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UBC Theses and Dissertations

Typogenetics : a logic of artificial propagating entities Morris, Harold Campbell


This thesis deals with abstract models of propagation (especially, self—replication). As some of these reflector borrow from nature, a summary of biology's current understanding of natural reproduction (mitosis) is provided for background. However, the predominant concern is with entities realized in uninterpreted symbolic systems, and associated philosophical and design problems. Thus the comparison that is made between artificial and natural modes of propagation is intended primarily to enhance conception of the former. Automata constitute one type of formal model. With a simple Turing Table the concept of a self-replicating string is illustrated. The idea of a logical universe in which propagating "virtual" entities emerge and interact is explored with reference to cellular automata. A formal system called Typogenetics provides the centerpiece of this thesis. The system, first presented in an incomplete form in Hofstadter (1979), is here fully developed (augmented with a useful program for personal computers). A Typogenetics string ("strand," in analogy to a DNA strand) codes for operations that act to transform that very strand into descendant strands. Typogenetics strands exhibited include, among others, a pallindromc self-replicator coding for operations sufficient to replicate itself; a "self-perpetuator" deforming and then reforming itself through fully compensatory operations; and an "infinitely fertile" strand bearing an infinitude of unique descendants. Meta-logical proofs establish certain general propositions about the Typogenetics system, e.g. that for every strand there is a mother strand. Redactio reasoning, of potential general is ability beyond Typogenetics, shows how a hypothetical strand can be ruled out by establishing the incommensurability of its two identities qua packet of operations and qua operand. A Russellian—type paradoxical strand that has all and only the non—self-replicating strands for offspring is considered (is it a self—replicator?), spurring discussion of the Theory of Types and Hofstadter's "strange loops."

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