Nietzsche's Recurrence Revisited: The French Connection

Notes and Discussions NIETZSCHE'S RECURRENCE REVISITED: THE FRENCH CONNECTION Joe Krueger's article is the latest and perhaps the best of a long series of attempts to explicate the historical background and philosophical significance of Nietzsche's theory of the Eternal Recurrence. I Yet, like almost all previous commentators, Krueger ignores what seems to me one of the most fascinating aspects of the subject: its relation to Henri Poincarr's recurrence theorem in mechanics. Since Nietzsche himself presented his theory as a deduction from physics, it would seem that the most obvious starting point for its interpretation is the physics of his own time; I agree with Krueger that Rose Pfeffer's claim for an adumbration of quantum concepts is not very plausible. While Nietzsche developed his theory at about the same time as Poincarr, it would not be accurate to speak of "simultaneous discovery" since his "proof" did not address the mathematical issueswhich Poincar6 considered crucial; moreover , the philosophical significance of the theory was almost exactly the opposite for Nietzsche and for Poincarr. Nevertheless the relations between the two may be of sufficient interest to readers of this Journal to justify a brief summary of Poincarr's version (assuming Nietzsche's to be already familiar). 2 One of the major objectives of eighteenth-century mathematical physics had been to prove that the stability of the solar system is a consequence of Newton's laws of motion. By the beginning of the nineteenth century this goal had apparently been reached by the work of such scientists as Lagrange, Laplace, and Joe Krueger, "Nietzschean Recurrence as a CosmologicalHypothesis," Journal of the History of Philosophy 16 (1978):435-44. In addition to the works cited in his first footnote see C. Andler, Nietzsche, Sa Vie et sa Pens~e (Pads: Bossard, 1928),IV, Livre 2, Chap. I; Oskar Becker, "Nietzsches Beweise ~r sein Lehre von der ewigen Wiederkunft," Bliittern fi~r Deutsche Philosophie 9 (1936):368-87; J. Delevsky, "L'idee du cycle eternal darts l'historie du monde," in Studies and Essays in the History of Science and Learning offered in Homage to George Sarton (New York: Henry Schuman, 1944),pp. 375-402; Walter Kaufmann,Nietzsche: Philosopher, Psychologist, Antichrist (Princeton, N.J.: Princeton University Press, 1950),Chapter 11;Stanley L. Jaki, Science and Creation: From Eternal Cycles to an Oscillating Universe (NewYork: Science History Pubs., 1974), Chapter 13; R. J. Hollingdale,Nietzsche: The Man and His Philosophy (London: Routledge and Kegan Paul, 1965),Appendix II; Joan Stambaugh, Nietzsche's Thought of Eternal Return (Baltimore : Johns Hopkins University Press, 1972). 2 For further details see S. G. Brush, The Temperature of History: Phases of Science and Culture in the Nineteenth Century (NewYork: Burt Franklin & Co., 1978),Chapter V; The Kind of Motion We Call Heat: A History of the Kinetic Theory of Gases in the 19th Century (Amsterdam: North-Holland Pub. Co., 1976),Chapter 14. The connection between Nietzsche's ideas and Poincar ~'s theorem is brieflynoted by M. Capek, The PhilosophicalImpact of Contemporary Physics (Princeton: Van Nostraad Co., 1961), pp. 125-26. [235] 236 HISTORY OF PHILOSOPHY Poisson. Hence it was generally befieved that the earth had remained at the same average distance from the sun for an indefinitely long time in the past, and that physical conditions on the surface of the earth had been roughly the same as they are now for countless millions of years. This assumption was the basis for the Hytton-Lyell "uniformitarian" theory of geology, developed in the first half of the nineteenth century. However, the assumption was challenged on severed grounds (such as the cooling of the earth and sun) by William Thomson in the 1860s. Thomson also noted that the calculations that predicted the stability of the solar system were only approximate, and failed to take account of irreversible dissipation effects. In fact, Thomson's general principle.of dissipation of energy (1852) was one of his weapons in his campaign against uuiformitarian geology and (indirectly) evolutionary biology.3 Thomson's dissipation principle was later incorporated into the generalized statement of the Second Law of Thermodynamics by Rudolf Clausius (1865): the entropy of the universe tends toward a maximum. In the final state of...