Symmetry in Science and Art by A. V. Shubnikov and V. A. Koptsik (review)

334 Books This will bring about an altogether different morality of science. He believes that the fragmentation ofphenomena brought about by ever-increasing abstraction is equivalent to conceptual alienation-which is one step removed from psychological alienation. He says that this moral crisis arose when science emerged triumphant. He answers in the negative the question: 'Can science fundamentally change itself by its own means?' Dennis C. Pirages, relates the existence of democratic institutions to affluence provided by technology, but he does not see the havoc caused by the misuse of technology on the bewildered citizens ofthe affluent societies and on other societies that they victimize. But I feel that he rightly questions the ability of democratically governed societies to control the misuse. Jerzy A. Wojciechowski in discussing the 'ecology' of knowledge asserts that science has been developing as if it were an autonomous, self-centered and self-justifying activity. But C. A. Hooker, as regards technology, raises the question: By whose values are the designs to be made; who is to control and how? Frank H. T. Rhodes, refering to Copernicus as the gentle revolutionary who moved the Earth and its inhabitants from the centre of the Universe, sees the best hope for the future of humanity in the reassertion of the humane basis that underlay the work of Copernicus. Symmetry in Science and Art. A. V. Shubnikov and V. A. Koptsik. Trans. from Russian by G. D. Archard. David Harker, ed. Plenum Press, New York, 1974. 420 pp., iIIus. $42.00. Reviewed by Marc H. Bomstein* Symmetry is special, a truism recognized as such by philosophers, physicists and psychologists. Symmetry is special both to the structure of material things and to the perception of that structure. Symmetrical figures are those that may be made to coincide with one another by one or more successive reflections in a plane. The earliest observations on symmetry were Pythagorean, and the study ofsymmetry has reflected interest in biological forms. though formal analysis and the laws of symmetry only 'arrived: with study of crystallography. Current symmetry theory has applications to physics, chemistry, mechanics, mathematics and, as the book under review endeavors to show, to art. In the U.S.S.R. particularly, symmetry is as much a philosophical principle as a set of mathematico-Iogical relations, since invariant and transformational laws, which apply in both spheres, are at the root of materialistic dialectics. Consequently, the Soviet Union has been particularly prominent in this field, and Symmetry in Science and Art is a second edition-expanded, updated and profusely iIIustrated-of a classic Russian text that treats the basic principles of symmetry comprehensively. The book begins with geometry and symmetry of single points and continues through 3-dimensional translations, networks, group theory and color to artistic implications. Minerals, plants and animals often tend towards symmetry, and, insofar as human-made constructions mimic life, machines and artistic works tend to be symmetric in structure. Specific discussion of the aesthetic implications of symmetry theory is relegated in this book, though, to the very end of the .very last chapter, where the authors make brief, if bold, forays into poetry, music, architecture and art. Escher is ofcourse discussed, but so are Bach and Pushkin. For example: Is it odd how asymmetrical Is 'symmetry'? 'Symmetry' is asymmetrical How odd it is. 'This stanza may be read word by word from the end to the beginning. It may be considered as ail invariant of the transformation of "compound inversion" A change in the direction of reading (from the end to the beginning) with a simultaneous change in the order of the letters in the words produces no change in the sense' (p. 360). The power ofstructural *Dept. of Psychology, Princeton University, Green Hall, Princeton, NJ 08540, U.S.A. analysis is such that the laws of invariance and transformation indigenous to symmetry and asymmetry extend to tonal music, metrics, analogies and metaphors, as well as to the rules of visual perspective. Although not discussed here, patterns that are symmetric are more salient and more readily detected; graphic compositions that are symmetric are more interesting and pleasing, more easily produced and reproduced, and better remembered. The regular disposition of parts of...