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AUTHOR: James W. McAllister TITLE: Is Beauty a Sign of Truth in Scientific Theories? SOURCE: American Scientist v86 p174-83 Mr/Ap '98 The magazine publisher is the copyright holder of this article and it is reproduced with permission. Further reproduction of this article in violation of the copyright is prohibited. When a new scientific theory is put forward, scientists wish to know how close it is to the truth. The most straightforward way of estimating how close a theory is to the truth is to test its predictions against empirical data. This procedure is often difficult to carry out, however. Some theories are so general and deep that they have no definite observational implications. Other theories yield predictions only when conjoined with auxiliary hypotheses that are themselves doubtful. The predictions of yet other theories apply to physical conditions that we are unable to recreate in the laboratory, or regions of the universe inaccessible to us in space or time. In even the simplest cases, gathering the data needed to test a theory's predictions may involve laborious, difficult or costly experiments. Finally, one can never be certain that an empirical test of a theory has yielded a conclusive verdict. The data may have been inaccurate or wrongly interpreted. These problems are especially severe for some of the most fundamental and fast-developing branches of physical science: string theory, elementary particle physics, astrophysics and cosmology. In such areas, ascertaining by empirical means how close a theory is to the truth can be practically impossible. Similar problems arise in evolutionary biology and earth science, whose subject matter includes events in the remote past. By contrast, it is not difficult to assess how beautiful an object is. The perceptual features of an object, which are relevant to an assessment of its beauty, are immediately accessible to us. All that is required of us is to scrutinize the object with our aesthetic judgment. A verdict can be reached virtually immediately. Moreover, there is no danger of its being overturned by subsequent discoveries. Once we have apprehended all the object's perceptual features, we are in a position to deliver a conclusive verdict about its beauty. In this light, it is tempting to wonder whether we may use our aesthetic judgment to ascertain how close a scientific theory is to the truth. This would enable us to learn easily, without the need for empirical investigation, whether a given theory has uncovered a deep truth about the universe or constitutes a wrong turn. Many scientists claim to be able to tell by means of aesthetic judgment how close a theory is to the truth. Roger Penrose puts it like this: It is a mysterious thing in fact how something which looks attractive may have a better chance of being true than something which looks ugly.... I have noticed on many occasions in my own work where there might, for example, be two guesses that could be made as to the solution of a problem and in the first case I would think how nice it would be if it were true; whereas in the second case I would not care very much about the result even if it were true. So often, in fact, it turns out that the more attractive possibility is the true one. P. A. M. Dirac had no doubts that beauty is a sign of truth: "It is more important to have beauty in one's equations than to have them fit experiment.... It seems that if one is working from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress." It was primarily on aesthetic grounds that Dirac became convinced of the truth of the general theory of relativity: "One has a great confidence in the theory arising from its great beauty, quite independent of its detailed successes.... One has an overpowering belief that its foundations must be correct quite independent of its agreement with observation." According to Steven Weinberg, the beauty of our theories shows that we are nearing the fundamental laws of nature: Time and again physicists have been guided by their sense of beauty not only in developing new theories but even in judging the validity of physical theories once they are developed. It seems that we are learning how to anticipate the beauty of nature at its most fundamental level. Nothing could be more encouraging that we are actually moving toward the discovery of nature's final laws. Although aesthetic factors are cited most often in physics, they appear to play a role in other sciences too: James D. Watson reports that, when Rosalind Franklin learned of his and Francis Crick's model of the structure of DNA, she "accepted the fact that the structure was too pretty not to be true." All such statements presuppose that beauty is indeed a sign of truth in scientific theories. But what is the evidence
