On Wed, Jan 21, 2015 at 7:26 PM, John Clark <johnkcl...@gmail.com> wrote:
> On 18 January 2015 at 18:27, Jason Resch <jasonre...@gmail.com> wrote: > > > Do you believe that *one and only one* of the following statements is >>> true? >>> the 10^(10^(10^100))th decimal digit of pi is 0 >>> the 10^(10^(10^100))th decimal digit of pi is 1 >>> the 10^(10^(10^100))th decimal digit of pi is 2 >>> the 10^(10^(10^100))th decimal digit of pi is 3 >>> the 10^(10^(10^100))th decimal digit of pi is 4 >>> the 10^(10^(10^100))th decimal digit of pi is 5 >>> the 10^(10^(10^100))th decimal digit of pi is 6 >>> the 10^(10^(10^100))th decimal digit of pi is 7 >>> the 10^(10^(10^100))th decimal digit of pi is 8 >>> the 10^(10^(10^100))th decimal digit of pi is 9 >>> Either you answer yes, or no to that question. If you answer yes, I >>> don't see how you can escape mathematical realism. >> >> > Seth Lloyd has estimated that the maximum number of computations that > could be performed in the visible universe is about 10^121 operations on > 10^90 bits, if this is insufficient to find your number is it meaningful > to say pi has a 10^(10^(10^100))th decimal digit? > If we run an AI in a restricted environment which only permits it to perform 10^5 computations, on 10^4 bits of memory, would that AI be correct in its belief that the millionth digit of Pi <http://www.wolframalpha.com/input/?i=one+millionth+digit+of+pi> is meaningless and does not have a definite value? To me that seems to lead to a "mathematical solipsism", where what would be true in math would depend on what each individuals believes is true and they are capable of proving. > I don't know, it depend on if mathematics gave rise to physics or physics > gave rise to mathematics. > > I think those might be disjoint questions. Many, and perhaps most physicists don't believe mathematics gave rise to physics, and yet hardly any of them are ultrafinitists. The only thing it depends on is whether or not mathematical objects have objective properties independent of us/the universe, and whether those properties exist regardless of our inclination or ability to find them. Jason -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
