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 thephilosophy of science. The � rst concerns what role aesthetics plays in scienti� c thinking. Thesecond is the problem of how logically testable ideas are generated (the so-called “psychology ofresearch” versus “logic of (dis)proof” problem). I argue that aesthetic sensibility is the basis forwhat scientists often call intuition, and that intuition in turn embodies (in a literal physiologicalsense) 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 andsensually, using visual and aural images, kinesthetic and other proprioceptive feelings, sensa-tions, 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 oneknows. Eminent scientists universally describe an explicitly secondary process in which suchpersonal 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 philosophersof science (as well as psychologists and arti� cial intelligence researchers) have had in makingsense of scienti� c thinking have arisen from confusing the form and content of the � naltranslations 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 isbeautiful is known by its sensory and emotional effects on our mind. Because of thisfoundation in sensation and emotion, aesthetic experiences have classically been limitedto experiences of natural phenomena and the products of the arts. But all humaninventions, including those stemming from science, mathematics, and engineering, canevoke the same range and types of aesthetic responses that a beautiful vista, a stunningpainting, or a moving symphony can do. Scientists, just as much as artists, will exclaimhow “beautiful” or “elegant” or “breathtaking” a result is (Tauber, 1996). Theexcitement accompanying the discovery or invention of new things is often described asbeing 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, insome 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 theStudy of Experimental Medicine that everything purposeful in scienti� c thinking beginswith feeling:

ISSN 0269-8595 print/ISSN 1469-9281 online/02/010061-17 Ó 2002 Inter-University FoundationDOI: 10.1080/02698590120118837

62 R. S. ROOT-BERNSTEIN

Just as in other human activities, feeling releases an act by putting forth theidea which gives a motive to action, so in the experimental method feeling takesthe initiative through the idea. Feeling alone guides the mind and constitutesthe primum movens of science. (Bernard, 1927, p. 43)

The mathematical physicist Wolfgang Pauli also maintained that scienti� c thinkingbegins within the “unconscious region of the human soul”, where, “the place of clearconcepts is taken by images of powerful emotional content, which are not thought, butare 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 herexperience,

new hypotheses come into the mind most freely when discursive reasoning(including its visual component) has been raised by intense effort to a level atwhich it � nds itself united indissolubly with feeling and emotion. When reasonand intuition attain this collaboration, the unity into which they merge appearsto 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 soundalmost artistic, Arber makes the conclusion explicit: “Emotion has function in [sci-enti� 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 haswritten 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 abystander watching it happen. Only later was I able to begin to formulate asystematic theory of structure, bonding and reactions for these unusualmolecules.… Was it science? Our later tests showed it was. But the processesthat 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 writtenthat the “scientist needs an artistically creative imagination” (Planck, 1949). Indeed,scientist and artist are kith and kin, for their motivations often begin in the samepre-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 knowssomething 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 andsensual 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 knowsconstitutes 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� caesthetics. Fourth, that aesthetic cognition precedes and is distinct from formal logic,and that an explicit translation process is therefore required before ideas can becommunicated and tested logically. In sum, aesthetic cognition combines knowledgeand feeling into synosic intuition that has an analyzable “meta-logic” which is the basisfor creative scienti� c thinking.

AESTHETIC COGNITION 63

The emotional and sensual basis of scienti� c intuition

Begin with the argument that despite its objective facade, all scienti� c thinking has anineluctable emotional and sensual component. Probably everyone who has studied thephilosophy 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 itbecause he takes pleasure in it; and he takes pleasure in it because it isbeautiful. If nature were not beautiful, it would not be worth knowing and lifewould not be worth living.… (Poincare, 1946, pp. 366–367)

What has been less well established is the degree to which Poincare’s sentiments areechoed 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 thecentral nervous system, was led to science through art. He was attracted as a boy todrawing 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 ofneurology holds out to the investigator captivating spectacles and incomparableartistic emotions. In it, my aesthetic instincts found full satisfaction at last. Likethe entomologist in search of brightly coloured butter� ies, my attentionhunted, in the � ower garden of the grey matter, cells with delicate and elegantforms, 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 inbuilding the cloud chamber had no scienti� c basis nor had he any inkling that it wouldone day be used to study the behavior of subatomic particles. Quite the contrary, it hadbegan in attempts to recreate the spectral beauties called glories and coronas that he hadwitnessed 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 youththrough his artistic hobbies: he made his own pastels and oil paints; invented a novelform of decalcomania (a form of transfer printing); synthesized his own collodion for hishome-made camera; and concocted his own � reworks. Despite his Nobel prize, hemaintained that art was what motivated his curiosity and claimed at the end of his lifethat his greatest contribution to humanity was actually his very in� uential work on colortheory (Ostwald, 1927). Fellow laureate, Robert B. Woodward wrote that his attractionto chemistry was similarly sensual:

