Aesthetic cognition

INTERNATIONAL STUDIES IN THE PHILOSOPHY OF SCIENCE, VOL. 16, NO. 1, 2002

Aesthetic cognition ROBERT S. ROOT-BERNSTEIN Department of Physiology, Michigan State University, East Lansing, MI 48824, USA

Abstract The purpose of this article is to integrate two outstanding problems within the philosophy of science. The rst concerns what role aesthetics plays in scienti c thinking. The second is the problem of how logically testable ideas are generated (the so-called “psychology of research” versus “logic of (dis)proof” problem). I argue that aesthetic sensibility is the basis for what scientists often call intuition, and that intuition in turn embodies (in a literal physiological sense) ways of thinking that have their own meta-logic. Thus, aesthetics is a form of cognition. Scientists think not in equations or words or other logical abstractions, but emotionally and sensually, using visual and aural images, kinesthetic and other proprioceptive feelings, sensations, patterns, and analogies. These aesthetic forms of thinking have their own logics that I call “synosia”, from the root words synaesthesia (a combining of senses) and gnosis, “to know”. Synosia denotes understanding that integrates feeling that one knows with feeling what one knows. Eminent scientists universally describe an explicitly secondary process in which such personal knowledge must be “translated” into a formal language, such as words or equations, in order to be communicated to other people. Many of the unsolved problems that philosophers of science (as well as psychologists and arti cial intelligence researchers) have had in making sense of scienti c thinking have arisen from confusing the form and content of the nal translations with the hidden means by which scienti c insights are actually achieved. Introduction: before logic Aesthetics is usually de ned as the study of that which is beautiful and that which is beautiful is known by its sensory and emotional effects on our mind. Because of this foundation in sensation and emotion, aesthetic experiences have classically been limited to experiences of natural phenomena and the products of the arts. But all human inventions, including those stemming from science, mathematics, and engineering, can evoke the same range and types of aesthetic responses that a beautiful vista, a stunning painting, or a moving symphony can do. Scientists, just as much as artists, will exclaim how “beautiful” or “elegant” or “breathtaking” a result is (Tauber, 1996). The excitement accompanying the discovery or invention of new things is often described as being literally orgasmic in intensity—physicist Subramahnyam Chandrasekhar calls it “shuddering before the beautiful” (quoted in Curtin, 1982, p. 7; Chandrasekhar, 1987). Intellectual understanding often begins with such emotional and sensual shudders. As ethologist Desmond Morris has written, “No one ever studies anything unless, in some way or other, they are deeply emotionally involved with it” (Morris, 1983, p. 101). Thus, Claude Bernard, the founder of modern physiology, wrote in his Introduction to the Study of Experimental Medicine that everything purposeful in scienti c thinking begins with feeling: ISSN 0269-8595 print/ISSN 1469-9281 online/02/010061-17 Ó DOI: 10.1080/02698590120118837

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Just as in other human activities, feeling releases an act by putting forth the idea which gives a motive to action, so in the experimental method feeling takes the initiative through the idea. Feeling alone guides the mind and constitutes the primum movens of science. (Bernard, 1927, p. 43) The mathematical physicist Wolfgang Pauli also maintained that scienti c thinking begins within the “unconscious region of the human soul”, where, “the place of clear concepts is taken by images of powerful emotional content, which are not thought, but are seen pictorially, as it were, before the mind’s eye” (Heisenberg, 1974, pp. 179–180; Chandrasekhar, 1987, p. 146). Similarly, botanist Agnes Arber argues that in her experience, new hypotheses come into the mind most freely when discursive reasoning (including its visual component) has been raised by intense effort to a level at which it nds itself united indissolubly with feeling and emotion. When reason and intuition attain this collaboration, the unity into which they merge appears to possess a creative power which was denied to either singly. (Arber, 1964, pp. 20–21) If Morris’s, Bernard’s, Pauli’s, and Arber’s statements go beyond aesthetics to sound almost artistic, Arber makes the conclusion explicit: “Emotion has function in [scienti c] discovery as it admittedly has in creative work in the arts” (Arber, 1964, p. 21). Chemist William Lipscomb agrees. Of his Nobel prizewinning research on boron he has written that he, felt a focusing of intellect and emotions which was surely an aesthetic response. It was followed by a ood of predictions coming from my mind as if I were a bystander watching it happen. Only later was I able to begin to formulate a systematic theory of structure, bonding and reactions for these unusual molecules.… Was it science? Our later tests showed it was. But the processes that I used and the responses that I felt were more like those of an artist. (Curtin, 1982, p. 19) Physicist Max Planck would not have been surprised. Many years before, he had written that the “scientist needs an artistically creative imagination” (Planck, 1949). Indeed, scientist and artist are kith and kin, for their motivations often begin in the same pre-logical sensations (Root-Bernstein, 1985, 1987). My purpose in this article is to explore the nature of this artistic, pre-logical, emotion-laden, intuition-based feeling of understanding—the sense that one knows something before one has the ability to express what one knows in words or equations. I call such pre-logical thinking “aesthetic cognition”. I propose four major arguments. First, all scienti c problem solving and problem generation involves emotional and sensual responses that are similar if not identical to those associated with the arts. Second, that the experience of knowing what one feels and feeling what one knows constitutes a speci c form of understanding that I call “synosia”. Third, there is a “meta-logic” to these intuitive responses that is embedded in what we call scienti c aesthetics. Fourth, that aesthetic cognition precedes and is distinct from formal logic, and that an explicit translation process is therefore required before ideas can be communicated and tested logically. In sum, aesthetic cognition combines knowledge and feeling into synosic intuition that has an analyzable “meta-logic” which is the basis for creative scienti c thinking.

