> On 22 May 2020, at 19:11, Jason Resch <[email protected]> wrote: > > > > On Fri, May 22, 2020 at 9:23 AM Bruno Marchal <[email protected] > <mailto:[email protected]>> wrote: > >> On 21 May 2020, at 21:43, Jason Resch <[email protected] >> <mailto:[email protected]>> wrote: >> >> >> >> On Thu, May 21, 2020 at 1:33 PM Bruno Marchal <[email protected] >> <mailto:[email protected]>> wrote: >> >>> On 20 May 2020, at 18:45, Jason Resch <[email protected] >>> <mailto:[email protected]>> wrote: >>> >>> >>> >>> On Wed, May 20, 2020 at 7:05 AM Bruno Marchal <[email protected] >>> <mailto:[email protected]>> wrote: >>> >>>> On 19 May 2020, at 05:20, Jason Resch <[email protected] >>>> <mailto:[email protected]>> 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/ >>>> <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) > > OK. > > > >> >> >> 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 >> <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. > > > I doubt this. Most subsequence of the Champernowne number are completely > random, and *very* long. Only the tiny initial segment does not look random, > when you know the algorithm to generate it. It can be proved that most > natural number have incompressible sequences. The number of compressed > algorithm grows much less that the numbers of number (for each finite > length). > > I think like Pi, reality itself could be generated by a short compressible > algorithm (like the UD).
Neither the mathematical reality, nor the physical reality can be generated by an algorithm. The physical reality emerges from all algorithm. Keep in mind that if you are cut and paste in two places at very different “moments of time” (like with delay of a billions years for one of the reconstitution), that delays is not first person knowable. So the number of steps is not relevant for a computational state to exist. What is relevant is the relative measure on the continuations, but we have to take them all into account, and that is not a recursive set, making the physical reality NOT Turing emulable. This means also that only the UD can bring it (or anything Turing equivalent at some level of description, like the collection of true sigma_1 sentences in arithmetic). If the physical reality was generated by a program, that would entail Mechanism, but Mechanism entails that the physical appearances cannot be Turing emulable, so the thesis that the physical universe if brought by a programs, or by a proper subset of programs is self-defeating. > > But also like Pi, if you find yourself at some arbitrary offset, it looks > like it is irreducibly random (like the quantum fluctuations that appear in > the distribution of galaxies and CMB of our universe). > > Perhaps there is some law where when you combine a deterministic process with > infinite steps, the result is random. Deterministic self-duplication, or the multiple preparation of identical state, by programs run in arithmetic, does that, but only from the first person point of view. Now, long complex program can certainly imitate some pseudo-random sequences. > I have some familiarity with the design of secure random number generates > computers use to generate encryption keys and other values that are necessary > for security. All are based on the process of taking a very large number (so > large it can't be guessed) then combining it with a deterministic, but > difficult-to-reverse (one-way) function. OK. > > The simplest example I cold easily describe is the one built into Java called > SHA1PRNG. It starts with a random number (a seed value) that is on the order > of 256 bits. Then to generate a sequence of random looking bits, it puts this > random number through a one-way hash function (called SHA1). The output of > this function only produces 160 random bits. If more are needed the random > seed value is incremented by 1, and the process is repeated. What seems > random is just counting and mixing up the result. Only it is counting from a > starting position so large it could only be guessed with negligible > probability. > > The hallmark of a secure random number generator, as opposed to an unsecure > one, is if it takes exponential time (in relation to the number of bits in > the seed value) to guess the next bit output by the generator with greater > than 0.5 probability, given all the bits output by the random number > generator so far. > > > >>> <snip> >> >> 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 >> <https://cse.buffalo.edu/~rapaport/111F04/lloyd-ng-sciam-04.pdf> > > Black hole are very interesting, including for the role they give to quantum > information. But, from a quick look at the paper this is till “digital > physicalism”, and it refutes itself. > > If I recall correctly the main