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Aesthetics: A Cognitive AccountAuthor(s): Robert DixonSource: Leonardo, Vol. 19, No. 3 (1986), pp. 237-240Published by: The MIT PressStable URL: http://www.jstor.org/stable/1578243

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Aesthetics:A Cognitive Account

Robert DixonAbstract-This essay recalls the original meaning of aesthetic as relating to objects and acts of senseperceptionas opposed o objectsand acts of formalknowledge.Thisdistinction s thenapplied o theproblemof definingart, so as to providean approachalongfundamental ognitive ines. Contemporaryrends n theteachingof mathematics,which often also isolate sense perception rom formalknowledge,are reviewed.Newdevelopmentsn mathematicswhichre-emphasize heimportanceof sensoryperception o mathematicsare then examined. The authorarguesthat a unifyingapproach o aesthetics,art and mathematics s calledfor.

I. INTRODUCTIONTheoriginalmeaningof aesthetic referredto sense perception in general,and not toany special qualities or categories ofartifactsor of naturalphenomena.That isto say, aesthetic = sensible [1].In contemporary usage, sensible isfrequently confused with reasonable-with which, however, it should moreproperlybe contrasted-while aesthetic scommonly regardedas denoting ideas ofbeauty and/or fine art.The latter corruption dates from theeighteenth century, when Baumgartenand Kant initiated a tradition ofphilosophical ideas about evaluativejudgements [2]. I would argue that thisproved to be unfortunate for two mainreasons: firstly, it obscured the originalmeaning; secondly, its restriction ofmeaning has ultimately led to confusion.

Reference to current Aesthetics [3] willshow that the philosopher's question ofbeauty has tended to become a study ofart criticism, which in turn reliesexclusively on the paradigm of fine art.Even if the threatened circularityof thisdevelopment is not complete, the two-fold loss of generalityof meaningleads toa loss of usefulness.The Shorter OxfordEnglish Dictionary[4] describes the original meaning ofaesthetic as "obsolete", yet it would seemto correspond to colloquial usage: "Thegarden gate is aesthetically pleasing aswell as being useful for keepingthe sheepout." Also, we have the precise usage ofmodern derivatives to guide us: e.g.anaesthetics, concerned with the controlof sensation; and kinaesthetics, con-cernedwith the sense of musculareffort,

Robert Dixon (computer artist), Department ofDesign Research, Royal College of Art, KensingtonGore, London, SW7, U.K.Received 20 May 1984.

through which we obtain our feeling ofweight, force and movement.I am not advocating a returnto originalusage so muchas warningagainstunclearusage of either art or aesthetic. Myconcern is to focus attention on thosecognitive distinctions that underlie theolder and/or fundamentalmeanings.ForI believe it is in these terms that thepresent split, as well as any futureunion,of art and science can be understood.

II. SENSE PERCEPTIONWe receive information about states ofthe world and our own body from thesense organs. Without them no inform-ation could pass to us, without sense therecould be no knowledge: all knowledge isconstructed from sense experience [5].This is both obvious and yet easily

overlooked. Even the purestmathematicsmakes 'sense' to us, as I shall arguelater.Formal accounts of knowledge, how-ever, as in mathematics, physics, chem-istry and so on, describe abstractsystemsor objective worlds, not ourexperienceofsuch things. Indeed, by definition,personal experience in itself is absentfrom scientific objectivity and for goodreasons. But it should be realised that thisdetachment is a potentially destructiveillusion [6]. It is the postulated objectivityof an incomplete epistemology.The cognitive significance of the termaesthetic is as a term of cleavage,contrasting with formal knowledge. Thesame contrast is marked by the distinc-tion between sense and reason, andbetween phenomena and theory. Thisdivision of human intelligence is remin-iscent of the much-publicizedwork with'split brain' patients, in whom the rightand left hemispheres of the brain hadbeen disconnected from each other bysurgery. Sperry [7], summarizing adecade of this work,generalizesthat right

and left hemispheric functions contrastwith each other in terms of a recognizableand broad division or polarity ofcognitive skills.Cross [8] links this polarity withpresent attempts to identify design as away of knowing. He describes howcontemporary education emphasizesformal modes of intelligenceat its upperlevels, while placing informal modeswithin a developmental schema (such asPiaget's) at the lower levels. There is, heargues, a need to discover the fullerimportance of informal modes of cog-nition. Our capacities for manipulatingobjects and images and for pattern-recognitionareprimaryways of knowing,not just PrimarySchool activities.The significance of objects and acts ofsense perception for higher levels ofknowledge may be summarized asfollows:

