e d "goo") is an u n t r a n s l a t a b l e French w o r d that reflects t h e full flavor e x p e r i e n c e , w h i c h is m o r e t h a n just a c o m b i n a t i o n of taste a n d a r o m a . Its untranslatability is verified by t h e fact that my c o m p u t e r spellchecker, with u n i n t e n t i o n a l h u m o r , keeps correcting the spelling to "gout." It m a y say s o m e t h i n g about cultural attitudes to food that BrillatSavarin's b o o k w a s not translated into English until 1884 (the American food writer M. F. K. Fisher's 1949 translation is n o w generally regarded as t h e best). If it w e r e not lor this book, his n a m e w o u l d live on only in t h e dish called a Brillat-Savarin, w h i c h is a m e t h o d of serving lamb in small pieces, a c c o m p a n i e d by d u c h e s s potatoes, loie gras, truffles, a n d green asparagus tips in butter. I find myself salivating at t h e very t h o u g h t of this dish, w h i c h is a n o t h e r e x a m p l e of t h e fact that good food is as m u c h a m a t t e r of e x p e c t a t i o n as e x p e r i e n c e . Brillat-Savarin's r e v e r e n c e for t h e aftereffects of eating w e r e reflected by Rossini, w h o w a s no m e a n g o u r m e t himself, in four musical pieces collectively entitled The Gourmet Life and i n t e n d e d to represent t h e process of digestion. Their subtitles w e r e , in sequence, Interrupted Contentment, Over-Indulgence, Juices (a piece w h i c h c o m b i n e d t h e s o u n d of h a r d w o r k i n g gastric juices with s o m e repetition in u n e x p e c t e d places), and Relief. I believe that I


149

149

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possess t h e world's only recording of this little-known set of pieces, kindly m a d e privately for me by t h e British c o m p o s e r Malcolm Hill. The Futurists. See Marinetti, Filippo Tommaso, The Futurist Cookbook, Brill, S., transl., Bedford Arts, 1989. A massively e n t e r t a i n ing a c c o u n t of "Food as a P e r f o r m a n c e M e d i u m " w a s published by Barbara Kirshenblatt-Gimblett in Performance Research, v o l u m e 4, page 1 ( 1 9 9 9 ) . Heston Blumenthal. B l u m e n t h a l is chef-proprietor of t h e Fat Duck r e s t a u r a n t at Bray (near Windsor), in t h e U.K. I am indebted to him lor m u c h information a n d m a n y enjoyable c o n v e r s a t i o n s a b o u t cooking styles. . . . garlic and coffee. Professional flavorists h a v e a similar concept of "bridging t h e gap" b e t w e e n t w o dissimilar a r o m a s to i m p r o v e t h e overall impression. the brain . . . can't decide whether it is experiencing garlic or coffee, and oscillates between the two. This " e x p l a n a t i o n " is a d m i t t e d l y speculative, a n d Gary B e a u c h a m p , director of t h e Monell Chemical Senses Institute, has cast s o m e d o u b t on it.

I 50

. . . the human brain loves surprises. Experiments at E m o r y University Health Sciences, reported on www.sciencedaily.com. Perhaps an alternative i n t e r p r e t a t i o n is that t h e brain h a t e s b o r e d o m and cuts out signals that h a v e b e e n a r o u n d too long. This obviously has survival v a l u e w h e n we a r e constantly b o m b a r d e d by lots of different a r o m a s . I am indebted to my friend a n d colleague Dr. Alan Parker, of F i r m e n i c h Pic, for m a k i n g this a n d a n u m b e r of o t h e r interesting p o i n t s a b o u t this chapter.

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. . . flavor scientists are making progress. A great deal of exciting w o r k in this area is e m a n a t i n g from t h e Monell Chemical Senses Institute in Philadelphia, led by Gary B e a u c h a m p , a n d t h e research laboratories of Firmenich Pic in G e n e v a , Switzerland, led by Tony Blake, a fount of information on m a n y things sensual.