focus of the paper is less about the nature of > reality (upon which it might speculate) and more about what are the physical > limits of computation in the universe. That’s the problem. It seems to take the notion of “universe” for granted. But as you say, it does not really address the fundamental question, although it might look that way. I have few doubt that black hole have a lot to say about physical information and physical computers. But to understand why things like black hole and computer exists, with mechanism, we have to derive them from arithmetic or combinators, or any non physical computer. > > Indeed, it entails computationalism, but computationalism entails that the > physical universe is not simulable exactly by a computer. Mechanism (aka > computationalism) entails that even to simulate a nanometer^3 of vacuum, you > need to run instantaneously the entire universal dovetailing, and compute the > probabilities from there, which is not possible. As far as the paper is > physically sound, if Mechanism ic correct, it can only be an approximation. > It is interesting for physics, but does not address the fundamental question, > like where there is a an appearance of a physical universe, and where does > all appearances come from. > > > > >> >> 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. > > That looks interesting, but if this is not derivable from Kxy = x + Sxyz = > xz(yz), it will have to eve abandoned. > > > Perhaps there is something about black holes and the physical limits of > computation there that could more easily be derived from Kxy = x + Sxyz = > xz(yz). If so, it could lend additional support. I am not sure it could be done “easily”, but it has to be done that way if we want to keep intact the difference between quanta and qualia, between first person experience and the first person plural one, etc. If we get different sort of black hole, or no black hole at all, we would got evidences to doubt Mechanism. > > > >> >> There are incredible relations between fundamental physics and computation >> which amaze me. > > > Honestly, how could that been amazing? If we assume mechanism in cognitive > science, the physical universe is entirely explainable in term of a > statistics on *all* computations. > > I don't know, there is something elegent about how deep the connection is. > Planck's constant directly determines maximum speed of computation per unit > of mass-energy in the universe. Mass times Volume directly tell us maximum > number of bits that can be stored. Except that for black hole it seems the information is on the surface of the volume (strangely enough). > Speed of light and G tell us the maximum speed of a serial computation. The > volume of the universe and Bekenstein bound tell us the number of bits that > are stored in the universe, and that each bit has flipped an average of > exactly once in the 13.8 billion years since the BB. I am not sure I can make sense of this, but it is very plausibly only due to my incompetence. > > It is more amazing perhaps starting from the view that the universe is not > derived from the machine self-reflection (where most people start). Then > these connections seem very mysterious. > > > In mathematics, “all computation” is the only place where “all” is well > defined, thanks to the “miracle” of the Church-Turing thesis. > > Have you understand that all computations are run in arithmetic? Here “in > arithmetic” can be replaced by “in all models of arithmetic” or “in the > standard model of arithmetic” or “provable in RA”, or provable in all > combinatory algebra, etc. > > > I subscribe to this idea. Well, those are theorem provable in very weak theories. It is more a question of grasping the proof than subscribing to a philosophical idea. That arithmetic executes all programs is a theorem similar to Euclid’s theorem that there is no biggest prima numbers. It is more a fact, than an idea which could be debated. I insist on this as I realise this is less known by the general scientists than 20 years ago. We knew this implicitly since Gödel 1931, and explicitly since Church, Turing and Kleene 1936. > I think it's the best hope at revolutionizing theoretical physics, which > seems preoccupied on the problem of how to make everything predictable in > finite time (i.e. string theory). Does COMP have anything to say about > whether such efforts can succeed? Should we expect there to be ways to chase > out the infinities? Are they in effect, is the string theory community > chasing for the equivalent of a classical algorithm for predicting the > behavior of a quantum computer? With COMP (aka digital mechanism), the laws of physics her to be explained from the laws of computations and numbers, which are not based on any physical