Abstract
'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.
- Arbib, M. A. (1966). 'Simple self-reproducing universal automata,' Information and Control.Google Scholar
- Arbib, M. A. (1967). 'Automata theory and development: Part 1,' Journal of Theoretical Biology.Google ScholarCross Ref
- Arbib, M. A. 'Self-reproducing automata--some implications for theoretical biology'.Google Scholar
- Biological Sciences Curriculum Study. (1968). Biological Science: Molecules to Man, Houghton Miffl in Co.Google Scholar
- Chaitin, G. J. (1966). 'On the length of programs for computing finite binary sequencest,' Journal of the Association for Computing Machinery.Google ScholarDigital Library
- Chaitin, G. J. (1969a). 'On the length of programs for computing finite binary sequencest: Statistical considerations,' ibid.Google Scholar
- Chaitin, G. J. (1969b). 'On the simplicity and speed of programs for computing infinite sets of natural numbers,' ibid.Google Scholar
- Chaitin, G. J. (1970). 'On the difficulty of computations,' IEEE Transactions on Information Theory.Google ScholarDigital Library
- Codd, E. F. (1968). Cellular Automata. Academic Press. Google ScholarDigital Library
- Kolmogorov, A. N. (1965). 'Three approaches to the definition of the concept 'amount of information' ', Problemy Peredach i Informatsii.Google Scholar
- Kolmogorov, A. N. (1968). 'Logical basis for information theory and probability theory,' IEEE Transactions on Information Theory.Google ScholarDigital Library
- Loveland, D. W. 'A variant of the Kolmogorov concept of complexity,' report 69-4, Math. Dept., Carnegie-Mellon University.Google Scholar
- Loveland, D. W. (1965). 'On minimal program complexity measures,' Conference Record of the ACM Symposium on Theory of Computing, May 1969. Google ScholarDigital Library
- Martin-Lof, P. (1966). 'The definition of random sequences,' Information and Control.Google Scholar
- Minsky, M. L. (1962). 'Problems of formulation for artificial intelligence,' Mathematical Problems in the Biological Sciences, American Math. Society.Google Scholar
- Moore, E. F. (1962). 'Machine models of self-reproduction,' ibid.Google Scholar
- Von Neumann, J. (1966). Theory of Self-Reproducing Automata. (Edited by A. W. Burks) University of Illinois Press.Google Scholar
- Solomonoff, R. J. (1964). 'A formal theory of inductive inference,' Information and Control.Google Scholar
- Willis, D. G. (1969). 'Computational complexity and probability constructions,' Stanford UniversityGoogle Scholar
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