1. Formal skills depend upon aestheticskills insofar as pattern-recognition is anecessary part of the use of symbols,whether visual or auditory.2. It is an educational truism that theacquisition of abstract understandingfollows from a grounding in concreteexperience. 'Seeing' (sensing) is not onlybelieving, it is also understanding.3. Validation in science requiresobservation and experiment, which ex-plains the proposition that theory refersultimately to phenomena. (The equiva-lent relation in mathematics will beexamined in more detail below.)4. The objects of technology demon-strate and record knowledge. The em-phasis we put upon formal expressionand documentation often belies the valueof, and ultimate dependence upon,concrete expression.5. Smith [9] offers a sustaineddiscussion of the proposition thataesthetics precedes technology, which inturn precedes science. Using the historyof metallurgy, he traces each major

? 1986 ISASTPergamon Journals Ltd.Printed in Great Britain.0024-094X/86 $3.00+0.00 LEONARDO, Vol. 19, No. 3, pp. 237-240, 1986 237

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technologicaldiscoverybackto an earliercuriosity in the sensible properties ofmaterials.

III. ARTThe same pattern of semantic collapsewhich associates aesthetic with art and

beauty is likely to be carried throughwhen it comes to interpretingthe wordart. Just as aesthetic comes to denote aspecial subset of sensible phenomena, soart comes to denote a special subset ofartworks. The descriptive term becomesevaluative. To avoid confusion, I will usethe capitalized Art to denote suchrestrictedconceptions of art.A recent (U.K.) Department of Educa-tion and Science reportentitled AestheticDevelopment[10] neatly and unwittinglyencapsulates this common loss of mean-ing. The report comes from the Assess-ment of Performance Unit (APU), andthe authorsultimatelyaddressthemselvesto the problem of assessment in thoseareas of curriculumcurrentlyassociatedwith the word aesthetic, the Arts.

Having ignored the original meaningof aesthetic, the APU first considers,andthen lays aside as too problematic, thesubject of beauty, before settling on thesubject of art and the artistic. But thisexplicit avoidance of the issue of valuejudgement only makesway for its implicitinclusion with the Arts.Although the APU says that "by thearts, here, we mean all areas of art anddesign, dance, drama, literature andmusic" [11], it is clear that they restrictthemselves to what I am here calling theArts. Here is a complete list of theexamples used in the report by way ofillustration: Picasso's Guernica;Impres-sionism; Fauvism; Cubism; Surrealism;Abstract Expressionism;High Realism;aBill Gibb garment;a Charles Mackintoshchair; Gershwin's "Summer Time";Elizabethan court dance; nineteenth-centuryAmericanfolk dance;Romeo andJuliet; Monet; Japanese prints;a Chopinwaltz; the paintings of Nash andNevinson; the poems of Owen.The patterns of evaluation governingthe inclusion or exclusion of various artforms from the Arts arefamiliarenough,even if the underlying logic proves moredifficult to obtain. But let us assume thatthe Arts form a subsclass of the arts and

proceed, in an effort to relate art toaesthetics, to ask what the more fund-amental concept implies.If we start from the other direction,from a position of wider meaning, andmove towards narrowing the definition,what do we find?

art [12]: 1. "practical skill, or itsapplication, guided byprinciples";2. "human skill and agency(opposed to nature)";3. "application of skill toproduction of beauty(especially visual beauty)and works of creativeimagination, as in finearts";4. "branch of learning..."

