Fabric of Knowledge

THE IFABRIG OF KNOWLEDGE a study of the relations between ideas

'Contemplate the formative principles of things bare of their coverings'

The Meditations of Marcus Aurelius book I 2 paragraph 8

First published in 1973 by Gerdd Duckworth & Co. Ltd., 43 Gloucester Grescent, London NWL.

All rights reserved. No part of this publication rnay be reproduced, stored in a retrieval system, or transmitted, in any form or by any rneans, electronic, mechanicd hotocopying, reeordlng 'P or otherwise, without prior permission of the copyright o m e r . ISBN O 7156 0714 6

Typesetting by Specidised Offset Services, Liverpool. Printed by kinwin Brothers Limited, Old Woking, Surrey

F O R E W CP R D by PREFACE

C.W. Kilmister

1

T H E A R R A N G E M E N T O F I D E A S . Standpoint - A history of an expepiment - The general pattern of ideas - Perception classes - Chains of notions Integrative levels - Formative grades - Artefacts Notation for levels and grades - Scmantic types Introduction of relations - Names m d notation for the types - Full code sequences - The holotheme: a provisional summary.

2

T H E D E V E L O P M E N T O F A L H E O R U . properties of

relaLions - Relation codes - Operations - Numbers - Mathematical structures - h t o the domain of physics - Relation codes and the holotheme - Rules for placing nolions - The pattern in brief.

40

3 B A C K G R O U N D A N D G O M M E N T . Some other views - l a w s of the levels - The arrival of new levels - Aggregates of matter - Photons - Bther r e c e n t w o r k - Earlier work - The Greeks Mediaevd to modern - Co-ordinate indexing - Data fields - Applications - Conclusion.

65

APPENDIXES

A . A Data Field and its Contents B . Examples of Placement

6 . Previous Notes on the Levels D . Summary of the Relation Code GENERAL INDEX PLACEMENT INDEX

The classification of the elernents of knowledge is largely the province of the librarian and the specialist in documentation, with help from the teacher and the linguist. Such people have sometimes developed a tendency to avoid one of the subjects they must classify, namely arithmetic and the more advanced mathematics built upon it. This attitude is not unreasonable in the light of the forbidding methods of teaching the subject to which they may have been exposed at school. Fortunately, matters are improving fast; but memwhile to present a classification based on a simple and easily rnemorised pattern is safe only so long as n o one hints that the pattern may be related to mathematics and its feIIow studies. Uet at bottom the classifier and the mathernatician are doing the sarne thing, finding and manipulating patterns. Mlhen I saw this book in draft my reaction was one of great pleasure at the pattern it put forward, and this was increased because the approach to my own subject came, as it were, from the side of the arts. It was a way to arrange ideas which arose from the notions used in everyday life, essayed the development of readily-followed rules, and almost as a by-product revealed a scheme for classifying the concepts of mathematics and using them as a means of ordering the other sciences. I hope that one day Mr Jolley wil1 turn his argument round, present it in the fonn of a hierarchy derived from mathematics and then test its applicability to the rest of knowledge. It has become clear that a systematic application of such a hierarchy is not only a vduable classification scheme but serves as a genuine research tool and an effective teaching aid. The advantages to research are gained from the way that a regular pattem reveals gaps where, if the pattern is consistent, something new ought to be found. The teaching advantages spring from the way a suitable framework makes things fit together, so that connections between ideas are easy to mernonse. One way of judging the value of a book is to see how much

furfier work it suggests. There is a great deal to be done in the present field of study; bui Mr Jolley has made the main lines clear. His range includes the social sciences, economics, politics and management, but perhaps I rnay be forgiven if I deal for a moment with my own subject. The non-mathematician rnay skip the next few sentences, in the knowledge that his or her special study is equally recondite, in its own way, though it wil1 seem easy t o those familiar with it. The order and system that MrJolley brings to the modem world of mathematics (specially algebra and analysis) is quite stnking. I t would not be true to say that there was previously chaos here, but the most avowedly systernatic account, say by the Bourbaki school, is of an unsatisfacto-). nature. A starting point for Bourbaki is what is known as a set, a co3lectPon of things of any sort whatever. Bourbaki defines structures within and between sets in such a way that the result is mathematics as we know it. But why does he choose to define these structures and not others? There seems to be no inner motivation: the object is sirnply to impose a pattern that wil1 produce the desired result. By contrast, an arrangement such as that here presented supplies a motive: an order of definition appears, based on the observed properties of the structures tBiemselves, and implies that these are the structures out of which the subject we know exfoliates. A good pattern, like that of the periodic table, must make its own way in &e world. It invites attempts to prove it mistaken, to question its assumptions, to show that its gaps are blemishes and not merely undiscovered country. No doubt, faced with the considerable novelty in these pages, the reader wil1 be tenipted (fairly, I hope) to test their claims. There is always the question of how much reserve should be accorded to a view when it may be mistaken but, equally, rnay just be unfmiliar. There is much here which is novel, not least the belief that a universal classification rnay at last be with us, whose rules are independent of the habits of the dassifier. The pattem presents a considerable challenge: may &e book inspire others to begin the large task that it delineates.