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The emotional and sensual basis of scienti c intuition Begin with the argument that despite its objective facade, all scienti c thinking has an ineluctable emotional and sensual component. Probably everyone who has studied the philosophy of science is familiar with Henri Poincare’s opinion that, The scientist does not study nature because it is useful to do so. He studies it because he takes pleasure in it; and he takes pleasure in it because it is beautiful. If nature were not beautiful, it would not be worth knowing and life would not be worth living.… (Poincare, 1946, pp. 366–367) What has been less well established is the degree to which Poincare’s sentiments are echoed by other eminent scientists. The drive to experience beauty has often resulted in Nobel prizes (Root-Bernstein, 1987). Santiago Ramon y Cajal, the Spaniard who rst laid bare the architecture of the central nervous system, was led to science through art. He was attracted as a boy to drawing and painting, a love that he rediscovered in neurological studies: It is an actual fact that, leaving aside the atteries of self-love, the garden of neurology holds out to the investigator captivating spectacles and incomparable artistic emotions. In it, my aesthetic instincts found full satisfaction at last. Like the entomologist in search of brightly coloured butter ies, my attention hunted, in the ower garden of the grey matter, cells with delicate and elegant forms, the mysterious butter ies of the soul. (Ramon y Cajal, 1937, pp. 36–37) Ramon y Cajal’s contemporary, C.T.R. Wilson, revealed similarly that his motivation in building the cloud chamber had no scienti c basis nor had he any inkling that it would one day be used to study the behavior of subatomic particles. Quite the contrary, it had began in attempts to recreate the spectral beauties called glories and coronas that he had witnessed while climbing the hills of Scotland (Rayleigh, 1942, p. 99). Similar aesthetic motivations underlie many other Nobel prizes. Wihelm Ostwald, the eighth Nobel laureate in chemistry became interested in chemistry as a youth through his artistic hobbies: he made his own pastels and oil paints; invented a novel form of decalcomania (a form of transfer printing); synthesized his own collodion for his home-made camera; and concocted his own reworks. Despite his Nobel prize, he maintained that art was what motivated his curiosity and claimed at the end of his life that his greatest contribution to humanity was actually his very in uential work on color theory (Ostwald, 1927). Fellow laureate, Robert B. Woodward wrote that his attraction to chemistry was similarly sensual: it is the sensuous elements which play so large a role in my attraction to chemistry. I love crystals, the beauty of their form—and their formation; liquids, dormant, distilling, sloshing!; swirling, the fumes; the odors—good and bad; the rainbow of colors; the gleaming vessels of every size, shape, and purpose. Much as I might think about chemistry, it would not exist for me without these physical, visual, tangible, sensuous things. (Woodward, 1984, p. 137) Sometimes unusual sensitivity to color has actually been the source of the research problem that has resulted in great breakthroughs. Nobelist Albert Szent-Gyorgyi, for example, revealed that color motivated his discovery of vitamin C: I was led by my fascination by colors. I still like colors; they give me a childish

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pleasure. I started with the question, “Why does a banana turn brown when I hurt it” … There are two categories of plants, you see—those that turn black on being damaged and those in which there is no color change.… Why no color in some damaged plants? (Szent-Gyorgyi, 1966, pp. 116–117) Nobel prizewinning chemist Alan MacDiarmid, who was one of the discoverers of conductive polymers, was also motivated by his love of color. “There were no scienti c reasons whatsoever”, he said for his studies of polyacetylene, the rst conductive polymer he discovered: “My motivations have been driven by curiosity and color. …” (Russo, 2000). The emotional experiences that attend the observation or interaction with nature are similar motivators. When physiologist and ecologist Bernd Heinrich was asked by graduate school examiners why he wanted to become a biologist, he recounted a spring day in a German forest as a boy, “bumblebees humming, willow warblers and pied ycathers snagging bugs among the pussy willows and being overcome by ‘a delicious, light-headed feeling”’ (Wolkomir, 1997, p. 100). For astrophysicist Allan Sandage it was stars at night. It was like going to a cathedral. I had the feeling that the world was magic … The world was spirit.… I couldn’t wait for night to come and for the stars to come out. I would stand in the backyard and look at the appropriate time and identify the stars as they became visible out of the twilight. It was like being, I suppose, in a sort of heaven. I can’t explain it in words even today. I had that internal feeling about everything—about physics, about the way the world works, and about why we are. (Allan Sandage in Lightman & Brawer, 1990, pp. 72–73) Or, as chemist Roald Hoffmann has written, “We feel that these molecules are beautiful, that they express essences. We feel it emotionally, let no one doubt that” (Hoffmann, 1989, p. 332). Nor let anyone doubt that these emotional feelings are integral to research itself. Richard Bing, a cardiology investigator and musical composer argues that his music bene ts his science: “It helps me emotionally to feel more about science. You see, I am a romanticist. I perceive science as an emotional exercise of searching the unknown” (Bing, 1981). Chemist Dudley Herschbach compares these emotions to being in love: A general characteristic of the Nobel laureates that I have met … [is that] you really have to become completely captivated by something, like falling in love with a certain young lady … You can’t imagine why everyone else isn’t chasing after this wonderful person. (Russo, 2000) Jonas Salk once summarized the same feelings to me by advising, “Do what makes your heart leap.” Emotions tell us what is important to us and therefore direct the course of our inquiries. Emotions, intuitions, and feelings, in short, lie as much at the heart of the sciences as at the heart of the arts. As Einstein said, “only intuition, resting on sympathetic understanding, can lead to [insight]; … the daily effort comes from no deliberate intention or program, but straight from the heart” (Hoffmann, 1972, p. 222). Poincare wrote similarly in Science and Method that [i]t is by logic that we prove, but by intuition that we discover … Logic teaches us that on such an such a road we are sure of not meeting an obstacle; it does