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for this proposition? To begin with, we must distinguish objective properties of theories from the subjective sense of beauty that a scientist may experience in contemplating a theory. Scientists working at different times disagree over what aesthetic properties a theory must possess to count as beautiful. Astronomers from antiquity to the time of Nicholas Copernicus had an aesthetic predilection for particular symmetries, in virtue of which they insisted that theories should account for the orbits of celestial bodies as combinations of circles. Mechanics in the 18th century was pursued largely in an abstract style, not dependent on visualization. In the 19th century, by contrast, physicists such as Lord Kelvin and Ludwig Boltzmann found aesthetic value in theories that offered mechanistic models and visualizations of phenomena. Dirac saw beauty in theories that contain simple mathematical equations, whereas Weinberg regards a theory as beautiful if there is a sense of aptness or inevitability about its principles. Yet other scientists experience a sense of beauty if a scientific theory accords with their metaphysical commitments, and aesthetic distaste if it does not. Among these was Albert Einstein, who found quantum theory aesthetically repulsive because of its incompatibility with determinism. As this list makes clear, virtually every theory exhibits properties to which some scientist would attach aesthetic value. It cannot be that all such properties are a sign of truth. This would entail that almost all theories are true. The question whether beauty is a sign of truth must therefore be understood as the question whether some particular aesthetic properties of theories are a sign of truth. Scientific communities through the centuries have been engaged in a systematic empirical search for the answer to this question, as we shall see. The outcome is still undetermined. In uncontroversial times, most scientists within a branch of science may agree that a particular aesthetic property--a certain from of simplicity or symmetry, for example--is a sign of truth in theories. But this agreement vanishes when it is found that theories showing this aesthetic property perform less well in empirical tests than competing theories in which this property is absent. Such a discovery often triggers a scientific revolution, in which scientists abandon their commitment to particular aesthetic properties in the pursuit of empirical success. The search for aesthetic properties of theories that show a preferential link with truth must then recommence. THE BEAUTY OF THE UNIVERSE
Any aesthetic properties that were a sign of truth in theories would have a unique and fundamental status. They would be the aesthetic properties of the complete true account of the universe. The universe would be characterized as deeply by this fact as by the structure of space-time or the values of the universal constants. Because of this, any aesthetic properties that were a sign of truth would have to be ingrained in the universe in some way. According to a view that has enjoyed great popularity through the centuries, the aesthetic properties that are a sign of truth in theories are those exhibited by the world itself. On this view, a theory is bound to be close to the truth if it shows the same aesthetic properties as the natural phenomena; otherwise it must be false. This view is expressed most often in regard to the properties of simplicity and symmetry. Many scientists believe that a theory that shows the same form of simplicity as the world is bound to be true. Physicists frequently describe Maxwell's equations in electrodynamics as showing the same symmetries that hold between electric and magnetic fields in electromagnetic waves, and regard this as evidence that Maxwell's theory is true. If this view were correct, we would be able to use our aesthetic sense both to ascertain which aesthetic properties are shown by the universe, and to check whether a given theory reproduces these properties and is thus likely to be close to the truth. This view cannot be correct, however, for two reasons. First, in order to provide an accurate description of a phenomenon, it is neither sufficient nor necessary for a theory to share the phenomenon's aesthetic properties. A complicated theory of a simple phenomenon may be closer to the truth than a simple theory of it. The fact that Maxwell's equations show particular symmetries does not ensure that they are correct. Conversely, the behavior of electromagnetic waves could be correctly described by a theory that does not embody their symmetries. Indeed, the demand that a theory should embody the aesthetic properties of its subject matter is in many cases unintelligible. The gravitational field of a point mass has spherical symmetry, but what would it mean to demand spherical symmetry of a theory of gravitation? Second, the idea that we can recognize that a theory is close to the truth on the grounds that it embodies the aesthetic properties of phenomena presupposes that we know which aesthetic properties the phenomena show. The aesthetic properties of physical objects such as crystals and landscapes are indeed apparent to the naked eye. But in most cases our belief that phenomena show particular aesthetic properties is based entirely on the theories whose proximity to the truth we are attempting to assess. For example, our sole basis for believing that a given phenomenon is to some degree simple is our best theory about that phenomenon. To argue that this theory is true on the grounds that it shows the same simplicity as its subject matter would therefore be circular. Likewise, our only grounds for believing that
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electromagnetic waves show particular symmetries are that Maxwell's equations tell us that they do. The belief that electromagnetic waves have these symmetries therefore cannot be cited as evidence that Maxwell's theory is close to the truth. In all these cases, the belief that the phenomena have particular aesthetic properties is an effect of choosing among given theories, and cannot provide a basis for such a choice. THE SPLENDOR OF TRUTH
