Despite the simplicity of the axioms governing evolution, the resulting behavior rapidly becomes so chaotic as to be actually unpredictable. It’s because the graph is interfering with itself, a short circuit. If we take this idea a little farther, and apply the cellular automata rules not only to a grid, but to a graph — no more than a series of points with connecting lines — a new ‘type’ of rule/behavior become available (transforming the connections between points) and with it a corresponding new kind of complexity.

Yet even the simple versions of these automata can be considered, in some sense anyway, as isomorphic to the ’system’ of computation itself. With a little skill in deciding the rules for interpretation, you can use the automata as little calculators for doing any computation you can formalize. Perhaps a little crack opens upon between P and NP, that in using the machine to ‘theorize’ itself, we manage to ‘think’ the boundary of computability — and so perhaps cross it…? Perhaps. This is the paradox of AI at its heart: as soon as we discover a new algorithm, we understand it, we ‘work it out’ and so it is no longer ‘truly’ AI: we will push this boundary back until we discover either something so simple it cannot be explained further, or something so complex it cannot be explained at all (I’m thinking here of quantum mechanics, for instance.)

Thanks for this!

Joe

http://www.elsewhere.org/cgi-bin/postmodern