> On 24 Aug 2019, at 23:18, John Clark <[email protected]> wrote: > > On Tue, Aug 20, 2019 at 8:27 AM Bruno Marchal <[email protected] > <mailto:[email protected]>> wrote: > > > The simplest thing which is non trivial and that I can conceive is > > elementary number theory. 2+2=4 is conceptually more simple than the > > quantum vacuum. > > I don't know if that's true, but if it is then the quantum vacuum behaves in > more complex ways and does more interesting things than elementary number > theory, things like intelagent behavior and consciousness.
The quantum vacuum is indeed Turing universal. But elementary arithmetic also, and with mechanism, the first must be justified from the second, or from *any* universal machinery. > > > Consciousness, intelligence and observable are indeed things to derive, and > > mechanism derive it from number relations, > > There is simply no way that could be correct. Consciousness changes, or at > least my consciousness does and so does physical relations, but numbers never > do. Like in relativity, the changes are relative, and based on indexicals. > > >> Experimental physicists measure physical magnitudes and describe what they > >> found in the language of mathematics. How could you even in theory measure > >> the numerical magnitude of the number 7? Does that magnature ever change? > > > The result is a number, then we can interpret the number in term of the > > magnitude of something, but the physicalist adds something by committing > > itself in the idea that the magnitude refer to a physical universe, > > Because a physicists can measure a voltage but he can't measure a pure number. He can only measure a pure number. Then he can interpret it in some metaphysics. The number measured are neutral on it. > > >> A book has no meaning to you if you don't know the language it's written in > > > Not really. The book might be without a meaning accessible to me, but still > > accessible to another one. We might decide that a book has meaning if there > > is one universal number making genuine sense from it. > > I googled "universal number" and all I got was stuff about numerology and the > way dentist refer to specific teeth. That says something about google, perhaps. The terming is not important. I use “universal number” because “machine” is misleading for some people who take a machine as a physical entity. The number x emulates the number y, on the number z, just means that phi_x(y, z) = phi_y(z), for some (fixed) universal machinery phi_i (like arithmetic, game-of-life, diophantine polynomial, combinators, etc.). A number x is a universal emulator if x emulates all numbers on any input. > > > Without physical implementation, there is no direct physical use, > > Without matter there is no physical or nonphysical use directly or indirectly. > > > but without a FORTRAN interpreter, no FORTRAN code could have meaning. > > Having a FORTRAN interpreter is necessary but not sufficient to obtain > meaning, and the same thing could be said of a Physical Turing machine. Both > are needed. If Fortran is not enough, Digital Mechanism is false. > > >> OK so 0=1, that's fine. > > > No, that is not fine. If 0=1, pigs have wings. > > Yes but that's OK too, if nothing physical exists then pigs and wings can't > cause problems because they don't exist. And there are no minds that might be > upset by paradoxes. Assuming a primary physical universe, yes, that’s correct, but then mechanism has to be abandoned. > > >> there would be no contrast. If nothing physical existed then pure numbers > >> would have the property of infinite unbounded homogeneity, so they > >> wouldn't exist . > > > Contrast comes from the fact that some arithmetical relation are true, or > > false, > > A physicist can say a voltage difference either exists or it doesn't, but all > a mathematician can say is if a arithmetical relation can be derived from a > set of agreed on axioms then its true, but derivation requires calculation > and without a Physical Turing Machine nothing can be calculated. All computations are emulated in all models of arithmetic. A model M of Peano arithmetic is another example of combinatory algebra. Just define, for x, y z in the model: xy = z by M satisfies Ec(T(x, y c) & z = U(c)), with T the Kleene’s predicate and U the result-extracting function (from the computation c). See Davis’s book for the detailed implementation of T and U in arithmetic (or see Gödel’s 1931 which does practically the same with the probability predicate). > > > If you have a physical definition of natural number, let me know, > > OK, the natural number 1 is exactly the number of seconds it takes light to > travel 299,792,458 meters, 1 is used in 299,792,458. > and the natural number n is exactly the number of seconds it takes light to > travel n times that distance. > > >>Nobody assumes time and space they observe them. > > > The whole point of Plato [...] > > My cue to skip to the next paragraph. > > >> are you really going to tell me with a straight face that your phantom > >> calculations can produce all the effects that INTEL's Silicon calculations > >> can? > > > Yes. It actually did. > > I hope you don't really mean that because if you do you've lost your mind. It can do this for an emulated observer. You have not proved that the “physical silicon” do anything more than that. > > > INTEL, silicon, matter are all in the head of the universal machine. The > > mathematical explains where INTEL comes from ... > > I don't want you to explain anything, I want you you to PERFORM a calculation > without using matter that obeys the laws of physics, and we both know you're > never ever EVER going to be able to do that. “Performing” is defined in arithmetic, with Mechanism (once well understood). It is a relative notion. > > > You need to first understand that (N, 0, s, +, *) satisfies the existence > > of all computations, > > All? (N, 0, s, +, *) satisfies ALL computations? Did I get that right, All > computations?! ALL? Why in your life did you ever waste money buying a > computer when (N, 0, s, +, *) can do ALL you want a computer to do? Yes. If phi_i(x) = y, whatever the universal machinery phi_i is, you can prove that (N, 0, s, +, *) satisfies it, and satisfy all the condition to say that the computation is implemented. Obviously, to make such a computation manifested relatively to you, you need to interpret it