it is the sensuous elements which play so large a role in my attraction tochemistry. I love crystals, the beauty of their form—and their formation;liquids, dormant, distilling, sloshing!; swirling, the fumes; the odors—good andbad; the rainbow of colors; the gleaming vessels of every size, shape, andpurpose. Much as I might think about chemistry, it would not exist for mewithout these physical, visual, tangible, sensuous things. (Woodward, 1984,p. 137)

Sometimes unusual sensitivity to color has actually been the source of the researchproblem that has resulted in great breakthroughs. Nobelist Albert Szent-Gyorgyi, forexample, 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


pleasure. I started with the question, “Why does a banana turn brown when Ihurt it” … There are two categories of plants, you see—those that turn blackon being damaged and those in which there is no color change.… Why no colorin some damaged plants? (Szent-Gyorgyi, 1966, pp. 116–117)

Nobel prizewinning chemist Alan MacDiarmid, who was one of the discoverers ofconductive polymers, was also motivated by his love of color. “There were no scienti� creasons whatsoever”, he said for his studies of polyacetylene, the � rst conductivepolymer he discovered: “My motivations have been driven by curiosity and color. …”(Russo, 2000).

The emotional experiences that attend the observation or interaction with natureare similar motivators. When physiologist and ecologist Bernd Heinrich was asked bygraduate school examiners why he wanted to become a biologist, he recounted a springday 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 wasstars at night.

It was like going to a cathedral. I had the feeling that the world wasmagic … The world was spirit.… I couldn’t wait for night to come and for thestars to come out. I would stand in the backyard and look at the appropriatetime and identify the stars as they became visible out of the twilight. It was likebeing, I suppose, in a sort of heaven. I can’t explain it in words even today. Ihad that internal feeling about everything—about physics, about the way theworld 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 musicbene� ts his science: “It helps me emotionally to feel more about science. You see, I ama 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] youreally have to become completely captivated by something, like falling in lovewith a certain young lady … You can’t imagine why everyone else isn’t chasingafter this wonderful person. (Russo, 2000)

Jonas Salk once summarized the same feelings to me by advising, “Do what makes yourheart leap.” Emotions tell us what is important to us and therefore direct the course ofour inquiries.

Emotions, intuitions, and feelings, in short, lie as much at the heart of the sciencesas at the heart of the arts. As Einstein said, “only intuition, resting on sympatheticunderstanding, can lead to [insight]; … the daily effort comes from no deliberateintention or program, but straight from the heart” (Hoffmann, 1972, p. 222). Poincarewrote similarly in Science and Method that

[i]t is by logic that we prove, but by intuition that we discover … Logic teachesus that on such an such a road we are sure of not meeting an obstacle; it does


not tell us which is the road that leads to the desired end. For this it isnecessary to see the end from afar, and the faculty that teaches us to see isintuition. Without it, the geometrician would be like a writer well up ingrammar but destitute of ideas. (Poincare, 1946, p. 438)

Indeed, it is possible to take my argument a step further to conclude that logicaldecision-making originates in emotion. The argument follows not only from thetestimonials given above, but from neurological research as well. Neurologist AntonioDamasio has found that patients whose emotional affect (that is, their ability to respondemotionally) is grossly impaired due to strokes, accidents, or tumors lose the ability tomake rational decisions and plans despite having intact rational function (Damasio,1994). Such patients can, for example, calculate accurately the odds of having a winningpoker hand, but cannot, in actual play, implement their calculations in a mannerdesigned to optimize their chances of winning. Unable to become emotionally involvedin their decisions, they fail to make good ones even when they can accurately describethe 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 thoughtand behavior; they are its basis. That which we feel strongly about is what is mostimportant 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 theproblems 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 tofeel 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 bea paradox—that rationality results from irrational means—is in actuality the con-sequence of thinking being founded in sense and sensation. Aesthetics again provides acornerstone for understanding this sensual basis. Many philosophers of aesthetics haveargued that the ultimate aesthetic experience is a synaesthetic one—that is to say, onein 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 aestheticexperience must combine sensation, craft, and understanding. Thus, a great piece ofmusic or science should not only move us, but also impress us with its use of the toolsof the trade and surprise us with new understanding (Root-Bernstein, 1997). I havecalled this combination of sense and sensibility synosia, from an elision of the wordssynaesthesis (to combine senses) and gnosis (to know) (Root-Bernstein, 1989; Root-Bernstein & Root-Bernstein, 1999). The best science, like the best art, is that whichappeals to the widest range of emotion and intellect.

