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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 Dixon

Abstract-This essay recalls the original meaning of aesthetic as relating to objects and acts of sense perception as opposed to objects and acts of formal knowledge. This distinction is then applied to the problem of defining art, so as to provide an approach along fundamental cognitive lines. Contemporary trends in the teaching of mathematics, which often also isolate sense perception from formal knowledge, are reviewed. New developments in mathematics which re-emphasize the importance of sensory perception to mathematics are then examined. The author argues that a unifying approach to aesthetics, art and mathematics is called for.

I. INTRODUCTION

The original meaning of aesthetic referred to sense perception in general, and not to any special qualities or categories of artifacts or of natural phenomena. That is to say, aesthetic = sensible [1].

In contemporary usage, sensible is frequently confused with reasonable- with which, however, it should more properly be contrasted-while aesthetic is commonly regarded as denoting ideas of beauty and/or fine art.

The latter corruption dates from the eighteenth century, when Baumgarten and Kant initiated a tradition of philosophical ideas about evaluative judgements [2]. I would argue that this proved to be unfortunate for two main reasons: firstly, it obscured the original meaning; secondly, its restriction of meaning has ultimately led to confusion.

Reference to current Aesthetics [3] will show that the philosopher's question of beauty has tended to become a study of art criticism, which in turn relies exclusively on the paradigm of fine art. Even if the threatened circularity of this development is not complete, the two- fold loss of generality of meaning leads to a loss of usefulness.

The Shorter Oxford English Dictionary [4] describes the original meaning of aesthetic as "obsolete", yet it would seem to correspond to colloquial usage: "The garden gate is aesthetically pleasing as well as being useful for keeping the sheep out." Also, we have the precise usage of modern derivatives to guide us: e.g. anaesthetics, concerned with the control of sensation; and kinaesthetics, con- cerned with the sense of muscular effort,

Robert Dixon (computer artist), Department of Design Research, Royal College of Art, Kensington Gore, London, SW7, U.K.

Received 20 May 1984.

through which we obtain our feeling of weight, force and movement.

I am not advocating a return to original usage so much as warning against unclear usage of either art or aesthetic. My concern is to focus attention on those cognitive distinctions that underlie the older and/or fundamental meanings. For I believe it is in these terms that the present split, as well as any future union, of art and science can be understood.

II. SENSE PERCEPTION

We receive information about states of the world and our own body from the sense organs. Without them no inform- ation could pass to us, without sense there could be no knowledge: all knowledge is constructed from sense experience [5]. This is both obvious and yet easily overlooked. Even the purest mathematics makes 'sense' to us, as I shall argue later.

Formal accounts of knowledge, how- ever, as in mathematics, physics, chem- istry and so on, describe abstract systems or objective worlds, not our experience of such things. Indeed, by definition, personal experience in itself is absent from scientific objectivity and for good reasons. But it should be realised that this detachment is a potentially destructive illusion [6]. It is the postulated objectivity of an incomplete epistemology.

The cognitive significance of the term aesthetic is as a term of cleavage, contrasting with formal knowledge. The same contrast is marked by the distinc- tion between sense and reason, and between phenomena and theory. This division of human intelligence is remin- iscent of the much-publicized work with 'split brain' patients, in whom the right and left hemispheres of the brain had been disconnected from each other by surgery. Sperry [7], summarizing a decade of this work, generalizes that right

and left hemispheric functions contrast with each other in terms of a recognizable and broad division or polarity of cognitive skills.

Cross [8] links this polarity with present attempts to identify design as a way of knowing. He describes how contemporary education emphasizes formal modes of intelligence at its upper levels, while placing informal modes within a developmental schema (such as Piaget's) at the lower levels. There is, he argues, a need to discover the fuller importance of informal modes of cog- nition. Our capacities for manipulating objects and images and for pattern- recognition are primary ways of knowing, not just Primary School activities.

The significance of objects and acts of sense perception for higher levels of knowledge may be summarized as follows:

1. Formal skills depend upon aesthetic skills insofar as pattern-recognition is a necessary part of the use of symbols, whether visual or auditory.

2. It is an educational truism that the acquisition of abstract understanding follows from a grounding in concrete experience. 'Seeing' (sensing) is not only believing, it is also understanding.

3. Validation in science requires observation and experiment, which ex- plains the proposition that theory refers ultimately to phenomena. (The equiva- lent relation in mathematics will be examined in more detail below.)

4. The objects of technology demon- strate and record knowledge. The em- phasis we put upon formal expression and documentation often belies the value of, and ultimate dependence upon, concrete expression.

