Chemical Education Today
Symmetries of Nature: A Handbook for Philosophy of Nature and Science Klaus Mainzer. Walter de Gruyter: Berlin, 1996. 3-11012990-6. (First English edition of Symmetrien der Natur. Walter de Gruyter: Berlin, 1988.) 659 pp + 20 pp. Index. Mainzer’s work is what it advertises itself to be: a compendious handbook of discoveries of symmetries, particularly in mathematics and the natural sciences, and their representation in theories, in philosophy of science, and to a lesser degree in technology and broader culture. Among over a hundred distinguishable areas of study considered are, for example, the following: illustrations and a cursory discussion of symmetrical art from Navajo, Aztec, Indian, and Chinese sources; a few pages on the mechanism of the ancient Chinese south-pointing carriage; twenty pages on the history of constructions of regular polygons and Platonic and other geometric solids; symmetries in historical and recent space-time theories and in thermodynamics and chaotic systems; antisymmetry in DNA synthesis and structural symmetries and asymmetries in organisms; and even metaphorical “symmetry breaking” in decentered postmodern art and critical theory. Symmetry has become a particularly important topic in philosophy of science, especially since the publication by Bas C. van Fraassen of Laws and Symmetry (Clarendon: Oxford, 1989.). Van Fraassen argues that the idea of necessity that underlies law explanation and causation is a vestige of 17th century science, and an account of science as a process of constructing models that express mathematical relations, symmetries, and invariances provides adequate representation of the phenomena of nature. Mainzer’s interest lies in a related project, determining the prospects for a unification of theories among the sciences, or the unification of models. His collection represents a useful resource for those attempting to understand the prospects for unification and the degree to which symmetry arguments pervade scientific explanation across fields. Mainzer is a philosopher of mathematics and physics, and his extended discussion of physics, especially quantum mechanics and particles, is the most developed portion of the volume, and provides a core that connects a good deal, though not all, of the balance of the handbook. Consequently, chemistry is considered primarily in a 30-page historical treatment of crystal classification, leading to a discussion of mathematical group theory, and molecular handedness. Homochirality in nature also comes in for brief treatment. A short discussion of molecular structures introduces the topic of the prospects and purposes of a unification of theories by a reduction of stereochemistry to quantum mechanics, given that “our models and images are always only more or less drastic simplifications and abstractions of complex relationships” in nature itself. Eric Palmer Department of Philosophy, Allegheny College, Meadville, PA 16335
Vol. 74 No. 4 April 1997 • Journal of Chemical Education
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