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Preformation of Ontogenetic Patterns

Published online by Cambridge University Press:  01 April 2022

Michael J. Katz  and
William Goffman
Michael J. Katz
Affiliation:
Division of Applied Mathematics, Brown University
William Goffman
Affiliation:
School of Library Science and Department of Biometry Case, Western Reserve University
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Abstract

Most patterns of an organism develop reproducibly and predictably. Thus, most biological patterns are largely predetermined by the nature of the zygote and by the nature of the surrounding world. Some ontogenetic patterns can also be considered to be preformed. Eighteenth and nineteenth century definitions of ‘preformation’ suggested that all aspects of a precursor pattern—its elements and its configuration—are preserved during development. Today, the idea of preformed configurations has been lost. To revive this lost idea, we offer the following biologically contemporary definition for preformed ontogenetic patterns: preformed patterns are those patterns with topologies that have been conserved during their ontogenies. This definition is presented in precise mathematical language, and its application is demonstrated in a system of developing, abstract patterns.

Type
Research Article
Information
Philosophy of Science , Volume 48 , Issue 3 , September 1981 , pp. 438 - 453
Copyright
Copyright © 1981 by the Philosophy of Science Association

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Footnotes

†

We are indebted to Prof. Ulf Grenander, to Prof. Raymond Lasek and to the journal referee for their comments which led to significant improvements in this manuscript. This work was supported by NIH grants NS 07118 and NS 06278 and by a grant from NSF.

References

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