> On 30 Aug 2019, at 19:36, John Clark <[email protected]> wrote: > > On Fri, Aug 30, 2019 at 11:26 AM Bruno Marchal <[email protected] > <mailto:[email protected]>> wrote: > > >> Euclid proved that IF numbers have nothing to do with physics then there > >> are infinitely many primes. But that's a big if. > > That is false. Or give the reference. > > I need to provide a reference for you to believe Euclid didn't mention > physics in his proof?!
You were ambiguous. But so we agree that Euclid didn’t mention physics, nor any physical assumption, in his proof on the prime numbers. > > > Euclid simply did not assume that numbers have nothing to do with physics. > > Then why didn't Euclid mention physics in his proof? Because physics is irrelevant for that issue. Your statement above was ambiguous, and give the pirmeression that Euclid assume *expliciltly* that numbers are independent of physics. > > > The numbers, informally, intuitively, as well as formally have no relation > > at all with any assumption concerning the existence of a physical reality, > > But the numbers we use DO have a hidden assumption about the existence of the > physical. Nope. > As children we are taught one way to measure the distance along the number > line, and measuring distance is important because it's the reason we say > 2+2=4. We say for example 300 is larger than 8/45 because it is further from > zero. However if there really are an infinite number of prime numbers then > with p-adic numbers there are an infinite number of ways to measure distance > and all of them are internally as self consistent as the distance measuring > procedure engineers use to build a bridge. For example if p is 3 then the > 3-adic distance between zero and 300 is 1/3 but the 3-adic distance between > zero and 8/45 is 9, so by the 3-adic measure 8/45 is much larger than 300. > Even though it's internally consistent only abstract mathematicians are much > interested in p-adic numbers because they're not much use in physics. That is like arguing that 1 + 1 = 1, because one cloud + one cloud is one cloud. That is not valid. It is like saying that group theory is false because 6 has no inverse in (N, +, *). > > > Then you should not use it to claim that only a primitively material > > computation can support consciousness. > > I have not made that claim, I don't even know what "primitively material > computation" means. It means a computation implemented in a physical reality supposed to have basic ontological reality. It is what you are using to say that the computation in arithmetic would be less real, or less able to support consciousness, than the physical computations. Bruno > > 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/CAJPayv1A9eA1yB_sd9iTHV0vqi%3DLSX7WhGSr5vYsCnwsnpaWkQ%40mail.gmail.com > > <https://groups.google.com/d/msgid/everything-list/CAJPayv1A9eA1yB_sd9iTHV0vqi%3DLSX7WhGSr5vYsCnwsnpaWkQ%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/5E4743CB-F7C3-425F-9C26-B3D9E92D9888%40ulb.ac.be.