C.W. ~ i l m i s t e r Professor of Mathematics King9sCollege, London.

The first two chapters of this book describe an inquiry into whether the elements of human knowledge may be arranged in an order which is not determined by personal opinion and which is capable of being venfied independently by different people. I t coneludes that this is possible and describes a theory which rnay serve the purpose. This part of the book is based on a paper presented at the First Ottawa Conference on the Conceptual Basis of the Ciassification of Knowledge, which was held in October 1971. 1 wrotc the paper during the summer of that year, using the results of work I had b e e n about twelve years earlier. Almost at the last moment I found myself unable to present it in person, and this task was undertaken at short notice by Robert Fairtllorne, t o whom I owe a considerable debt of gratitude. The third chapter is a commentary, intended to supply a background to the theory, to cornpare my present views with those of others, and to suggest applications of the work to practica1 problems. I should like to thank ASLIB Proceedings and Classqication Society Bulletin, in whose pages some of the material here printed first appeared, and the organisers of the Ottawa Conference, vvithout whose invitation much of this book would still be in the form of disorganised notes in trays on rny study floor.

I The Arrangement of Ideas have been trying for fifteen years to find out how people think. I do not mem how nervous impulses travel about their brains, or how they reason, or whether they visudize, though d l these are part of the problem - that part which is to do with methods and processes. My o m concern has been with a different aspect of the matter: with the materids they use. These materids are ideas, mental images or representations of what may (or at times may not) exist in the world about us. The questions I asked were, what sort of ideas exist, how c m we classify Lhem, and how can we be sure that none have een overlooked? I also wanted to know how simple ideas were assembled into the more complicated sort. I needed this wledge for a highly practica1 puvose: I was concerned a special type of information retrieval which relied for ffectiveness on the assembly of simple notions to form licated descriptions. Systems of this sort demand that ers can put their hands on ideas when they want thern constmction work they have In mind. Pn consequente sential to find a helpful order for the notions &ey Sometirnes the dphabet wil1 do; but this has its ns. To start with, it arranges words, each with one or eas tagging after it, and the ideas take up a random ement which makes it impossible to find them if their ed words are unknown or forgotten. Gonsequently,

other patterns are sought. Most other patterns are equdly arbitrary, based on the rnere decision of an expert or a comrnittee; but even so they are rernarkably helpful, once they have been learned in outline. Any pattern is better than none. However, if it is possible to find an arrangement which is inherent in tihe ideas themselves, this should offer advantages far in excess of those provided by patterns imposed by any personal opinion. It seems clear that the development of a universal ordering of ideas must be based on a study of the notions we believe correspond to the contents of the real world about us. This inquiry must supply rules whereby the notions may be placed in positions which they cannot help but hold. So far as is possible, personal opinion must be ruled out as a reason for placement: the only help must be that which comes from a careful exarnination of the structure of the ideas themselves. Such a scheme of notions wil1 bear directly on linguistics, since it wil1 be tke image which speech must represent, and indeed may even turn out to be the so-called Ueep structure of language' - the external pattem our notions imitate and which must in its turn be symbolized by speech. It will also be relevant to other disciplines, which it TNill support much as the periodic table underlies chemistry. No doubt its gaps wil1 dways be more impofiant than its areas of completeness, for they wil1 correspond to those places where research is still to be done. It wijl have especial value for those whose work is to catdogue m d to classify what we cunenely know. The documents they index and file deal with topics which have a place in it, and the retrieval systems they create wil1 be the more efficient for being more closely moulded to it. I suspect that a most-exact model of this type wil1 also display great economy and coherente of pattern, so that it may 'be of considerable use in the field of education. It is iiikely to set the major subjects of the school and college curriculum in an obvious, understandable, sensible relationship to each other, so that the bewildered scholar may the

The Arrangement of Ideas

13

more readily see where his studies fit in tke vast field of knowledge offered t o him. This is consistent vvith the recent trend towards ernphasizing the unity of knowledge as opposed to the differences between the traditiond main subjects of school curricula. So much for rny standpoint, except for this: exploration and adgustment of such a pattem may never be completed, but I think we now know enough to get the outline right. It is to this matter that this book is directed.