Although they point in differentdirections, these four definitionsdo agreeon the element of human agency. Theinclusion of skill and learning threatensto add questions of evaluation to adescriptive category of artifacts. Such acompound meaning would exclude thepossibility of unskillful art and raisequestions of degree of skill and point ofview. The definitions do not agree,however, as to whether the artifact ispractical or theoretical, aesthetic orformal.In order to draw useful and funda-mental distinctions and avoid having artembraceall acts and artifacts in the wordart, I propose focusing upon artifactsthatspecifically or largely addressour senses.This is how a working printer woulddistinguish between artwork and text. Ofcourse, the art of typography is instru-mental in making and improving lingui-stic communication; but the informationcarried by the text is formally encoded,whereas pictures are immediate. Anarchaeologist would classify items un-earthed from an ancient civilization

similarly,separatingartfromengineering,say, in the broadest possible way.I suggest that the concept of artencompasses all possible media, styles,contents, standards,ideologies, qualities,moods, methods, and functions. It mustinclude modern advertising images [13]along with the prehistoric bison ofLascaux [14], technical diagrams withsensual reveries, canonic icons withpersonal doodles, patterns with pictures,and so on. An artifactis to be classifiedasart on the basis of cognitive category andnot on any question of value or purpose.Accordingly, a mathematical diagram isan artwork (Fig. 1), whereas a formulaisnot.

IV. MATHEMATICSIt is perhaps mathematics, more thanany other discipline, which so keenlydraws the line between symbol and icon,between logic and intuition, betweenreason and sense. Students of elementarygeometry, for example, are taught torecognize valid arguments based onformal definitions as distinct from

impressions arising from diagrams. In-deed, the whole process of mathematicallearning, both historically and individ-ually, seems to be one of isolatingmathematical meaning within its formalsymbolism.The chief gain in this process isincreased generality and greater logicalprecision. The price paid, however, is aloss of immediacy.Mathematics teaches us how to reasonwith numbers and magnitude. It is

Fig. 1. SphericalSymmetry, computer-generated rtworkmass-reproduced s alithographpostcard.The subject is sphericalsymmetry,the icosahedraldocecahedral group.

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therefore inherently abstract and logicalin purpose. Yet abstraction impliesparticular and concrete origins. More-over, if mathematics is to serve animmediate purpose, then this lies in itsapplicability to phenomena, most in-fluentially through the sciences, but alsothrough the arts.The very idea of mathematics as aseparate departmentof knowledge beliesits origins and purposes. The develop-ment of mathematical ideas is inextri-cably bound up with concrete problems.A history of mathematics-Boyer [15],for example-is also a story of problemsset and solved in such practical activitiesas weights and measure, time and motion,accountancy, surveying, calendrics, en-gineering, architecture, navigation, as-tronomy, physics, gambling and pers-pective painting.The present state of mathematicalteaching clearly reflects a tendency toisolate a body of exclusively mathe-matical knowledge. There is therefore acharacteristic emphasis on symbolic,logical and abstract aspects. The need todivorce reason from sense has oftenseemed to be an importantmathematicalgoal. Hahn [16] gives severalexamplesofthe pitfalls of intuitive and visualapproaches to formal mathematics, thusemphasizingthe care needed in obtaininglogically valid arguments.But it is equallyclear to anyone who has ever learnt ortaughtmathematics hat concreteexamplesand an intuitive grasp are necessary forabstract understanding.Kline [17]gives a detailedhistoryof thedrive to isolate a body of purely logicalmathematics and examines limitationsinherent in so doing. His evidenceincludes not only those explicit limitsdiscovered by such logicians as Russelland Godel but also, and perhaps moresignificantly, numerous admissions bymathematicians themselves as to the vitalrole played by physical intuition inguiding and testing mathematical dev-elopment.Kitcher [18] challenges the aprioristaccount of mathematical propositionscustomarily given by philosophers andsketches an alternative in which mathe-matical knowledge is ultimately based insense-experience. He does not offer adetailed account of the sensory links, butdoes demonstrate effectively the histori-cal and social dimensions of mathe-matical learning.Davis and Hersh [19] question atraditional myth of mathematicsas purelogic and call for a more open-mindedattitude to its nature. Their manyexamples bringout the diversityof stylesin mathematical thinking and illustrate

