On Thu, May 21, 2020 at 1:33 PM Bruno Marchal <marc...@ulb.ac.be> wrote:
> > On 20 May 2020, at 18:45, Jason Resch <jasonre...@gmail.com> wrote: > > > > On Wed, May 20, 2020 at 7:05 AM Bruno Marchal <marc...@ulb.ac.be> wrote: > >> >> On 19 May 2020, at 05:20, Jason Resch <jasonre...@gmail.com> wrote: >> >> I recently wrote an article on the size of the universe and the scope of >> reality: >> https://alwaysasking.com/how-big-is-the-universe/ >> >> It's first of what I hope will be a series of articles which are >> largely inspired by some of the conversations I've enjoyed here. It covers >> many topics including the historic discoveries, the big bang, inflation, >> string theory, and mathematical realism. >> >> >> >> >> It has not been proved that the decimal expansion of PI contains all >> (finite codes of all) sequences. >> > > I understand that Pi is proven to be normal, > > > (Oops I meant to say "Pi is not proven to be normal" somehow I deleted the *not* while refactoring the sentence) > > But that is not the case. Pi win all experimental test, but the normality > of basically all irrational numbers are open problems. It is generally > conjectured that they are all normal. > For the Champernow number, the normality is easy to prove, but it has been > build that way. > > > > but is it true for the irrational numbers (Pi, e, sqrt(2), etc.) that > probabilistically the chance of not finding a given finite sequence of > digits goes to zero? > > > Most would bet that this is indeed the case, but that is unsolved today. > > > > Is it correct to say that almost surely > <https://en.wikipedia.org/wiki/Almost_surely> any sequence can be found? > > > Hmm… “almost” has already a technical meaning in computer science. It > means for all but a finite number exceptions. It existential dual is > “there is infinitely many …”. > > Then, I don’t want to look like pick nicking, but “almost” and “sure” > seems a bit antinomic. > > Some intuition of infinite decimal series, and of irrational numbers > (which have no infinite repetition, etc.) gives a feeling that it would be > quite astonishing that it is not the case, even for sqrt(2), and we can say > that this has been experimentally verified, but mathematicians ask for > proof, and some ask for an elementary proof (not involving second order > arithmetic or analysis). > > > > > If it does not hold for Pi, are there other numbers that would be better > examples for the type of analogy I am making? > > > > The Champernowne Number > > https://mathworld.wolfram.com/ChampernowneConstant.html > > > > > I want to show why statistically an infinite space leads to near certainty > of repetitions of material arrangements assuming some kind of infinite > uniformity, just like the infinity of random-looking digits of an > irrational number leads to infinite repetitions among any finite sequence. > > > > You get this with Champernowne number. It is normal, despite > extraordinarily compressible. It is about equal to 0.123.., but all kids > can easily write the decimals without ending! It is obviously normal, as > it goes through all the numbers, and thus all the sequences. > But the universe appears more random than something so well structured like the Champernowne constant. What about Chaitin's Omega? Hasn't Chaitin proved a certain randomness for that digits of that constant? > > It has not be confused with a universal dovetailing which is a computation > which happens to execute all computations, which are peculiar number > relations. > > The problem is that each of us (us, the universal number) are implemented > in many computations, and indeed, below our substitution level, we get > infinitely many computations). Physics, conceptually, becomes a statistical > measure on uncertainty on which are our most probable computations, as > “seen from inside”. Here the mathematical logicians have a tool which lacks > to the physicalists, which is “transparent” mathematical theory of > self-reference, indeed, they get both the machines’ own theory (G) and the > true theory (G*), and the difference (G* minus G) which is so important to > get the difference between the quanta and the qualia. > > > > > > > >> >> It is easy to fiw, as you can take the number of Champernow, which >> trivially contain all sequences: >> >> C = 0,12345678910111213141516…. >> >> OK? >> >> Now, this is different from the universal dovetailing, which *executes* >> (semantically) all computations, and makes unavoidable that to solve the >> mind body problem, we have to extract the believes in bodies from the >> statistics on the first person continuation determined by all computations. >> It is here that it is crucial to distinguish between a computation (a >> notion involving counterfactuals) and a description of a computation, which >> does not. >> > > Indeed. To be clear I am not making the case here that our universe is > contained within Pi, only showing that infinity leads to repeats so long as > the description is finite, be it a volume of matter and energy, or a finite > length of decimal digits. > > > As long as you don’t assume simultaneously Mechanism and some “physical > universe” (making it or its elements primitive), there is no (logical) > problem. > > With mechanism, the laws of physics emerges from the statistics on the > dreams/computations of the natural number. > > The “god” of the universal Löbian machine, G*, provides the truth, the > believable, the knowable, the