The view that the aesthetic properties of natural phenomena themselves are a sign of truth in scientific theories therefore cannot be maintained. By what other approach could we ascertain which aesthetic properties, if any, are a sign of truth? Since any such aesthetic properties would have to be ingrained in the universe, it should be possible to discover which they are by induction. If an aesthetic property were a sign of truth, a theory that exhibited that property would necessarily be true, and would therefore show the best empirical performance conceivable. In contrast, a property that has no link with truth may be found in theories of all degrees of empirical adequacy. Thus, we may recognize a property that is a sign of truth from the fact that its presence in a theory is correlated with good empirical performance. We now unearth a remarkable discovery about scientific practice. Scientists are engaged--albeit for the most part unconsciously--in a systematic inductive search for aesthetic properties of theories that constitute a sign of truth. This search exploits the fact that any such property would be correlated with good empirical performance. The procedure by which scientists form and update their aesthetic preferences among theories appears to have been designed expressly to bring this search to a successful conclusion. As is well known, a theory that is aesthetically innovative strikes most scientists as ugly when it is first put forward. If such a theory demonstrates substantial empirical success, however, it comes gradually to be regarded as beautiful. Examples are plentiful. At first, many astronomers regarded Johannes Kepler's theory of planetary motions as ugly for portraying the planetary orbits as ellipses rather than combinations of circles. Isaac Newton's theory of gravitation struck many of his contemporaries as aesthetically unacceptable for postulating action at a distance. And many physicists--most notably Dirac--regarded quantum electrodynamics as ugly for relying on nonstandard mathematical operations in renormalization. But as they built up their impressive empirical track record, all these theories came gradually to be seen as aesthetically pleasing. These examples illustrate a crucial fact. Scientists' aesthetic preferences respond inductively to the empirical performance of theories. More precisely, scientists attach aesthetic value to an aesthetic property roughly in proportion to the degree of empirical success scored by the set of theories that exhibit that property. If a property is exhibited by a set of empirically very successful theories, scientists attach great aesthetic value to it, and thus see theories that exhibit that property as beautiful. If a property has no association with empirical success, either because theories exhibiting that property have been demonstrated inadequate, or because such theories have as yet no empirical track record, scientists attach no aesthetic value to it, and thus feel no aesthetic attraction for theories that exhibit it. This inductive procedure greatly influences the development of science. If a given theory scores notable empirical success, its aesthetic properties win increased favor among scientists' aesthetic preferences. Scientists will consequently tend to prefer theories that show these properties to theories that do not, and will strive to formulate further theories that satisfy this preference. As long as such theories remain successful, their aesthetic properties will acquire greater and greater favor. When such theories cease to demonstrate empirical success, the properties that they exhibit will lose favor relative to any other properties whose correlation with empirical success appears stronger. Because of this inductive mechanism, if there exists an aesthetic property that is a sign of truth, then scientists' aesthetic preferences will converge on it. Suppose that, by chance, scientists one day formulate a theory that exhibits such a property. Since any such theory must be true, it will score great empirical success. Scientists will attach aesthetic value to the property in question, and will seek to formulate further theories exhibiting it. Since these further theories must likewise be true, the aesthetic value attributed to the aesthetic property will increase without limit. Beauty will indeed have become the splendor of truth. BEAUTY AND SEXUAL SELECTION
Scientists' practice of choosing among theories on aesthetic criteria is analogous to the process of mate choice under sexual selection. In certain species, a male or female chooses among potential mates partly on the basis of traits that may be described as aesthetic: the color and condition of fur or plumage, size of horns or antlers, length of tail, degree of body symmetry and quality of vocalization and display. What evolutionary advantage is conferred by such choice? Each organism is predisposed to maximize the spread of its genetic material. An organism therefore has an interest in ensuring that its mate has the greatest possible reproductive potential. To determine the reproductive potential of several prospective mates conclusively, an organism would have to interbreed with them all--an impractical
