On Friday, January 23, 2015, John Clark <[email protected]> wrote: > > On Thu, Jan 22, 2015 at 4:46 PM, Jason Resch <[email protected]> wrote > >>> >> Do we know that? Do we know that such a digit exists? >> >> > It follows from the axioms that there is a certain definite digit. > > They show you how to generate terms in a sequence and if you add up enough of them you'd get the the 10^(10^(10^100))th decimal digit of pi; but it assumes that there is no barrier that makes doing that impossible and states that assumption with 3 little dots (...). I don't know for certain but those 3 little dots *might* be saying something that is logical nonsense, I do know for certain that the first mathematicians who used those 3 little dots knew nothing about quantum mechanics or the computational limit of the universe, and that gives me pause. >
What I explained is that if you think there is a largest number *that* is what definitely leads to logical nonsense. Say there is a largest number N, such that N+1 is not a bigger number, but is still N. That means N+0 = N+1. Now subtract N from both sides. >> >> > Or do you propose there is some last digit of Pi which varies from place to place according to the available local computing resources of one's local environment? > > I wouldn't call the entire universe a local environment. Even with accelerating expansion? What about AIs trapped in simulations? > And if what mathematicians have been saying for years is really true (and I'm not saying it is true but it might be) and math is a language then any digit of pi that requires more than 10^121 calculations to compute , like the 10^(10^(10^100)) digit, is as fictitious as the last digit of pi in conventional pre-quantum physics mathematics. Then e^(2*pi*i) wouldn't equal 1. Nor would a circles diameter / pi yield it's diameter. > >> >> > Neither has to be more fundamental than the other. Mathematics only needs to have an independent existence. > > If mathematics is a language then it needs something to talk about, and like any language you can write fiction or nonfiction. If it's just a language then mathematics can talk about the physical world (non-fiction) but it can also be used to write fiction. So some or the more esoteric and abstract areas of mathematics, and perhaps even something as mundane as the Real Numbers, *might* be rather like a mathematical version of a Harry Potter novel. > No, fiction like Harry Potter doesn't kick back. If you can simply make up the largest Mersenne prime then do so, there's a lot of prize money being offered for it. >> >> > So either one must say mathematics is independent of physics, > > That can't be, the two are clearly related, but what is not known is if physics gave rise to mathematics or mathematics gave rise to physics. > >> > or accept some ultrafinitism philosophy of mathematics which is incompatible with existing axiomatic systems. > > Yes, but just because something is a axiom doesn't necessarily mean it's true, and one of the axioms are those 3 little dots, and that axiom might not *correspond* with reality. > >> >> > Here is another example to ponder: >> I find two prime numbers A and B, each about a million digits long, multiply them together to get a composite number C, write down C, then throw the computer used to generate those A and B into a black whole which won't evaporate until long after all protons in the universe have decayed. > > Protons will decay in only about 10^40 years and even the larges black Hole will decay in about 10^99 years, a blink of a eye compared with eternity; or at least it is if mathematics is more fundamental than physics, otherwise eternity, a infinite number of years, does not exist. > >> >> >The number C is so large it can't be factored in the life of the universe. Do you believe A and B have definite values despite our inability to compute them? > > If mathematics is just a language and if factoring that composite number would exceed the computational capacity of the entire universe and if you really can destroy information (and nearly all physicists think that you can not) then yes, A and B would no longer have definite values; I mean if you destroy something then obviously it no longer exists. But if you can destroy information then all sorts of other very weird things could happen too. However I don't think you can destroy information. I wasn't asking whether you thought they were destroyed but whether or not the factors of C still had definite values or not. Jason > > John K Clark > > > > > > > -- > 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 [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/d/optout. > -- 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
