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But my guess is that among appropriate classes of rules there will actually be quite a large number that lead to universes which share at least some features with our own. Much as the same laws of continuum fluid mechanics can emerge in systems with different underlying rules for molecular interactions, so also I suspect that properties such as the existence of seemingly continuous space, as well as certain features of gravitation and quantum mechanics, will emerge with many different possible underlying rules for the universe.

But my guess is that when it comes to something like the spectrum of masses of elementary particles—or perhaps even the overall dimensionality of space—such properties will be quite specific to particular underlying rules.

In traditional approaches to modelling, one usually tries first to reproduce some features of a system, then goes on to reproduce others. But if the ultimate rule for the universe is at all simple, then it follows that every part of this rule must in a sense be responsible for a great many different features of the universe. And as a result, it is not likely to be possible to adjust individual parts of the rule without having an effect on a whole collection of disparate features of the universe.

So this means that one cannot reasonably expect to use some kind of incremental procedure to find the ultimate rule for the universe. But it also means that if one once discovers a rule that reproduces sufficiently many features of the universe, then it becomes extremely likely that this rule is indeed the final and correct one for the whole universe.

And I strongly suspect that even in many of the most basic everyday physical processes, every element of the underlying rule for the universe will be very extensively exercised. And as a result, if these basic processes are reproduced correctly, then I believe that one can have considerable confidence that one in fact has the complete rule for the universe.

Looking at the history of physics, one might think that it would be completely inadequate just to reproduce everyday physical processes. For one might expect that there would always be some other esoteric phenomenon, say in particle physics, that would be discovered and would show that whatever rule one has found is somehow incomplete.

From Stephen Wolfram: A New Kind of Science [citation]