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suggestion. Organisms therefore choose mates partly on the basis of indicators that are diagnostic of good reproductive potential. Indicators of good reproductive potential include, of course, traits that are functional to actual interbreeding. But they may also include traits that are only contingently correlated to good reproductive potential in a species at a certain time. For example, although large antlers or bright plumage are not functional to actual interbreeding, they may be signs of vigor or resistance to parasites, and thus be correlated to good reproductive potential. This correlation is only contingent, however. An organism's physiological investment in antlers or plumage may become so great as to depress its reproductive potential. A species gains greatest evolutionary advantage if its members are predisposed to choosing mates on the basis of traits that are, as a matter of fact, strongly correlated with good reproductive potential at the time at which the choice is performed. To this end, species are endowed with what is in effect an inductive mechanism for updating members' aesthetic preferences. Organisms whose mates have good reproductive potential produce on average more offspring than other members of their species. Thus, if these organisms choose their mates partly out of a preference for a particular aesthetic trait, and this preference is heritable, then this preference will become more widespread in the next generation. As long as the trait remains correlated with good reproductive potential, mate choice will yield beneficial results. If the correlation declines, however, as happens when antlers grow so large as to hamper movement, organisms that continue to prefer this trait will find themselves at a reproductive disadvantage compared to members of their species that switch to other criteria. Likewise, scientists wish to adopt theories that will have the greatest empirical success. Testing available theories exhaustively is in many cases impractical. Scientists therefore resort to choosing among theories on the basis of indicators that are diagnostic of empirical success. Such indicators include some features of theories that are functional to empirical performance, such as predictive accuracy, predictive scope and logical consistency. But they also include features that are correlated with empirical success only contingently. Among such features are aesthetic properties of theories. Scientists, like organisms in sexual selection, are therefore endowed with an inductive mechanism for updating their aesthetic preferences. They attribute aesthetic value to an aesthetic property proportionally to the empirical success scored by theories that exhibit that property. The obvious dissimilarity between the two cases is that, whereas aesthetic preferences in sexual selection are genetically encoded and thus can evolve only with the passing of generations, a scientist's aesthetic preferences are culturally acquired and therefore can be revised as circumstances change. SCIENTIFIC REVOLUTIONS
The inductive mechanism by which scientists' aesthetic preferences evolve ensures that they are conservative. Scientists' aesthetic criteria attribute value to theories that reproduce the aesthetic properties of empirically successful theories of the recent past. Because of this conservative bias, aesthetic preferences can become outdated and cease to reflect the state of empirical development of a science. In such cases, aesthetic preferences begin to hinder scientific progress. The result is a scientific revolution. Suppose that a long sequence of empirically successful theories shows particular aesthetic properties. Scientists will come to endow these properties with great aesthetic value. They will see theories that exhibit these properties as beautiful and other theories as ugly. Suppose that experimentalists then uncover some empirical findings of a radically new sort. These findings cannot be explained by any theory showing the familiar aesthetic properties, but only by a new theory whose aesthetic properties are unprecedented. In such an event, theory choice becomes controversial. Proponents of the new theory will point to its success in explaining the new findings, but other scientists will reject this theory on aesthetic grounds, since it fails to exhibit the aesthetic properties that have until recently been associated with empirical success and that they find aesthetically pleasing. This situation has occurred many times. From 1687, when Newton published the Principia, to 1900, classical physical theories built up an unparalleled empirical track record. Such theories--which included classical electrodynamics and statistical thermodynamics as well as Newtonian mechanics--shared some pronounced aesthetic properties. They were deterministic, and they offered visualizations of all phenomena in everyday terms. From 1897, when the electron was discovered, even subatomic particles were visualized as miniature versions of macroscopic bodies. Thanks to the empirical success of classical theories, physicists had come to see determinism and visualization as conferring beauty to theories, as well as being deeply associated with empirical success. If physicists in 1900 had been asked whether determinism and visualization were signs of truth, most would have replied vehemently in the affirmative. Within a few years, however, it became clear that classical physical theory was unable to explain empirical findings about some important subatomic phenomena, including black-body radiation, the photoelectric effect and the
