In lieu of an abstract, here is a brief excerpt of the content:

Reviewed by:
  • Symmetry: Cultural-Historical and Ontological Aspects of Science-Arts Relations: The Natural and Man-Made World in an Interdisciplinary Approach
  • István Hargittai
Symmetry: Cultural-Historical and Ontological Aspects of Science-Arts Relations: The Natural and Man-Made World in an Interdisciplinary Approach by György Darvas. Translated from the Hungarian by David Robert Evans. Birkhäuser, Basel, Boston, MA, and Berlin, 2007. xi + 508 pp. 10: 3-7643-7554-X; 13: 978-3-7643-7554-6.

György Darvas has been a dedicated organizer of symmetry meetings and editor of the periodical Symmetry. His enthusiasm has now spilled over into a 500-page book whose material is divided into five parts: Introductory chapters; Interdisciplinary Applications; Symmetry in Inanimate Nature; The Road from Nature to Man; and Human Creativity. The text is illustrated by a plethora of quotations and images. The end matter contains a Bibliography; Sources of Illustrations; Subject Index; Index of Names; and some 30 pages of color plates. Unfortunately, the book lacks a clear formulation of purpose, systematic elucidation and reliability in the details of discussion. Only a few examples will be given here for illustration. Sadly, the confusion starts with basic notions.

Darvas assigns dissymmetry to examples where “an object displays symmetry, but this symmetry is broken in one of its characteristics or a not too significant detail” (p. 21; see also p. 60) His examples include “a bubble in a diamond” and “a freckle on a face” (p. 21). He cites another example from Thomas Mann’s The Magic Mountain: a passage in which Hans Castorp understands why the builders of antiquity introduce minute variations in their columnar structures as a protest of the lifelessness of too much regularity (p. 23). All these are good examples of distortion or violation of symmetry to smaller or greater extent, but dissymmetry is something else; it has a well-defined meaning from which there is no reason to depart. Darvas refers copiously to A.V. Shubnikov’s teachings [1], so let us see what dissymmetry is according to Shubnikov. It is the absence of certain symmetry elements, for example a symmetry plane. Shubnikov called dissymmetry the falling out of one or another element of symmetry from a given group.

Pasteur used the term dissymmetry for the first time to designate the absence of a symmetry plane in a figure. Accordingly, dissymmetry did not exclude all elements of symmetry, only the absence of certain symmetries. Darvas quotes Pierre Curie correctly but misinterprets his teaching. Curie suggested a broad application of the term dissymmetry. He called a crystal dissymmetric in the case of the absence of those elements of symmetry upon which depends the existence of one or another physical property in that crystal. In Curie’s original words: “Dissymmetry creates the phenomenon” (“C’est la dissymétrie qui crée le phénomène”) [2]. That is, a phenomenon exists and is observable due to dissymmetry, due to the absence of some symmetry elements from the system. The misunderstanding of the fundamental notion of dissymmetry does a conceptual disservice to the whole book.

The discovery of the double helical structure of DNA was, among other things, a triumph of symmetry considerations. Darvas brings up this question but treats it superficially, which results in misunderstanding. There is more than one kind of symmetry in the DNA structure. There is the helical symmetry and the presence of overall twofold symmetry. One of the co-discoverers, [End Page 185] James D. Watson, never gave much importance to the twofold symmetry of the structure. He has stated explicitly, “I never used the dyad [the presence of twofold symmetry] to find the structure” [3]. In contrast, Francis Crick, on seeing Rosalind Franklin’s results, realized that her C2 symmetry of the A form of DNA implied two chains running in opposite directions. Watson had been trying two-chain models, but had them running in the same direction [4]. These distinctions are important here. Darvas quotes at length (pp. 336–337) from various sections of Watson’s book The Double Helix (without giving exact references), but this side of the story remains murky. On page vii, it is not clear which writing...

pdf

Share