A history of an expe.piment My concern with this problem started in 1959. Bt was a spare-time affair, rnuch intenupted, and it comprised three stages. During the first, which llasted for several years, I examined ideas taken from large numbers of classifications and word Ests which I encountered in my daily Ilfe as an indexing consultant. My aim was to find what major varieties of idea could be distinguished, starting with as few opinions on the matter as possible, and consequently treating a'U other witings on the subject with reserve. P Look no steps t o avoid other peoples9 opinions when they came rny way, but I did not carry out a jiterature search or sit at the k e t of any teacher. Indeed, it was some time beforc I realized I had ernbarked on any special voyage of discovery; when I did so, well on rny journey. When the true position dawned on t seemed better to go forward than to return to find charts of the unknown seas. I think this choice was . Most of the arrangements of knowledge which I met in Iife were n0 more relevant to rny rieeds than the of signatures is to the classification of plants. I had as innocendy as I could, and to compare results with ose of other workers when results were to hand. I decided ould in any case be a wortk-while experiment to go where subject took me, and then, at a suitable moment, "c see wel1 my expenence ageed with that of others. Later, I

14

The Fabric of Kno wledge

read extensively in the field of the classlfication of ideas, and found I was part of a great stream of effort and speculation whose headwaters were lost in the past. Fortunately, I did not then find anything which made me fee1 my results had been reached before. This was indeed good luck: I would very seldom recommend that a study should begin like mine, without a full survey of existing views: the chance of spending years doing work whlch is already done is far too great. The o u t c o m of this period was a general pattem which appeared to be complete, repetitive and interndly consistent; but it was based entirely on observation and cried out for a f o m a l theory, for mathematical underpinning. The second stage of niy inquiry began wïth a search for this. Quite suddedy, in 1965, I redized that set theory provided the pattem I sought. I fastened on this and worked upon it, referring back and forth between the textbooks and rny obsemations, trying to develop a sirnple, ianderstandable terminology with which to talk of what I was about. As rny confidence grew, I began at last to read the history of the matter, and to relate other people9s views to rny own experienee. By 1967 I was satisfied Mrith the formalism, and the present stage could start. This is concerned with consolidation, drawing conclusions, finding applications and developing rules of the sort h i c h may one day grace a textbook on holothemics, by which is meant the study of the whole set of notions we may Ionn. Typical rules are concerned Mrith finding the position occupied by an idea ~ t h i nthe general pattern. Such rules can be reduced to a series of choices between alternatives which come in pairs and are mutually exclusive. Consequently they can generate series of b i n a v digits, which may fit wel1 in the memo-. of a computer. This property may have a special appeal for those who are concerned with handling infomation by electronic rneans. Rules of this sort place ideas according t o five main

The Arrangement of ldeas

15

categones. These are concemed with each notion's perception class, integrative level, formative rank and gade, and sernantic type. Glass, level, rank, gade and type rnay now be described - first briefly, as more or less bald assertion, and then in greater detail.

The general pattern of ideas The concept of a perception class provides the first and most general distinction between the various types of notion we may form. It is based on the difference between the plain ordinary certainties of the world, which are accepted quite generally, and ideas which are held by at least one large group of sane people to conespond to no reality, os whose conespondenee with reality is unproven or agreed to be non-existent. These are special ideas, which may be known to be fantasy, or rnay be hypotheses awaiting proof, or rnay be unprovable though many people assert thern to be true. This sort of speciality has nofiing to do with abstraction. Nurnbers are abstract, but they are universauy held to exist, none the less. They are not doubted or denied as one rnight doubt or deny the existence of the Great God Thor. By contrast, religieus beliefs are special. Believers may be sure they are true, but there are also unbelievers. The proper way to accommodate both is to give a special status to faith, rnaking it quite distinct frorn hypothesis and fiction, yet none îhe less to do with how we interpret the world, how we two classes of notions may be distinpuished: the e, which is lower, and the special, which is higher, ng ideas which are often achieved by our imagination upon and seeking insight into the lower. The main of ideas with which this book is concerned is the r. I t is this lower, mundme, class which most readily ories rnentioned above: those of level, , grade and type. These categones are to do with

