I close this brief review with two final remarks relating to Genetic Relativism.
Firstly, von Neumann himself seems to have discounted even the possibility of Genetic Relativism being applicable to his models. In his discussion of different kinds of mutations, he stated explicitly that mutations affecting that part of a description tape coding for the core part of the self-reproducer (i.e. coding for in the terms used above) would result in the production of ``sterile'' offspring (von Neumann, 1949, p. 86): the implication is that this would always be the outcome of such mutations. I suggest that such a claim is too strong, in general. My view is that, on von Neumann's model, it is probably fair to say that such mutations would almost always yield sterile offspring--but that, depending on the detailed design of the constructive automaton, and the nature of the particular mutation, there might be exceptional cases where the offspring would still be an self-reproducer, but containing an altered core constructive automaton.
Secondly, when tackling von Neumann's problem within the framework of Genetic Absolutism, it was necessary to assume a degree of compositionality in the genetic language, to assure that there would exist a range of mutations not affecting the core constructive automaton in a self-reproducer; without this assumption it would be difficult, if not impossible, to argue that the set of self-reproducers anchored on this single core general constructive automaton would be connected under mutation. This compositionality assumption is more or less equivalent to the biological hypothesis of Genetic Atomism, which holds that genomes may be systematically decomposed into distinct genes which, individually, have absolute effects on phenotypic characteristics (see McMullin 1992b, p. 11; Dawkins 1989, p. 271). This again represents a divergence between von Neumann's pragmatically convenient solution schema for his particular problem, and the realities of the biological world (where any simple Genetic Atomism is quite untenable). I conjecture therefore that, should we wish to move away from a strict Genetic Absolutism in our formal or artificial systems we might well find it useful, if not essential, to abandon simple compositionality in our genetic language(s) (i.e. Genetic Atomism) also. This, in turn, would ultimately lead away from self-reproducer architectures in which there is any simple or neat division between the core constructive automaton and the rest of the automaton (though there might still be a fairly strict separation of the description tape--i.e. a genotype/phenotype division).
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