[NKS 2004: How big a possibility space?] - A New Kind of Science: The NKS ForumA New Kind of Science: The NKS Forum
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NKS 2004: How big a possibility space?
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Posted by: Jason Cawley
Wolfram in the second half of the morning session addressed in passing the size of a practical possibility space for NKS work, with current computing power. He explained a few examples, involving a few trillion possible rules - each of course with many initial conditions, which can be evolved for many steps.
That is the size of space it is practical to explore, by sampling and filtering etc. "So operationally, that is what we mean by "simple"", he said. Naturally, smaller spaces can be explored more extensively. When one gets down to tens of thousands, one can employ exhaustive search.
How does one get a tractable possibility space, in a system with many elements? One must focus on just the essential features of the phenomenon one wants the model to capture, and idealize away the remaining details. To answer a different question, one may need a different model making different idealizations. One wants the model to be isomorphic to some subsystem or internal logic of the real system. But there may be others - at different scales, for example - that one just leaves out.
This is similar to the problem of picking a dependent variable and isolating critical system parameters in traditional science. When a few numbers are supposed to capture what a system is doing, they will inevitably leave out some aspects of system behavior, or only characterize some average about them. If the right parameters are chosen, though, they will still tell you important things about the system.
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