151 . . . putting a few coffee beans under the grill. A n o t h e r way to fool people w i t h instant coffee is to add a little g r o u n d c a r d a m o m , filtering off t h e residue before serving. 152 The gravy project. This w a s s p o n s o r e d by Bisto, m a k e r s of a range of instant gravies. The difference b e t w e e n such c o m m e r c i a l gravies and t h o s e p r e p a r e d by cooking a little flour in m e a t juice lies mainly in t h e fact t h a t t h e starch usually c o m e s from a different source in t h e c o m m e r c i a l gravy, and t h e c o m m e r c i a l gravy is fatfree, an a d v a n t a g e for health, but a d i s a d v a n t a g e w h e n it c o m e s to flavors that only dissolve in fats. 152

Peter Barham.

Barham

is

the

author

of

The

Science

of Cooking

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(Springer-Verlag, 2 0 0 1 ) , and is also t h e p e r s o n w h o i n t r o d u c e d me to t h e w o n d e r f u l world of g a s t r o n o m i c a l science. 15 3 The Gravy Equation:

w h e r e Wis t h e wet (or u n c o o k e d ) weight of t h e food, D is t h e dry (or cooked) weight, a n d 5 is t h e s h r i n k a g e factor. I published t h e details in "The T h e o r y of Gravy," Annals of Improbable Research, vol. 7, 6, N o v e m b e r / D e c e m b e r 2 0 0 1 , p. 4. 153 One food that didn't make it to the final gravy report. Popcorn was the most p o r o u s food material that we could t h i n k of, a n d therefore t h e o n e likely to take up t h e highest p e r c e n t a g e of gravy. It did — it took in six times its o w n weight. W e n d y o p i n e d that t h e taste of gravy and p o p c o r n is disgusting, a n d that individual Yorkshire p u d d i n g s , w h i c h take up 90 p e r c e n t of their o w n weight, w e r e m u c h t o b e preferred. S h e was very disappointed w h e n w e t h r e w t h e p u d d i n g s o u t after we had w e i g h e d t h e m . Peter had to cook some more. 155 . . . unanswered questions. I h a v e n o t had a c h a n c e to r e t u r n to t h e s e q u e s t i o n s , a l t h o u g h 1 h a v e passed t h e information on to a few chefs, a n d also published t h e data in t h e aptly n a m e d Annals of Improbable Research. 155

The Devil's Dictionary. The Unabridged Devil's Dictionary, Bierce, Ambrose, Schultz, D. G., a n d Joshi, S. T, eds., University of Georgia Press, 2 0 0 2 . 1 56 The X-ray video of a chewing head. The video was s h o w n by Professor Robin H e a t h of t h e Royal L o n d o n School of Medicine and Dentistry. Robin m a k e s a particular study of p r o b l e m s in eating, w h i c h are surprisingly c o m m o n , especially a m o n g older people. The m a i n p r o b l e m , he tells m e , is an increasing inability to secrete sufficient saliva, a p r o b l e m often exacerbated by particular drugs. Robin did a s u r v e y of w h i c h food patients found easiest to eat, and w a s surprised to find that t h e h a r d a n d brittle g i n g e r s n a p cookie c a m e high on t h e list. These cookies can s u p p o r t a weight of five kilograms w h e n s u s p e n d e d across a gap, so Robin had every right to be surprised. He e v e n t u a l l y discovered that n o n e of his patients had t h o u g h t t o m e n t i o n that t h e y d u n k e d t h e cookies in tea to m a k e t h e m softer before eating t h e m . 158

"shear-thickening" and "shear-thinning." The bolus b e c o m e s m o r e c o h e r e n t as we chew, w h i c h m a k e s it h a r d e r to distort. The terms that I h a v e used to describe this h a v e a m o r e precise scientific m e a n i n g , w h i c h m a y or m a y not strictly apply.


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1 59 this part of the tongue . . . first encounters the lactose (one of the sweetest of sugars) in mother's milk. This is only t r u e if t h e infant licks before suckling. O n c e suckling starts, t h e milk is expressed to t h e back of the m o u t h . 165 Menthol modulates oral sensations of warmth and cold. Details ol this can be found in Green, Barry, Physiology and Behaviour, vol. 35, 1985, p. 4 2 7 . 165 Chili pepper hotness. This is m e a s u r e d in "Scoville units," a m e a s u r e of t h e c o n c e n t r a t i o n of capsaicinoids. The p o p u l a r j a l a p e n o chilis weigh in at up to 5000 Scoville units, but for real h e a t try the waxy, t h u m b - s i z e d h a b a n e r o (up to 3 0 0 , 0 0 0 ) . Pure capsaicin registers a staggering 15 million. Like m a n y of t h e a r o m a molecules, capsaicinoids are soluble in oil, but insoluble in w a t e r or cold beer. For t h e n o n - c h i l i p e p p e r addict, or t h e addict w h o has h a d e n o u g h , t h e secret to clearing chili p e p p e r heat from t h e m o u t h is to drink plenty of milk. Coc o n u t also w o r k s because it is loaded with oil. O v e r c o n s u m p i i o n oi chili peppers, incidentally, can lead to h e m o r r h o i d s . 167