constmction, w i t h intemal state or structure. For example, an i n t e p t i v e level m a y b e defined as a consecutive sequence o f sixteen degrees o f complexity. B y contrast w i t h perceplion classes, o f which ( o n t h e definition above) tkere are only t w o , integrative levels are fairly numerous. Eight c m b e defined, each being well k n o m as t h e province o f one or more major sciences. A s a result, three choices are needed i n order t o place an idea i n its level. Fortunately, these generally appear i n t h e guise o f a single choice between eight dternatives. T h u s there is a level concerned Mrith atoms and molecules, and n o laborieus decision procedure is needed t o conclude that t h e concept o f an acid radicd appears there. T h e forrnative grades are t h e sixteen degrees o f complexity within each level. T h e y are divided i n t o t w o ranks, i n each o f which eight o f t h e grades are found. T h u s a level consists o f eight grades whicl-i f o r m its lower rank, and eight which f o r m its higher. A single choice is needed i n order t o determine rank; three are needed t o decide u p o n g a d e ; i n b o t h cases &e declsions are based o n familiar properties o f relations, which are dealt with later i n this account. It is n o t surprising that t h e properties o f relations are relevant i n this context, for i f ideas are t o b e $ven places i n some m a y b y rneans which are n o t arbitrary t h e n t h e y must be placed according t o their nature, which arises f r o m their internal constmction. T h e relations between their parts are therefore o f central is w h y mathernatics, as t h e study o f sact structure, m a y b e expected t o have something y about t h e f o m a l i v e ranks and grades. g a d e contains examples o f eight different , which are t h e semanfic types whose languages t o develop t h e different parts o f verbs, adjectlves. An idea's t y p e , Iike its ious, b u t i n difficult cases a routine o f ons m a y b e called for, and i n these cases r decision m a y b e felt t o b e very like those

FIGURE 1: A hierarchy showing the pattern of ideas as described opposite with numerals attached as explained later

I -1

DIRECTION OF INCREASING COMPLEXITY COMPLETE RANGE OF IDEAS

.. . . . . . . . . . . . . . . . . .. .. .. .. .. .. . ... .... ... . . . . . . . . . . . . . . . . . . .;L~ssES':;:::~,::',:;::,,,~:::::::: j,: : l: : .................................................

I

I

..nvo ~ E

O : MUNDANE

R ~ ~ P ; . ~ ( ~ ~

I

I : SPECIAL

helium . zinc - carbon - tin - iron

...

.l 1

18

The Fabric of Knowledge

employed in grammar t o determine a word's type according to the part it plays in expressing a train of thought. These, then, are the categories of notion round which my inquiry suggested a structure of knowledge might be built.

Perception classes To take things in due order, a more detailed treatment of the categories of notion must begin with a note on the perception classes as such, although the main emphasis of the work must be on the levels, grades and types which appear in them. Utopia, mallom trees, Mr Bumble, the coming of the eoquecigmes, phlogiston, Osiris, vital spirits, Ragnarok, these are examples of notions whose home is in the upper perception class. They are now generally accepted as flction, even those which were once matters of faith, like the existence of Osiris, or of firmly held hypothesis, like the existence of vital spirits. Othcrs, more important in this class, are the notions which are alive in the great world religions: redemption, the hereafter, reincarnation, the Church Triumphmt. These, the concern of theology, I laid aside during my inquiry - at first unconsciously, and later in the belief that they nicht repeat, at a higher position, the patterns I encountered in more mundane affairs. In practice, I found myself beginning my task by contemplating notions of a sort I was later to cal1 'objects'. These were passive rmndane entities with boundaries. Nations, plants and people are examples, and it is clear that notions of this sort appear in the special perception class also: Mr Bumble is modelled on a person, Utopia on a nation, mallom trees on trees of our world of everyday. As T grew to be aware of what I was doing, the distinction between special and mundane grew important to me, and it seemed useful to symbolize it. I made use of a binary notation, simply because there were only two choices. T allotted the numeral O to the mundane, and 1 to the special,

