On Sun, Jul 17, 2011 at 2:54 PM, meekerdb <meeke...@verizon.net> wrote:
> On 7/17/2011 11:50 AM, Jason Resch wrote: > >> For Euler's identity to hold, Pi must exist in its infinitely precise >> form, but Pi does not exist in its infinitely precise form anywhere in this >> universe. >> > > You don't know that, since space may well be a continuum (c.f. the recent > paper by Feeney et al). Pi is a number, that space may be a continuum doesn't make this number appear anywhere in the universe. We can point to two electrons and say that is an instance of the number 2, but where would we see a physical instance of the number Pi? > > > Ben believes mathematical truth only exists in our minds, but does Pi >> really exist in our minds, or only the notion that it can be derived as the >> ratio between a plane circle and its diameter? >> > > But that's the characteristic of mathematics, its statements are notions > and notions are things in minds. So there is no difference between the > notion of pi existing in our minds and pi "really" existing in our minds. Is there no difference between the notion of the moon existing in our minds and the moon "really" existing? We say the moon exists because it has properties which are objectively observable. Mathematics, like physics i a source of objective observations and therefore part of reality. What makes the moon more real than the number 5? If you say it is because the moon is some place we can go to or see with our eyes, then what makes the number 5 less real than the past, or that beyond the cosmological horizon, or other branches of the wave function? > > > Pi is so big that its digits contain all movies and all books ever >> created, surely this is not present within our minds, >> > > Expressing pi as a sequence of digits is a notion in our minds. That Pi takes an infinite number of bits to describe, and an infinite number of steps to converge upon, is more than a notion in our minds, it is an incontrovertible fact. > The sequence is no more in our minds than is 10^10^100. Pi is not special, there are many numbers which exists that are beyond the physics of this universe. I consider this further evidence of mathematical realism. If you say a Googolplex exists, then where is it? There are not a Googolplex things in this universe to count. Therefore if you think a Googleplex exists, then numbers exist independently of physical things to count. Even if there was a universe with nothing in it at all, the numbers would still exist. > > > but it is exactly what must exist for e^(2*Pi*i) = 1. >> > > I disagree. For Euler's identity to hold just means that if follows > logically from some axioms we entertain. > > > There are other ways to prove Euler's identity, but for that equation to be true, those irrational numbers (e and Pi) must be used with infinite precision. I have two questions for you: Do you believe Pi has an objective magnitude? Do you believe humans know what that magnitude is? Jason -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
