means is that any simplicity observed in known physical laws may have little connection with simplicity in the underlying rule.

Indeed, it turns out that simple overall laws can emerge almost regardless of underlying rules. And thus, for example, essentially as a consequence of randomness generation, a wide range of cellular automata show the simple density diffusion law on page 464—whether or not their underlying rules happen to be simple.

So it could be that the laws that we have formulated in existing physics are simple not because of simplicity in an ultimate underlying rule, but rather because of some general property of emergent behavior for the kinds of overall features of the universe that we readily perceive.

Indeed, with this kind of argument, one could be led to think that there might be no single ultimate rule for the universe at all, but that instead there might somehow be an infinite sequence of levels of rules, with each level having a certain simplicity that becomes increasingly independent of the details of the levels below it.

But one should not imagine that such a setup would make it unnecessary to ask why our universe is the way it is: for even though certain features might be inevitable from the general properties of emergent behavior, there will, I believe, still be many seemingly arbitrary choices that have to be made in arriving at the universe in which we live. And once again, therefore, one will have to ask why it was these choices, and not others, that were made.

So perhaps in the end there is the least to explain if I am correct that the universe just follows a single, simple, underlying rule.

There will certainly be questions about why it is this particular rule, and not another one. And I am doubtful that such questions will ever have meaningful answers.

But to find the ultimate rule will be a major triumph for science, and a clear demonstration that at least in some direction, human thought has reached the edge of what is possible.

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