The mathematician Stanislaw Ulam provided an interesting insight into how thiscombination of sense and sensibility can arise. He began experimenting as a child withcalculating “not by numbers and symbols, but by almost tactile feelings combined withreasoning, a very curious mental effort” (Ulam, 1976, p. 17). Years of thinking aboutthinking convinced him that most human thought occurs through such sensualimaginings—“pictorially, not verbally”. Although Ulam does not elaborate, one canimagine that he may have performed his sensory “calculations” as someone might use


an abacus (that is, as a series of tactile motions that represent arithmetic units andoperations) or simply with reference to how numbers might “feel” if converted intoweights that one imagined in one’s hands. All of us make such “calculations” every timewe throw an object at a speci� c target without actually measuring anything or using anymathematics. With experience, most of us become reasonably accurate in our throwingskill, demonstrating that we can understand things without being able to measure orcalculate in the formal mathematical or logical senses of the terms (Root-Bernstein,1990).

Francis Galton, one of the founders of cognitive psychology, demonstrated morethan a century ago that almost everyone develops such visual and kinesthetic ways ofthinking about numbers (Galton, 1874) and I have found more recently that the mostsuccessful scientists take advantage of an unusually wide range of such non-symbolicmodes of thinking (Root-Bernstein et al., 1995). Formal schooling teaches us to ignorethem, but severe dyslexia has required Cambridge mathematician Kalvis Jansons toenhance them. Since he � nds it extremely dif� cult to read words or equations, he saysthat he does most of his mathematics using kinesthetic feelings. Just as most of usremember how to make knots, tie our shoes and ties, or ride a bicycle using our “musclememory”, so Jansons remembers and manipulates mathematical functions concerningknot 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 theknot 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 extremelyhard to describe and remember in words [or equations], and people who attempt to doso usually forget them very quickly and are poor at spotting similarities betweencomplicated knots” (Wieskrantz, 1988, p. 503). Jansons � nds the similarities by com-paring the common series of movements that he must perform to make knots that maylook visually quite different.

Thus, Jansons’ description of mathematical thinking is very similar to Ulam’s, whoargued that thinking is a

succession of operations with symbolic pictures, a sort of abstract analogue ofthe Chinese alphabet … except that the elements are not merely words butmore like sentences or whole stories with linkages between them forming a sortof 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 termsdemonstrates that this meta- or super-logic of manipulative processes exists and can leadto 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 workedto develop a “real feeling” in the muscular sense for the physical interrelationshipsbetween the various physical measurements that he needed to model.

I found out that the main ability to have was a visual, and also an almosttactile, way to imagine the physical situations, rather than a merely logicalpicture of the problems.… I discovered that if one gets a feeling for no morethan a dozen … radiation and nuclear constants, one can imagine the sub-atomic world almost tangibly, and manipulate the picture dimensionally andqualitatively, before calculating more precise relationships. (Ulam, 1976, 148)

He also discovered that many of his distinguished colleagues, including John von


Neumann and Robert Oppenheimer lacked this “feel”. They were able to participate inthe 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 issurprising (Root-Bernstein, 1990, 1996, 1997). Many of the best scientists acquire sucha 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 theperspective 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 ofan object, a pillar or a crystal or the branch of a tree, or even of an animal ora man, and as it were to trace it from within, understanding the formation andmotoriality (Bewegtheit) of the object with perceptions of one’s own muscles: itmeans 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 feellike it. Instead of viewing the animal from a human standpoint—and makingserious anthropomorphic errors in the process—I attempted as a researchethologist, to put myself in the animal’s place, so that its problems became myproblems, and I read nothing into its lifestyle that was alien to its particularspecies. (Morris, 1979, p. 58)

Nobel laureate Barbara McClintock similarly took the time to “become friends” withher corn plants, developing what she called “a feeling for the organism”:

