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Dynamics of Dissymmetry

Published online by Cambridge University Press:  01 July 2024

Roger Caillois
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It is not impossible, it is almost inevitable, to conjecture the existence of laws so general that their jurisdiction would be affected neither by the nature nor the scale nor the level of their object—so that they would apply equally to the relations of numbers or of inert or organic matter, to the progression of rigorous thought or the flights of an amused or charmed fancy. If such laws did not govern the whole extent of the real, possible or conceivable world, or if, although autonomous, they could not be inferred from one another by some system of relations or transfers, I fear that human reflection, in spite of its partial successes, might seem condemned to reveal itself vain, since gaps, or fundamental absences of relationship, could put its cogency into question in a decisive fashion.

Type
Research Article
Information
Diogenes , Volume 19 , Issue 76 , December 1971 , pp. 62 - 92
Copyright
Copyright © 1971 Fédération Internationale des Sociétés de Philosophie / International Federation of Philosophical Societies (FISP)

References

* The present memoir develops the text of the exposé presented June 8, 1971 as the annual Zaharoff Lecture, under the title of “Balance and Dissymmetry in Nature and Art.” I am indebted to the Board of Directors of the Taylor Foundation for having entrusted Diogenes with its publication in extenso.

1 Vitruvius, De architectura, I, 2.

2 Kant, Prolegomena… I, § 13: "On the first foundation of the difference between the regions of space." Cf. Vilma Reich, La Gauche et la droite, Paris, 1967, pp. 183-202.

3 Supporting the opposite thesis: W. von Engelhardt, Studium Generale, II, July 1949.

4 List with descriptions and examples in Fr. H. Pough, Guide des roches et minéraux, French translation, Neuchâtel, 1969, Pp. 64-76.

5 P. Lépine, "Les virus," in Biologie, Encyclopédie de la Pleiade, Paris, 1965, pp. 1894-1896.

6 Exposé of the thesis (and discussion, after I had conveyed my objections to the author) in Michel De Wolf, "Sur une des formes les plus élémentaires de la symbolisation," in Cahiers internationaux de symbolisme, nos. 19-20, 1970, pp. 102-106.

7 H. Hécuen, "La symétrie en neuropsychologie," in Totus Homo, vol. II (1970), no. 1, pp. 8-15.

8 A few definitions or conventions are needed here. In man, right and left determine themselves, as they do by similarity among the higher animals, thanks to the direction in which we walk. For a conch or other shell the movement is said to be dextrorotary, or right-coiled, if, when the object is placed oppo site the observer, with its point at the top, it appears to him to be coiled clockwise, that is to say, from left to right, from its origin. Hence a dextrorotary shell is one whose orifice in seen at the right. The direction of rotation of a crystal is determined by supplementary, oblique facets located between the longitudinal faces and the terminal pyramids. Held vertically, the crystal is right-handed if, as they approach the pyramids, the upper facets are inclined toward the observer's right; it is left-handed if they are turned to the left. Because of the symmetrical arrangement of the facets, the direction remains the same if the crystal is inverted. These choices are not entirely arbitrary: they are all derived from correspondences with the upright posture and bilateral symetry of man.

9 Herman Weyl, Symétrie et mathématique moderne, Paris, 1964, p. 45.

10 Zoologie, Encyclopédie de la Pléiade, t. II, Paris, 1963, p. 682.

11 Pasteur, Oeuvres Complètes, t. I, "Dissymétrie moléculaire," Paris, 1922, p. 343.

12 Quoted by Vilma Reich, ibid., p. 69.

13 Pasteur, ibid., p. 338. See also pp. 341-342, 369.

14 J. Nicolle, "Questions relatives à la symétrie," Zeitschrift für Aesthetik und allgemeine Kunstwissenschaft, XIV, 1 (1969), p. 21.

15 Vilma Reich, op. cit., pp. 118-119.

16 Hermann Weyl, op. cit., p. 38.

17 Quoted by Jacques Nicolle, "On Symmetry," in Diogenes, no. 12, Winter 1955, p. 87.

18 A. Dauvillier, "L'Origine de la vie," in Biologie, op. cit., p. 1865-1866. Cf. Jacques Monod, Le Hasard et la nécessité, Paris, 1970, pp. 161-162.

19 Jacques Monod, ibid., pp. 62-67.

20 Louis Leprince-Ringuet, "Leçon inaugurale au Collège de France," Paris, 1959, pp. 31-35, where the author clearly explains how the non-conservation of parity when mesons and hyperons are disintegrated led scientists to abandon, at least partially, "one of the most naturally supported laws of physics."

21 A recent development, limited to the field of politics, tends to give a favorable meaning to the left. With the left are associated ideas of progress, generosity, reforms, social justice and, more generally, an ideal and the future, whereas the right evokes stagnation and egoism, the maintenance of unjust privileges, and in any case order, experience and the past. We know that the designation of parties and movements by the epithet "left" is purely fortuitous (it happens that the deputies in question are seated to the left of the president of the Assembly), but the fact is that this designation has consolidated and perpetuated itself, and has even spread beyond the frontiers of France. The analyses of sociologists predicted the contrary, and would have led us to expect "that the right would be the side of freedom and action, and the left the side of passivity and dependence" (H. C. Van der Meer, Polarisation droite-gauche de l'espace phénoménal, Groningen, 1958, quoted by Vilma Reich, ibid., p. 85). It would be interesting to find out whether this break with usage was possible only because people's linguistic consciousness did not associate the new and quite accidental meaning of the word with the usual, long-accredited connotations, or whether it soon acquired the character of an act of defiance—the taking over of a world that was cursed, disdained, suspect, and miserable in the double sense of arousing pity and scorn.