well how logic and intuition interact.Stewart also observes this confusedregard for the relation between logicaland intuitive aspects of mathematics:although "one of the more noticeableaspects of modern mathematics is atendency to become increasinglyabstract" [20], most mathematicians"think in pictures; their intuition isgeometrical" [21]. He states that it isintuition which enables mathematiciansto "see that a theorem is true, withoutgiving a formal proof, and on the basis oftheir vision produce a proof that works"[22].I have no doubt that increasingspecialization and departmentaldemarc-ation give rise to a loss of unity.Optimistically, Bohm writes that "thesharp break between abstract logicalthought and concrete immediate experi-ence that has pervadedour culturefor solong, need no longerbe maintained"[23].Within his holistic perspective theendemic 'fragmentation' is a product ofthought and has no basis in reality.A growing tradition of work in thetwentieth century explicitly re-empha-sizes the primary importance of sensoryexprience and natural phenomena tomathematics. Two contemporary geo-meters addressing this issue are BenoitMandelbrot and Rene Thom, whodemonstrateindifferentways the creativeand illustrative power of visual thinkingfor mathematics.Both hail astheirmodelthe work of D'Arcy Thompson [24], inwhich naturalmorphology is the objectofmathematical investigation.

Mandelbrot makes extensive use ofcomputer graphics in the developmentofhis fractal theory (fractalform= a featureat every scale) [25], noting that

there s noquestionhatanyattemptoillustrategeometryinvolves a basicfallacy. For example, a straight line is,strictly speaking, unbounded and in-finitely thin and smooth, while anyillustration is unavoidably of finitelength, of positive thickness, androughedged. Nevertheless, a rough evocativedrawingof lines is felt by many o beusefulandby some to be necessarynorder o buildup intuition ndhelp nthe search for a proof. And of course,when it comes to providingageometricmodelof athread, roughdrawingsinfact more adequate ... It suffices for allpractical purposes that a geometricconcept and its image should fit withina certain range of characteristic sizes[26].

Mandelbrot expressesa passionate andhigh regard for sense perception. Hebalances the usefulness of mathematical

analysis with a clear statement that "theeye has enormous powers of integrationand discrimination"[27]. Indeeditwouldbe fair to say that his work is as much acontribution to aesthetics as it is tomathematics. He is as prepared todescribe his work a 'vision' as to call ittheory.Thom's catastrophe theory developsideas fromsingularity heoryand different-ial topology to address problems inmorphogenesis. Concrete applicationsare demonstrated in areas as different asembryology and sociology [28].Thom criticizes the excessive abstrac-tion of 'modern' mathematics teachingand challengesthe proposed set-theoreticbasis [29]. He deploresthe consequentde-emphasis of geometry in the elementarycurriculum and insiststhat "geometryis anatural and possibly irreplaceable inter-mediary between ordinary language andmathematical formalism" [30]. He pres-ses his point firmlywith the reminder hat"according to a now-forgotten etymo-logy, a theorem is above all the objectof avision" [31].As well as affirming the fundamentalplace of sense perception in epistem-ology, twentieth-centurywork on naturalmorphology greatly restores the balanceof mind evident in that ancient insight,traditionally ascribed to Pythagoras, ofmatching perceived patternswith numer-ical patterns. Key episodes in thisapproach, such as musical harmony andpictorial perspective, provide clear anti-dotes to the dominant abstraction [32] ofour school mathematics. As a finalexample of the unifying approach tomathematics and aesthetics, it might beworth citing Smith [33] and Mandelbrot[34], who independently of each otherobserved structural hierarchy both inartworks and in natural forms and thusbrought mathematics into the study ofpictorial composition and visual texture,and vice versa.

V. CONCLUSIONMathematics provides a fitting context

in which to define visual art across thecurriculum. This is done by drawingthecognitive distinction between, for ex-ample, picture versus text or betweenform versusformula, and so on. Theoriesof learningrecognizethis samedivisionasbeing between primaryversus secondaryways of knowing. Secondary ways ofknowing involve encoded information,whereas primary ways of knowing areaesthetic, in the original meaning of thisword, denoting that which is sensible asopposed to that which is reasonable.

