Leonardo

ning and M.A.Hartley, "Symmetry and Ornamentation Are Correlated to the Peacock's Train," Animal Behavior42 (1991) p. 1020; AC. liggett, "Fluctuating Asymmetry in Scatophaga Stercoraris L.: Successful Males Are More Symmetrical," AnimalBehavior45 (1993) p. 1041; A.P.Moller, "Female Preferences for Apparently Symmetrical Male Sexual Ornaments in the Barn Swallow Hirundo rusuca," BehavioralEcology and Sociobiology 32 (1993) p. 371; P.Arcese, "Harem Size and Horn Symmetry in Oribi," Animal Behaviour48 (1994) p. 1485; AK. Eggert and S.K.Sakaluk, "Fluctuating Asymmetry and Variation in the Size of Courtship Food Gifts in Decorated Crickets," TheAmericanNaturalist 144 (1994) p. 708;].P. Swaddle and I.C. Cuthill, "Preferences for Symmetrical Males by Female Zebra Finches," Nature 367 (1994) p. 165. 4. D. Cougar, "Sex and the Symmetrical Body," NewScientist146 (1995) p. 40. 5. A. McLachlan and M. Gant, "Small Males Are More Symmetrical: Mating Success in the Midge," AnimaiBehaviour50 (1995) p. 841. 6. EJ. Oakes and P. Barnbard, "Fluctuating Asymmetry and Mate Choice in Paradise Whydas, Vidua Paradisaea: An Experimental Manipulation," AnimalBehaviour48 (1994) p. 937. 7. R.A Johnstone, "Female Preferences for Symmetrical Males as a By-Product of Selection for Mate Recognition," Nature272 (1994) p. 172. 8.]. Mollon, In Colour: Art and Science (Oxford, U.K.: Cambridge Univ. Press, 1995). 9. R. Dawkins, The SelfISh Gene(Oxford, U.K.: Oxford Univ. Press, 1967). 10. For a brief review of some suggestive brain studies in aesthetics and the brain, see P.van Sommers, "Observational, Experimental and Neuropsychological Studies of Drawing," in C. LangeKuttner and G.V. Thomas, eds., Drawingand Looking(London: Harvester Wheatsheaf, 1995) chapter 4, p. 44. 11. S. Brenner, quoted in R. Levin, "WhyIs Development so Illogical?", Science 224 (1984) p. 327. 12. F.Jacob, "Evolution and Tinkering,:" Science 196 (1977) p. 161. RESPONSE TO PETER VAN SOMMERS The editor of Leonardo has kindly invited me to write a short commentary on Peter van Sommers's commentary on Alexander Voloshinov's article "Symmetry as a Superprinciple of Science and Art" (Leonardo 29, No.2, 1996). I appreciate this opportunity because nowadays we are witnessing a welcome proliferation of the interest in and application of the symmetry principle, while there is also the danger of overextending the inferences that may stem from such applications. On the one hand, it is wonderful that even TheNew York Times [1] and Newsweek (and, subsequently, Reader's Digest) [2] discuss the importance of symmetry in mate selection. But, on the other hand, it bothers me when well-funded studies at respectable universities find a direct correlation between the ages of loss ofvirginity and intercourse frequency of university coeds and the degree of geometrical symmetry of their faces. To reduce human mate selection to this degree is counterproductive from the point ofview of recognizing the utility of the symmetry concept in human relations. Van Sommers finds an esoteric, metaphysical drift in Voloshinov's approach of "superprinciple of symmetry ." On the contrary, I find it an oversimplification. It seems to me that Voloshinov is reading a bit too much into the role of the symmetry concept, although he does it in an engaging and enthusiastic way. There are some fundamental terms that need clarification. Voloshinov is given to definitions of such basic ingredients as, for example, geometrical symmetry. He says that it is the "invariance of geometrical objects with regards to certain transformations of geometrical space." I claim that the true attribute of geometrical symmetry has nothing to do with whether the object of transformation is geometrical or not. What is important is the rigor of the transformation in geometrical symmetry. Symmetry in this narrow sense, however, has very restricted utility and is capable of giving merely yes or no answers. The application of the symmetry concept is taking off so strongly today because we have learned to relax this rigor and have replaced the ''yes/no'' restricted alternative by "and" degrees. I find crucial from this point ofview what van Sommers calls "the symmetrical structure at one level." Yes,the presence and degree of symmetry depends a great deal on the scale of operations . Perfect symmetry at one level loses its perfection at a greater magnification , at a closer look. I think that Eugene Wigner...