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absorption and emission spectra of atoms. Quantum theory, which emerged in the mid-1920s, proved capable of accounting for these findings. But quantum theory showed aesthetic properties radically different from those of classical physical theories. It was indeterministic and revealed itself unamenable to consistent visualization. This development split the physics community into two. One faction, led by Niels Bohr and Werner Heisenberg, judged the loss of determinism and visualization a price worth paying for an empirically successful theory of subatomic phenomena. They placed little weight on aesthetic criteria for judging theories, seeing that aesthetic properties hailed as "signs of truth" were generally reflections of past empirically successful theories, and could not be taken as guides in uncertain times. The other group, which included Einstein and Erwin Schrödinger, acknowledged the empirical successes of quantum theory but found the theory aesthetically unattractive in virtue of its abandonment of the classical style of theorizing. Schrödinger was repelled especially by quantum theory's abstractness. He strove to find a visualization of the Schrödinger equation in classical terms, but it quickly emerged that none could be provided. By contrast, Einstein was displeased by the theory's indeterminism. For him the beauty of the world would be marred if God decided occurrences on the cast of a die. Both groups could claim to be acting rationally. Bohr and Heisenberg followed sound empiricist principles in embracing the best-performing theory of subatomic phenomena available. But the other faction too could claim good inductive support--to them the lesson of classical physics seemed to be that determinism and visualization are correlated with empirical success, and that subsequent theories would stand a better chance of empirical success if they too were deterministic and visualizing. Unfortunately, the correlation between determinism, visualization and empirical success turned out to be spurious. Quantum theories continued to score striking empirical successes, unmatched by any classical theory of the subatomic domain. Before long, all mainstream physicists had accepted quantum theory. To do so, they were compelled to abandon their long-standing aesthetic preference for determinism and visualization. This was the truly revolutionary act. Just as styles of theorizing in science are defined by the entrenchment of particular aesthetic preferences, so a scientific revolution is marked by the abandonment of aesthetic commitments. In his book The Structure of Scientific Revolutions, the late Thomas S. Kuhn suggested that revolutions are induced by aesthetic factors and inhibited by empirical factors. He argued that, since an established paradigm's empirical track record is invariably superior to that of a newly formulated competitor, scientists are never driven to undertake a revolution for empirical gain. Rather, they are attracted to a new paradigm by its aesthetic properties. But Kuhn's view cannot be correct if scientists' aesthetic preferences are formulated by induction on the empirical performance of theories--aesthetic factors must always exercise a conservative, inhibiting role in a revolutionary crisis. The quantum revolution is a good illustration. Quantum theory was adopted specifically on the strength of its empirical performance in accounting for subatomic phenomena, whereas its aesthetic properties weighed against its acceptance. Kuhn's model of revolutions has a further shortcoming. According to Kuhn, there can be no rational reason for undertaking a revolution. Every paradigm holds to its own criteria for comparing the worth of theories and portrays its own theories as the best. A revolution is therefore a capricious act. By contrast, if revolutions are episodes in which scientific communities shake off aesthetic commitments that are hindering the pursuit of empirical performance, there is a good reason for undertaking a revolution. Scientific revolution becomes rational. APPLIED ART
Aesthetic judgment responds to empirical performance not only in science but also in the applied arts, such as architecture and industrial design. Every material used in architecture--wood, masonry, iron and steel, concrete, plate glass--has a distinctive set of technical characteristics that allows particular practical needs to be met. For the virtues of a material to be exploited, however, it must be used in an appropriate design. When a new material is introduced, the designs that are best suited to exploiting its capabilities frequently strike conservative architects and the public at first as ugly. This aesthetic resistance is overcome only gradually, as the new material demonstrates its utility. The mechanism by which aesthetic canons are updated in architecture is inductive, like its analogue in science. Cast iron provides a good example. The structural use of cast iron was pioneered in Britain in the Industrial Revolution. The material was first used in bridges, beginning with the Coalbrookdale bridge (1779) over the River Severn in Shropshire, and in the frames of industrial buildings such as textile mills and warehouses. Cast iron allowed bridges of longer spans than were possible in stone, and it enabled multistory mills and warehouses, whose frames had traditionally been of wood, to be made fireproof. The designs of these early iron structures were innovative, shaped by the need to exploit the technical capabilities of the material to the fullest. However, their designers were not architects but engineers, such as Thomas Telford and James Watt, and bridges and industrial buildings were considered to lie outside the purview of architectural design. They therefore had no effect on established aesthetic canons in architecture, which had been formulated with pre-existing materials such as stone and brick in mind.
