On Sun, Sep 1, 2019 at 8:41 AM Bruno Marchal <[email protected]> wrote:
> > *so we agree that Euclid didn’t mention physics, nor any physical > assumption, in his proof on the prime numbers.* > Yes Euclid said nothing about physics in his proof, but he should have. A proof is only as good as the assumptions it starts out with and Euclid assumed physics could be ignored. > *> Because physics is irrelevant for that issue.* > The very nature of prime numbers depends on physics. A number is prime if it can't be divided by any number except itself and 1, and so it is claimed by mathematicians that if n is prime then n+1 can not be prime because it can be divided by 2. But if the computational resources of the expanding accelerating universe is finite then there must exist a very large but finite prime number N such that the universe is unable to divide N+1 by 2 even in theory. >> 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.* > With a cloud sometimes it's 1 and sometimes it's 2, but with fingers and rocks and many other things there is an invariance, it's always 2, and 2+2 is always 4. We get these answers because we've agreed on a way that is internally self consistent to measure how far a number is from zero. Using that distance measure we say 300 is much further from zero than 8/45 and is therefore larger, but there are plenty of other ways to measure distance, if we used the 3-adic way for example then 8/45 is larger than 300. So why don't we use 3-adic arithmetic and teach it to children? Because although it's just as self consistent intuitively it seems wrong and because it is useless in dealing with physical objects like fingers. > *>>> 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. * > I don't insist that the material computation we see around us be the basic reality, maybe it is but maybe it's not and we're in a simulation. However I do insist numbers can't be the basic reality. *> 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. * > I'm saying there is no such thing as numbers and only numbers doing computation so it can't support consciousness or intelligence or anything else. 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 view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAJPayv392eunXzL6oHfwbyAtsBeMb4mfek%2BJa8vA64fN9CKvrw%40mail.gmail.com.
