> On 26 May 2018, at 01:43, John Clark <[email protected]> wrote: > > On Thu, May 24, 2018 at 1:18 PM, Bruno Marchal <[email protected] > <mailto:[email protected]>> wrote: > > > I have provided definition of computations, and explicit examples, > > I’m not interested in your definitions, examples are VASTLY more important. > Definitions can't conjure anything into existence except for more > definitions.
You ask me examples of computations? OK, that is fair enough. Let me give you some example. In the Turing formalism, with combinators, and with elementary arithmetic, and an informal one with Diophantine polynomial. 1) With Turing machine, which are set of quadruple q_i S_j S_k q_r. (The qs are state, the Ss are symbols tape). The computation start from some instantaneous tape description, with the machine in state q_1, and this can be written q_1S_nS_mS_l …. S_h. (It means that the machine is scanning the first element of its tape containing S_n, and it looks if it has a quadrupent beginning with q_1 S_n, and operates accordingly (see my preceding post on this). So, a computation, which is an abstract sequence of instantaneous description of the machine enforced by its quadruplet. It will looks like: q1S2S0S5S3 S2q1S0S5S3 S2S0q1S5S3 S2S0S5q2S5 S2S0q3S5S5 More on this in Davis little book “Computability and unsolvability”. See especially the chapter 4 which explains in all details how this is entirely translatable in Arithmetic, using Gödel’s numbering ¨*and* computational isomophism. 2) with combinators. I recall that S and K are combinators, and that if x and y are combinators so is (x y), abbreviated by xy (we suppress all left parentheses for reason of readability (aaa(bbb)aaa must be read as if it is ((((a a) a)((b b) b))((a a ) a)). The axioms of reduction aare Kxy => x and Sxyz => xz(yz). In this case, it happens that a computation is a sequence of combinators, each resulting from the preceding one by the application of the axioms of reduction. Example SS(KI)(KK)(SS) S(KK)(KI(KK)))(SS) S(KK)I(SS) KK(SS)(I(SS) KK(SS)(SS) K(SS) The computations should be identified with their description, but only with their abstract sequence when a universal number, like the combinators axioms, related them. Amazingly, it can be shown that Turing machine can mimic exactly the combinators, and that the combinators can mimic exactly the Turing machine computations, and that a universal number cannot distinguish its base computations by introspection. > Definitions of computation without the use of matter That is not the interesting or relevant point. He important point is that the definition of computation, including their existence do not *assume* the existence of anything physical. The definition can be done with our without matter, but what is important is that the computation themselves does not require the assumption of a physical reality. Eventually, with mechanism, it is the physical reality which is emergent from the first person statistics on all computation (and this is conformed by the fact that []p & p, []p & <>t, and []p & <>t & p, obeys to quantum logics when p is restricted to the sigma_1 sentences (which correspond to the computable states by Kleene Normal Form theorem). > that obeys the laws of physics exist, but that certainly doesn't means > computations without the use of matter that obeys the laws of physics exists; > that's why I want an EXAMPLE not another silly definition. But you can't > provide one nor can anyone else. I just did. Both examples can be translated into pure number theoretical relation, preserving the computational isomorphism that Gödel discovered between partial computability and the arithmetic reality, although this will be made utterly precise by Kleene’s normal form theorem. I let you give a computation with elementary arithmetic, or just with the addition axioms: x + 0 = x x + s(y) = s(x + y) Try to compute s(0) + (s0). Again the key point is that Logic + the axioms: 0 ≠ s(x) s(x) = s(y) -> x = y x = 0 v Ey(x = s(y)) x+0 = x x+s(y) = s(x+y) x*0=0 x*s(y)=(x*y)+x Provides a Turing-complete (but not Löbian) theory, that is, a universal machinery and machine. As you can see, no assumption on a physical reality is made. This is needed only to ensure the existence of a physical computation, which is a much more particular concept. It will of course be defined only after we have derived the sum on all computations. > > > > and explicit examples, with the combinators, (may be you were not yet in > this list), with numbers, with LISP and lambda-expressions, > > That is an excellent example of something that has never calculated a goddamn > thing and never will. It is a description of how matter that obeys the laws > of physics can make a calculation if it is organized in a certain way. > Specifically a structure made of matter can calculate if and only if its > logical operational structure in its simplest most essential form is a Turing > Machine. And yes I know, the authors of many computational papers never > specifically mention matter or the laws of physics, they take that as a given > too obvious to mention, No. > and that is exactly why numbers, with LISP and lambda-expressions by > themselves can't calculate a goddamn thing . I mean, do the programers at > Microsoft really have to constantly remind their bosses that for the computer > code they’ve just written to actually do what they claim it can do it must > first be run on a computer?? That is not relevant for the logical point. You cannot attribute thought on people, nor invoke the fact that a computation can be implemented in nature to say that the computation notion assumes some nature, which is just not the case. You are always begging the question by invoking your personal belief. That is not how science proceed. > > > I am not inclined to repeat this, > > Thank god! > > > Let me quote Gödel What matter in a computation is that at some (relative > > )instant, some proposition are true, like “the content at place 3 of the > > register R is 5” , > > For that to be relevant to our topic Godel would first have to