To a mathematical definition of 'life'

'Life' and its 'evolution' are fundamental concepts that have not yet been formulated in precise mathematical terms, although some efforts in this direction have been made. We suggest a possible point of departure for a mathematical definition of 'life'. This definition is based on the computer and is closely related to recent analyses of 'inductive inference' and 'randomness'. A living being is a unity; It is simpler to view a living organism as a whole than as the sum of its parts. If we want to compute a complete description of a region of space-time that is a living being, the program will be smaller in size if the calculation is done all together, than if it is done by independently calculating descriptions of parts of the region and then putting them together.

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

[2]  Gregory J. Chaitin,et al.  On the Length of Programs for Computing Finite Binary Sequences , 1966, JACM.

[3]  Donald W. Loveland,et al.  A Variant of the Kolmogorov Concept of Complexity , 1969, Information and Control.

[4]  Per Martin-Löf,et al.  The Definition of Random Sequences , 1966, Inf. Control..

[5]  E. F. Moore Machine Models of Self-Reproduction , 1962 .

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

[7]  P. H. A. Sneath Planets and Life , 2019, Fundamental Planetary Science.

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

[9]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[10]  Andrei N. Kolmogorov,et al.  Logical basis for information theory and probability theory , 1968, IEEE Trans. Inf. Theory.

[11]  J. Schwartz,et al.  Theory of Self-Reproducing Automata , 1967 .

[12]  Gregory J. Chaitin,et al.  On the difficulty of computations , 1970, IEEE Trans. Inf. Theory.

[13]  E. Wright,et al.  An Introduction to the Theory of Numbers , 1939 .

[14]  John von Neumann,et al.  Theory Of Self Reproducing Automata , 1967 .

[15]  Gregory J. Chaitin,et al.  On the Simplicity and Speed of Programs for Computing Infinite Sets of Natural Numbers , 1969, J. ACM.

[16]  Donald W. Loveland,et al.  On minimal-program complexity measures , 1969, STOC.

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

[18]  David G. Willis,et al.  Computational Complexity and Probability Constructions , 1970, JACM.

[19]  Michael A. Arbib,et al.  Automata theory and development: Part I , 1967 .

[20]  Claude E. Shannon,et al.  The Mathematical Theory of Communication , 1950 .

[21]  Gregory J. Chaitin,et al.  On the Length of Programs for Computing Finite Binary Sequences: statistical considerations , 1969, JACM.

[22]  Godfrey H. Hardy,et al.  A mathematician's apology , 1941 .

[23]  E. F. Codd,et al.  Cellular automata , 1968 .