The nature of number
August 24, 2012 at 12:51 pm
(This post was last modified: August 24, 2012 at 12:56 pm by Categories+Sheaves.)
(August 24, 2012 at 10:49 am)whateverist Wrote: Really? I've never heard or thought about this. I can't think how General Relativity (or anything else) prevents pi from occupying one unique location on the number line. How can it not be a constant? I am intrigued. [But I have only begun reading this tread so perhaps this has already been discussed.]If some neighborhood of spacetime has a nontrivial curvature, any 'circles' you encounter there may not satisfy everybody's favorite equations involving pi (like the one relating radius to circumference, etc.). So in some sense it isn't very good at being an observable physical constant. But pi shows up in a bunch of equations relating to curvature anyway (exemplo gratis) so pi's existence as a fixed/abstract constant is even more important in general relativity