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not tell us which is the road that leads to the desired end. For this it is necessary to see the end from afar, and the faculty that teaches us to see is intuition. Without it, the geometrician would be like a writer well up in grammar but destitute of ideas. (Poincare, 1946, p. 438) Indeed, it is possible to take my argument a step further to conclude that logical decision-making originates in emotion. The argument follows not only from the testimonials given above, but from neurological research as well. Neurologist Antonio Damasio has found that patients whose emotional affect (that is, their ability to respond emotionally) is grossly impaired due to strokes, accidents, or tumors lose the ability to make rational decisions and plans despite having intact rational function (Damasio, 1994). Such patients can, for example, calculate accurately the odds of having a winning poker hand, but cannot, in actual play, implement their calculations in a manner designed to optimize their chances of winning. Unable to become emotionally involved in their decisions, they fail to make good ones even when they can accurately describe the positive and negative outcomes associated with their decisions. Damasio’s work, along with that of neurologist Richard Cytowic (1993) and writer Edmund B. Bolles (1991) suggests that our feelings and intuitions are not impediments to rational thought and behavior; they are its basis. That which we feel strongly about is what is most important to us. That which is most important is that which we act upon. Therefore, our emotions and feelings are essential motivators for scienti c work, determining the problems we will address and the direction our work will take. Synosia: to feel is to know and to know is to feel One can summarize the preceding points by concluding that to know is to feel and to feel is to know. Scientists combine a multitude of sensual feelings, emotions, desires, and intuitions in order to devise rational explanations of nature. What may seem to be a paradox—that rationality results from irrational means—is in actuality the consequence of thinking being founded in sense and sensation. Aesthetics again provides a cornerstone for understanding this sensual basis. Many philosophers of aesthetics have argued that the ultimate aesthetic experience is a synaesthetic one—that is to say, one in which all of the senses are intermingled to create a complete mind–body experience (Richards et al., 1925; Odin, 1986). Beyond the experiential aspects of aesthetics, however, most philosophers and practitioners also argue that a complete aesthetic experience must combine sensation, craft, and understanding. Thus, a great piece of music or science should not only move us, but also impress us with its use of the tools of the trade and surprise us with new understanding (Root-Bernstein, 1997). I have called this combination of sense and sensibility synosia, from an elision of the words synaesthesis (to combine senses) and gnosis (to know) (Root-Bernstein, 1989; RootBernstein & Root-Bernstein, 1999). The best science, like the best art, is that which appeals to the widest range of emotion and intellect. The mathematician Stanislaw Ulam provided an interesting insight into how this combination of sense and sensibility can arise. He began experimenting as a child with calculating “not by numbers and symbols, but by almost tactile feelings combined with reasoning, a very curious mental effort” (Ulam, 1976, p. 17). Years of thinking about thinking convinced him that most human thought occurs through such sensual imaginings—“pictorially, not verbally”. Although Ulam does not elaborate, one can imagine that he may have performed his sensory “calculations” as someone might use

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an abacus (that is, as a series of tactile motions that represent arithmetic units and operations) or simply with reference to how numbers might “feel” if converted into weights that one imagined in one’s hands. All of us make such “calculations” every time we throw an object at a speci c target without actually measuring anything or using any mathematics. With experience, most of us become reasonably accurate in our throwing skill, demonstrating that we can understand things without being able to measure or calculate in the formal mathematical or logical senses of the terms (Root-Bernstein, 1990). Francis Galton, one of the founders of cognitive psychology, demonstrated more than a century ago that almost everyone develops such visual and kinesthetic ways of thinking about numbers (Galton, 1874) and I have found more recently that the most successful scientists take advantage of an unusually wide range of such non-symbolic modes of thinking (Root-Bernstein et al., 1995). Formal schooling teaches us to ignore them, but severe dyslexia has required Cambridge mathematician Kalvis Jansons to enhance them. Since he nds it extremely dif cult to read words or equations, he says that he does most of his mathematics using kinesthetic feelings. Just as most of us remember how to make knots, tie our shoes and ties, or ride a bicycle using our “muscle memory”, so Jansons remembers and manipulates mathematical functions concerning knot and set theory by imagining the physical feel of the processes they represent. Thus, he spends hours tying knots, and when he does not have a piece of rope in his hands, he remembers them by “imagin[ing] the nger movements involved and the feel of the knot being tied without picturing it in my mind or moving my hands at all” (Weiskrantz, 1988, p. 503). “Knots”, Jansons explains, “are examples of things that are extremely hard to describe and remember in words [or equations], and people who attempt to do so usually forget them very quickly and are poor at spotting similarities between complicated knots” (Wieskrantz, 1988, p. 503). Jansons nds the similarities by comparing the common series of movements that he must perform to make knots that may look visually quite different. Thus, Jansons’ description of mathematical thinking is very similar to Ulam’s, who argued that thinking is a succession of operations with symbolic pictures, a sort of abstract analogue of the Chinese alphabet … except that the elements are not merely words but more like sentences or whole stories with linkages between them forming a sort of meta- or super-logic with its own rules. (Ulam, 1976, p. 183) The fact that knot theory can be translated into formal mathematical and logical terms demonstrates that this meta- or super-logic of manipulative processes exists and can lead to important insights. Moreover, it can be developed and mastered through practice. Thus, when Ulam began working at Los Alamos in the 1940s, he says that he worked to develop a “real feeling” in the muscular sense for the physical interrelationships between the various physical measurements that he needed to model. I found out that the main ability to have was a visual, and also an almost tactile, way to imagine the physical situations, rather than a merely logical picture of the problems.… I discovered that if one gets a feeling for no more than a dozen … radiation and nuclear constants, one can imagine the subatomic world almost tangibly, and manipulate the picture dimensionally and qualitatively, before calculating more precise relationships. (Ulam, 1976, 148) He also discovered that many of his distinguished colleagues, including John von