The ment 167 The idea food

collapse of an aqueous draining film. My results for this experiw e r e reported in Colloids and Surfaces, vol. 52, p. 163. "spraying" of droplets containing aroma molecules. The original t h a t a r o m a droplets m i g h t s o m e h o w be "sprayed" t r o m a bolus was suggested to me by Professor Robin H e a t h .

c h a p t e r 9: the p h y s i c s of sex Page 171

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/ was once asked to give a talk. The aim of my talk, a n d of this c h a p ter, was to m a k e science accessible a n d to use t h e j o u r n e y of t h e s p e r m to s h o w that science is n o t divided into watertight c o m p a r t m e n t s labeled "physics," "biology," "chemistry," etc. It was not my i n t e n t i o n to give scientific a n s w e r s to sexual p r o b l e m s , alt h o u g h a surprising n u m b e r of people h a v e asked me to do just that. My a n s w e r has always b e e n that I am not qualified in this area, and have never w o r k e d in it professionally. The best I can offer is information that people m a y be able to use to help t h e m to f o r m u l a t e t h e right q u e s t i o n s to s o m e o n e suitably qualified. There were more teachers than students present. Middle-aged male teachers m a y h a v e had a special interest. According to my Bristol University colleague, Professor Shah Ebrahim, middle-aged m e n w h o h a v e sex t h r e e or m o r e times a w e e k are half as likely to h a v e strokes or heart attacks as t h o s e w h o are sexually inactive (con-

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Uniting studies on 2 4 0 0 Welsh m e n , reported at t h e World Stroke Congress in N o v e m b e r 2 0 0 0 ) . Ebrahim's results are in stark contrast to t h e belief of J o h n Harvey Kellogg, i n v e n t o r of Kellogg's Cornflakes, that t h o s e w h o e n gage in sex, e v e n for procreative p u r p o s e s , s h o u l d limit their activities or insanity w o u l d result (Kellogg, J. H., Plain Facts for Old and Young, Senger, Burlington, Iowa, 1882). 171 The radioactive watch and telephone book stories. These w e r e reported in a survey for Doctor, a w e e k l y n e w s p a p e r for t h e British medical profession ( q u o t e d in The Editor, 21 July 2 0 0 1 ) . Reports of t e e n a g e m i s u n d e r s t a n d i n g s a b o u t sex a r e endless. Two of my favorites c o m e from M i a m i . O n e p r e g n a n t t e e n a g e r att e n d i n g a M i a m i Beach clinic insisted that she had suffered from contraceptive failure. "What m e t h o d did you use?" she was asked. "Jelly," she replied. " W h a t type of jelly?" "Grape." The s a m e clinic gave a s e v e n t e e n - y e a r - o l d boy a d e m o n s t r a t i o n of h o w to use a c o n d o m . "I've b e e n doing it w r o n g for t w o years," he said. "I t h o u g h t y o u h a d to p o k e a hole in it so y o u r testicles wouldn't explode." 172 Sex is even now regarded as a somewhat dubious topic for a scientist to be discussing. A history of sex research is given by t h e American acad e m i c Vern Bullough in Science in the Bedroom (Basic Books, 1994). Professor Bullough claims that a great deal of t h e stigma still associated w i t h sex research goes back to St. A u g u s t i n e ' s doctrine "that t h e sin of A d a m a n d Eve is t r a n s m i t t e d from p a r e n t s to child r e n t h r o u g h t h e sexual act, w h i c h , by virtue of t h e lust that acc o m p a n i e s it, is i n h e r e n t l y sinful." My o w n belief is that a great m a n y people in t h e W e s t e r n world still subscribe to this doctrine implicitly, e v e n if t h e y do not do so explicitly. Some of the people at t h e talk to which I referred may have been a little shocked w h e n I introduced a study by Swedish scientists w h o p e r s u a d e d a couple to m a k e love in a hospital MRI s c a n n e r of t h e type used to study brain abnormalities. In this case, t h e couple's sexual organs w e r e t h e focus of attention. O n e can only admire their dedication to d u t y as they m a n a g e d to have intercourse while being b o m b a r d e d by a series of instructions t h r o u g h a m i c r o p h o n e . 173 Blood pressure generated by pumping of the heart. The blood pressure is kept w i t h i n " n o r m a l " limits by t h e elastic stretching of t h e blood vessels with e a c h p u m p i n g stroke. If it w e r e not for this, t h e systolic blood pressure (the h i g h e r of t h e t w o readings normally q u o t e d ) w o u l d be incredibly high, because liquids are virtually in-