Th e Arrangement of ldeas

19

w i t h t h e result that t h e special appeared i n t h e numericdly later or higher Position. Clearly, any further notation produced as a result o f 'further uiquirjr, could remaln w i t k i n this framework. I thought o f t h e entire set o f notions w e rnight f o n n - t h e holotheme - as potentially suited t o continued division o f this sort, d t h o u g h I &d n o t expect this division t o b e simple. I looked for great complexity, and indeed began b y using an alphabetic notation o n t h e ground that a mere t e n n u m e r d s were unlikely t o b e enough. T h e persistent d u d i t y o f things surprised m e w h e n I encountered it. This binary e f f e c t established itself dunng rny examination o f t h e passive entities o f ordinary life, t o which i t is time t o turn.

Ghains of notions T h e essential process i n t h e study o f integrative levels is that o f rnaking chains o f ideas such that each earlier notion is a constnicrive part o f each later concept, just as bricks m a y b e part o f a house. This is work which is fairly easy t o d o , i f bounded rnaterial bodies - objects - are considered. I was fortunate t o have selected these as t h e first sort o f n o t i o n I would exarnine. T h e follouving is a chain o f objects: a proton an atomic nucleus a carbon a t o m a methyl g o u p a phospholipid molecule a lipoprotein membrane a mitochondrion a rnuscle cel1 a muscle fibre a muscle a heart

a cardiovascular system a human being a degreasing section a painting department a production line a factory a neighbourhood a town a county a nation an alliance the United Nations It is interesting to form other chains and to compare them, setting sirnilar notions together. For example, an electron rnight occupy the same line as a proton, and a plant cel! might appear on the sarne line as an animal cell. M e n this is done, some chains d l 1 be found to have gaps in thern; others wil1 seem t o have a superabundance of ideas. Here is a cornparison of chains: a carbon atom a methyl group a phospholipid molecule a lipoproteh membrane a mitochondnon a muscle cel1

a magnesium atorn a chlorophyll molecule a chloroplast a chloroplast layer a leaf cel1

It is clear that each chain calls for an expansion of the other. When enough chains of this sort have been made, regularities appear. At intervals, the notions foming the basis of important disciplines occur: sub-atornic particles; atoms; molecules; organelles; cells; organs of the body; entire plants or animals; organized human groups; nations. This list is not complete, but it offers a starting point. At an early stage in my study, I named ideas of this sort "units', and I wondered

The Arrangement of Ideas

21

whether there was a general property by which they could always be recognized. The answer, it seemed, was provided by the concept of homeostasis, as first applied in the field of biology. AI1 the units possessed this property to a high degree: @ven favour&le circumstances, they remained in balance with their surroundings. If not too severely damaged, they mended themselives. Even atoms, lacking electrons, trapped them if they could; and if a trade union Post its general secretary it appointed another. Units demanded completeness, and completeness appeared to be judged by degree of ability to survive. However, frorn this point of view some units fared better than others. Molecules were more independent than atoms: they &d not rush into partnership as readily as did atoms, although they too could interact. Gells were more independent than the organelles they contained, which mostly relied on the cells for survival. Leaves and flowers rnight die but the plant coulid still continue. An industrial company rnight close d o m a department, a state might extinguish old divisions, but the company and the state could both live on.

Integrative levels

I remember my s u p n s e when I saw that the more and the less dependent units dternated dong the entire length of any chain Mnthin which no units were omitted. This is the sort of reguj2arity whicfi entourages myone looking for a pattern, because it appears Mrithout being forced, and justifies the procedure of simply gazing at one's problem in a questioning way. My o m first list of units ran as fouovvs: photons PARTICLES

( ~ t rest h mass)

atom MOLECULES

The Fabric of Knowledge organelles CELLS

QrganS PLANTS AND ANIMALS

departments GOMMUNITIES

locd governrnents NATIONS

I noticed with interest that it was notably organic. It did not deal with artefacts, which I w u l d have to examine later. Also, I observed a second pattern in the chain. Every fourth unit seemed in some way to be enninent, to be a culrnination of the ideas which went before. The physical sciences aspired to molecules and molecular substances; the life sciences rose to the study of living beings; the social sciences culminated in the politic-d, social and econoniic behaviour of nations and of their unions and alliances. Such effects as this made it seem very rnuch as if the underlying pattem was binary. If this was so, then it was hard to resist the view that a list containing twelve units was incomplete. There ought to be sixteen. The positions held by the remaining four might, of course, come after that held by nations; but this view had littPe to recommend it counpared with the alternative, that they came before photons and were, in fact, to do with rnathematics. I remernbered reading specuIations that physicists might one day have to make matter out of space, and I guessed that two units concerned with geometnes rnight precede the photons and particles of sub-atomic physics, while two units of even greater simplicity occupied the two positions at the very start of the chain. I therefore added the following t o rny list: members of sets FULL SETS