5. Smith [9] offers a sustained discussion of the proposition that aesthetics precedes technology, which in turn precedes science. Using the history of metallurgy, he traces each major

? 1986 ISAST Pergamon 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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technological discovery back to an earlier

curiosity in the sensible properties of materials.

III. ART

The same pattern of semantic collapse which associates aesthetic with art and beauty is likely to be carried through when it comes to interpreting the word art. Just as aesthetic comes to denote a special subset of sensible phenomena, so art comes to denote a special subset of artworks. The descriptive term becomes evaluative. To avoid confusion, I will use the capitalized Art to denote such restricted conceptions of art.

A recent (U.K.) Department of Educa- tion and Science report entitled Aesthetic Development [10] neatly and unwittingly encapsulates this common loss of mean- ing. The report comes from the Assess- ment of Performance Unit (APU), and the authors ultimately address themselves to the problem of assessment in those areas of curriculum currently associated with the word aesthetic, the Arts.

Having ignored the original meaning of aesthetic, the APU first considers, and then lays aside as too problematic, the subject of beauty, before settling on the subject of art and the artistic. But this explicit avoidance of the issue of value judgement only makes way for its implicit inclusion with the Arts.

Although the APU says that "by the arts, here, we mean all areas of art and design, dance, drama, literature and music" [11], it is clear that they restrict themselves to what I am here calling the Arts. Here is a complete list of the

examples used in the report by way of illustration: Picasso's Guernica; Impres- sionism; Fauvism; Cubism; Surrealism; Abstract Expressionism; High Realism; a Bill Gibb garment; a Charles Mackintosh chair; Gershwin's "Summer Time"; Elizabethan court dance; nineteenth- century American folk dance; Romeo and Juliet; Monet; Japanese prints; a Chopin waltz; the paintings of Nash and Nevinson; the poems of Owen.

The patterns of evaluation governing the inclusion or exclusion of various art forms from the Arts are familiar enough, even if the underlying logic proves more difficult to obtain. But let us assume that the Arts form a subsclass of the arts and proceed, in an effort to relate art to aesthetics, to ask what the more fund- amental concept implies.

If we start from the other direction, from a position of wider meaning, and move towards narrowing the definition, what do we find?

art [12]: 1. "practical skill, or its

application, guided by principles";

2. "human skill and agency (opposed to nature)";

3. "application of skill to production of beauty (especially visual beauty) and works of creative imagination, as in fine arts";

4. "branch of learning..."

Although they point in different directions, these four definitions do agree on the element of human agency. The inclusion of skill and learning threatens to add questions of evaluation to a

descriptive category of artifacts. Such a

compound meaning would exclude the

possibility of unskillful art and raise questions of degree of skill and point of view. The definitions do not agree, however, as to whether the artifact is practical or theoretical, aesthetic or formal.

In order to draw useful and funda- mental distinctions and avoid having art embrace all acts and artifacts in the word art, I propose focusing upon artifacts that

specifically or largely address our senses. This is how a working printer would distinguish between artwork and text. Of course, the art of typography is instru- mental in making and improving lingui- stic communication; but the information carried by the text is formally encoded, whereas pictures are immediate. An

archaeologist would classify items un- earthed from an ancient civilization

similarly, separating art from engineering, say, in the broadest possible way.

I suggest that the concept of art

encompasses all possible media, styles, contents, standards, ideologies, qualities, moods, methods, and functions. It must include modern advertising images [13] along with the prehistoric bison of Lascaux [14], technical diagrams with sensual reveries, canonic icons with

personal doodles, patterns with pictures, and so on. An artifact is to be classified as art on the basis of cognitive category and not on any question of value or purpose. Accordingly, a mathematical diagram is an artwork (Fig. 1), whereas a formula is not.

IV. MATHEMATICS

It is perhaps mathematics, more than any other discipline, which so keenly draws the line between symbol and icon, between logic and intuition, between reason and sense. Students of elementary geometry, for example, are taught to

recognize valid arguments based on formal definitions as distinct from

impressions arising from diagrams. In- deed, the whole process of mathematical learning, both historically and individ- ually, seems to be one of isolating mathematical meaning within its formal symbolism.

The chief gain in this process is increased generality and greater logical precision. The price paid, however, is a loss of immediacy.

Mathematics teaches us how to reason with numbers and magnitude. It is

Fig. 1. Spherical Symmetry, computer-generated artwork mass-reproduced as a lithograph postcard. The subject is spherical symmetry, the icosahedraldocecahedral group.