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Neumann and Robert Oppenheimer lacked this “feel”. They were able to participate in the analytical, but not in the creative aspects of the physics (Ulam, 1976, pp. 147, 151–152). The range of feelings used by scientists to perform their mental calculations is surprising (Root-Bernstein, 1990, 1996, 1997). Many of the best scientists acquire such a complete “feel” for the systems they study that they actually report being able to “become” part of the system, imagining what it is like to experience the world from the perspective of some component. Philosophers have labeled this cognitive process “empathizing” or “sympathizing”. As Martin Buber explained, Empathy means to glide with one’s own feeling into the dynamic structure of an object, a pillar or a crystal or the branch of a tree, or even of an animal or a man, and as it were to trace it from within, understanding the formation and motoriality (Bewegtheit) of the object with perceptions of one’s own muscles: it means to “transpose” oneself over there and in there. (Buber, 1920, p. 34) Ethologist Desmond Morris provides an illustration: With each animal I studied I became that animal. I tried to think like it, to feel like it. Instead of viewing the animal from a human standpoint—and making serious anthropomorphic errors in the process—I attempted as a research ethologist, to put myself in the animal’s place, so that its problems became my problems, and I read nothing into its lifestyle that was alien to its particular species. (Morris, 1979, p. 58) Nobel laureate Barbara McClintock similarly took the time to “become friends” with her corn plants, developing what she called “a feeling for the organism”: I found that the more I worked with [chromosomes] the bigger and bigger they got, and when I was really working with them, I wasn’t outside, I was down there. I was part of the system.… these were my friends … As you look at these things they become part of you. And you forget yourself. The main thing is you forget yourself. (Keller, 1983, p. 117) Empathizing is an extremely common strategy adopted by successful scientists. Virologist Jonas Salk reported that, “I would picture myself as a virus or a cancer cell, for example, and try to sense what it was like to be either and how the immune system would respond” (Salk, 1983, p. 7). Molecular biologist Jacques Monod says that in his studies he had “to identify myself with a molecule of protein” in order to understand its functions (Monod, 1970, p. 170). Organic chemist Peter Debye said: “You had to use your feelings—what does the carbon atom want to do?” (Debye, 1966, p. 81). Sabrumanyan Chandrasekhar made many of his discoveries in astrophysics by imagining the universe “from the point of view of the star” (Chandrasekhar, 1987, p. 67). Richard Feynman revolutionized quantum physics with insights that often came from asking himself, “If I were an electron, what would I do?” (Gleick, 1992, pp. 142, 394) and his colleague Hannes Alfven has written that many of his insights have come by imagining what it is like to be a charged particle: Instead of treating hydromagnetic equations I prefer to sit and ride on each electron and ion and try to imagine what the world is like from its point of view and what forces push to the left or to the right. This has been a great advantage because it gives me a possibility to approach the phenomena from another

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point of view than most astrophysicists do and it is always fruitful to look at any phenomenon under two different points of view. (Alfven, 1988, p. 250) Both scientists and philosophers have therefore advised students of science to adopt empathizing as an important tool in the mental arsenal. Molecular biologist Joshua Lederberg has written that, A scientist needs to be able to become an actor.… One needs the ability to strip to the essential attributes of some actor in a process, the ability to imagine oneself inside a biological situation; I literally had to be able to think, for example, “What would it be like if I were one of the chemical pieces in a bacterial chromosome?” and try to understand what my environment was, try to know where I was, try to know when I was supposed to function in a certain way, and so forth. (Judson, 1980, p. 6) Similarly, Karl Popper once suggested that, I think the most helpful suggestion that can be made … as to how one may get new ideas in general [is] … 0 sympathetic intuition” or “empathy”.… You should enter into your problem situation in such a way that you almost become part of it. (Krebs & Shelley, 1975, p. 18) The problem with the literature on empathizing is that, as with Ulam’s meta-logic of tactile calculating, very few people have elaborated on what it means to become the object they are studying. There is, in fact, little mystery. To imagine how an object would react requires the building up of a series of functional hypotheses or mental models about its behavior in certain situations. Like Ulam’s kinesthetic calculating, these hypotheses or models need not be numerically accurate, but they must be order-of-magnitude approximations informed by accurate analogies. A scientist trying to understand “what the carbon atom wants to do” will combine formal knowledge about valences and af nity with a series of analogies to magnetic attraction, stickiness, and related macroscopic concepts informed by kinesthetic experiences of how these concepts feel bodily to be a human being. Such feelings provide guides to the qualitative differences between covalent and hydrogen bonds (super glue versus rubber cement), or a sense of how increased thermal energy will cause increased vibrations that result in “shaking off” bonded components just as a suf ciently hard shake can cause two objects held together by Velcro to separate. Physicist Richard Feynman gave an excellent example of how he used such mental models to ponder his own mathematical puzzles. I had a scheme, which I still use today when somebody is explaining something that I am trying to understand: I keep making up examples. For instance, the mathematicians would come in with a terri c theory, all excited. As they are telling me the conditions, I construct something [in my mind] which ts all the [mathematical] conditions. You know, you have a set (one ball)—disjoint (two balls). The balls turn colours, grow hairs, or whatever, in my head, as they put more conditions on. Finally they state the theorem, which is some dumb thing about the ball which isn’t true for my hairy green ball thing, so I say “False”! (Feynman, 1985, p. 85) “I can only think in pictures”, he said. “It’s all visual” (Feynman, 1988, p. 54). “[I see] the character of the answer, absolutely. An inspired method of picturing, I guess”