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compressible, as a n y o n e w h o has ever belly-flopped from a high diving board will k n o w . O n e of t h e causes of high blood pressure is in fact a gradual stiffening of t h e blood-vessel walls so that t h e y are u n a b l e to dilate sufficiently. 173 Hormones . . . relax the smooth muscle of the artery walls. In fact, t h e y stimulate the release of nitric oxide, a small molecule w h o s e chemical symbol (NO) rings r a t h e r oddly in this context. It is nitric oxide that p r o d u c e s t h e relaxation. The nitric oxide is e v e n t u ally destroyed by a d r e n a l i n e , or m e n w o u l d be sporting day-long erections. 174 Vacuum device for passive erection. Researchers at the Novosibirsk Research Institute in Russia claim that a course of this t r e a t m e n t , c o m b i n e d with t h e use of an infrared laser to irradiate the top of t h e penis tor five m i n u t e s each time, eventually leads to a situation w h e r e t h e v a c u u m device is no longer necessary because t h e laser t r e a t m e n t p r o d u c e s "a massaging of t h e veins which leads to increased metabolism a n d n u t r i t i o n of t h e tissue." 174

There is no such thing as an aphrodisiac. There are, however, materials that can p r o d u c e orgasms in s o m e people. The antidepressant c l o m i p r a m i n e m a k e s s o m e w o m e n have a n orgasm w h e n they y a w n or sneeze {New Scientist, 27 March 1998, p. 27). A friend of o n e sufferer asked w h a t she w a s taking for it. She answered, "Pepper" (New Scientist, 20 J u n e 1998, p. 56). O t h e r a n t i d e p r e s s a n t s h a v e t h e opposite side effect. At least o n e - t h i r d of p e o p l e taking a n t i d e p r e s s a n t s along t h e lines of Prozac suffer a loss of libido or have difficulty attaining orgasm (New Scientist, 29 S e p t e m b e r 2 0 0 1 , p. 17).

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Fancied resemblance to a penis or a vagina. The range was fairly wide. In the w o r d s of Piet Hein's little "grook" (Hein, P., Grooks, MIT Press, Cambridge, Mass., 1966): Everything's e i t h e r c o n c a v e or -vex. So w h a t e v e r you d r e a m will be s o m e t h i n g with sex.

174 Aphrodisiacs. Ginseng has recently been s h o w n to reduce t h e n u m ber of s p e r m e n t e r i n g t h e cervical m u c u s . O n e of t h e m o r e u n u s u a l "aphrodisiacs," described in t h e Kama Sutra, consists of a p o w d e r e d m i x t u r e of t h e dried plant Vajnasunhi (its Sanskrit n a m e — 1 h a v e b e e n u n a b l e to find t h e English equivalent), red arsenic ( A s S ) , a n d sulphur. The mixture is set on fire. If t h e m o o n , viewed t h r o u g h t h e exceedingly poisonous smoke, a p p e a r s golden, t h e n t h e a m a t o r y experience will be successful. T h e r e is s o m e fascinating physics involved here, since t h e 2

