Birkhoff revisited: beauty as a function of effect and means.

The beauty of visual patterns is quantified, starting from the assumption that beauty is maximal when a maximum of effect is attained with a minimum of means applied. Birkhoff has based his theory of beauty on this assumption, but his specification of means and effect differs from the one presented here. In our conception, effect is specified as the number of independent regularities (R) of a pattern not accounted for by the simplest interpretation of the pattern. This variable is closely allied to the concept of conjunctive ambiguity. The irregularities of a pattern that are not constrained by additional regularities (P) make up the means term of the means-effect analogy. An index of beauty (M) is defined, M = R - P. It is shown that there is substantial correlation between M and preference judgments for a set of Birkhoff's polygons. It is further demonstrated that M has relevance to describe properties of the relation of beauty to complexity, data of experiments on the aesthetic attractivity of combinations of patterns, and preferences for certain proportions of simple figures above others.

[1]  O. Reiser,et al.  Principles Of Gestalt Psychology , 1936 .

[2]  R. Ogden.  Naive Geometry in the Psychology of Art , 1937 .

[3]  Hans J. Eysenck,et al.  The empirical determination of an aesthetic formula. , 1941 .

[4]  Helmut Kuhn,et al.  A History of Aesthetics. , 1941 .

[5]  H. J. Eysenck,et al.  The experimental study of the 'good Gestalt'--a new approach. , 1942 .

[6]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[7]  Claude E. Shannon,et al.  The Mathematical Theory of Communication , 1950 .

[8]  J. Hochberg,et al.  A quantitative approach to figural "goodness". , 1953, Journal of experimental psychology.

[9]  R. Arnheim.  Art And Visual Perception , 1954 .

[10]  W. N. Dember,et al.  Response by rats to differential stimulus complexity. , 1957, Journal of comparative and physiological psychology.

[11]  Elliot Aronson,et al.  The effect of severity of initiation on liking for a group. , 1959 .

[12]  Charles Bouleau,et al.  The Painter's Secret Geometry: A Study of Composition in Art , 1963 .

[13]  Harry Munsinger,et al.  Uncertainty, structure, and preference. , 1964 .

[14]  P. Vitz,et al.  PREFERENCES FOR RATES OF INFORMATION PRESENTED BY SEQUENCES OF TONES. , 1964, Journal of experimental psychology.

[15]  W. Kessen,et al.  Age and uncertainty: Developmental variation in preference for variability☆ , 1964 .

[16]  P. Vitz.  Preference for different amounts of visual complexity. , 1966, Behavioral science.

[17]  D D Dorfman,et al.  Pattern preference as a function of pattern uncertainty. , 1966, Canadian journal of psychology.

[18]  D. Berlyne,et al.  The semantic differential and other measures of reaction to visual complexity. , 1966, Canadian journal of psychology.

[19]  H. Day.  Evaluations of subjective complexity, pleasingness and interestingness for a series of random polygons varying in complexity , 1967 .

[20]  F. Attneave.  Triangles as ambiguous figures. , 1968, The American journal of psychology.

[21]  H J Eysenck,et al.  An experimental study of aesthetic preference for polygonal figures. , 1968, The Journal of general psychology.

[22]  Harold J. McWhinnie,et al.  A review of research on aesthetic measure , 1968 .

[23]  E. Leeuwenberg.  Quantitative specification of information in sequential patterns. , 1969, Psychological review.

[24]  J. Reich,et al.  Stimulus Properties, Frequency of Exposure, and Affective Responding , 1970, Perceptual and motor skills.

[25]  H. Eysenck,et al.  Training in art as a factor in the determination of preference judgements for polygons. , 1970, British journal of psychology.

[26]  L. Zusne.  Visual perception of form , 1970 .

[27]  John M. Kennedy,et al.  Optics Painting and Photography , 1970 .

[28]  E. Walker.  COMPLEXITY AND PREFERENCE IN ANIMALS AND MEN * , 1970 .

[29]  D. Berlyne,et al.  Aesthetics and Psychobiology , 1975 .

[30]  E. Leeuwenberg.  A perceptual coding language for visual and auditory patterns. , 1971, The American journal of psychology.

[31]  D. Berlyne,et al.  Hedonic effects of uniformity in variety. , 1971, Canadian journal of psychology.

[32]  D. Berlyne,et al.  Uniformity in variety: extension to three-element visual patterns and to non-verbal measures. , 1972, Canadian journal of psychology.

[33]  Herbert A. Simon,et al.  Complexity and the representation of patterned sequences of symbols. , 1972 .

[34]  S. Ertel.  CHAPTER 5 – Exploratory Choice and Verbal Judgment1 , 1973 .

[35]  S. Kreitler,et al.  Psychology of the arts , 1974 .

[36]  H. Franke,et al.  Ästhetik als Informationsverarbeitung , 1974 .

[37]  W. R. Garner.  The Processing of Information and Structure , 1974 .

[38]  S. Kreitler,et al.  Psychology of the arts , 1974 .

[39]  W. R. Garner.  Uncertainty and structure as psychological concepts , 1975 .

[40]  Earl A. Alluisi,et al.  Studies in the New Experimental Aesthetics , 1975 .

[41]  D. Dörner,et al.  Ästhetische Befriedigung und Unbestimmtheitsreduktion , 1975 .

[42]  Stuart Margulies,et al.  Principles of Beauty , 1977 .

[43]  M. P. Friedman,et al.  HANDBOOK OF PERCEPTION , 1977 .

[44]  Julian Hochberg,et al.  Chapter 10 – ART AND PERCEPTION* , 1978 .

[45]  Benoit B. Mandelbrot,et al.  Fractals: Form, Chance and Dimension , 1978 .

[46]  R. Nicki,et al.  Uncertainty and preference for ‘ambiguous’ figures, ‘impossible’ figures and the drawings of M. C. Escher , 1979 .

[47]  Ernst Gombrich,et al.  The Sense of Order. , 1980 .

[48]  I C McManus,et al.  The aesthetics of simple figures. , 1980, British journal of psychology.

[49]  J. Wohlwill.  The place of order and uncertainty in art and environmental aesthetics , 1980 .

[50]  Harrie F J M van Tuijl.  Perceptual interpretation of complex line patterns. , 1980 .

[51]  E. Leeuwenberg,et al.  Coding theory of visual pattern completion. , 1981, Journal of experimental psychology. Human perception and performance.

[52]  R. Nicki,et al.  Ambiguity, cubist works of art, and preference , 1981 .

[53]  J. Beck.  Organization and representation in perception , 1982 .

[54]  Over visuele schoonheidservaring , 1982 .

[55]  R. F. A. Collard,et al.  Minimization of structural information: A set-theoretical approach , 1983, Pattern Recognit..

[56]  Ambiguity, beauty, and interestingness of line drawings. , 1983 .

[57]  Frans Boselie,et al.  The aesthetic attractivity of the golden section , 1984 .

[58]  F. Boselie.  Complex and Simple Proportions and the Aesthetic Attractivity of Visual Patterns , 1984, Perception.