Abstract
IN this memoir M. Yermoloff applies Cantor's theory of number to problems of evolution with the object of deciding whether the processes of evolution have been continuous, connex, or discontinuous. He regards the successive generations of a natural order, such as the, Diatomaceae, as an aggregate which can be treated by Cantor's methods. If there be continuity, this aggre gate is infinite and non-enumerable, and its power is 2N”, where NO denotes Cantor's smallest transfinite cardinal number Alef-zero; if there be connexity, the aggregate is infinite, but enumerable, and its power is NO; if finally there be discontinuity, the aggregate is finite, and its power is the total number of generations. With the last alternative the time required for the evolution of a given variety will be finite, but with the other two infinitely great, and much more difficult to account for. Thus the conclusion is reached that evolution has taken place by step-by-step “mutation “rather than by continuous, or even connex, “varia tion.” If any criticism is to be offered of this interest ing and suggestive memoir, it is that few of the bio logists for whom, presumably, it is intended are likely to possess a sufficient knowledge of higher mathematics to appreciate the argument fully, in spite of the fact that quite one-half of the memoir is devoted to an exposition of Cantor's methods.
Y a-t-il continuié dans le monde physique?
Nicolas
Yermoloff
Par. Pp. x + 48. (Paris: Gaston Doin, 1923.) 3.50 francs.
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Y a-t-il continuié dans le monde physique?. Nature 113, 158 (1924). https://doi.org/10.1038/113158b0
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DOI: https://doi.org/10.1038/113158b0