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Architects were drawn to cast iron by its obvious utilitarian advantages. But at first they were unwilling to acknowledge its aesthetic consequences; they wished any cast-iron structures to conform to traditional aesthetic canons. A common solution was to conceal them behind masonry fa¸cades. For example, Henri Labrouste's Bibliothèque Sainte-Geneviève (1843-1850), Paris, has a vaulted reading room whose airy and graceful look is owed to its slender iron columns and arches, but its stone fa¸cade has a generally conventional neo-Renaissance form. Likewise, St. Pancras Station (1864) in London consists of a cast-iron train shed designed by the engineer William H. Barlow, which has the widest span that had yet been achieved, but this is concealed from the street by the massive neo-Gothic terminal building in masonry designed by George Gilbert Scott. Only gradually did the conviction grow that cast-iron structures should be given the style most suited to the material, rather than forms appropriate to previous epochs, and should appear openly, not hidden behind a fa¸cade. An important stage was represented by the Eiffel Tower, erected for the Universal Exhibition of 1889, which forcefully displayed many of the design principles implicit in cast iron. The tower was initially considered hideous by many, but it gradually came to be valued on aesthetic grounds. By the end of the 19th century, cast iron and steel were admitted into civic architecture in France as well as Britain, and used openly in commercial and domestic buildings. The rise of aesthetic canons attuned to cast iron constituted a revolution in architecture, just as the abandonment of determinism and visualization constituted a revolution in 20th-century physics. Earlier contributions to each domain--masonry buildings in architecture, classical theories in physics--had enjoyed great practical success, which ensured that their aesthetic properties were accorded great value. When contributions of a new kind--cast-iron structures in architecture, quantum theories in physics--emerged, their aesthetic properties were regarded as ugly, as they violated established aesthetic preferences. The new contributions were obliged to prove their worth, by demonstrating successes that could not be replicated by the established approach. Only then did their aesthetic properties come to be seen as beautiful. The cast-iron revolution in architecture is vividly illustrated by the contrast between the Eiffel Tower and a structure that had been erected only five years earlier to serve a similar celebratory function, the Washington Monument in Washington, D.C., which is a white marble obelisk. The Washington Monument conforms to aesthetic canons first formulated in ancient Egypt, whereas the Eiffel Tower embodies new problem-solving techniques and consequently displays unprecedented aesthetic properties. A close parallel can be found in the quantum revolution. Ernest Rutherford's atomic theory of 1911, which pictured the atom as a miniature classical planetary system, is the counterpart of the Washington Monument. Its conservative appearance accords with long-established aesthetic canons. By contrast, the atomic theory that Bohr put forward a few years later, which explained the spectral lines of atoms on the assumption that the energy of electrons is quantized, is the analogue of the Eiffel Tower--although initially regarded as iconoclastic, it defined the style that would dominate subsequent decades. THE SCIENTIST'S DILEMMA
To what extent may a scientist rely on his or her aesthetic judgment in assessing whether a theory is close to the truth? If a theory strikes a scientist as beautiful, is that good reason for thinking that it is true? For a scientist's aesthetic judgment to be a reliable indicator of truth, two conditions must be satisfied. First, one or more aesthetic properties of theories must be signs of truth. Second, a scientist's aesthetic judgment must be tuned to those aesthetic properties rather than to others--in other words, theories that exhibit a property that is a sign of truth must seem to a scientist to be beautiful. The evidence that any aesthetic property of theories is a sign of truth is at present scarce. Any such property would be strongly correlated with empirical success. But today empirical success appears to accompany different aesthetic properties in different branches of science. A certain form of visualization is correlated with empirical success in cosmology but not in quantum theory; a certain form of logical simplicity is correlated with empirical success in relativity theory but not in cosmology; a certain form of mathematical simplicity is correlated with empirical success in quantum theory but not in relativity theory. In this light, the conviction of Einstein, Dirac and others that aesthetic signs of truth have already been identified cannot be endorsed. If this had occurred, the empirical utility of choosing theories on particular aesthetic criteria would be far more obvious than it is. On the other hand, we cannot rule out that some