I found that the more I worked with [chromosomes] the bigger and bigger theygot, and when I was really working with them, I wasn’t outside, I was downthere. I was part of the system.… these were my friends … As you look at thesethings they become part of you. And you forget yourself. The main thing is youforget yourself. (Keller, 1983, p. 117)

Empathizing is an extremely common strategy adopted by successful scientists. Virolo-gist Jonas Salk reported that, “I would picture myself as a virus or a cancer cell, forexample, and try to sense what it was like to be either and how the immune systemwould respond” (Salk, 1983, p. 7). Molecular biologist Jacques Monod says that in hisstudies he had “to identify myself with a molecule of protein” in order to understand itsfunctions (Monod, 1970, p. 170). Organic chemist Peter Debye said: “You had to useyour feelings—what does the carbon atom want to do?” (Debye, 1966, p. 81). Sabru-manyan Chandrasekhar made many of his discoveries in astrophysics by imagining theuniverse “from the point of view of the star” (Chandrasekhar, 1987, p. 67). RichardFeynman revolutionized quantum physics with insights that often came from askinghimself, “If I were an electron, what would I do?” (Gleick, 1992, pp. 142, 394) and hiscolleague Hannes Alfven has written that many of his insights have come by imaginingwhat it is like to be a charged particle:

Instead of treating hydromagnetic equations I prefer to sit and ride on eachelectron and ion and try to imagine what the world is like from its point of viewand what forces push to the left or to the right. This has been a great advantagebecause it gives me a possibility to approach the phenomena from another


point of view than most astrophysicists do and it is always fruitful to look at anyphenomenon under two different points of view. (Alfven, 1988, p. 250)

Both scientists and philosophers have therefore advised students of science to adoptempathizing as an important tool in the mental arsenal. Molecular biologist JoshuaLederberg has written that,

A scientist needs to be able to become an actor.… One needs the ability to stripto the essential attributes of some actor in a process, the ability to imagineoneself inside a biological situation; I literally had to be able to think, forexample, “What would it be like if I were one of the chemical pieces in abacterial chromosome?” and try to understand what my environment was, tryto know where I was, try to know when I was supposed to function in a certainway, 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 getnew ideas in general [is] … 0 sympathetic intuition” or “empathy”.… Youshould enter into your problem situation in such a way that you almost becomepart of it. (Krebs & Shelley, 1975, p. 18)

The problem with the literature on empathizing is that, as with Ulam’s meta-logic oftactile calculating, very few people have elaborated on what it means to become theobject they are studying. There is, in fact, little mystery. To imagine how an objectwould react requires the building up of a series of functional hypotheses or mentalmodels about its behavior in certain situations. Like Ulam’s kinesthetic calculating,these hypotheses or models need not be numerically accurate, but they must beorder-of-magnitude approximations informed by accurate analogies. A scientist trying tounderstand “what the carbon atom wants to do” will combine formal knowledge aboutvalences and af� nity with a series of analogies to magnetic attraction, stickiness, andrelated macroscopic concepts informed by kinesthetic experiences of how these conceptsfeel bodily to be a human being. Such feelings provide guides to the qualitativedifferences between covalent and hydrogen bonds (super glue versus rubber cement), ora 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 objectsheld together by Velcro to separate.

Physicist Richard Feynman gave an excellent example of how he used such mentalmodels to ponder his own mathematical puzzles.

I had a scheme, which I still use today when somebody is explaining somethingthat I am trying to understand: I keep making up examples. For instance, themathematicians would come in with a terri� c theory, all excited. As they aretelling me the conditions, I construct something [in my mind] which � ts all the[mathematical] conditions. You know, you have a set (one ball)—disjoint (twoballs). The balls turn colours, grow hairs, or whatever, in my head, as they putmore conditions on. Finally they state the theorem, which is some dumb thingabout 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”


(Gleick, 1992, p. 245). He felt and heard the answers, too, once reporting that he usedkinesthetic feelings and acoustic images to solve problems. He would, in fact, rollaround on the � oor, tap out patterns with his hands and feet, whoop and click and makeother sounds, translating the problems upon which he was working into sensualequivalents that he could model and act out (Gleick, 1992, passim). These were thethings that gave him a literal feel for his problem.

