TOWARD A MATHEMATICAL DEFINITION OF “ LIFE ”

In discussions of the nature of life, the terms “complexity,” “organism,” and “information content,” are sometimes used in ways remarkably analogous to the approach of algorithmic information theory, a mathematical discipline which studies the amount of information necessary for computations. We submit that this is not a coincidence and that it is useful in discussions of the nature of life to be able to refer to analogous precisely defined concepts whose properties can be rigorously studied. We propose and discuss a measure of degree of organization

[1]  F. S.,et al.  A Mathematician's Apology , 1941, Nature.

[2]  E. T..  An Introduction to the Theory of Numbers , 1946, Nature.

[3]  C. O. Oakley,et al.  The Enjoyment of Mathematics. , 1957 .

[4]  Ernan McMullin,et al.  The Physicist’s Conception of Nature , 1958 .

[5]  J. Neumann.  The General and Logical Theory of Au-tomata , 1963 .

[6]  Ray J. Solomonoff,et al.  A Formal Theory of Inductive Inference. Part I , 1964, Inf. Control..

[7]  G. J. Chaitin,et al.  TO A MATHEMATICAL DEFINITION OF “ LIFE ” , 1970 .

[8]  Herbert A. Simon,et al.  The Sciences of the Artificial , 1970 .

[9]  Arthur W. Burks,et al.  Essays on cellular automata , 1970 .

[10]  L. Orgel.  The Origins of Life: Molecules and Natural Selection , 1973 .

[11]  Patrick Billingsley,et al.  The Probability Theory of Additive Arithmetic Functions , 1974 .

[12]  Gregory J. Chaitin,et al.  Information-Theoretic Computational Complexity , 1974 .

[13]  G. Chaitin.  Randomness and Mathematical Proof , 1975 .

[14]  G. Chaitin.  A Theory of Program Size Formally Identical to Information Theory , 1975, JACM.

[15]  Aaron D. Wyner,et al.  The common information of two dependent random variables , 1975, IEEE Trans. Inf. Theory.

[16]  Rolf Landauer,et al.  Fundamental Limitations in the Computational Process , 1976 .

[17]  H. Witsenhausen.  Values and Bounds for the Common Information of Two Discrete Random Variables , 1976 .

[18]  H P Yockey,et al.  A calculation of the probability of spontaneous biogenesis by information theory. , 1977, Journal of theoretical biology.

[19]  C. Sagan.  The Dragons of Eden: Speculations on the Evolution of Human Intelligence , 1977 .

[20]  J. Schwartz,et al.  A note on monte carlo primality tests and algorithmic information theory , 1978 .

[21]  G. Hardy,et al.  Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work , 1978 .

[22]  N. Costa,et al.  Non-Classical Logics, Model Theory and Computability , 1980 .