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REFERENCES AND NOTES1. Chambers TwentiethCentury Dictionary(Edinburgh: 1972) gives three distinctmeanings for aesthetic: (a) originallyrelating to perception by the senses; (b)generally relating to possessing, orpretending to, a sense of beauty; (c)artistic or affecting to be artistic.2. Anthony Flew, A Dictionary of Philo-sophy(London:Pan, 1979).Kantstronglydisapprovedof this corruption,however.3. Flew [2], for example, or HaroldOsborne, Aesthetics (Oxford: OxfordUniversity Press, 1972).4. The Shorter Oxford English Dictionarygives: "Aesthetic ... things perceptibleby the senses, as opposed to thingsthinkable or immaterial. Misapplied inGerman by Baumgartento 'criticism oftaste', and so used in English since1830..."5. It is instructive to realise that there aremore than the proverbial five senses:sight, hearing, smell, taste and touch; weshould also note kinaesthetics, the senseof heat, the sense of pain, the sense ofgravitationalorientation,sense of hunger,sense of thirst, and so on.6. R.D. Laing, The Voice of Experience(Harmondsworth: Penguin, 1983).7. R.W. Sperry, "Lateral Specialization inthe Surgically Separated Hemispheres",in The Neurosciences:Third Study Pro-gramme, F. O. Schmitt and F.G.Worden, eds. (Cambridge, MA: MITPress, 1975).8. Nigel Cross, "Designerly Ways of

Knowing", Design Studies 3, No. 4(1982).9. Cyril Stanley Smith, In Search ofStructure (Cambridge, MA: MIT Press,1982).10. U.K. Department of Education,Aesthet-ic Development, 1983.11. Ref. [10] p. 2.12. Chambers TwentiethCenturyDictionary[1].13. John Berger, Ways of Seeing (Har-mondsworth, Middlesex: Pelican, 1972).14. Ernst Gombrich, The Story of Art(London: Phaidon, 1964).15. Carl B. Boyer,A History of Mathematics(New York: Wiley, 1968).16. Hans Hahn, "The Crisis in Intuition", inThe Worldof Mathematics Vol. 3, J.R.Newman, ed. (New York: Simon &Schuster, 1956).17. Morris Kline, Mathematics-The Loss ofCertainty (Oxford: Oxford UniversityPress, 1980).18. Philip Kitcher, The Nature of Mathe-matical Knowledge (Oxford: OxfordUniversity Press, 1983).19. Philip J. Davis and Reuben Hersh, TheMathematical Experience (Brighton:Harvester, 1981).20. Ian Stewart, Concepts of ModernMathe-matics (Harmondsworth, Middlesex:Pelican, 1975) p. 1.21. Stewart [20] p. 5.22. Stewart [20] p. 4.23. David Bohm, Wholenessand the Impli-cate Order(London: Ark, 1983) p. 203.24. D'Arcy Wentworth Thompson, OnGrowth and Form (Cambridge: 1917,1942).

25. A fractal curve is one which has infinitelymany bends, and a fractal surface is onewhich has infinitely many hills andvalleys. Typically, these features areexhibited at everyscale of magnification;and nature, according to Mandelbrot,abounds in fractal forms. Thus, forexample, coastlines have promontoriesand inlets ranging from the size ofcontinents down to microscopic irregu-larities.26. Benoit B. Mandelbrot, The FractalNature of Geometry (San Francisco:Freeman, 1982) p. 22.27. Benoit B. Mandelbrot, Fractals (SanFrancisco: Freeman, 1977)p. 24.28. Ren6 Thom, Structural Stability andMorphogenesis Reading, MA:Benjamin,1972).29. Ren6 Thom, "'Modern' Mathematics:An Educational and PhilosophicalError?", American Scientist 59 (1971).Thom's own work derives inspirationfrom such simple phenomena as lightcaustics in coffee cups and wavesbreaking on the beach. See ChristopherZeeman, Catastrophe Theory (Reading,MA: Addison-Wesley, 1977); and P.T.Saunders,AnIntroduction o CatastropheTheory (Cambridge: Cambridge Uni-versity Press, 1980).30. Thom [29] p. 698.31. Thom [29] p. 697.32. Seymour Papert, Mindstorms(Brighton:Harvester, 1982).33. Smith [9].34. Mandelbrot [26].

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