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174 175 176

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m o o n will a p p e a r golden only if t h e s m o k e particles are t h e s a m e size as t h e w a v e l e n g t h of b l u e - g r e e n light (about 500 n m ) , so that t h e y will scatter this light but leave t h e r e d / y e l l o w e n d of the s p e c t r u m relatively unaffected. The m i x t u r e is also u n u s u a l in that it can be t u r n e d into an anaphrodisiac by a d d i n g m o n k e y e x c r e m e n t and t h r o w i n g it over t h e m a i d e n . This e n s u r e s that she will not be given in marriage to a n y o n e else, w h i c h is h a r d l y surprising. Spanish fly and French troops. Reported by Meynier, Dr. J., Archives of Military Medicine and Pharmacology, vol. 22, 1893, p. 52. "Cupid's Nightcap." New Statesman and Nation. 1 N o v e m b e r 1953. Effects o]"Viagra on cut flowers. British Medical Journal, vol. 313, 1999, p. 274. T h e FDA site for c o n s u m e r information on medical aspects of Viagra is: http://www.fda.gov/cder/consumerinlo/viagra/default.htm. Viagra acts by slowing t h e degradation of nitric oxide. It is not the only orally administered drug that can help sufferers of impotence. Losartan, a d r u g used to combat high blood pressure, was found in a clinical trial to help nearly ninety percent of sufferers (Capo et al„ American Journal of Medical Sciences, vol. 321, 2 0 0 1 , p. 336). The physics of ejaculation. I h a v e used t h e e x a m p l e of ejaculation with s o m e success to teach N e w t o n ' s Laws of M o t i o n to an o t h e r wise reluctant class of first-year university s t u d e n t s . The speed w i t h w h i c h t h e ejaculate e m e r g e s can be w o r k e d out by t h e a p plication of N e w t o n ' s Second Law of Motion (force = mass X acceleration), w h i c h can be used to calculate t h e vertical speed of a projectile from t h e m a x i m u m height that it attains. In this case t h e "projectile" is a teaspoonful of ejaculate. The only published description I could find a b o u t t h e height it can attain a p p e a r s in Philip Roth's Portnoy's Complaint, w h e r e P o r t n o y is reported to h a v e hit t h e light bulb. Information from o t h e r sources, h o w e v e r , revealed that t h e average m a l e is unlikely to be able to l a u n c h his teaspoonful of ejaculate m o r e t h a n a foot or so straight up into t h e air. In this case, N e w t o n ' s Second, Law says that its initial velocity m u s t be a r o u n d t w o m e t e r s / s e c o n d , i.e., a r o u n d seven kilometers per h o u r , w h i c h is a fast walking speed. This d o e s n ' t create too m a n y p r o b l e m s on Earth, but it does add an interesting twist to t h e p r o b l e m of m a k i n g love in space. The p r o b l e m is not just an a c a d e m i c o n e — NASA has n o w b e g u n to issue p r e g n a n c y testing kits to female p e r s o n n e l on t h e I n t e r n a tional Space Station, t h e r e b y a d m i t t i n g that a g r o u p of m e n and w o m e n cooped up t o g e t h e r for five m o n t h s in space might get up to m o r e t h a n a bit of m e t e r - r e a d i n g a n d dial-twisting.


241

According to NASA technician Harry Stine (in Stine, G. H., Living in Space, M. Evans 8- Co., 1997), NASA has already c o n d u c t e d g r o u n d - b a s e d e x p e r i m e n t s on t h e feasibility of m a k i n g love in space. The e x p e r i m e n t s w e r e c o n d u c t e d in a b u o y a n c y t a n k , alt h o u g h t h e n a m e s of t h e v o l u n t e e r s are u n f o r t u n a t e l y n o t on public record. The conclusion w a s that m a k i n g love in weightless conditions is barely feasible, b u t that it is m a d e m u c h easier if a third person is present to hold o n e of t h e bodies in place. Whales found this out eons ago, and m a n y species of w h a l e use the practice to this day. In physical terms the third person (or whale) is there to provide a defense against Newton's First Law of Motion, which says that if you p u s h on something, it will accelerate a w a y unless there is a balancing force that stops it from doing so. In space, t h e r e is a n o t h e r of N e w t o n ' s Laws to be considered — his Third Law, w h i c h says that action a n d reaction are e q u a l . This principle explains w h y a shell fired from a c a n n o n p r o d u c e s a recoil that drives t h e c a n n o n b a c k w a r d s . The principle applies equally well to gases and predicts, for e x a m p l e , t h a t b u r n i n g fuel ejected from a rocket will p r o d u c e a recoil that drives t h e rocket forward. It also applies to liquids, including t h o s e p r o d u c e d d u r ing ejaculation. T h e exact a m o u n t of of t h e c o n s e r v a t i o n of m o m e n t u m (i.e., mass anced by t h e b a c k w a r d

recoil can be calculated from t h e principle m o m e n t u m , w h i c h says that t h e forward x velocity) of t h e ejaculate m u s t be balm o m e n t u m of t h e body ejecting it.

