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So in the end I strongly suspect that the basic rules by which human memory operates can almost always be viewed as being essentially fixed—and, I believe, fairly simple.
A description based on output from a cellular automaton rule that one has never seen before is thus for example not likely to be useful.
But for each specific computation we wanted to do, we always set up a cellular automaton with a different set of underlying rules.
And it leads to an explanation of how we as humans—even though we may follow definite underlying rules—can still in a meaningful way show free will.
For example, as I discussed at the end of Chapter 7 , models based on traditional mathematical equations often give constraints on behavior rather than explicit rules for generating behavior.
The underlying rules for the Turing machine then define constraints on which sequences of such statements can be true.
And with the cellular automaton being a universal one such as rule 110 this implies that the axioms of arithmetic can support universality.
For the point is that instead of handling objects like integers directly, axiom systems can just give abstract rules for manipulating statements about them.
The functions are numbered like 2-neighbor analogs of the cellular automaton rules of page 53 .
And indeed the Principle of Computational Equivalence implies that a vast range of systems—even ones with very simple underlying rules—should be equivalent in the sophistication of the computations they perform.