----- Original Message ----- From: "Dan Asimov" <dasimov@earthlink.net> To: "math-fun" <math-fun@mailman.xmission.com> Sent: Wednesday, September 26, 2007 2:07 PM Subject: Re: [math-fun] Mathematical cosmos article by Max Tegmark
Er, I meant to send that to Rich first, but instead sent it directly to all of math-fun. Oh, well.
A friend sent me that Tegmark article from the Sept. 14 New Scientist magazine, and the idea that physics is ultimately nothing more than the underlying mathematics seemed worth sending on to math-fun.
I'd be very curious to learn people's reactions to that article.
--Dan
An interesting idea. Suppose I posit that Peano's Axioms = Theory of Everything. Peano's Axioms are consistent, and described undefined entities (natural numbers) by their interrelationships. It merely remains to figure out what aspects of natural number theory map to observables in the universe, and BAM, we're done. But, aye, there's the rub. Those stinking observables. Our mathematical universe must have buried within it some model of the observables. Maybe the author is advocating some method of sieving all possible theories for ones that can model the observables, but methinks that this is folly from a practical standpoint, especially given that the observables reveal not a single clue about their true relationships. To my knowledge, all of today's pet physical theories have frayed edges, i.e, scales at which they fail to describe phenomena accurately. This implies that the theories are not globally accurate, they are only approximations to the truth, and in that sense no better than classical mechanics. So in our mathematical universe, we know neither where the observables are, nor do we know how the observables are related so that we can even begin to look for them. After all this time, we really still do know nothing about physics, sometimes very accurately, but nothing nonetheless. Since the only way to verify that our mathematical universe is correct would be to identify the observables within it and compare those with actual observations, and given that the observables cannot be located within the theory, it seems we are stuck with working from the observables to the theory, the time-honored methodology.