points LINES, LINEAR SPACES

Two domains of the INANIMATE KINGDOM

Two domains of the ANIMATE KINGDOM

The Arrangement of ideas

25

purpose. I began by considering those ideas which came immediately after units in my chains. There was an immediate result: my colliection of ihese contained a marked preponderance of what I cdled %ssemblies9:groups of units in which no precedence could be found. The two electrons in the innemost orbit of an atom afford an example; so do the members of a leaderless group of people involved in a general discussion; so do a pair of eyes, the atoms in a hydrogen molecule; the sides of a hexagon, a pair of cuffllnks, a swarrn of midges, the voters in an election when each has one vote only . The notions which followed assemblies also had something in common, Sequence, precedence, order appeared in them. Examples are afforded by a production line in a facto-., the digestive system of an animal, the rainwater system of a house. I found the name 'system9 was so frequently used in connection G t h them that for a time I adopted it; but in due course it began to seem better to kmphasise the seriality of the collections of units involved, so I began to use the word 'series' for notions of this type. When units, assemblies and series had been removed from my chains of ideas very little remained. That little, however, was of considerable interest. Pt consisted of reciprocal or interactive series (I thought of them as assemblies of series), and it introduced an effect of feedback. Examples are: the afferent and efferent nervous systems taken together (and generally, with the brain and the spinal cord, called the central nervous sy stem) ; the transmission, ignition, braking and other systems, taken LogeSier, of a motor vehicle without its bodywork (I have often seen those driven past my tvlndow on their way from the engineer to the coachbuilder); the two series of unit parts which between them make two-way conversation possible by telephone. At first, after some hesitation, I called these reciprocal series 'combines9; but when unidirectional sequences had been named 'series' the word Csystem9became free and I applied it to assemblies

26

The Fabric of Knowledge

of series which displayed this internal balancing tendency. It chimed in wel1 with cument practice: general systems theory is concerned with interacting series. Notions of this sort are central to the study of cybemetics. I t is hard t o overrate their

importante. When sufficient series are brought together in this way, the resulting complex system is sufficiently interactive to produce a new unit, ensuring its homeostasis by the co-operation of its many trains of elements. This method of examining ideas reveals four steps, including a lower unit, assembly, series and system, before a higher unit is reached, and since I had found two units, a major and a nunor, in my integrative levels P concluded that each level contained eight steps of this sort. Of these, the first four led up frorn the lower unit to the unit which, being major, I thought of as central t o the level; the second four led on to the lower unit of the next level upward. I found it helpful to think of these as formative stages, stages in the fomation of higher things from lower. Soon each of these eight was to be divided in two, to form sixteen in all. Meanwhile I added a little to my teminology, calling a unit of a lower rank a subunit, an assembly of a lower rank a subassembly, and so on. With this convention, an atom becarne a molecular subunit and the alimentary canal of a human being becarne a subseries in the level of plants and anirnals. To proceed, a new distinction must be called into play. As an immedate example, consider the differente between an atom of copper and copper as a substance. 6)ne is an object; the other is a large collection of such things, an idea vvithout bounds, copper atoms on and on til1 we stop bothering to think about them, copper atoms to infinity. TFbe Same situation is found at other levels: electricity is a boundless collection of electrons, space can be thought of as a boundless collection of points, mist is a boundless collection o1 droplets, water a boundless collection of molecules of that