Many scientists place the insights obtained by such empathetic intuitions abovethose obtained through logic. Perhaps the most revealing story in this regard has beentold by physicist Mitchell Wilson, who worked as a postdoctoral fellow with EnricoFermi during the latter half of the 1940s. Wilson recounts witnessing a meeting at whichFermi, I.I. Rabi, and Leo Szilard attempted to solve one of the outstanding problemsof nuclear reactor design. Rabi went up to the blackboard and wrote a series ofequations attempting to prove some point. Szilard disagreed and wrote his own series ofequations. Then came Fermi’s turn. Fermi took a very different tack. Stanislaw Ulamhas said that Fermi had a “whole arsenal of mental pictures, illustrations, as it were, ofimportant laws or effects” that he used in preference to his also very highly developedmathematical techniques (Ulam, 1976, p. 163). In this case, Fermi examined his arsenalof mental models and proclaimed that both Rabi and Szilard were wrong. They askedhim how he knew. “Intuition”, he replied. Wilson started to laugh. The notion ofrebutting a formal mathematical argument with “intuition” struck him as comical. Thenhe realized that Rabi and Szilard did not consider Fermi’s reply a joke at all. Theycapitulated 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 providesone window on why Rabi and Szilard may have capitulated to Fermi’s intuition.Einstein provides further enlightenment. When faced with an abstruse mathematicaldemonstration that he considered overly abstract, Einstein would often tell his math-ematical collaborators, “I am convicted but not convinced” (Whitrow, 1967, p. 78).Einstein’s collaborator Ernest Straus explained that what Einstein meant was that “hecould no longer get out of agreeing that it was [logically] correct, but he did not feel thathe understood why it was so” (Whitrow, 1967, p. 78, emphasis added). This feelingwas, as Einstein said himself in his Autobiographical Notes, what differentiates under-standing from mere fantasizing:

Concepts and propositions get “meaning” or “content,” only through theirconnection with sense experiences. The connection of the latter to the formeris purely intuitive, not itself of a logical nature. The degree of certainty withwhich this connection, or intuitive linkage, can be undertaken, and nothingelse, 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 Reasonthat “The intellect can intuit nothing. The senses can think nothing. Only through theirunion can knowledge arise” (Arber, 1964, p. 124). Rabi and Szilard must have realizedthat their mathematical formalisms were like those that convicted but did not convinceEinstein—devoid of sensual connections to the physical world. They were thereforewilling to accept Fermi’s “intuitive” rejection of their logical arguments based on hisexamination of his “feel” for similar systems.

Why is this “feel” for the system so important? Wolfgang Pauli suggested that it isrelated to experiencing beauty. Only when there is a “congruence of preexisting internalimages of the human psyche with external objects and their behavior”, does one


experience “understanding in nature, together with the joy that man feels in under-standing” (Heisenberg, 1974, pp. 179–180). In order to shudder before beauty, it is notenough to be convicted. One must also be convinced. And one must be convinced—onemust feel—in order to act upon one’s knowledge.

Intuition is one of the reasons that scientists value elegance so highly. Elegantresults are like poems. They distill a huge amount of meaning into a very small spacewhile simultaneously making a large number of connections to other results. The abilityto concentrate meaning and connections maximizes understanding and its emotionalimpact, whereas simply following a logical path to a conclusion often yields neitherinsight, connections, surprises, nor joy. Science, being a human endeavor, requires thelatter characteristics to make it interesting and fun. Only when we feel that we know andknow 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 linkedthrough aesthetic considerations. My third argument is therefore that “emotion has alogic of its own”, to quote Cytowic (1993, Part 2, Chap. 7). Actually, I prefermathematician Stanislaw Ulam’s use of the term “meta-logic” to describe aestheticcognition. By “meta-logic”, Ulam meant that it is possible to understand things—andhere I use the term understand to mean suf� cient knowledge to act upon an object orthrough a process to obtain a desired end—in a completely sensual way independent oflinguistic, mathematical, or other formal logical structures. Another common term forthis form of understanding is “intuition”. Einstein is again instructive. In describing hisscienti� c aesthetics, Einstein maintained that, “A theory is the more impressive thegreater the simplicity of its premisses, the more different kinds of things it relates, andthe more extended its area of applicability” (Einstein, 1949, p. 31). The problem withlogical arguments that convict but do not convince is that they fail to satisfy Einstein’saesthetic 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 thepictures, feelings, and emotional states by which he solves problems so that the class ofsuch pictures, feelings, and emotions is tapped and similarities revealed.

