An interesting rereading of von Neumann and Burks on the theory of
self-reproducing cellular automata. The author explores an
illuminating evolutionary perspective on von Neumann's
accomplishment, with a nontrivial, but still not entirely satisfying
conclusion, namely that von Neumann's universal constructor allows
for evolutionary paths that include construction of successively more
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Very interesting paper. Recommendation of short talk comes not from lack of quality, but belief that essential point can be made relatively succinctly. Other comments:
Author gives a good discussion of evolutionary perspective on von Neumann's construction, but could go further, particularly elucidating further issues that remain after this discussion. E.g.:
1. Evolution by a mutation process on the code for the vN constructor still presupposes the existence of the constructor. Is there a path to "generically" construct the constructor? This is a gap that I don't believe vN managed to fill.
2. One approach to this question could come from the author's comments on vN's comments ("he consistently pointed out how his CA space could support an indefinite variety of quite arbitrary machine configurations and behaviors..."). The inference being that if you take a random configuration on an infinite plane, then with probability one a vN constructor exists somewhere in the configuration. Actually, a full-blown vN self-reproducing universal machine exists somewhere with probability one. But is this a useful observation? If we consider the biosphere, the probabilities of "happening to find" a full-blown cell with reproductive mechanism would probably require a system the size of many universes insead of merely the size of the earth's surface. But I haven't done even a seat of the pants calculation of these probabilities; I just want to illustrate how the train of thought could play out.
3. I agree with the author's own statement of the most important shortcoming of his analysis (in conclusion): namely that demonstrating the possibility of a pathway that could result in "organisms" with increasing complexity is not as compelling as showing that such a pathway will actually be explored with high probability.
I tend to think of the shortcomings in my points 1 and 3 as shortcomings of vN's approach/mode of analysis, rather than shortcomings of the author's analysis. Where does the author come down on this issue?