concept. To study the physical reality, we must do physics. Using comp is just the only way to address the relation between first person plural physical prediction, and the first person confirmation. The goal is to understand why there is something instead of nothing, and this in a way which does not eliminate consciousness and persons, like materialism is enforced to do. To sump up the reason in a "physicalist terms”, no laws of physics can predict any first person confirmation without integrating on all “Boltzmann Brain” which are all executed in arithmetic. The physical reality is a sum on all dreams/consistent-histories/computations-seen-from-inside. The goal is not find new physics, although that might happens some day, but to solve the mind-body problem, and this without eliminating mind, which eventually forces us to eliminate matter from the ontology. > > > We don’t need to postulate a physical universe, nor even induction axioms, to > explain where the quantum computations come from, and why we tend to trust > the induction axioms. > > But in theology (aka philosophy of mind, metaphysics) the situation is worst > than that/ We just cannot postulate a physical universe, if we want it to be > related to any conscious first person experience by machines. > > > > >> >> >> 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. > > Interesting. > > >> If you could somehow still that motion, we'd weigh only a few pounds. >> Something to ponder next time we step on a scale. :-) > > Is there some mass which is not kinetic energy in disguise? > > I suspect that too. That all apparent mass is just confined energy moving at > C. Have you seen how mass appears in a "light box" > https://www.youtube.com/watch?v=gSKzgpt4HBU > <https://www.youtube.com/watch?v=gSKzgpt4HBU> ? Very good video indeed, but it will take a lot of work to get this from mechanism. Energy remains pretty mysterious. It has to be related with fundamental symmetries, and why the physical laws are (or should be) time symmetrical. There is no Kestrel (Kxy = x) nor Starling (Sxyz = xz(yz)) in the physical universe . K eliminates information/energy, and S duplicates it, which is eventually impossible physical events. Th reason might be related to the necessity of group theory in physics. The measure one might necessitate some Lie group role in the picture. Why SU(1) or SO(3)? It is here that I suspect the number 24 to play a key role, for gravitation. The progress here will still comes from physics for a very long time I’am afraid. Or worst: from Number theory, which might might again demotivate people for theology (if 1500 years of lie was not enough!). Recently, I have come up with some possible reason why the physical should appear three dimensional, and this could be related to some relations between prime number and knots. This again suppose the existence of braids in the theory Z1* and X1*, which unfortunately remains based on intractable conjectures. This could give some reason why we have no qualia corresponding to 4 dimensional geometry. That is a big mystery. I use it often to explain qualia. We do have qualia for 0, 1, 2, 3 dimensions, and not for those > 3, which is a bit mysterious. Can we program a machine to have 4D qualia? I thought so but now I got the shadow of a reason to doubt this, and this would explain the 3D appearances in the available physical reality for numbers… Bruno > > Jason > > > If yes, I will have to revise my understanding of the Higgs-Englert-Brout > boson ... > > Bruno > > >> >> 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 [email protected] >>> <mailto:[email protected]>. >>> 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 [email protected] >> <mailto:[email protected]>. >> 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. >> 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/CA%2BBCJUgZr_0%3DfqFpdw6W-QBeT3hBbjET0OmMD%3D3iBWwPDMJPMw%40mail.gmail.com >> >> <https://groups.google.com/d/msgid/everything-list/CA%2BBCJUgZr_0%3DfqFpdw6W-QBeT3hBbjET0OmMD%3D3iBWwPDMJPMw%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] > <mailto:[email protected]>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/30AB1C3C-7EEF-4A64-923C-6F2DA3D6E368%40ulb.ac.be > > <https://groups.google.com/d/msgid/everything-list/30AB1C3C-7EEF-4A64-923C-6F2DA3D6E368%40ulb.ac.be?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] > <mailto:[email protected]>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/CA%2BBCJUjNes2EY7%2BVfwxJbpK6CxS8Hb3cD%3Dr%2B_xhtaF5kxehc9A%40mail.gmail.com > > <https://groups.google.com/d/msgid/everything-list/CA%2BBCJUjNes2EY7%2BVfwxJbpK6CxS8Hb3cD%3Dr%2B_xhtaF5kxehc9A%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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