This process of � nding similarities through such intuitive means is literally the wayin 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 picturesform sequences, each member of which calls forth another, this too is not yet“thinking.” When, however, a certain picture turns up in many such se-quences, then precisely by such return—it becomes an organizing element forsuch sequences, in that it connects sequences in themselves unrelated to eachother. Such an element becomes a concept. (Einstein, 1949, p. 7)

Thus, like Ulam, Einstein told several interviewers that he used pictorial images andkinesthetic feelings rather than words or equations when solving problems. He went sofar 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 throughrepeated analogical connections.


This feeling of analogy or association is necessary to place the set of impres-sions 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. Insome, 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: “Thereis”, he said,

a way of “writing” abstract ideas in a kind of shorthand which is almostorthogonal to the usual ways in which we communicate with each other bymeans 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, thegreatest 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, isthat we do not think about just anything; we think about problems. As Einstein himselfsaid at one point, de� ning a problem is often more valuable than solving it, because oncethe 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 thethings we need to consider is the possibility that the purpose of cognitive aesthetics isless to solve problems than to raise them. How, after all, do we know that we are facinga 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 gooddecision-making. We must feel that there is something wrong in order to be motivatedto study the problem, and the nature of the problem de� nition will come from our senseof the disjunction or anti-aesthetic quality of the situation as it exists. Thus, BertrandRussell once said, “In all the creative work that I have done, what has come � rst is aproblem, a puzzle involving discomfort” (Hutchinson, 1959, p. 19).

Mathematician Norbert Weiner provided an excellent example of how such feelingsof discomfort, or what he calls “hypnogogic images”, can actually become the organizingprinciple for thinking creatively, taking the place of muscular or visual images. At onepoint in his career, Weiner records that he so overworked himself that he developedpneumonia.

It was impossible for me to distinguish among my pain and the dif� culty inbreathing, the � apping of the window curtain, and certain as yet unresolvedparts of the potential problem on which I was working. I cannot say merely thatthe pain revealed itself as mathematical tension, or that the mathematicaltension symbolized itself as a pain: for the two were united too closely to makesuch a separation signi� cant. However, when I re� ected on this matter later, Ibecame aware of the possibility that almost any experience may act as atemporary symbol for a mathematical situation which has not yet been orga-nized and cleared up. I also came to see more de� nitely than I had before thatone of the chief motives driving me to mathematics was the discomfort or eventhe pain of an unresolved mathematical discord. I became more and moreconscious of the need to reduce such a discord to a semipermanent andrecognizable terms before I could release it and pass on to something else.Indeed, if there is any one quality which marks the competent mathematician


more than any other, I think it is the power to operate with temporaryemotional symbols and to organize out of them a semipermanent, recallablelanguage. If one is not able to do this, one is likely to � nd that his ideasevaporate from the sheer dif� culty of preserving them in an as yet unformu-lated shape. (Weiner, 1956, pp. 85–86)

Thus, Weiner and Russell tell us that we identify the existence of scienti� c problems bythe anti-aesthetic feelings of discomfort or even pain that they induce in us, and thespeci� c nature of these feelings become the genesis of creative thought.

The realization that we recognize problems through our anti-aesthetic response tothem provides an important clue as to how we go about de� ning the nature of theproblem and recognize its solution. The nature of the disjuncture between our aestheticexpectations and what we observe or think we know reveals the detailed characteristicsof 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 thelogic of disproof that so many philosophers make. The recognition of the existence ofa problem (i.e. the disproof of the existing problem-solving model or demonstration ofthe inadequacy of available data) creates the context of discovery by generating a speci� cdisjuncture between the known and the unknown. The speci� c nature of this disjuncturede� nes not only the speci� c outlines of the problem to be resolved, but de� nes theaesthetic criteria that must be satis� ed by a solution and creates the aesthetic angstrequired to motivate the search for a solution. Thus, scientists with the most rigorouslydeveloped sense of scienti� c aesthetics are often the most successful scientists and manyof the most productive periods in the history of science are characterized by the kindsof aesthetic con� icts that are represented by the Ptolemaic–Copernican con� ict overcircular and elliptical orbits in astronomy or the Bohr–Einstein con� ict over the statusof statistical versus causal approaches to physics. Changes in scienti� c aesthetics gohand in hand with major shifts in both the philosophy of science and the actualmechanics 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 logicof research, however, and actually informs it. Thus the formal results of logic stem fromthe informal insights of aesthetic intuition. That there is a necessary and important linkbetween the two is undeniable: experience demonstrates that intuitions can be translatedinto formal logical or linguistic terms. The reasoning here is simple. We all know thatclear writing re� ects clear thinking. Ideas that are not well organized in the mind do notcome out on paper in a clear fashion. The same thing is true of scienti� c ideas. Poorlyconstructed hypotheses yield poorly organized research. Moreover, the translation froman hypothesis to an experiment, or from one language into another, can only beachieved if there is, in fact, a correspondence between the nature of the ideas expressedin the two languages. Thus, idioms are often untranslatable, just as some scienti� cconcepts have no physical equivalents and are therefore untestable. These everydayexamples provide the basis for arguing that there must be a logic to aesthetic cognitionbecause the results of such cogitation are translatable into formal linguistic andmathematical terms. Were no logic inherent in aesthetic cognition, then it is dif� cult toimagine how logical results would result from its machinations.


