> On 4 Sep 2019, at 19:36, John Clark <johnkcl...@gmail.com> wrote: > > On Wed, Sep 4, 2019 at 11:31 AM Bruno Marchal <marc...@ulb.ac.be > <mailto:marc...@ulb.ac.be>> wrote: > > >> The reality of being prime means being unable to be divided by any integer > >> except for itself and 1, > > >OK. > > >> and if the amount of computation possible in the expanding accelerating > >> universe is finite then beyond a finite point no integer can be so divided, > > >More precisely; no integer can be divided by a physical instantiation of > >some program. > > I see no reason to think your language was more precise than mine.
The point is that the size of the universe, or even its existence is relevant to say that beyond some point a number is no more physical divisible by some instantiation of a physical computers, but that is irrelevant with the validity of Euclid’s argument that there are infinitely many primes. Unless you assume that there is a physical primary universe of some sort, in which case Mechanism becomes inconsistent or spurious (given that such universe cannot act on the presence of absence of consciousness in the computation realised in the arithmetical models (logician sense).. > > >> so EVERY integer beyond that is prime. > > > Which is of course absurd, > > No, it just means the concept of prime has reached the limit of its > applicability. May be in physics, although String theory provides an amazing counter-intuitive-exemple, by using the zeta-regularisation, which is based on the existence of the full (infinite) distribution of primes. > Newton's theory wasn't absurd, it's just not the appropriate thing to use > where gravity is super strong or things move super fast. > > >> Meaning needs contrast, if every number has the property of being prime > >> then beyond that point the very concept of prime loses its meaning. > > > Absolutely. > > So, assuming the universe really is incapable of making a infinite number of > calculations, only use the concept of prime for numbers less than that point, > and that point, although finite, will be huge to the huge power. I prefer to simply not assume a physical universe. Eventually such notions does not fit consistently with mechanism. You have not yet explain how a physical universe can make a material computation more real. With mechanism, we do understand how the physical makes a computation relatively more probable. That physicalness is no more primary though. > > > Here either you lie, or you confuse against the hypothesis of indexical > > digital mechanism (YD + CT), > > And you forget IHA. > > > and its conclusion “physics is a ranch of machine’s theology” [...] > > And that is my cue to skip to the next paragraph. > > > Some natural numbers are universal Turing machine > > A universal Turing machine, or any sort of machine for that matter, needs to > be able to *do* something, and numbers, natural or otherwise, can't *do* > anything. That is ridiculous, numbers do tuns of things, including all computations, when taken in relation with other numbers. You meant “cannot do something physical”. Then you are right, but the physical is still itself made up by the numbers, with mechanism. > > > I have given the (rather standard) definitions, > > And I have said examples are what's important, all definitions are derivative > and dreaming up a new definition in no way enhances our understanding of how > the world works. > > > See Davis’ book, or Gödel’s 1931 paper > > Can Davis’ book or Gödel’s 1931 paper make a calculation? This question is beyond ridiculous. > > > The successor function, which sends n on n+1 [...] > > Stop right there! Sends? How does the function "send" anything anywhere, how > exactly does it *do* that? Does the function need energy to *do" it? Is it > instantaneous or does it take time? And after the function turns 5 into 6 > does that mean the integer 5 no longer exists? And what happened to the old > #6 after the new guy moved in? That is elementary mathematics, or you are playing with the words. And, no, computations, even physical does not require energy, except for the read and the write. Only erasing information requires energy, and we can compute without ever erasing information. A good thing, given that we have reason to believe that the physical universe never destroy information (cf the battle between Susskind and Hawking). > > > Elementary Arithmetic, like LISP, Fortran, the game of life, or even quite > > amazingly the Diophantine polynomials, are all example of Turing universal > > system. > > I agree, and a crucial part of the system is a computer (or a brain) made of > matter that obeys the laws of physics to run the software on. A LISP interpreter is a computer, in the sense of a universal “Turing” machine. You can run it on *any* universal system. Of course if you want physical output, you need to implement it physically, but the point is that with mechanism, that physicalness is explained itself by number (program, words, digital-machine) relations. > > > The Newtoinian world does violate the physics extracted from Mechanism, > > Who knows? who cares? The definition of "Mechanism" in English is "a system > of parts working together in a machine", but that's not what it means in > Brunospeak, last week it meant "saying yes to the digital doctor”, It has always meant that. You just confused the Mechanist Hypothesis with its logical *consequences* Bruno > however this week "Mechanism" is defined differently in Brunospeak and I > refuse to study it because you'll just change it to something else next week. > > 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 everything-list+unsubscr...@googlegroups.com > <mailto:everything-list+unsubscr...@googlegroups.com>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/CAJPayv1SDQ22Uyu%3D50kX4FTNy_LBgcvWZGeYEy-DhnUVQ8GbyA%40mail.gmail.com > > <https://groups.google.com/d/msgid/everything-list/CAJPayv1SDQ22Uyu%3D50kX4FTNy_LBgcvWZGeYEy-DhnUVQ8GbyA%40mail.gmail.com?utm_medium=email&utm_source=footer>. -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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