Wolfram Science Group
Phoenix, AZ USA
Registered: Aug 2003
Paul - yes simplicity is likely to be a good guide. Wolfram suspects that even the initials of a fundamental rule will be simple - or at least, that we won't find it unless the initial and rule are both simple, a significantly easier claim. But the underlying rule is likely to be universal.
Why? Well, if every phenomenon nature shows were simple, then I'd agree with your argument, that universality would be "formal overkill". But instead we see all classes of behavior. And we know which class of formal system exhibits all classes of behavior, and it is not the simplest class.
The math of traditional physics stresses all sorts of symmetries, in part because those make it much easier to solve things. But while we see gobs of symmetry at a fundamental rule level, the universe is not remotely simple, symmetry, periodic, fixed point-ee, or anything of the sort.
And we have formal precedent for systems evolving according to simple underlying rules, with plenty of low level structure and regularity caused by the form of the rule, that nevertheless generate elaborate complexity and variety, even from very simple initial conditions. They are computationally irreducible underlying rules.
That is enough to suspect that the underlying rules, whatever they are, will be at least that high in the computational behavior scale. Whether irreducible and universal usually coincide, is of course an open NKS question, and Wolfram's PCE amounts to the conjecture that they will. If that is true, then the previous will extend to "the underlying rule is probably universal".
Which doesn't mean that it will have some incredibly elaborate initial, exploiting that inherent flexibility. You can start a universal rule off simply. When you do, you still get lots of its inherent potential variety, since subpieces of the evolution pop up here or there in the pattern, that mimic different initials (or more strictly, pieces thereof). That's the idea. It is a possible explanation for the mix of variety and simplicity we see in nature.
It could be wrong, of course. It is a conjecture, and a fairly heroic one, as extrapolations go. But we have evidence against overly symmetric and simple alternatives, from the lack of perfect simplicity or regularity seen in the history of the universe.
Now, sure, some alternate explanations have other ways of generating that from relatively simple formalisms. But if they invoke objective chance to get there, they haven't really explained it. Instead they underspecify a universe. You can get a nice symmetric ensemble of possibles and just let objective chance pick one, but then the symmetry is entirely imposed, really.
I suppose I should add that you are right that too much should not be hung on universality alone. If someone seeking fundamental computational rules for physics just relies on an argument of the form, "rule X is universal, so it has some possible initial condition in which a computation parallel to the universe can in principle be found", that is a weak argument.
The NKS book does not do this. Instead, Wolfram considers and rejects numerous possible computational schemes as unpromising, when known physical relations or symmetries would be too artificial in that set up. E.g. straight CA models do not naturally produce spatial isometry (they tend to have preferred directions along lattice "grains"), so they are out. He wants a set up in which curved space is natural, relativity works, etc. In that sense, you are right that a focus on known simplicities has to guide any search for a computational model for physics.
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