The fact that the results of aesthetic cognition must be translated into formallanguages in order to be communicated to other people explains why intuition haslargely been ignored by philosophers. The mental images, physical and muscularfeelings, emotions, and intuitions that Einstein, Ulam, Weiner and the others describeare what Michael Polanyi has called “personal knowledge” (Polanyi, 1958). Insightarrives through private mental means using mental “languages” that are often inventedfor individual, personal use. The scientist feels that he knows and may even know whathe feels, but feelings are not capable of direct communication to other people. So, it isnecessary to translate personal knowledge into public formulations such as words,equations, and diagrams. I am told by physicists and mathematicians at CalTech andMIT that one of the major dif� culties encountered by their students is making theconverse translation: students who cannot translate equations and words back into theimages and feelings that motivated their invention are unable to understand the contentof their courses. Like such students, many philosophers have understandably focused onthe communicable formulations of scienti� c ideas rather than their personal and privatecognitive manifestations, but have thereby missed both the reasons for the invention ofthe formal results and the sensual meanings of their content.

My fourth argument is therefore that there is a fundamental distinction between thecreative stage of scienti� c thinking that I have been describing and its translation intoa form acceptable for communicating insight to other people. The problem that everyscientist must address is how to move from the private sensory feelings he uses forthinking to the public languages we share for communicating what we think. Only whenwe explicitly recognize that the “tools of thinking” and the “tools of communication” aredistinct can we understand the intimate, yet tenuous, connection between thought andlanguage, imagination and logic.

Many scientists have commented on the distinction between the private, nonverbalphase of scienti� c problem solving and the translation of ideas into language. Ulam, asI noted above, said that he used “visual algorithms” for thinking, which he consideredto be a “kind of shorthand which is almost orthogonal to the usual ways in which wecommunicate with each other” (Ulam, 1976, p. 183). He would use his images to geta 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, “incertain problems that I have done, it was necessary to continue the development of thepicture as the method, before the mathematics could really be done”. And Einsteinwrote that his thinking was totally visual and sensual, and that mathematics and logicwere performed explicitly as secondary steps: “Conventional words or other signs[presumably mathematical ones] have to be sought for laboriously only in a secondarystage, when the associative play [between images] already referred to is suf� cientlyestablished and can be reproduced at will” (Hadamard, 1945, pp. 142–143). Einsteinexplained 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 twotriple 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 wasmerely a later formulation of the subject matter, just a question of how thething could best be written … but in this process they [the ideas] did not growout of any manipulation of axioms. (Wertheimer, 1959, p. 228, n. 7)

Metallurgist Cyril Stanley Smith of MIT had the same experience as Einstein: “The


stage of discovery was entirely sensual and mathematics was only necessary to be ableto communicate with other people” (Smith, 1981, pp. 353–354). Werner Heisenbergwrote similarly that in the revolution in physics he helped to create,“mathematics.… played only a subordinate, secondary role. Mathematics is the form inwhich we express our understanding of nature; but it is not the content of thatunderstanding” (Heisenberg, 1974, p. 146).

Biologists note the same translation problem. Nobel laureate Barbara McClintocksaid, “you work with so-called scienti� c methods to put it into their frame after youknow” (Keller, 1983, p. 203). Agnes Arber also notes that the records kept by scientistsare things “very remote from the original”, a mere “translation of his perception intoanother medium” (Arber, 1964, p. 67). The most dif� cult problem that must beaddressed in this translation process for Arber is that words and equations express onlylinear 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 singleline … 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 wordsor 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 theliterally physical embodiment of the actual process of creation.

