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New Perspectives in Nonlinearity or What to do When the Whole is More than the Sum of its Parts

Published online by Cambridge University Press:  28 February 2022

John H. Holland
John H. Holland*
Affiliation:
The University of Michigan
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Extract

Before starting, I would like to beg the reader's indulgence. This paper is not a survey, or even a balanced account mentioning related work. It is simply an exposition of one approach to the problem. As such it contains only three references — all to my own work! Mea culpa.

In each of the sciences there are pivotal problems which can be formalized as searches for the global optimum of a function f: A→R, where A is an appropriately chosen domain of elements and R is the set of positive real numbers. In genetics, for example, A becomes the genotypes (combinations of genes) of interest and f assigns to each genotype its fitness; in economics (von Neumann's model), A becomes mixes of economic activities and f assigns to each mix its utility; in game playing, A becomes the possible strategies and f assigns to each strategy its minimax value; and so on.

Type
Part VII. Mathematics and Philosophy of Science
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1976 , Issue 1: Volume One: Contributed Papers 1976 , 1976 , pp. 240 - 255
Copyright
Copyright © 1976 by the Philosophy of Science Association

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Footnotes

1

Much of the research reported here was supported by National Science Foundation Grant DCR71-01997.

References

Holland, J.H. Adaptation in Natural and Artificial Systems. Ann Arbor: The University of Michigan Press, 1975.Google Scholar
Holland, J.H. “Adaptation.” In Progress in Theoretical Biology, 4. Edited by R. Rosen. New York: Academic Press, 1976. Pages 263-293.CrossRefGoogle Scholar
Holland, J.H. “Studies of the Spontaneous Emergence of Self- Replicating Systems Using Cellular Automata and Formal Grammars.” In Automata, Languages, Development. Edited by Lindemayer, A. and Rozenberg, G.. Amsterdam: North-Holland Publishing Co., 1976.Google Scholar