observable, and the one which feels. And > this, modulo Mechanism at the metalevel, assuming only two equations, like > Kxy = x, and Sxyz = xz(yz). > > > > > > > > >> >> With Mechanism, physics is reduced to number psychology or theology, and >> theology is reduced to arithmetic (through the Gödel-Löb-Solovay theorems). >> > > I am working on a post now which will get more into this, about why there > is something rather than nothing. How to bootstrap reality and universes > from arithmetical truth will be part of that. :-) > I appreciate your comments. Thank you. > > > > The discovery of the universal machine, and especially the Löbian one, is > an event more important than the Big Bang. Of course, that discovery is > made an infinite number of times in very elementary arithmetic. > > The Lôbian machines are the universal machines which knows (even in a > rather weak sense) that they are universal, and they know the complicated > consequences that happens, especially if they want to remain universal > …They oscillate easily between freedom and security in a not entirely vain > attempt to fill the gap between G* and G and their necessary intensional > variants. > > With universality, you get free will, but you need löbianity, to get > responsibility. All universal machine, like RA, with enough induction > axioms, like PA, is Löbian. > > Their weakness? They are credulous, and hallucinate easily, like seeing > far away galaxies, sun, moon, and Higgs bosons…, but eventually they can > explain the why and the how of all sharable aspect of their experiences, > and detect possible oracles, who knows. > > The G*/G gap is really the difference between Computer Science (where > there is no hallucinations) and Computer’s Computer Science, which can > contains many hallucination, like notions of some absolute harwdare. > > With Mechanism, the laws of physics does not depend on the universal > machinery chosen for the ontology. The choice of a universal machinery, is > equivalent with the choice of a base for the recursive enumeration of all > partial computable functions. > > Thanks to QM, Nature fits well with the most startling aspect of mechanism > (or self-multiplication at the basic level). > The theology of machine will not replace physics, on the contrary, it > predicts that larger and larger part of mathematics will be “known” > “experimentally” (betting). > > Concerning our local cosmos, I am fascinated by the black holes, but very > ignorant, I see it implies multiverses of different kinds, super-imposed to > the Everett-Omen-Griffith entangled consistent histories. With Mechanism, > it is an open problem to just define a notion of a singular physical > universe, without mentioning the complex “intermediate histories” between > Earth and Heaven … > I read this lately, and found it very interesting: https://cse.buffalo.edu/~rapaport/111F04/lloyd-ng-sciam-04.pdf Among some of the most interesting conclusions: quantum mechanics/Planck's constant imposes an upper bound on the speed of computation, general relativity/Newton's constant imposes an upper bound on the density of computation. There are various intermediate possibilities of parallel vs. sequential computing, but the maximum sequential information processing speed is reached only for black holes. There the number of bits that can be processed per step is given by Bekenstein's bound, and the "clock cycle" is the amount of time it takes light to cross the diameter of the black hole. Another fascinating consequence: given that the matter-energy density of the universe as a whole is right at the cusp of gravitational collapse, the total mass of the observable universe is exactly equal to the density of a black hole of the same volume of the observable universe. The estimated number of bits within the universe is also exactly equal to the total number of bit operations that have occurred in the universe since the big bang. In other words: for every one of the 10^120 bits in the universe, each has been processed (flipped) exactly once (on average) in the time since the big bang. There are incredible relations between fundamental physics and computation which amaze me. > > Did you know that contrary to some myth (that I were “almost sure” > about), even quarks can maintain the social distancing, if you provide > enough energy! That is what happen in the gluon-quark plasma! I guess that > is very hot. > I read recently <https://frankwilczek.com/Wilczek_Easy_Pieces/342_Origin_of_Mass.pdf> that it's estimated 90% of our mass comes from the relativistic speed of quarks and other particles inside the nucleus. If you could somehow still that motion, we'd weigh only a few pounds. Something to ponder next time we step on a scale. :-) Jason > > Bruno > > > > > Jason > > > -- > 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. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/CA%2BBCJUh%2BtsA_wSHxvZxNidKkmXTPx_M%2BnLdbh0GkqOyzRvGGoQ%40mail.gmail.com > <https://groups.google.com/d/msgid/everything-list/CA%2BBCJUh%2BtsA_wSHxvZxNidKkmXTPx_M%2BnLdbh0GkqOyzRvGGoQ%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 everything-list+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/4D675133-9010-4911-BB1D-6B0AEB9BC168%40ulb.ac.be > <https://groups.google.com/d/msgid/everything-list/4D675133-9010-4911-BB1D-6B0AEB9BC168%40ulb.ac.be?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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