According to my calculations, if an eighty-kilogram m a n ejects t h r e e g r a m s of ejaculate traveling at seven kilometers p e r hour, he will recoil at an initial speed of (0.003 X 7/80) = 0.00026 k i l o m e ters per hour. In a gravitational field this d o e s n ' t m a t t e r too m u c h . If t h e s p e r m is directed d o w n w a r d s , for e x a m p l e , t h e m a n will recoil u p w a r d by a m a x i m u m distance of five m i c r o m e t e r s before being b r o u g h t back to e a r t h u n d e r t h e influence of gravity. I n space, t h o u g h , t h e m a n will k e e p m o v i n g , covering o n e m e ter every t h r e e h o u r s , until he hits o n e of t h e walls of t h e spaceship. It t h e spaceship is eight m e t e r s long, he could take as long as t w e n t y - f o u r h o u r s to reach t h e far wall — j u s t nice time for t h e libido to build up for a r e t u r n b o u t . 177

Chances of conception after discontinuation of intrauterine and oral contraception. These w e r e reported by C. Tietze in t h e International Journal of fertilization, vol. 13, October-December 1968, p. 385. 177 . . . with a flattish wedge-shaped head like a mini-surfboard. The actual d i m e n s i o n s are typically 4.5 m i c r o m e t e r s long by 2.5 m i c r o m e t e r s w i d e by 1.5 m i c r o m e t e r s thick.

242


177 The semen pool. This is actually below t h e external os if t h e female p a r t n e r is lying on h e r back. The cervix relaxes afterwards for t h e e x t e r n a l os to dip i n t o t h e pool. 178 Seminal plasma gelling. The gelling reaction occurs w h e n p r o t e i n s from o n e accessory gland c o m e into contact with e n z y m e s secreted by a n o t h e r accessory gland. In technical terms, t h e crosslinking m o l e c u l e is 6- (y glutamyl) lysine from t h e seminal vesicle, and t h e e n z y m e is a c a l c i u m - d e p e n d e n t t r a n s g l u t a m i n a s e . 178 The Billings test and "ferning." These are described in the World Health Organization Laboratory Manual for the Examination of Human Semen and Sperm Cervical Mucus Interaction, 4th edition, Cambridge University Press, Cambridge, 1999. 179 Ferning. W h e n I first c a m e across this lest, no o n e could tell me w h a t t h e crystals w e r e . I had t h e m analyzed, a n d found that t h e y w e r e s o d i u m chloride — in o t h e r w o r d s , c o m m o n salt, t h e principal salt in o u r b o d y fluids. Why, t h o u g h , should c o m m o n salt form needle-like, b r a n c h e d crystals, r a t h e r t h a n t h e small cubit ones that we find in o u r salt s h a k e r s ? The a n s w e r is that t h e surfaces of t h e crystals, identical to the eye, are chemically different. Mucopolysaccharides stick preferentially to s o m e laces, p r e v e n t ing t h e m from g r o w i n g further, so t h e crystal grows u n e q u a l l y in different directions. This principle of controlled crystal g r o w t h is n o w recognized to p e r m e a t e n a t u r e . It a p p e a r s to underlie, lor exa m p l e , t h e d e v e l o p m e n t of t h e shapes of seashells. It is u n c l e a r w h y "ferning" relates to t h e "goodness" of t h e m u cus. P r e s u m a b l y it is a m a t t e r of t h e h y d r a t i o n and unfolding of t h e m u c o p o l y s a c c h a r i d e s , w h i c h affects both t h e consistency of t h e m u c u s a n d t h e ability of t h e molecules to stick to different crystal faces. This is a Ph.D topic waiting for a c a n d i d a t e . 180 Lateral pressure in a protein film on an oil drop. Fisher, L. R., Mitchell, E. E., a n d Parker, N. S., "A critical role for interfacial compression and coagulation in t h e stabilisation of e m u l s i o n s by proteins," Journal of Colloid and Interface Science, vol. 119, 1987, p. 592. 182 Ability of spermatozoa to fertilize the egg. It still seems to be an open q u e s t i o n as to w h a t p r o p o r t i o n of t h e s p e r m a t o z o a that p e n e t r a t e t h e cervical m u c u s are actually capable of fertilizing t h e egg. Robin Baker, in Sperm Wars (Basic Books, 1997), puts the p r o p o r tion as low as ten p e r c e n t . 182

