> On 6 Aug 2019, at 15:25, John Clark <[email protected]> wrote: > > On Tue, Aug 6, 2019 at 3:55 AM Bruno Marchal <[email protected] > <mailto:[email protected]>> wrote: > > >> If nobody can find a computation that is not realized by some physical > >> object, and nobody can, > > > Everybody can do that, in the samùesense that everybody can find a prime > > number. > > Yes, everybody can find prime numbers because everyBODY has a body made if > matter that obeys the laws of physics.
That makes a human body able to find some prime number, but the prime number notion is not transformed into a physical notion through this. Same with computation. All the proposition making some computation into arithmetical existence are true, independently of the laws of physics, like the arithmetical proposition making 17 into a prime number, do not depends on human existence. We need human existence only to assert that some human grasp the notion of prime, but the prime numbers does not need human to be prime. Insects have used the primality of 13 and 17 well before human did mathematics, for example. > > >A computation can be realised physically, but also arithmetically, as shown > >in all elementary textbook. > > Oh god here we go again!! Here we go with elementary textbooks making > physically realizable calculations Not at all. The elementary textbook just explain in detail that the notion of computation is available in arithmetic, independently on any physical laws. You will need physical laws only to implement some computation physically; like you need arithmetic to see that they are all emulated in arithmetic. > that for some never explained reason INTEL and its competitors have never > taken advantage of even though the technique would make them masters of the > universe. > > > I do not assume the existence of the physical object, > > That's OK, physical objects don't care if you assume them or not, they just > keep on doing what they do. Like the prime numbers do not care about mathematicians studying them. > > > that is insisting on your confusion between computation and physical > > computations. > > When it comes to discerning the difference between a real calculation and > ridiculous phantom calculations your confusion is epic. Use of “real” is invalid here. > > >> Mathematical language can describe a computation > > > Sure. But a computation is not the same as a description of computation, > > I know, that was my point. The Mathematical language can describe a > calculation but it can not make a calculation anymore than the English > language can produce a flesh and blood cat from the letters C, A and T. Yes, but you cannot deduce from this that a mathematical structure cannot emulate a computation. Indeed, all models of the arithmetical theories emulate, in the precise sense of Church, Turing and Co. all computations. A mathematical structure is not to be confused with the language describing that mathematical structure. > > > like the fact that 1 + 1 is 2 is different from the sequence of symbols "1 > > + 1 is 2”. > > "1+1=2" is what a computation produces, and that is the ONLY reason it is a > fact. Since Gödel we know that whatever produces “1+1=2” will be unable to prove some arithmetical statement which is true, showing that truth (of an arithmetical proposition) is not the same as proof of such proposition in some theory. The arithmetical truth os independent of all theories build to explore it. > And the ONLY way to make a calculation is with matter that obeys the laws of > physics. That is the only way to make a physical computation. But you don’t need to make an arithmetical computation. They are just there in the same sense that the prime numbers are well determined independently of the human existence, or even the physical universe possible existence. > Actually it's even more restrictive than that, the matter must be organized > in certain specific ways to make a calculation, if you organize it in the > form of a logic textbook it won't work, if you organize it in the form of a > Silicon Microprocessor it will. But the computation exists in arithmetic, independently of its emulation by a physical processor, like we can be sure that there is a prime number bigger than 10^(10^1000), independently of the fact that we might perhaps never find it. > > >> just as the English language can describe a cat, but the three letter > English word "cat" is not an animal and is not alive. > > > Yes, some language used in mathematics can describe a computation, but that > > does not make a > computation the same as a description of a computation. > > I know, that was my point. But you restrict that point of the physical reality, and dismiss it on the arithmetical reality. > > > You confuse again a model and a theory, semantic and syntax, > > You again confuse the fact that the semantic meaning of any language > including the Mathematical language ultimately comes from calculation, That is wrong. On the contrary the semantic of any theory escape the syntactical abilities of that theory. That comes from incompleteness. In fact, no theory at all can even defined its own semantics. > and the only way to make a calculation is with matter that obeys the laws of > physics. > > > I think that you are stuck into your idea that mathematics is a language. > > A language needs a vocabulary and a grammar, and mathematics has both. And much more than that. > I am certainly not the first to say that, neither was Galileo who said: > "Mathematics is the language in which God has written the universe". > > >>The type of Turing Machine that can