On Wed, Nov 28, 2018 at 9:31 AM James Propp <jamespropp@gmail.com> wrote:
Julia Robinson has a good quote: "What is proved about numbers will be a fact in any universe."
Though I suppose there could be universes harboring intelligent life in which the laws of physics are such that pi isn't seen as a very interesting number until fairly late in a culture's development, and facts about pi are seen as arcane and boring.
That's still the case for the vast majority of humans. In hyperbolic space, the circumference is 2 pi R sinh r/R, where R is the Gaussian curvature of the plane, so perhaps an inhabitant of such a space would consider (pi R) more fundamental. Also seems like a q-deformed exponential function wouldn't have period 2 pi. So while pi would still be pi, it wouldn't necessarily have the same physical significance.
By the way, have any of you read the R. A. Lafferty short story in which some people discover some small integers (less than ten) that had hitherto gone unnoticed? The relevant phrase is something like "involutive number series" but I couldn't dig up any information with Google.
There's a popular hypnosis trick where people are made to forget a number below ten and then count their fingers: https://www.google.com/search?q=hypnotized+to+forget+the+number+6 -- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike https://reperiendi.wordpress.com