> On 1 Sep 2019, at 17:58, John Clark <[email protected]> wrote: > > On Sun, Sep 1, 2019 at 8:41 AM Bruno Marchal <[email protected] > <mailto:[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.
He assumed also that Christian, and Islamic and many other theologies/metaphysics can be ignored. That is ridiculous. He proves things from what he is assuming, like any logician or mathematician would do. That he is not assuming your materialist religion is, simply, not relevant at all. Euclid assumes only what has been formalised since; that is no more than elementary arithmetic (see my precise account on this in preview post, or in may longs texts). > > > Because physics is irrelevant for that issue. > > The very nature of prime numbers depends on physics. Are you trying to win the argument of the most ridiculous statement ever asserted. Of course an expression like “very nature” is enough fussy to claim what you want, but the reality is that being prime or not is independent of any physical laws, except in the sense that if Mechanism is true, the physical laws might depend on the prime numbers (in that direction!). Indeed that can be said illustrated from the fact that in string theory, to get the mass of the photon right, we use 1+2+3+4+5+… = -1/12, which is a statement about the prime numbers, just a little bit disguised. So physics can depends on math, explainingly so with mechanism, but with or without Mechanism, math is independent of 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. Of course, if your god cannot do something then it is impossible, even with holy water. May be it is time to choose some other god, perhaps. Or better, it is better to avoid invoking our personal opinion when doing science. Have you try that? > > >> 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. A (serious) question; are the 3-adic numbers Turing universal, when accompanied with addition and multiplication? Real numbers and similar are usually Not Turing universal. They are not rich enough. I assume a universal machinery, and I chose natural numbers, because everyone is familiar with them, but very often, I suggest using the combinators (cousin of the lambda expressions, which are simpler to related to computations, proofs, and diverse chapters of mathematical logics. > > >>> 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. How could any digital machine distinguish between being implemented in this or that Turing universal machinery, once you accept the idea that we are in a simulation? Still doubting that elementary arithmetic is Turing universal? If not, you have to show me how a universal machine can distinguish between being implemented by this or that universal machine/numnber, and if you succeed, then you have to show me your contract with the doctor, and the mention that you exige some *special* universal machine (but then you already are out of the mechanist hypothesis, which can be used too show that such a distinction is not available from the first pov of any digital machine). Isuepect you invoke your “god” implicitly, but that is not valid here. > > > 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 Explain this to my tax inspector! Bruno > 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] > <mailto:[email protected]>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/CAJPayv392eunXzL6oHfwbyAtsBeMb4mfek%2BJa8vA64fN9CKvrw%40mail.gmail.com > > <https://groups.google.com/d/msgid/everything-list/CAJPayv392eunXzL6oHfwbyAtsBeMb4mfek%2BJa8vA64fN9CKvrw%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]. 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