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And I have little doubt that all sorts of such systems can be identified both terrestrially and extraterrestrially—and certainly require nothing like the elaborate history of life on Earth to produce.
sorts of practical processes in which bias or deadlock can be avoided by using randomness, or in which one wants to generate behavior that is somehow too complex for an adversary to predict.
And so as one example page 249 shows a two-dimensional cellular automaton often called the Game of Life in which all sorts of localized structures occur even on a white background.
Indeed, it is a general feature of class 4 cellular automata that with appropriate initial conditions they can mimic the behavior of all sorts of other systems.
And while ordinary integers still satisfy all the constraints, the system is sufficiently incomplete that all sorts of other objects with quite different properties also do.
But it turns out that there are all sorts of other axioms that also do this.
For though there are connections of all sorts, this book is first and foremost about a fundamentally new intellectual structure, that needs to be understood in its own terms, and cannot reasonably be fit into any existing framework.
So given, say, an ordinary piece of rock in which there is all sorts of complicated electron motion this may in a fundamental sense be doing no less than some system of the future constructed with nanotechnology to implement operations of human thinking.
One can represent the inside of such a system much like a sorting network from page 1142 —but with s -input s -output gates instead of pair comparisons.
Arithmetic systems [emulating register machines]
Given the program for a register machine with nr registers in the form on page 896 , an arithmetic system which emulates it can be obtained from
RMToAS[prog_, nr_] := With[{p = Length[prog], g = Product[Prime[j], {j, nr}]}, {p g, Sort[Flatten[MapIndexed[ With[{n = First[#2] - 1}, #1 /.