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(Gleick, 1992, p. 245). He felt and heard the answers, too, once reporting that he used kinesthetic feelings and acoustic images to solve problems. He would, in fact, roll around on the oor, tap out patterns with his hands and feet, whoop and click and make other sounds, translating the problems upon which he was working into sensual equivalents that he could model and act out (Gleick, 1992, passim). These were the things that gave him a literal feel for his problem. Many scientists place the insights obtained by such empathetic intuitions above those obtained through logic. Perhaps the most revealing story in this regard has been told by physicist Mitchell Wilson, who worked as a postdoctoral fellow with Enrico Fermi during the latter half of the 1940s. Wilson recounts witnessing a meeting at which Fermi, I.I. Rabi, and Leo Szilard attempted to solve one of the outstanding problems of nuclear reactor design. Rabi went up to the blackboard and wrote a series of equations attempting to prove some point. Szilard disagreed and wrote his own series of equations. Then came Fermi’s turn. Fermi took a very different tack. Stanislaw Ulam has said that Fermi had a “whole arsenal of mental pictures, illustrations, as it were, of important laws or effects” that he used in preference to his also very highly developed mathematical techniques (Ulam, 1976, p. 163). In this case, Fermi examined his arsenal of mental models and proclaimed that both Rabi and Szilard were wrong. They asked him how he knew. “Intuition”, he replied. Wilson started to laugh. The notion of rebutting a formal mathematical argument with “intuition” struck him as comical. Then he realized that Rabi and Szilard did not consider Fermi’s reply a joke at all. They capitulated instantly, proclaiming that further work was clearly needed on the problem (Wilson, 1972, p. 14). Feynman’s description of his imagistic testing of mathematical theorems provides one window on why Rabi and Szilard may have capitulated to Fermi’s intuition. Einstein provides further enlightenment. When faced with an abstruse mathematical demonstration that he considered overly abstract, Einstein would often tell his mathematical collaborators, “I am convicted but not convinced” (Whitrow, 1967, p. 78). Einstein’s collaborator Ernest Straus explained that what Einstein meant was that “he could no longer get out of agreeing that it was [logically] correct, but he did not feel that he understood why it was so” (Whitrow, 1967, p. 78, emphasis added). This feeling was, as Einstein said himself in his Autobiographical Notes, what differentiates understanding from mere fantasizing: Concepts and propositions get “meaning” or “content,” only through their connection with sense experiences. The connection of the latter to the former is purely intuitive, not itself of a logical nature. The degree of certainty with which this connection, or intuitive linkage, can be undertaken, and nothing else, differentiates empty fantasy from scienti c truth. (Einstein, 1949, p. 11) We can hear here various resonances with Kant’s dictum in his Critique of Pure Reason that “The intellect can intuit nothing. The senses can think nothing. Only through their union can knowledge arise” (Arber, 1964, p. 124). Rabi and Szilard must have realized that their mathematical formalisms were like those that convicted but did not convince Einstein—devoid of sensual connections to the physical world. They were therefore willing to accept Fermi’s “intuitive” rejection of their logical arguments based on his examination of his “feel” for similar systems. Why is this “feel” for the system so important? Wolfgang Pauli suggested that it is related to experiencing beauty. Only when there is a “congruence of preexisting internal images of the human psyche with external objects and their behavior”, does one

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experience “understanding in nature, together with the joy that man feels in understanding” (Heisenberg, 1974, pp. 179–180). In order to shudder before beauty, it is not enough to be convicted. One must also be convinced. And one must be convinced—one must feel—in order to act upon one’s knowledge. Intuition is one of the reasons that scientists value elegance so highly. Elegant results are like poems. They distill a huge amount of meaning into a very small space while simultaneously making a large number of connections to other results. The ability to concentrate meaning and connections maximizes understanding and its emotional impact, whereas simply following a logical path to a conclusion often yields neither insight, connections, surprises, nor joy. Science, being a human endeavor, requires the latter characteristics to make it interesting and fun. Only when we feel that we know and know what we feel do we truly understand. The meta-logic of aesthetics And so we return to our theme that understanding and emotion are inextricably linked through aesthetic considerations. My third argument is therefore that “emotion has a logic of its own”, to quote Cytowic (1993, Part 2, Chap. 7). Actually, I prefer mathematician Stanislaw Ulam’s use of the term “meta-logic” to describe aesthetic cognition. By “meta-logic”, Ulam meant that it is possible to understand things—and here I use the term understand to mean suf cient knowledge to act upon an object or through a process to obtain a desired end—in a completely sensual way independent of linguistic, mathematical, or other formal logical structures. Another common term for this form of understanding is “intuition”. Einstein is again instructive. In describing his scienti c aesthetics, Einstein maintained that, “A theory is the more impressive the greater the simplicity of its premisses, the more different kinds of things it relates, and the more extended its area of applicability” (Einstein, 1949, p. 31). The problem with logical arguments that convict but do not convince is that they fail to satisfy Einstein’s aesthetic criteria. In order for a theory or explanation or model to be widely applicable, the scientist using it must be able to translate its symbolic representation into the pictures, feelings, and emotional states by which he solves problems so that the class of such pictures, feelings, and emotions is tapped and similarities revealed. This process of nding similarities through such intuitive means is literally the way in which Einstein de ned thinking: What precisely is “thinking”? When on the reception of sense impression, memory pictures emerge, this is not yet “thinking.” And when such pictures form sequences, each member of which calls forth another, this too is not yet “thinking.” When, however, a certain picture turns up in many such sequences, then precisely by such return—it becomes an organizing element for such sequences, in that it connects sequences in themselves unrelated to each other. Such an element becomes a concept. (Einstein, 1949, p. 7) Thus, like Ulam, Einstein told several interviewers that he used pictorial images and kinesthetic feelings rather than words or equations when solving problems. He went so far to assert to his colleague Leopold Infeld that, “no scientist thinks in formulae” (Infeld, 1941). Ulam agreed. He too considered thinking to be the linking of sense images through repeated analogical connections.

