> On 28 Aug 2019, at 21:21, John Clark <[email protected]> wrote: > > On Wed, Aug 28, 2019 at 1:15 PM Jason Resch <[email protected] > <mailto:[email protected]>> wrote: > > >> And both the Axiom Of Choice and the Continuum Axiom involve infinity and > >> physics has no use for infinity so physics doesn't care if those axioms > >> are true or not, so there is no way to independently determine their > >> truth, so stuff based on them are the equivalent to mathematical Harry > >> Potter stories. > > > Is this to say you agree? > > You mean you agree with me? > > > If you disagree with anything I said that missed it. > > I disagree if you still think a program doesn't need to be running to *do* > something.
It is just obvious that a program needs to be run to do something. But only a universal number/machine can run something. And indeed, all the universal machine eventually run all programs, already in the arithmetical reality. Physics emerges from that. If your conception of mathematical existence was right, mathematics would be founded on physics. Unfortunately, physics, the science, assume the numbers at the start. Bruno > > It is true we never access truth, but the same dilemma haunts us in physics. > > It's not perfect but it's all we've got, Physics is the only way we have of > determining even the approximate truth. You hold up 2 physical fingers and > then you hold up 2 more physical fingers and you see there are 4 and not 5 or > 3. Why else would you be so convinced that 2+2 is 4, and why else would > mankind pick only those axioms and rules of operation that make things come > out that way? > > > Have I changed your mind regarding what Minsky said regarding possible > > programs? > > No but I don't want to argue over what Minsky's words did or did not mean as > if it were the talmud and not just a very smart man giving an interview. > > > Regarding axiom of choice, I believe it's independent of ZFC, but that > > doesn't imply it's independent of another more powerful system. > > If the axiom of choice is true Banach and Tarski proved you can cut up a > solid 3D sphere into as few as 5 pieces and then by just moving the pieces > around and rotating them (and not changing the pieces size or shape) you can > reassemble those 5 pieces in such a way that you end up with 2 spheres each > one identical to the original sphere. And if you had a tiny sphere and a huge > sphere you could cut up and reassemble the tiny sphere so it's identical to > the huge sphere and cut up and reassemble the huge sphere so it's identical > to the tiny sphere. But that's not the way our world works, that's not the > way physics works, so any proof that starts with the assumption the axiom of > choice is true is like a book that starts with the assumption a boy could be > a wizard, such proofs are mathematical Harry Potter stories. The book may > have no plot holes and the proof contain no errors but both are fiction > nevertheless. > > I should add that neither Euclid's geometry or Einstein's Non-Euclidean > geometry need the axiom of choice, nothing in Physics does. > > 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] > <mailto:[email protected]>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/CAJPayv3udzu9Fm3JN17FcB81MF97-0SPKyi77ud4_iZEE9G4uw%40mail.gmail.com > > <https://groups.google.com/d/msgid/everything-list/CAJPayv3udzu9Fm3JN17FcB81MF97-0SPKyi77ud4_iZEE9G4uw%40mail.gmail.com?utm_medium=email&utm_source=footer>. -- 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 view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/9B7DC3A9-0B04-4E5D-8E5F-97094C60BD50%40ulb.ac.be.
