> On 2 Sep 2019, at 21:14, John Clark <[email protected]> wrote: > > On Mon, Sep 2, 2019 at 11:57 AM Bruno Marchal <[email protected] > <mailto:[email protected]>> wrote: > > >> 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. > > > That he is not assuming your materialist religion is [...] > > My cue to skip to the next paragraph. > > > the reality is that being prime or not is independent of any physical laws, > > The reality is 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. > so EVERY integer beyond that is prime. Which is of course absurd, and this illustrates well the inappropriateness to define mathematical concept through physical implementation of digital machine. > 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. All this is a good argument to defend the idea that “being prime” is better defined, like you did above, by having exactly two divisors. In that case, we get Euclid back. Good! > > > if Mechanism is true [...] > > I said I believed Mechanism was true because I would say yes to the digital > doctor, but that was on Thursday and today is Monday. In Brunospeak what does > "Mechanism" mean on Monday? Here either you lie, or you confuse against the hypothesis of indexical digital mechanism (YD + CT), and its conclusion “physics is a ranch of machine’s theology”. > snip > > >>> 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, > > No, but natural numbers are not Turing universal either, but a Turing Machine > with a natural number of states is Turing universal. Some natural numbers are universal Turing machine, other are universal fortran interpreter, some are quantum universal dovetailer, All Turing machine have a natural number of state, but only some of them are Universal Turing machine. I have given the (rather standard) definitions, working with any fixed enumeration of the partial computable function phi_i. A natural number x emulate a natural number y on the input z, means that phi_x(y, z) = phi_y(z). A natural number u is Turing-Universal, or Church-Turing Universal if it can emulate all numbers. See Davis’ book, or Gödel’s 1931 paper to see how to translate the talk on the phi_i in the (pre) arithmetical language (that is using classical first order language + the symbol s, 0, +, *. We can show that if phi_i(j) = r, then M satisfies phi_i(j) = r, where M is any model of Peano arithmetic, or of Robinson Arithmetic. > > > I assume a universal machinery, > > And natural numbers are not machinery and no other sort of number is either. > Machinery needs change and change needs matter. The successor function, which sends n on n+1, or n on s(n), provides enough change in the digital realm. It is just a theorem of basic computer science, even the oldest one (if we abstract that Gödel missed the Church’s thesis and did not realise he showed that). Elementary arithmetic is Turing universal. Interestingly, if you suppress any one axiom among the seven axioms given by Robinson, you lose the Turing universality. Are there are: 1) 0 ≠ s(x) 2) x ≠ y -> s(x) ≠ s(y) 3) x ≠ 0 -> Ey(x = s(y)) 4) x+0 = x 5) x+s(y) = s(x+y) 6) x*0=0 7) x*s(y)=(x*y)+x > > > and I chose natural numbers, because everyone is familiar with them, > > Everyone is familiar with natural numbers because that's what they were > taught, they are extraordinarily useful in describing the physical world so > taxpayers were willing to pay people to teach it to their children. But > p-adic numbers, unlike natural numbers and real numbers and imaginary > numbers and complex numbers, have little or no connection to the physical > world. So p-adic numbers are only taught to graduate students who want to be > pure mathematicians of the most abstract sort, but they're just as internally > consistent as any other sort of number. > > > 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? > > I'll be damned if I can see why that is relevant to the question at hand, but > we might be able to detect errors and glitches in the program that's > simulating us if we look closely enough at the sub atomic level. Preston > Greene makes the point that if you want to test the efficiency of a new drug > it is important that the subjects not know if they are receiving the drug or > a placebo, in the same way... > > "if our universe has been created by an advanced civilization for research > purposes, then it is reasonable to assume that it is crucial to the > researchers that we don’t find out that we’re in a simulation. If we were to > prove that we live inside a simulation, this could cause our creators to > terminate the simulation — to destroy our world." > > Are We Living in a Computer Simulation? Let’s Not Find Out > <https://www.nytimes.com/2019/08/10/opinion/sunday/are-we-living-in-a-computer-simulation-lets-not-find-out.html> > > > Still doubting that elementary arithmetic is Turing universal? If not, you > > have to show me how a universal machine can [...] > > I can't say anything about that until I know it you're talking about > elementary arithmetic or a Universal Turing Machine. Elementary Arithmetic, like LISP, Fortran, the game of life, or even quite amazingly the Diophantine polynomials, are all example of Turing universal system. A polynomial of degree 4 can simulate exactly, i.e. emulate, the extremely fast growing function which send n on n^(n^(n^(n^n)…)))). And all Turing universal system can emulate each other, in the sense defined above. We can test if we are in a designed simulation, indeed by “discovering the pixels”, or more precisely by discovering that the “physical laws” in the simulation are not the one given by the measure on all relative computations (it violates the material self-referential mode). The Newtoinian world does violate the physics extracted from Mechanism, but Quantum Mechanics does not, until now. If we were in a Newtonian world, we could infer that either Mechanism is false, or we are in a designed simulation. Bruno > > > you invoke your “god” implicitly, but [...] > > And that is my cue to say goodnight. > > 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/CAJPayv3182VLmWR9sEwQHkaNH5CSt3pdaradwK4Ho%2BxXDwmZiQ%40mail.gmail.com > > <https://groups.google.com/d/msgid/everything-list/CAJPayv3182VLmWR9sEwQHkaNH5CSt3pdaradwK4Ho%2BxXDwmZiQ%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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