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This feeling of analogy or association is necessary to place the set of impressions correctly on the suitable end points of a sequence of branches of a tree. And perhaps this is how people differ from each other in their memories. In some, more of these analogies are felt, stored, and better connected. (Ulam, 1976, p. 183) He, too, rejected the notion of thinking in terms of words, numbers, or logic: “There is”, he said, a way of “writing” abstract ideas in a kind of shorthand which is almost orthogonal to the usual ways in which we communicate with each other by means of the spoken or written word. One may call this a “visual algorithm”. (Ulam, 1976, p. 183) Jansons would call it a kinesthetic one. No matter. Virtually without exception, the greatest mathematicians and scientists assert that the development of this pictorial, visual, kinesthetic, or generally sensual algorithm is the basis for scienti c thinking. What is missing from both Einstein’s and Ulam’s accounts of thinking, however, is that we do not think about just anything; we think about problems. As Einstein himself said at one point, de ning a problem is often more valuable than solving it, because once the correct problem is formulated there are often many people capable of solving it, whereas genius often consists in seeing the problem in the rst place. So one of the things we need to consider is the possibility that the purpose of cognitive aesthetics is less to solve problems than to raise them. How, after all, do we know that we are facing a problem except in terms of the discontent we feel looking at the situation as it exists? Here we return to the neurologists’ observation that feeling and emotion underlie good decision-making. We must feel that there is something wrong in order to be motivated to study the problem, and the nature of the problem de nition will come from our sense of the disjunction or anti-aesthetic quality of the situation as it exists. Thus, Bertrand Russell once said, “In all the creative work that I have done, what has come rst is a problem, a puzzle involving discomfort” (Hutchinson, 1959, p. 19). Mathematician Norbert Weiner provided an excellent example of how such feelings of discomfort, or what he calls “hypnogogic images”, can actually become the organizing principle for thinking creatively, taking the place of muscular or visual images. At one point in his career, Weiner records that he so overworked himself that he developed pneumonia. It was impossible for me to distinguish among my pain and the dif culty in breathing, the apping of the window curtain, and certain as yet unresolved parts of the potential problem on which I was working. I cannot say merely that the pain revealed itself as mathematical tension, or that the mathematical tension symbolized itself as a pain: for the two were united too closely to make such a separation signi cant. However, when I re ected on this matter later, I became aware of the possibility that almost any experience may act as a temporary symbol for a mathematical situation which has not yet been organized and cleared up. I also came to see more de nitely than I had before that one of the chief motives driving me to mathematics was the discomfort or even the pain of an unresolved mathematical discord. I became more and more conscious of the need to reduce such a discord to a semipermanent and recognizable terms before I could release it and pass on to something else. Indeed, if there is any one quality which marks the competent mathematician

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more than any other, I think it is the power emotional symbols and to organize out of them language. If one is not able to do this, one is evaporate from the sheer dif culty of preserving lated shape. (Weiner, 1956, pp. 85–86)

to operate with temporary a semipermanent, recallable likely to nd that his ideas them in an as yet unformu-