The most frustrating part of aesthetic cognition for scientists is that it may yieldinsights that are not immediately amenable to translation. Friedrich Gauss oftencomplained that “I have had my results for a long time; but I do not yet know how Iam to arrive at them” (Beveridge, 1950, p. 145). Lord Kelvin similarly “had at times todevise 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 suchas the four-color map theorem or Fermat’s last theorem, the results of intuition may becorrect but the translation into linear forms of reasoning so complicated that it may takedecades or even centuries for the conversion to become possible. These problemssuggest that a more in-depth understanding of the meta-logic of aesthetic cognition mayprovide 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 oflogic at work in every creative act, whether in science or in any other subject, and thoseare the meta-logical forms of thinking that are embedded in what we call intuitivethought and the formal logical forms in which we communicate. Thus, there aremeta-logical “tools for thinking” and logical “tools for communicating” that needseparate philosophical approaches (Root-Bernstein & Root-Bernstein, 1999). One rea-son that the philosophy of science has failed to come to grips with the creative aspectsof the scienti� c enterprise is that it has thus far focused mainly on the logic behindpublic tools for communicating rather than on the meta-logic of private tools forthinking.

Conclusions: beyond the psychology of discovery

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


Thus, this article identi� es a phenomenon that de� nes a new area for philosophicalresearch with many interesting aspects.

Perhaps the most important implication of aesthetic cognition is that it underminesa widely held belief among some philosophers, logicians, and linguists that, that whichcannot be said, cannot be thought. To take such a position is to ignore a vast literatureon nonlinguistic forms of thinking that include visual and other forms of imaging,kinesthetic thinking, sensual thinking, modeling, and the use of emotions and intuitionby scientists and mathematicians (e.g. Weiskrantz, 1988). It is clear that most creativescientists understand things before they are able to express what they know in anyformal language, even to themselves. Thus, to understand the nature of thinking,we must abandon the preconception that thinking must involve words or otherlogical symbols and accept that images, feelings, sensations, and emotions also embodylogics.

Aesthetic cognition therefore makes the body part of the mind, creating newapproaches 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 distinctionbetween mind and body is quite impossible. Feeling must be a form of thinking andthinking cannot be divorced from feeling. The very best scientists seem to be telling usthat 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 ofideas, 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-logicto describe the nature of sensual, aesthetic, emotional thinking. The fact that aestheticshas had a formal presence in philosophy since its origins, and that the aesthetics of artand the aesthetics of science appear to be very similar, at least in outline (Root-Bernstein, 1997), suggests that such a formal meta-logic is possible.

Undoubtedly the evolution of an aesthetic meta-logic will be gradual. It will growand diverge just as formal mathematical logic has done. And undoubtedly there will bethe same inability to create an unambiguous, noncontradictory meta-logic as there hasbeen for mathematical logic. But the implications of formalizing such a meta-logic mightbe as important for promoting creative or intuitive thinking as logic itself has been forproviding clear tests of reasoning. Working hand in hand, the two might be synergistic.

One � nal note: the concept of aesthetic cognition may have extremely importantimplications for devising arti� cial intelligence machines. Such machines can, at present,convict, but never convince. They are currently unable to invent problems; cannotchoose a problem to work on; have no means of evaluating which of several problemsis most likely to be interesting; cannot bring the kind of intuitive physical understandingthat 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 butfrom meta-logical or aesthetic ones. Thus, arti� cial intelligence will fail to provideinsights into human thinking or model its capabilities until aesthetic cognition is itselfunderstood suf� ciently to be modeled and implemented by computers.

What we must always remember is that behind every human action there ismotivation, and that motivations are always based in the aesthetic sensibility andemotional feelings. Far from being antithetical to philosophy, the meta-logic of suchmotivations must become part of it. “Can you understand that it is not only scienti� cresults that are the recompense for all this trouble and annoyance,” wrote ethologistKonrad Lorenz of his love of animals, “but more, much, much more?” (Konrad Lorenz,


1952, p. 9). Is a philosophy of science that cannot account for why or how scientists doscience worthy of the name philosophy?

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Note on contributor

Robert Root-Bernstein is a Professor of Physiology, an historian and philosopher of science, and an amateurartist 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]

Aesthetic Cognition

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