# The Probability of the Existence of a Self-Reproducing Unit

## Abstract

IN his ‘Analytical Study’ of life and the multiplication of organisms,^{1} Elsasser analyses the way in which the information is stored in the germ-cells which enables these germ-cells to develop into organisms similar to the parent—similar also in their ability to produce in their turn, germ-cells containing the same type of information. Although no clear-cut proof is presented, a good deal of weighty evidence is adduced^{2} to show ‘that the structure of a butterfly, a snake, a tree, or a bird cannot be deduced mathematically from some relatively compact body of basic data stored in the chromosomes’; the ‘maintenance of information is ... not adequately described in terms of the mechanistic approximation’. The present writer has also been baffled by the miracle that there are organisms—that is, from the point of view of the physical scientist, structures—which, if brought into contact with certain nutrient materials, multiply, that is, produce further structures identical with themselves. He felt that it is, according to the known laws of physics, infinitely unlikely that structures of this nature exist and the present article is a report on the considerations and calculations which he undertook in this connection.^{3} Actually, the point of view is somewhat different from Elsasser’s: Elsasser considers the way in which the information necessary to develop the adult specimen is stored in the germ-cells and shows that the germ-cells do not have properties which the physicist would expect to be suitable for storing large amounts of information. We shall be concerned, on the other hand, with what appears to be a miracle from the point of view of the physicist: that there are structures which produce further identical structures.^{4}

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## Reference

- 1.Walter M. Elsasser,
*The Physical Foundations of Biology*. London, Pergamon Press, 1958.Google Scholar - 2.Since the whole book (cf. Ref. 1) is built around this theme, it is not possible to point to definite passages which contain all the evidence presented. Nevertheless, pages 124–32 are perhaps most characteristic of the trend of thoughtGoogle Scholar
- 3.The results of these considerations were mentioned already in the author’s article The Unreasonable Effectiveness of Mathematics in the Natural Sciences’,
*Communications in Pure and Applied Mathematics*,*13*, 1960, p. 1.Google Scholar - 4.M. Polanyi’s review of G. Himmelfarb’s
*Darwin and the Darwinian Revolution*,*The New Leader*,31 August 1959, p. 24, expresses similar doubts concerning the possibility of explaining the phenomenon of life on mechanistic grounds.Google Scholar - 5.J. VON Neumann,
*Mathematische Grundlagen der Quantenmechanik*,Berlin, Julius Springer, 1932 (English translation, Princeton, Princeton University Press, 1955), Chapter VI. Heisenberg (*Daedalus, 87*,1958, p. 100), puts it even more concisely and picturesquely: ‘The conception of objective reality ... has thus evaporated ... into the transparent clarity of a mathematics that represents no longer the behaviour of elementary particles but rather our knowledge of this behaviour.’Google Scholar - 6.For this concept, see, e.g. E. Wigner,
*Gruppentheorie*, etc., Braunschweig, Friedr. Vieweg, 1931 ( English translation, New York, Academic Press, Inc., 1959 ), Chapter XII.Google Scholar - 7.
- 8.The only paper that is available on this subject seems to be ‘The General and Logical Theory of Automata’ in
*The Hixon Symposium*(edited by L. A. Jeffress), New York, John Wiley and Sons, 1951, p.1. However, C. E. Shannon’s discussion of von Neumann’s work*(Bull. Amer. Math. Soc.*,*64*,1958, p. 123, draws attention to further unpublished papers. In connection with the reliability problem, to be discussed below, see ’ Probabilistic Logics and the Synthesis of Reliable Organisms from Unreliable Components,’ in*Automata Studies*(edited by C. E. Shannon and J. McCarthy), Princeton, Princeton University Press, 1956, p. 43.Google Scholar - 9.Elsasser, op. cit., p. 129.Google Scholar
- 10.It must suffice to mention a few of the pertinent papers here and the knowledge of most of these I owe to Dr. H. Jehle of George Washington University: F. H. C. Crick and J. D. Watson,
*Nature*,*171*,1953, p. 737;*Proc. Roy. Soc. A 223*,1954, p. 80; G. Gamow,*Biol. Medd. Danske Vid. Selskab*,*22*,1954, No. 2;*22*,1955, No. 8; F. H. C. Crick, J. S. Griffith and L. E. Orgel,*Proc. Nat. Acad. Sc.*,*43*,1957, p. 416; M. Delbrück, S. W. Golomb, L. R. Welch,*Biol. Medd. Danske Vid. Selskab*,*23*,1958, No. 9. See also H. J. Muller,*Proc. Roy. Soc. B.*134, 1947, p. 1.Google Scholar - 11.