change with time, that is to say > the type that can actually *do* something, the type that is amenable to > the scientific method, MUST be made of matter that obeys the laws > of physics. No exceptions. > > > Well, I guess, for a believer. I am not. > > Well, I guess that's the difference between you and me. I believe in both the > value of induction and of the Scientific Method. You do not. I do. I would not have consecrated 35 years of my life to show that Mechanism is empirically testable/refutable if that was not the case. The difference between you and me is that you assume that the physical reality is primary, and I show that this is inconsistent once you assume the digital Mechanist hypothesis. > > >> Matter may or may not be the ultimate in primitive, but if matter can do > even one thing that numbers can't (and even you admit that pure numbers > can't generate power but matter can) then matter must be more primitive > than numbers. > > > Pure numbers cannot generate primitive energy or primitive matter, …, but > > who said that such things exist. > > As your body temperature skyrockets from megawatts of electrical power > milliseconds after you've been hit by a bolt of lightning it will male little > difference if you've said such things can exist or not. > > > pure number relations can generate the illusion of primitive energy, > > I have debated philosophy for a long time and I've noticed that nobody uses > the word "illusion" in an argument unless they are backed into a corner and > are desperate, > > >> Maybe our world and even we ourselves are all a simulation, but if so the > the cosmic virtual reality program MUST be running on a computer made > of matter that obeys the laws of physics because matter has one key > attribute that arithmetic lacks, matter can change but arithmetic can't. > And you can't have computation without change. > > > The change x -> s(x) is quite enough, to explain the psychological illusion > > of relative change. > > What you need to do now is write "x -> s(x)" on a postcard and mail it to > INTEL, I'm sure they will be very grateful to you for revolutionizing their > industry. Of course, they already know, and use this all the time. It is a primitive of all assembly language. > > > If some “matter” plays a role in computation, then lambda calculus cannot > > be Turing universal, nor Turing machine, which are equivalent with respect > > to computations and digital processes to lambda calculus. > > Bruno, that statement does not make one bit of sense. If lambda calculus is > equivalent to a Turing Machine, and it is, then whatever I say about a Turing > Machine is equally true for lambda calculus, and I say the only type of > Turing Machine that can actually *do* things like make a calculation is one > made of matter that obeys the laws of physics. Assuming such matter exists, you can implement a computation with it, but that does not make the computation more real. It makes its output available to you. But you cannot know if you are not also the product of some computation in arithmetic (unless some mysterious mystic power). In that simulation of you in arithmetic, you are still correct when arguing that you need a physical computation (relatively to you) to be able to use the output of that computation. This shows that your invocation of “real” for “physical” is not valid. > > >There is just no physical postulate in the theory of computability. > > And the theory of computability can not compute anything, no theory can. The theory of computability is not supposed to be able to compute, here. Incidentally, they can. Sigma_1 provability is equivalent with mlamnda calculus and Turing machine, with respect to computability. Any machine (arithmetical or physical) which can find a natural number having a decidable property can be shown to be Turing universal. So the theories RA and PA can compute, and all their computations are realised in virtue of some sigma_1 proposition to be true. > That's why you need physical Turing Machines like microprocessors that use > energy and produce heat if you want to mine for Bitcoins, and that's why > textbooks on computer theory can't mine a damn thing. > > > You come back with the knocking argument, which has been debunked by the > > Indian and greeks amore than 2000 years ago. > > The "knocking argument" is just an insulting name for Induction It is not an insult, but you can see as an exemple of wrong induction, especially when you are using that argument in a dream, or in arithmetic. Infinitely many John Clark use it in arithmetic to claim that a computation needs matter to be real, and of course, “we” know that those John Clark are wrong. > and the Scientific Method, and if the ancient Greeks had not "debunked" it > 2500 years ago Science would not have stagnated for 2000 years. ? > > > I suggest you reread those old text, > > I would rather have my teeth drilled. Stagnation has begun with the interdiction to read those greek text, and partially stopped when we have come back again to them, tanks to the Arab translations of the greek texts (not just Plotinus, but also mathematicians like Diophantus). 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 view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/CAJPayv3nmu_RACsWTYjAsc2yzUG-%3DXjD_9841A0Jf0m86JZ7qw%40mail.gmail.com > > <https://groups.google.com/d/msgid/everything-list/CAJPayv3nmu_RACsWTYjAsc2yzUG-%3DXjD_9841A0Jf0m86JZ7qw%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]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/3E60D66E-C6AE-4151-A464-B64D152E432E%40ulb.ac.be.
