The laws of physics are time-varying? That seems like... well, let's at least call it not a mainstream opinion.<p>> The universe exists apart from being evoked by the human imagination, while mathematical objects do not exist before and apart from being evoked by human imagination.<p>Smolin says this in his conclusion. But when people talk about the unreasonable effectiveness of mathematics (at least when I've heard it), <i>this</i> is what they're talking about - not that mathematical objects exist in some nonphysical platonic space, but that they exist <i>in our heads</i> as a game we play - a formal axiomatic system. The question is, why does our formal game, which we think is mostly abstract, suddenly and surprisingly turn out to work so well to model the physical universe? (We don't find that chess works as a model, for example.)<p>Smolin answers that, sort of. He says that since the basics of mathematics are in nature, it's reasonable that as math progresses, it will continue to correspond to nature. But it seems to me quite a stretch to say that, because the natural numbers correspond to the existence of countable things in nature, and natural objects take up space, therefore pseudo-Riemannian manifolds will correspond to general relativity. To say that is reasonable, it seems to me, requires making a mysticism around nature.
I just saw that this was a submission to the FQXi contest on "Trick or Truth: the Mysterious Connection Between Physics and Mathematics". I've only read 1st and 2nd place and this piece by Smolin yet, but I'm sure a lot of the other submissions are worthwhile to read as well:<p><a href="http://fqxi.org/community/forum/category/31424" rel="nofollow">http://fqxi.org/community/forum/category/31424</a>
> everything that exists is part of the
natural world, which makes up a unitary whole.<p>That would cause problems for super-string theory, the big bang and many other models of the origin of the universe.
I got a couple pages in before giving up. The question of existence/non-existence of theorems simply isn't as important as he makes it out to be, and I say this as somebody who's read a fair amount of relevant philosophy.