aesthetic property will soon reveal a much stronger correlation with empirical success. Until such a time, for a scientist to trust his or her aesthetic preferences in assessing whether a theory is close to the truth involves some risk. The benefits depend on the subsequent strength of the correlation between the aesthetic properties that the scientist cherishes and empirical success. In 1700, physicists who attached aesthetic value to determinism and visualization stood at the threshold of a 200-year period throughout which these aesthetic properties were to show a strong correlation with empirical success, acting effectively as signs of truth. But those who adopted these same preferences in 1900 were less fortunate. They were soon to be hindered from joining the quantum
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revolution. Scientists who allow their theory choices to be determined by their aesthetic preferences cannot know which of these scenarios resembles their own situation more closely. Scientists who allow their theory choices to be determined by their aesthetic preferences will enjoy one great advantage. The theories that they formulate and advocate will conform to established aesthetic canons, and will thus appear beautiful. They will find their theories more readily accepted by their colleagues, and they will win praise for the elegance of their work. In a nonrevolutionary phase, moreover, they will incur no empirical penalty for their preference, since in such a phase there is no conflict between empirical and aesthetic concerns. Scientists who conduct theory choice on aesthetic criteria during a revolution, however, are treated less kindly by history. When a revolutionary theory is put forward, such scientists will object that--regardless of its empirical success--it cannot be correct because it exhibits novel aesthetic properties. Instead, they will prefer theories showing familiar aesthetic properties, even though they are empirically inferior. These scientists will be remembered as supporters of the old order--their conservatism will appear tragically misguided, like Einstein's resistance to quantum theory. To avoid this fate, some scientists may be tempted to remove all weight from aesthetic preferences, and conduct theory choice exclusively on empirical criteria. But then they are precluded from capitalizing on any correlation between aesthetic properties and empirical success that may emerge, and they may be seen by their peers as failing to conform to the dominant style of theorizing. More seriously, in fields such as string theory, where there are few opportunities to test theories against empirical data, such a decision would deprive scientists of the sole effective basis for choosing between competing theories. Added material James W. McAllister is university lecturer in the Faculty of Philosophy at the University of Leiden. He received his Ph.D. from the University of Cambridge in 1989. He is the author of Beauty and Revolution in Science, published by Cornell University Press, 1996, on which this article is based. Address: Faculty of Philosophy, University of Leiden, P.O. Box 9515, 2300 RA Leiden, The Netherlands. Internet:
[email protected]. Figure 1. Raphael's The Three Graces (circa 1504) illustrates the ancient doctrine of the unity of the virtues. The doctrine is embodied in the classical Greek term kalos kagathos, which means "both good to look at and manifesting goodness in action." A moral variant of the doctrine holds that handsomeness or comeliness accompanies moral virtues or spiritual nobility in persons. An epistemological variant proposes that beauty accompanies truth, sometimes expressed in the motto Pulchritudo splendor veritatis ("Beauty is the splendor of truth"). Both variants of this doctrine were popular in the Renaissance. Although few people in our century would explicitly accept the moral variant, many notable scientists still believe that the epistemological variant applies to scientific truths. In the light of the history of science, however, this belief cannot be sustained. (With permission of the Musée Condé, Chantilly, France.) Figure 2. Copernicus's model of the motions of the celestial bodies prevailed over the Ptolemaic system not by virtue of its empirical adequacy, but because it was regarded by many contemporaries to be aesthetically superior. The principal reason is that Copernicus dispensed with the equant point, a geometrical construction that Ptolemy had invented. Since Copernicus's theory--notwithstanding its heliocentrism--maintained aesthetic continuity with Aristotelian cosmology, it cannot be considered to have triggered a scientific revolution. Beauty is ascribed to scientific theories to the extent that they accord with the scientific community's preexisting aesthetic canons, and is not a reliable guide to truth. (From Copernicus's De Revolutionibus Orbium Caelestium, 1543.) Figure 3. Kepler's laws of planetary motion--which describe the movements of the planets in terms of elliptical orbits--were initially unappealing to many of his contemporaries because an ellipse was considered