... time.¹

Note that there are still inward, degenerative, pathways shown here; the claim is only that this graph permits the possibility of a growth in complexity; whether it actually will grow is a different question, and an altogether more difficult one. I will return to this briefly in the conclusion.

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....²

It is neither trivial nor obvious that there exists a general constructive automaton within any given $M$; this is why the bulk of von Neumann's unfinished manuscript is taken up with the detailed design of a particular example $u_0$ to establish this result for his particular $M$.

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... right.³

Indeed, we call such changes ``mutations'' precisely because they can ``breed true'' in the offspring.

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... processors.⁴

Here, of course, I am referring to the so-called ``von Neumann computer architecture'' [22] (which was not, by any means, solely von Neumann's invention) rather than to his very different work on cellular automata.

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