The Arrangement of ldeas

27

substance, yeast a b o u n d e s s collection o f yeast plants. Further, n o t al1 substances are simple i n t h e sense o f being made o f units o f one sort only. Others are mixtures: air is an example. U e t others have an even more complex internal structure - consider plywood. In t h e case o f plywood t h e substance is bounded i n o n e dimension buk n o specific bounds are set i n t h e other t w o . There is a significant comparison t o b e d r a m between units and assemblies, o n t h e one side, and simples and mixtures, o n t h e other. Units and assemblies are concerned urith objects; simples and mixtures are concemed w i t h substances. There is n o necessary order about tlie internal stmcture o f simples or rnixares; b u t i f sheedike or larriinar substances are considered t h e n an order can b e made: i n t h e case o f &ree-ply plywood &is m a y be: first ply - rniddle ply - last ply. Suppose that sheets are equated t o series, accordingly: can w e t h e n find something which m a y b e equated t o systems? Sheets are bounded i n one dimension: perhaps materials which are bounded i n t w o dimensions might fill this higher r o k . Examples are afforded b y hosepiping, rope, cinematograph film. These are o f indeterrninate l e n g h , b u t breadth and thickness are assumed. A f t e r trying various names for t h e m , I ended b y called t h e m 'stretchesp. T o take this t o a conclusion: Sie n e x t m o v e should b e t o consider substances bounded i n three dimensions. These, however, apped t o u s ceirectly as objects. T h e y are clearly units, as indeed might b e expected, since at this point o n t h e upward path m o t h e r rank ( m o t h e r lower or upper half-level) becomes available. This line o f a r g m e n t led m e t o divide each formative stage i n t o t w o , o n e part serving t o accornmodate objects and t h e other t o accommodate substances. These parts I named k a d e s ' , and it is f r o m this division that t h e sixteen grades o f each integrative level are derived: eight grades i n each rank o f t h e level.

FIGURE 3:The sequence of formative grades in any level, showing its binary pattern, with octal and binary notation as described later first appearance in level of

I

I

I

boundlessness, infinity (after one grade)

subsimpie

reciprocity, symmetry (after two grades)

u d

0.4

2

subseries

0.1 00

0.5

subsheet

0.101 I

0.6

I

subsystem

0.110 l

l

1 1 1 1

0.7

1

order (after four grades)

I

I

U

0.11'1

I substretch

1.000

unit

1.001

simple

1 1

completion (of main unit) (after eight grades)

In this table, reciprocity is shown as a property which first appears in subassemblies: it is to be thought of as a relationship between the things concerned (as one is to the other, so the other is to the one). In this sense, 'symmetry' is another name for it. Note that the g a d e names are chosen with respect to objects and substances: other grade names may be more helpful for other types of idea.

The Alrangement of ldeas

29

Considera~onof rnaterials - vvire, rubber and the like - led me to become concemed vvith the placing of artefacts in my eihain of integrative levels. Books, cups and saucers, chairs, pianos, roofing tiles, bottles of weedkiller, the Venus de Milo, transistors, Jet engines, f o o t b d boots, electric slravers and battleships al1 required a home. It was a land of pitfals. I h e w , for example, that an ìdea was not more advanced than another idea simply beeause it physically contained that other idea: tortoises are contained in shePls, but they are more advanced than the shells whieh contain them. Again, I knew that physical size was nothing to go by: îhe sun, for al1 its irnmerisity, is not as advanced as a bol1 weevil. I suspected that a hinge, iricorporating the facility of movement, might be higher than the door m d door frame which it served to connect, however complex these might be, so long as they were rigid in themselves. Such things as hinges, scissors, locks, latches and the Iike T caliied "djustable devices'. In the end I set up the hypothesis that the two levels between that of rnolecu8es m d that of communities were occupied, on the mechanic slde, by two pairs of units (vvith their appropriate assemblies, series and systerns) as foIIows: single-piece parts ADJUSTABEE DEVICES engines and other organs of machines MACHINES At the level of communities the two branches of the chain came together: a farm, for instance, consists not o d y of people, other animds and plants, but also of buildings, tractors and harvesting machinery, After experimenting wit21 more chains of ideas I concluded that this was satisfactory, thocagh it seemed that unitary completeness could not be judged In the light of homeostasis on the mechanic side. lhnstead, Pt was something to do vvith

fitness for purpose. None the less, T believed I could recognize a unit artefact when I saw one. My lavvnmower ceased to be one when its handle broke away. M i l e I was looking at this part of the problem, I was met several times by the question Why, if tools and machines are inanimate, should they occupy levels which are mainly concemed with life?' There certainly seems to be a good common-sense argument for placing implements and machinery of al1 kinds at some inanimate physical level, moving off sideways, so to speak, from the main stern of the patterii as it rises through the grades. The argument which decided the matter for me may have been somewhat childlike: tools are extensions of the animal. A bicycle is an improved pair of legs, a pair of pliers is a hand with a stronger