Dixon, Aesthetics 238

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therefore inherently abstract and logical in purpose. Yet abstraction implies particular and concrete origins. More- over, if mathematics is to serve an immediate purpose, then this lies in its applicability to phenomena, most in- fluentially through the sciences, but also through the arts.

The very idea of mathematics as a separate department of knowledge belies its 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 problems set and solved in such practical activities as 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 mathematical teaching clearly reflects a tendency to isolate a body of exclusively mathe- matical knowledge. There is therefore a characteristic emphasis on symbolic, logical and abstract aspects. The need to divorce reason from sense has often seemed to be an important mathematical goal. Hahn [16] gives several examples of the pitfalls of intuitive and visual approaches to formal mathematics, thus emphasizing the care needed in obtaining logically valid arguments. But it is equally clear to anyone who has ever learnt or taught mathematics that concrete examples and an intuitive grasp are necessary for abstract understanding.

Kline [ 17] gives a detailed history of the drive to isolate a body of purely logical mathematics and examines limitations inherent in so doing. His evidence includes not only those explicit limits discovered by such logicians as Russell and Godel but also, and perhaps more significantly, numerous admissions by mathematicians themselves as to the vital role played by physical intuition in

guiding and testing mathematical dev- elopment.

Kitcher [18] challenges the apriorist account of mathematical propositions customarily given by philosophers and sketches an alternative in which mathe- matical knowledge is ultimately based in sense-experience. He does not offer a detailed account of the sensory links, but does demonstrate effectively the histori- cal and social dimensions of mathe- matical learning.

Davis and Hersh [19] question a traditional myth of mathematics as pure logic and call for a more open-minded attitude to its nature. Their many examples bring out the diversity of styles in mathematical thinking and illustrate

well how logic and intuition interact. Stewart also observes this confused

regard for the relation between logical and intuitive aspects of mathematics: although "one of the more noticeable aspects of modern mathematics is a tendency to become increasingly abstract" [20], most mathematicians "think in pictures; their intuition is geometrical" [21]. He states that it is intuition which enables mathematicians to "see that a theorem is true, without giving a formal proof, and on the basis of their vision produce a proof that works" [22].

I have no doubt that increasing specialization and departmental demarc- ation give rise to a loss of unity. Optimistically, Bohm writes that "the sharp break between abstract logical thought and concrete immediate experi- ence that has pervaded our culture for so long, need no longer be maintained" [23]. Within his holistic perspective the endemic 'fragmentation' is a product of thought and has no basis in reality.

A growing tradition of work in the twentieth century explicitly re-empha- sizes the primary importance of sensory exprience and natural phenomena to mathematics. Two contemporary geo- meters addressing this issue are Benoit Mandelbrot and Rene Thom, who demonstrate in different ways the creative and illustrative power of visual thinking for mathematics. Both hail as their model the work of D'Arcy Thompson [24], in which natural morphology is the object of mathematical investigation.

Mandelbrot makes extensive use of computer graphics in the development of his fractal theory (fractal form = a feature at every scale) [25], noting that

there is no question that any attempt to illustrate geometry involves a basic fallacy. For example, a straight line is, strictly speaking, unbounded and in- finitely thin and smooth, while any illustration is unavoidably of finite length, of positive thickness, and rough edged. Nevertheless, a rough evocative drawing of lines is felt by many to be useful and by some to be necessary in order to build up intuition and help in the search for a proof. And of course, when it comes to providing a geometric model of a thread, a rough drawing is in fact more adequate ... It suffices for all practical purposes that a geometric concept and its image should fit within a certain range of characteristic sizes [26].

Mandelbrot expresses a passionate and high regard for sense perception. He balances the usefulness of mathematical

analysis with a clear statement that "the eye has enormous powers of integration and discrimination" [27]. Indeed it would be fair to say that his work is as much a contribution to aesthetics as it is to mathematics. He is as prepared to describe his work a 'vision' as to call it theory.

Thom's catastrophe theory develops ideas from singularity theory and different- ial topology to address problems in morphogenesis. Concrete applications are demonstrated in areas as different as embryology and sociology [28].

Thom criticizes the excessive abstrac- tion of 'modern' mathematics teaching and challenges the proposed set-theoretic basis [29]. He deplores the consequent de- emphasis of geometry in the elementary curriculum and insists that "geometry is a natural and possibly irreplaceable inter- mediary between ordinary language and mathematical formalism" [30]. He pres- ses his point firmly with the reminder that "according to a now-forgotten etymo- logy, a theorem is above all the object of a vision" [31].