Thus, Weiner and Russell tell us that we identify the existence of scienti c problems by the anti-aesthetic feelings of discomfort or even pain that they induce in us, and the speci c nature of these feelings become the genesis of creative thought. The realization that we recognize problems through our anti-aesthetic response to them provides an important clue as to how we go about de ning the nature of the problem and recognize its solution. The nature of the disjuncture between our aesthetic expectations and what we observe or think we know reveals the detailed characteristics of the speci c problem that presents itself. Thus, I have argued in a previous book (Discovering, 1989) that there is no distinction between the context of discovery and the logic of disproof that so many philosophers make. The recognition of the existence of a problem (i.e. the disproof of the existing problem-solving model or demonstration of the inadequacy of available data) creates the context of discovery by generating a speci c disjuncture between the known and the unknown. The speci c nature of this disjuncture de nes not only the speci c outlines of the problem to be resolved, but de nes the aesthetic criteria that must be satis ed by a solution and creates the aesthetic angst required to motivate the search for a solution. Thus, scientists with the most rigorously developed sense of scienti c aesthetics are often the most successful scientists and many of the most productive periods in the history of science are characterized by the kinds of aesthetic con icts that are represented by the Ptolemaic–Copernican con ict over circular and elliptical orbits in astronomy or the Bohr–Einstein con ict over the status of statistical versus causal approaches to physics. Changes in scienti c aesthetics go hand in hand with major shifts in both the philosophy of science and the actual mechanics by which science is pursued at any given time in history (Kuhn, 1959; McAllister, 1996). Translating from aesthetic cognition to logical forms My contention is that the meta-logic of aesthetic cognition actually precedes the logic of research, however, and actually informs it. Thus the formal results of logic stem from the informal insights of aesthetic intuition. That there is a necessary and important link between the two is undeniable: experience demonstrates that intuitions can be translated into formal logical or linguistic terms. The reasoning here is simple. We all know that clear writing re ects clear thinking. Ideas that are not well organized in the mind do not come out on paper in a clear fashion. The same thing is true of scienti c ideas. Poorly constructed hypotheses yield poorly organized research. Moreover, the translation from an hypothesis to an experiment, or from one language into another, can only be achieved if there is, in fact, a correspondence between the nature of the ideas expressed in the two languages. Thus, idioms are often untranslatable, just as some scienti c concepts have no physical equivalents and are therefore untestable. These everyday examples provide the basis for arguing that there must be a logic to aesthetic cognition because the results of such cogitation are translatable into formal linguistic and mathematical terms. Were no logic inherent in aesthetic cognition, then it is dif cult to imagine how logical results would result from its machinations.

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The fact that the results of aesthetic cognition must be translated into formal languages in order to be communicated to other people explains why intuition has largely been ignored by philosophers. The mental images, physical and muscular feelings, emotions, and intuitions that Einstein, Ulam, Weiner and the others describe are what Michael Polanyi has called “personal knowledge” (Polanyi, 1958). Insight arrives through private mental means using mental “languages” that are often invented for individual, personal use. The scientist feels that he knows and may even know what he feels, but feelings are not capable of direct communication to other people. So, it is necessary to translate personal knowledge into public formulations such as words, equations, and diagrams. I am told by physicists and mathematicians at CalTech and MIT that one of the major dif culties encountered by their students is making the converse translation: students who cannot translate equations and words back into the images and feelings that motivated their invention are unable to understand the content of their courses. Like such students, many philosophers have understandably focused on the communicable formulations of scienti c ideas rather than their personal and private cognitive manifestations, but have thereby missed both the reasons for the invention of the formal results and the sensual meanings of their content. My fourth argument is therefore that there is a fundamental distinction between the creative stage of scienti c thinking that I have been describing and its translation into a form acceptable for communicating insight to other people. The problem that every scientist must address is how to move from the private sensory feelings he uses for thinking to the public languages we share for communicating what we think. Only when we explicitly recognize that the “tools of thinking” and the “tools of communication” are distinct can we understand the intimate, yet tenuous, connection between thought and language, imagination and logic. Many scientists have commented on the distinction between the private, nonverbal phase of scienti c problem solving and the translation of ideas into language. Ulam, as I noted above, said that he used “visual algorithms” for thinking, which he considered to be a “kind of shorthand which is almost orthogonal to the usual ways in which we communicate with each other” (Ulam, 1976, p. 183). He would use his images to get a feel for the systems he was working on “before calculating more precise relationships” (Ulam, 1976, p. 148). Feynman, another visual/kinesthetic thinker, also noted that, “in certain problems that I have done, it was necessary to continue the development of the picture as the method, before the mathematics could really be done”. And Einstein wrote that his thinking was totally visual and sensual, and that mathematics and logic were performed explicitly as secondary steps: “Conventional words or other signs [presumably mathematical ones] have to be sought for laboriously only in a secondary stage, when the associative play [between images] already referred to is suf ciently established and can be reproduced at will” (Hadamard, 1945, pp. 142–143). Einstein explained more fully to Max Wertheimer that the series of equations and axioms you nd in physics books have no resemblance to creative thinking: No really productive man thinks in such a paper fashion. The way the two triple sets of axioms are contrasted in [my physics book with Leopold Infeld] is not at all the way things happened in the process of actual thinking. This was merely a later formulation of the subject matter, just a question of how the thing could best be written … but in this process they [the ideas] did not grow out of any manipulation of axioms. (Wertheimer, 1959, p. 228, n. 7) Metallurgist Cyril Stanley Smith of MIT had the same experience as Einstein: “The