Pushing into cervical mucus. The force that a sperm s w i m m i n g at 3 m m / m i n can exert is given by: Force = 6TT X radius of head x viscosity of medium x velocity of sperm = 10"'° Newtons


243

The s a m e result has b e e n obtained by direct e x p e r i m e n t s , w h e r e motile spermatozoa w e r e stuck to a tiny spring a n d t h e force g e n erated calculated from t h e deflection of t h e spring. T h e pressure that this force p r o d u c e s is simply t h e force divided by t h e crosssectional area of t h e head, a n d c o m e s to 300 Pascals (i.e., a b o u t one three-hundredth oi atmospheric pressure). A simplified picture of sperm penetration is that this pressure will enable the s w i m m i n g s p e r m a t o z o o n to p u s h its way into a n y t h i n g with a yield stress of less t h a n a third of this value, i.e., 100 Pascals. 182 Effect of female sexual enjoyment on sperm penetration. Results of a survey by Jacky Boivin of Cardiff University, reported in New Scientist, 12 S e p t e m b e r 1998, p. 20. 182 Swimming in cervical mucus. We n o r m a l l y t h i n k of s w i m m i n g in t e r m s of t h e c o n s e r v a t i o n of m o m e n t u m . A s w i m m e r " t h r o w s " w a t e r b a c k w a r d s , and gains an e q u i v a l e n t forward m o m e n t u m . If t h e s w i m m e r stops m o v i n g t h e a r m s , he or she will glide forward u n d e r his or her o w n m o m e n t u m for several body lengths before being b r o u g h t to a stop by t h e viscous drag of t h e water. S o m e o n e carried forward u n d e r their o w n m o m e n t u m is said to be u n d e r t h e influence of inertial forces. The relative i m p o r t a n c e of inertial forces a n d viscous forces is given by t h e Reynolds number, w h i c h is simply t h e ratio of t h e t w o forces. For a p e r s o n s w i m m i n g , t h e Reynolds n u m b e r is b e t w e e n ten t h o u s a n d and a million, w h i c h explains w h y t h e p e r s o n can glide forward u n d e r their o w n m o m e n t u m w i t h o u t being dragged to an a b r u p t halt by viscous forces. For a s w i m m i n g s p e r m a t o z o o n , t h o u g h , t h e Reynolds n u m b e r is b e t w e e n 0.1 a n d 0 . 0 1 , and viscous forces d o m i n a t e . U n d e r t h e s e conditions, t h e s p e r m a t o z o o n can only "coast" u n d e r its o w n m o m e n t u m for a distance given by: distance = (2 X initial velocity X radius X density) / viscosity of liquid 2

This formula tells us that a s p e r m a t o z o o n s w i m m i n g at 3 m m / m i n can only "coast" t h r e e m i c r o m e t e r s in water, i.e., a b o u t a t w e n t i e t h of its o w n length, before being b r o u g h t up short by viscous drag on t h e h e a d . If viscous drag on t h e n o w - m o t i o n less tail is a d d e d in, t h e distance will be e v e n shorter. 183 Mucopolysaccharide molecules from bundles. See review article by Carlstedt, I., a n d S h e e h a n , J. K., in Symposium of the Society for Experimental Biology, vol. 4 3 , 1989, p. 289. 184 The shear-thinning behavior of cervical mucus. This has been reported by Ford, W. C, Ponting, F. A., McLaughlin, E. A., Rees, J. M., and Hull, M. G., in International Journal of Andrology, vol. 15, 1992, p. 127.

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