As well as affirming the fundamental place of sense perception in epistem- ology, twentieth-century work on natural morphology greatly restores the balance of mind evident in that ancient insight, traditionally ascribed to Pythagoras, of matching perceived patterns with numer- ical patterns. Key episodes in this approach, such as musical harmony and pictorial perspective, provide clear anti- dotes to the dominant abstraction [32] of our school mathematics. As a final example of the unifying approach to mathematics and aesthetics, it might be worth citing Smith [33] and Mandelbrot [34], who independently of each other observed structural hierarchy both in artworks and in natural forms and thus brought mathematics into the study of pictorial composition and visual texture, and vice versa.

V. CONCLUSION

Mathematics provides a fitting context in which to define visual art across the curriculum. This is done by drawing the cognitive distinction between, for ex- ample, picture versus text or between form versus formula, and so on. Theories of learning recognize this same division as being between primary versus secondary ways of knowing. Secondary ways of knowing involve encoded information, whereas primary ways of knowing are aesthetic, in the original meaning of this word, denoting that which is sensible as opposed to that which is reasonable.

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REFERENCES AND NOTES

1. Chambers Twentieth Century Dictionary (Edinburgh: 1972) gives three distinct meanings for aesthetic: (a) originally relating to perception by the senses; (b) generally relating to possessing, or pretending to, a sense of beauty; (c) artistic or affecting to be artistic.

2. Anthony Flew, A Dictionary of Philo- sophy (London: Pan, 1979). Kant strongly disapproved of this corruption, however.

3. Flew [2], for example, or Harold Osborne, Aesthetics (Oxford: Oxford University Press, 1972).

4. The Shorter Oxford English Dictionary gives: "Aesthetic ... things perceptible by the senses, as opposed to things thinkable or immaterial. Misapplied in German by Baumgarten to 'criticism of taste', and so used in English since 1830..."

5. It is instructive to realise that there are more than the proverbial five senses: sight, hearing, smell, taste and touch; we should also note kinaesthetics, the sense of heat, the sense of pain, the sense of gravitational orientation, 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 in the Surgically Separated Hemispheres", in The Neurosciences: Third Study Pro- gramme, F. O. Schmitt and F.G. Worden, eds. (Cambridge, MA: MIT Press, 1975).

8. Nigel Cross, "Designerly Ways of

Knowing", Design Studies 3, No. 4 (1982).

9. Cyril Stanley Smith, In Search of Structure (Cambridge, MA: MIT Press, 1982).

10. U.K. Department of Education, Aesthet- ic Development, 1983.

11. Ref. [10] p. 2. 12. Chambers Twentieth Century Dictionary

[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", in

The World of Mathematics Vol. 3, J.R. Newman, ed. (New York: Simon & Schuster, 1956).

17. Morris Kline, Mathematics-The Loss of Certainty (Oxford: Oxford University Press, 1980).

18. Philip Kitcher, The Nature of Mathe- matical Knowledge (Oxford: Oxford University Press, 1983).

19. Philip J. Davis and Reuben Hersh, The Mathematical Experience (Brighton: Harvester, 1981).

20. Ian Stewart, Concepts of Modern Mathe- matics (Harmondsworth, Middlesex: Pelican, 1975) p. 1.

21. Stewart [20] p. 5. 22. Stewart [20] p. 4. 23. David Bohm, Wholeness and the Impli-

cate Order (London: Ark, 1983) p. 203. 24. D'Arcy Wentworth Thompson, On

Growth and Form (Cambridge: 1917, 1942).

25. A fractal curve is one which has infinitely many bends, and a fractal surface is one which has infinitely many hills and valleys. Typically, these features are exhibited at every scale of magnification; and nature, according to Mandelbrot, abounds in fractal forms. Thus, for example, coastlines have promontories and inlets ranging from the size of continents down to microscopic irregu- larities.

26. Benoit B. Mandelbrot, The Fractal Nature of Geometry (San Francisco: Freeman, 1982) p. 22.

27. Benoit B. Mandelbrot, Fractals (San Francisco: Freeman, 1977) p. 24.

28. Ren6 Thom, Structural Stability and Morphogenesis (Reading, MA: Benjamin, 1972).

29. Ren6 Thom, "'Modern' Mathematics: An Educational and Philosophical Error?", American Scientist 59 (1971). Thom's own work derives inspiration from such simple phenomena as light caustics in coffee cups and waves breaking on the beach. See Christopher Zeeman, Catastrophe Theory (Reading, MA: Addison-Wesley, 1977); and P.T. Saunders, An Introduction to Catastrophe Theory (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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