inferior to a circle, which for centuries was believed to be the only perfect figure. Kepler's laws were ultimately accepted, however, because they could account for the motion of the planets better than competing theories. History suggests that scientists ascribe increasing aesthetic value to theories as they achieve greater empirical success. Here Kepler's illustration explains how an elliptical orbit accounts for the annual changes seen in the velocity of a planet, such as Mars, as it moves across the sky. (From Kepler's Astronomia Nova, 1609.) Figure 4. Symmetries are often seen in nature, as exemplified by this remarkable bracken frond (top). Some scientists believe that a theory is bound to be true if it replicates the symmetry properties of the phenomena that it describes. Thus, the symmetries of Maxwell's equations (bottom) are frequently cited as an indicator of their correctness. Close scrutiny of this argument, however, fails to support the idea that a scientific theory is bound to be true if it manifests the aesthetic properties of natural phenomena. Chinch Gryniewicz; Ecoscene/Corbis Figure 5. Sexual selection in certain animal species, such as the peafowl, serves as an analogy for the aesthetic decisions made by scientists choosing among theories. Choosing a mate on the basis of a physical trait, such as the ostentatious display of a peacock, will be beneficial for the peahen if the trait is correlated with good reproductive
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potential. For such traits, the correlation may be only contingent rather than necessary. Similarly, scientists tend to look for aesthetic qualities in theories that may only be contingently correlated with empirical success. Much like peafowl, scientists have an inductive ability to update their aesthetic preferences. Scientists may alter their aesthetic preferences by cultural change, however, whereas organisms such as the peafowl may only do so by biological evolution over generations. The Purcell Team/Corbis Figure 6. Ernest Rutherford's model of the atom as a miniature solar system with electrons (black) orbiting the nucleus (blue and green) is aesthetically appealing for its classical visualizability, but it conflicts with data. As we now know, quantum particles are not like billiard balls, they do not have precise boundaries, and they do not follow precisely localized paths. The fact that a theory offers a visualization of phenomena does not guarantee its success. Figure 7. Wave mechanics--which attempts to explain the behavior of elementary particles in terms of "wave packets"--was devised by Erwin Schrödinger in response to Werner Heisenberg's matrix mechanics, which suggested that quantum mechanical processes could not be visualized. Although Schrödinger's equation was quickly accepted by physicists, no consistent visual interpretation of quantum theory has been found. Such failures have convinced scientists that visualization is not a necessary property of an empirically successful theory. Figure 8. Feynman diagram depicts the interactions among elementary particles in space and time. Whereas Feynman diagrams do not provide full visualizations of submicroscopic phenomena in classical terms, as Rutherford's model of the atom attempted to do, they represent to some extent a return to visual imagery in quantum theory. Figure 9. Architectural aesthetics, as embodied in the Washington Monument (left) and the Eiffel Tower (right), can change with the discovery of a material's structural utility--much like the aesthetic appeal of a scientific theory, which seems to grow with every empirical success. The Washington Monument (1884), a white marble obelisk, pays homage to the aesthetic canons of ancient Egypt. In contrast, the Eiffel Tower, which was built a mere five years afterward, is an iconoclastic cast-iron structure that displayed aesthetic properties unprecedented in its day. Cast-iron architecture eventually attained wide use, and a broad aesthetic appeal, as its utility was discovered. Neil Rabinowitz/Corbis Dave Bartruff/Corbis BIBLIOGRAPHY
Andersson, M. 1994. Sexual Selection. Princeton: Princeton University Press. Dirac, P. A. M. 1963. The evolution of the physicist's picture of nature. Scientific American 208(5):45-53. Dirac, P. A. M. 1980. The excellence of Einstein's theory of gravitation. In Einstein: The First Hundred Years, ed. M. Goldsmith, A. Mackay and J. Woudhuysen. Oxford: Pergamon Press; pp. 41-46. Kuhn, T. S. 1962. The Structure of Scientific Revolutions. Second edition, 1970. Chicago, Ill.: University of Chicago Press. McAllister, J. W. 1996. Beauty and Revolution in Science. Ithaca, N.Y.: Cornell University Press. Penrose, R. 1974. The rôle of aesthetics in pure and applied mathematical research. Bulletin of the Institute of Mathematics and Its Applications 10:266-271. Watson, J. D. 1968. The Double Helix: A Personal Account of the Discovery of the Structure of DNA. Ed. G. S. Stent. London: Weidenfeld and Nicolson. Weinberg, S. 1992. Dreams of a Final Theory. New York: Pantheon Books. WBN:
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