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But if one has a system that yields the same causal network independent of the scheme used to apply its underlying rules, then the situation is different.
As one example, the pictures on the facing page were all generated by starting from a single black cell and then applying very simple two-dimensional cellular automaton rules.
starting with a single black cell and then applying a simple two-dimensional cellular automaton rule 250 times.
specific process one can apply it to a piece of raw data, and then see how the results compare with those obtained from all possible sequences.
Human Thinking
When we are presented with new data one thing we can always do is just apply our general powers of human thinking to it.
For all the other methods that we have discussed effectively operate by taking each new piece of data and separately applying some fixed procedure to it.
And so if we study computation at an abstract level, we can expect that the results we get will apply to a very wide range of actual systems.
But the ideas that I have developed are general enough that they do not apply just to nature.
At first biology seems to do better by repeatedly making random modifications to genetic programs, and then applying natural selection.
Mathematica works by taking its input and repeatedly applying transformation rules—a process which normally reaches a fixed point that is returned as the answer, but with definitions like x = x + 1 ( x having no value) formally does not.