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ON LIMITATIONS OF THEORIES OF BIOLOGY JOHN M. MYERS* I. Introduction During the past year I have been trying to prepare a formulation of a theoretical attack on problems of biological organization, with a special emphasis on handling perception in biological systems. Severe difficulties have been encountered, mostly witfi respect to having to decide what are the "significant" abstractions, and no particular formulation has been obtained . However, some interesting considerations have come into focus during the effort, and it now seems appropriate to present a discussion ofwhat one might reasonably hope for from such a theory, at least from my point ofview. We begin with some general considerations. The forces which give meaning to our perceptions of biology are so ramified and interrelated that the boundaries by which we isolate biological entities (cell, organ, organism, species, etc.) are boundaries ofour patience, not boundaries on the relations. The more exacting we become, the more smeared these boundaries get. This is one of the most salient features of the biological world. A related feature is that nothing in it is static, that its very essence is transformation. The current view, for example, as expressed by Oparin [i] and many others, is that of a competition among dynamic patterns, with the competition proceeding in an interrelated way on all levels from chemical through species and even broader interplays. The meaning of any aspect ofan organism, etc., is in the context ofall the competitions in which it plays a part and in their history. The broadest question which I wanted to examine was this: Can we construct a mathematical notion oftransformations and relations between them such that these generate abstract structures corresponding to the * Raytheon Research Division, Waltham, Massachusetts. 238 John M. Myers · Theories ofBiology Perspectives in Biology and Medicine · Winter 1967 biological world in its function, development, and evolution? It was a priori obvious that the knowledge on which to ground such a construction is not yet at hand, but one could look for a theoretical apparatus into which one could incorporate new knowledge and corrections in old knowledge as they occur. The total body of biological knowledge is already enormous, so that one would in a sense be trying to design a library system for biological relations. One would thus be able to look up a particular transformation and be able to call from the library, presumably automated,1 the ramifications of assorted transformations to the extent ofone's interest and patience. The central goal was not merely to amass and store biological data but to examine the possibility of finding generating principles with which one could derive large ramifications of relations starting with a much smaller body ofthem. It seemed that one could derive an algorithm for, say, a growing tree by a process ofsuccessively refining a set ofrelational rules. For instance, one could postulate growing (vertically) as a zeroth order approximation, then incorporate branching, add the relation that a branching event ought to inhibit more branching in that neighborhood, etc. With refinement, one would perhaps be able to generate not just a single shape but a whole family of shapes corresponding to the family one recognizes as a given kind oftree. By this means, one might obtain a relational characterization leaving out the irrelevant detail ofan overly metric description, somewhat in the spirit of a caricature. There were three reasons for desiring this type of description. The first was to characterize the relational character ofbiology in more universal and succinct terms, for instance, by finding significant widely occurring complexes ofcontrol relations. The second was to hunt for sets ofrelational couplings and control relations which could be applied to the evolution, generation, and function ofengineering devices for visual processing, artificial intelligence, etc. The third reason was the hope that, by emphasizing the relational rather than the metric character, one could find an expression of biology that was somehow more "fundamental" than that now available and from which the sizes and shapes we see would eventually be derivable. Even at the almost embarrassingly oversimplified level ofour discussion ofa tree, difficulties ofcomplexity were visible. The form ofa tree does 1 For discussion ofautomated libraries, see [2]. 239 not have much meaning except in...

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