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stage of discovery was entirely sensual and mathematics was only necessary to be able to communicate with other people” (Smith, 1981, pp. 353–354). Werner Heisenberg wrote similarly that in the revolution in physics he helped to create, “mathematics.… played only a subordinate, secondary role. Mathematics is the form in which we express our understanding of nature; but it is not the content of that understanding” (Heisenberg, 1974, p. 146). Biologists note the same translation problem. Nobel laureate Barbara McClintock said, “you work with so-called scienti c methods to put it into their frame after you know” (Keller, 1983, p. 203). Agnes Arber also notes that the records kept by scientists are things “very remote from the original”, a mere “translation of his perception into another medium” (Arber, 1964, p. 67). The most dif cult problem that must be addressed in this translation process for Arber is that words and equations express only linear reasoning, whereas “the experience of one’s own thinking suggests that it moves, actually, in a reticulum (possibly of several dimensions) rather than along a single line … A reticulum.… cannot be symbolized adequately in a linear succession of words” (Arber, 1964, pp. 45–46). Thus, we must accept the fact that what we can say in words or express in logical formulations is but a shadow of what we have actually imagined. To analyze scienti c thinking from these faint shadows on paper is therefore to miss the literally physical embodiment of the actual process of creation. The most frustrating part of aesthetic cognition for scientists is that it may yield insights that are not immediately amenable to translation. Friedrich Gauss often complained that “I have had my results for a long time; but I do not yet know how I am to arrive at them” (Beveridge, 1950, p. 145). Lord Kelvin similarly “had at times to devise explanations of that which had come to him in a ash of intuition” (Thompson, 1910, p. 1126). Sometimes, as in the case of Fermi described above, or in instances such as the four-color map theorem or Fermat’s last theorem, the results of intuition may be correct but the translation into linear forms of reasoning so complicated that it may take decades or even centuries for the conversion to become possible. These problems suggest that a more in-depth understanding of the meta-logic of aesthetic cognition may provide more direct means of both communicating and analyzing the results of intuition. My point is that we must formally recognize the existence of two different forms of logic at work in every creative act, whether in science or in any other subject, and those are the meta-logical forms of thinking that are embedded in what we call intuitive thought and the formal logical forms in which we communicate. Thus, there are meta-logical “tools for thinking” and logical “tools for communicating” that need separate philosophical approaches (Root-Bernstein & Root-Bernstein, 1999). One reason that the philosophy of science has failed to come to grips with the creative aspects of the scienti c enterprise is that it has thus far focused mainly on the logic behind public tools for communicating rather than on the meta-logic of private tools for thinking.

Conclusions: beyond the psychology of discovery It should be obvious from the preceding that the outlines of aesthetic cognition and the private mental “tools” by which intuition and emotion are harnessed can be de ned rigorously (Root-Bernstein, 1989; Root-Bernstein & Root-Bernstein, 1999). Similarly, the meta-logic behind aesthetic cognition has been outlined by many scientists and philosophers. It remains to reify this meta-logic as a set of rules, axioms, or practices.

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Thus, this article identi es a phenomenon that de nes a new area for philosophical research with many interesting aspects. Perhaps the most important implication of aesthetic cognition is that it undermines a widely held belief among some philosophers, logicians, and linguists that, that which cannot be said, cannot be thought. To take such a position is to ignore a vast literature on nonlinguistic forms of thinking that include visual and other forms of imaging, kinesthetic thinking, sensual thinking, modeling, and the use of emotions and intuition by scientists and mathematicians (e.g. Weiskrantz, 1988). It is clear that most creative scientists understand things before they are able to express what they know in any formal language, even to themselves. Thus, to understand the nature of thinking, we must abandon the preconception that thinking must involve words or other logical symbols and accept that images, feelings, sensations, and emotions also embody logics. Aesthetic cognition therefore makes the body part of the mind, creating new approaches to the mind–body problem. If, in scienti c thinking, thought and sensation, rationality and emotion, logic and beauty, are all bound inextricably, then the distinction between mind and body is quite impossible. Feeling must be a form of thinking and thinking cannot be divorced from feeling. The very best scientists seem to be telling us that the greatest scienti c discoveries come from the most complete melding of the two. Thus, we may have to rethink the nature of logic as being not a test for the validity of ideas, but rather a test for the possibility of clear communication of ideas. One can then take yet another step: it may be possible to devise a formal meta-logic to describe the nature of sensual, aesthetic, emotional thinking. The fact that aesthetics has had a formal presence in philosophy since its origins, and that the aesthetics of art and the aesthetics of science appear to be very similar, at least in outline (RootBernstein, 1997), suggests that such a formal meta-logic is possible. Undoubtedly the evolution of an aesthetic meta-logic will be gradual. It will grow and diverge just as formal mathematical logic has done. And undoubtedly there will be the same inability to create an unambiguous, noncontradictory meta-logic as there has been for mathematical logic. But the implications of formalizing such a meta-logic might be as important for promoting creative or intuitive thinking as logic itself has been for providing clear tests of reasoning. Working hand in hand, the two might be synergistic. One nal note: the concept of aesthetic cognition may have extremely important implications for devising arti cial intelligence machines. Such machines can, at present, convict, but never convince. They are currently unable to invent problems; cannot choose a problem to work on; have no means of evaluating which of several problems is most likely to be interesting; cannot bring the kind of intuitive physical understanding that Einstein demanded to any equation they may output; cannot interpret their output; and have no means to evaluate which of several possible answers is most useful. Oddly, all of these very practical functions in science come not from logical decisions but from meta-logical or aesthetic ones. Thus, arti cial intelligence will fail to provide insights into human thinking or model its capabilities until aesthetic cognition is itself understood suf ciently to be modeled and implemented by computers. What we must always remember is that behind every human action there is motivation, and that motivations are always based in the aesthetic sensibility and emotional feelings. Far from being antithetical to philosophy, the meta-logic of such motivations must become part of it. “Can you understand that it is not only scienti c results that are the recompense for all this trouble and annoyance,” wrote ethologist Konrad Lorenz of his love of animals, “but more, much, much more?” (Konrad Lorenz,

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Note on contributor Robert Root-Bernstein is a Professor of Physiology, an historian and philosopher of science, and an amateur artist whose books include Discovering (Harvard University Press, 1989; reprinted by Baker & Taylor, 1997); Rethinking Aids (Free Press, 1993); and, with his wife Michele, Honey, Mud, Maggots and other Medical Marvels (Houghton Mif in, 1997; Macmillan, 1998) and Sparks of Genius (Houghton Mif in, 1999). Correspondence: Department of Physiology, 313 Giltner Hall, Michigan State University, East Lansing, MI 48824, USA. E-mail: [email protected]