establish that > "register R" actually exists independently of atoms that obey the laws of > physics, and that register R had at least 3 places in it, and the contents of > the third place in that register is 5. And Godel did not do any of that, he > just made a definition, nobody has ever done that and nobody has ever done > anything even a little bit like that and nobody ever will. And it may be true > that Godel gave definitions of things without referring to physics but > definitions alone don't automatically cause things to spring into existence. Gödel, on the contrary defines the register R in arithmetic, explicitly, and its existence is a simple consequence of the fundamental theorem of arithmetic. He represented to symbols use in the computation by a number (as there is no other choice), and a register by a number whose unique ordered decomposition into prime factors mimic exactly what the register is supposed to do. So the existence here follows just the logical axiom we accepted for our axiomtaization used to define computation. The details of this are necessarily tedious, but see Davis Chapter 4, or just Gödel’s 1931 paper. > > JK Rowling defined Harry Potter as a boy wizard and gave a detailed > description of him in 7 books, but Rowling did not prove that Harry Potter > actually exists. Just as with the English language both fiction and > nonfiction can be written in the language of mathematics. Sure. Gold you see that there is difference between the arithmetical reality of the natural numbers, like Ex(x + 1 = 5), and fiction like Ex(x + 5 = 1). > Just as with English fiction mathematical fiction may be very interesting and > it may sometimes provide poetic insights and hints about the real world, but > that doesn’t change the fact that Harry Potter doesn’t exist. No problem with this. > > > > > John, if you don’t buy some book and study, you will just look like a liar. > > Buy the Dover book by Davis “The Undecidable” > > Stop talking down to me, I’ve been listening and from everything I've heard I > must conclude that I have a deeper understanding of mathematical logic than > you do. You have shown for some time that you have not even read any paper in mathematical logic, as what I explain here is the basic. You assume a computation needs a physical reality to exist, but that is sheer nonsense for a mathematical logician. There are very interesting things to say on physical computation, like the fact that it does not need energy (energy is used only to erase, but erasing is not necessary to get Turing Universality, as has Wang proved in the 50s). My work is at the intersection of metaphysics/theology and mathematical logic, and the foundation of physics. Mathematical logic belongs to pure mathematics, and has nothing to do with metaphysical assumption (be it Mechanism or Materialism). > I make no claim of being particularly smart but I have done something you > have not, I've avoided a fundamental blunder, the same blunder any good > freshman student would be able to avoid by his second day studying the > subject, I understand that defining X is not the same thing as proving X > exists independently of matter that obeys the laws of physics. I use existence as given by the axioms I start with. You use existence by invoking a god (in the greek original sense), that is a “reality”. That is just not science. My work has been defended as aPhD in computer science, and has been peer reviewed by many people. Yes, some academics dislike it a lot, but have failed to find any error. Then some use defamation to hide some of their personal wrongdoings, bu that it small history. My point is that you fail also, but for some reason, deny the fact. > > > > you will just look like a liar > > At least I haven't been educated beyond my intelligence. I don't know much > but what little I do know I know in some depth. > > > Apple would not exist if Turing and other mathematician did not discovered > > the universal machineries and machines. > > True, we need mathematicians to describe to us how to organize matter OK, but matter is not necessarily primitive, (and indeed cannot be with mechanism), but the point is that we can prove that computation exist (and are done, executed) in arithmetic, in the relative indexical way, which is also how Everett retrieved the appearance of collapse from the wave. My point is “just” that Everett’s work has to be pursued to retrieve the wave formalism itself from arithmetic, which I have partially done. > so it can calculate. So it can calculate relatively to us. > It is also true that Apple would not exist if physicists like Brattain, > Shockley and Bardeen hadn't invented the transistor because a description of > a computation is just not good enough to get the job done, you've got to > actually make the calculation, you’ve got to get an answer, and that can't be > done without matter and physics. That is true for the physical computations, but has no relevance for or against the arithmetical computations. Then with mechanism we retrieved the physical computations from all computations in arithmetic. > > > The “theology” of the machine is [...] > > Sorry, I haven’t been updated so I don’t know what the word “theology” means > in Brunospeak today, so I can’t comment. I told you that I use the term in the sense of a millenium of theological science. Not in the sense of 1500 years of dogmatic materialism. > > > Let me quote Gödel (footnote 9) of its 1931 paper “In other words the above > > described procedure provides an isomorphic image of PM (principal > > mathematical) in the domain of arithmetic, and all metamathematical > > arguments can equally well be conducted in this isomorphic image”. > > Principal mathematical? I assume you mean " Principia Mathematica " the > massive book by Russell and Whitehead, as Godel mentions it in the very title > of his famous 1931 paper that you're talking about, and Russell said that as > far as he knew there were only three people in the entire world who read all > three volumes of that gargantuan tome from cover to cover, the two authors > and Kurt Godel. Well its true that on page 379 of volume 1 of Principia > Mathematica it gets deep enough into mathematics and defines what “1” and > “+” and “=“ and “2” mean in sufficient detail to be able to show that 1+1=2; > but Principia Mathematica didn't make that calculation because a book can’t > calculate; the matter in the brains of Russell' and Whitehead did the > calculation. And a Xerox of Principia Mathematica is a isomorphic image of > it, but neither the Xerox nor the century old dusty book can calculate a > goddamn thing. You don’t address the key oint in the quote. The existence of the isomorphism between the (sigma_0) arithmetical reality, and the primitive recursive functions, extended implicitly to the sigma_1; as will done explicitly, and very elegantly, by Kleene. > > > You seem to take the arithmetical reality like if it was a book, but it is > > a reality, it can kicks back, > > Arithmetical reality can't kick back an answer to the question "How much is > 1+1?” without the help of physics. In your christian theology where primary matter is *assumed*. > > > You confuse a computation, which is an abstract relation of silencing of > > states relatively to a universal machine, with either the physical > > computations, > > I'm not confused about the difference between those two at all, its clear as > a bell, one can make a calculation and one can’t. For a non doubter in nature, and only for the particular notion of physical computation. But that beg the question. > > >> You've got it backwards, numbers emerge from physics. > > > That would be explaining the simple from the difficult. > > Like it or not the physical world we live in Assuming your christian theology, to make it primary. You really talk like a dogmatic believer. It is up to you to define primary matter, gives at least some argument what that would exist, and then, if you keep assuming mechanism, how it affects the consciousness of a digital machine. I have explained the rather insuperable difficulties awaiting you here. > IS difficult and immensely complex, numbers were invented to simplify it > enough so we could approximately understand how at least part of it works. > And it turned out mathematics was a wonderful language for explaining how the > physical world operates, it is much better at it than a language like > English. > > > We need a physical reality, yes, > > That is true, but you have never been able to explain why that is true. ? I did. Even in a testable way. I predicted the non-cloning theorem from mechanism many years before quantum physics got it. And I know only of Mechanism being capable of explaining why there is a physical reality at all, assuming no more than the Q theory above. > > > but that does not imply that it does not emerge from something non physical, > > I think it does because nobody has ever found a single example of something > non physical doing ANYTHING, Doing anything physical, you mean. 2 divides 6. That is something. > and even if there is something more fundamental than physics it wouldn’t > prove computations can exist without physics. Computations is not purely mathematical notion. You are the one invoking your god. Please stop doing that, because it is just not valid. You cannot invoke a miracle or a deity, or a metaphysical assumption, like primary matter, to change an original definition. > Life emerged from something non biological, chemistry, but that doesn’t mean > cocker spaniels were around 4 billion years ago just because the laws of > chemistry did. > > > You are the one who seem to have that belief in some primary matter, > > I humbly suggest it would be wise of you to stop talking about "primary > matter" until you learn what the term means, because yes, I do indeed believe > in something close to what Leibniz called "primary matter" because, although > I reject the idea of a soul, I do believe in information and that is as close > as you can get to a soul and remain in the scientific method. I believe in > primary matter because I believe the form, memory, intelligence and > consciousness of a person can be separated from his body and therefore can be > duplicated. You don't know it because you haven't bothered to learn what it > means but whenever you cast scorn on "primary matter" you are saying > consciousness can't be separated from a specific piece of matter, and that > would make you far more of a materialist than I am. > > > I just pointed out that your reasoning was assuming primary matter, and > > there is no problem with that, except if you believe in both Church thesis, > > and that you can survive a digital brain transplant. > > If primary matter doesn't exist then only secondary matter does, and that > would mean soul (aka information) can't be separated from matter, and that > would mean I would not survive a brain transplant. But primary matter does > exist. > > > you need to explain how they made some computations realer than other, and > > this without using “self-multiplication” as arithmetic doe that too. > > Huh? You need to explain what I need to explain. I did, but you stopped at step 3 without succeeding to explain to anybody why. You did get the point from times to time, though, but then refuse to tackle the step 4, without giving any reason, so ... > > > you show that you have no idea of what a computation is. > > I do have one idea what a computation is, getting an answer to a question, > how much is 1+1 for example That is close to the exercice above. I let you do it, but I don’t expect you will try to see the point, as your method seems to be just lying about what what is a computation, and refusing to verify your statements in the literature, so there are not much thing I can do to help you. Bruno > > 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 post to this group, send email to [email protected] > <mailto:[email protected]>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <https://groups.google.com/d/optout>. -- 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]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