in the physical reality. All sound universal numbers, in arithmetic, knows that. It does not make the physical reality primary. > > > and then to explain me what is your stuff, with definition or example, > > I've answered that question before, John K Clark is the way matter behaves > when it is organized in a johnkclarkian way. The question was not about John Clark, but about the stuff you are using. What is it, and how does it make a computation more real. We already know how it makes the computation looking more real relatively to you. > > you seem to accept mechanism, > > Yes and I've accepted it more than most, I spent $80,000 on it. > > > which force you to accept some computationalist account of consciousness, > > My fundamental axiom is consciousness is the way data feels when it is being > processed. I am OK with this, although that is a bit vague. It applies to all data processed through the sigma_1 arithmetical relations. > If you think about it although we strongly disagree about a lot of stuff I > wouldn't be surprised if that's your fundamental axiom too. After all, what > is the alternative? Yes, we agree on this. We disagree only that you invoke some impersonal god, Matter to make the processing more real, but then that appears to be invalid. If that was true, that matter would need magical, non Turing emulable, element, to make some computation more real, but the Mechanism can no more be true. > > > but then, that theory of consciousness will applied to the (relative) > > numbers. > > That would be valid if numbers could process data but they can't because they > can't change, They can’t change in the absolute way, nor can the block space-time universe of GR. But they can change in the relative way. Indeed that the point of proving that arithmetic is Turing universal. > only matter that obeys the laws of physics can perform calculations because > matter can change. Matter can do computations because it is Turing universal. But the same is true for all combinatory algebra, all model of arithmetic, etc. > We may use numbers to describe the pattern in space of voltages that are > inside a computer, but it always comes down to voltages not numbers. Only when you interpret the numbers through electricity. But you can build a Babbage machine, or just look inside arithmetic to see the emulation of electrical machine, Babbage machine, combinators, etc. > > >> I am a Turing Machine but I am not a Universal Turing Machine or a "Löbian > >> machine”because there are some problems that a Turing Machine can solve > >> with a *finite* amount of tape that I can not because my tape is too > >> short. So I can't prove I'm universal because I'm not. And yet I'm > >> conscious. > > > A universal Turing machine is a finite object. > > Something can be finite and still be much much larger than me. Back in 2010 a > Universal Turing Machine calculated the 2,000,000,000,000,000th digit of pi, > it turned out to be 0. I could not have done that, not even if I had pencil > and paper to help me. > > > It might (and will) sooner or later asks for more memory space. > > I can ask for more memory space but unlike a UTM I won't get it, and even if > I did there wouldn't be enough space for it to fit inside my skull. That why the biological universal entity develop brains, add neurons, or begin to use the wall of the cave as memory extension, until they discover paper, … magnetic tape. All universal machine want always more memory. > > > But the memory space is in the environment, not in the definition of the > > finite set of quadruplet. > > That's OK because I don't give a damn about the definition of the finite set > of quadruplets, I'm not interested in any definition I'm interested in > PERFORMING calculations. That si what the quadruplets do, relatively to the universal machinery implementing it, be it arithmetic, etc. > > > Nor do I assume a primitive physical universe in the thought experience. > > That's just silly, nobody assumes an experience. Nor did I do that. > And no amount of assumptions or definitions can add 2 and 2 without physics. 2+2=4 independently of anyone verifying the fact. > > >> If that huge number can change then so can any number, so when the number > >> 7 changes to something else the number 7 no longer exists. So in this new > >> reality how much is 4+3? > > > Changes are defined in the relative way, like in Block-Universe view of GR. > > Einstein made it clear that the Block-Universe is not homogeneous but changes > along the time dimension and along each of the 3 spatial dimensions. Like the numbers. > You think the number 7 changes relative to something. What is that something? 7 is 6 “after” 1 is added, like 8 is 7, when 1 is added. > And you never answered my question, after the number 7 changes to something > else how much is 4+3? If the register as change its content 7 by 8, 7 +1 in a further instruction could become 8 + 3. Number are not changed, but memory content can change, and they can be represented by numbers. I have explained a bit more on this already. > > > Hardware and software are relative notion, except for the physical hardware, > > Yes! > > > which is not a software at all, > > Yes! > > > but a phenomenological perception by the universal numbers. > > Numbers that can perceive things? In English the term "universal numbers" is > only meaningful in the world of astrology and dentistry, however nobody but > Bruno knows what "universal numbers" means in Brunospeak. Other logicians have used that expression, like Smullyan in its last book. But scientist hate vocabulary discussion. The key point is that the digital machine are arithmetical concept. See the paper recently cited by called, which shows, in passing, how PA proves the Turing universality of some machine:number. > > >> If you really believe, and apparently you do, that a proof has been found > >> that pure numbers can change > > > Relatively to other number, through number relations. > > Relative to the number 11 how has the number 7 changed? 4 > > > Obviously “a number can change” is nonsense, but in the course of a > > computation, even, made in arithmetic, a number can change. > > I see, obviously a number changing is nonsense but a number can change. No, I > take that back, I don't see. A number can represent a register. This is sometimes written like x := x + 1, and it means that we add 1 to the register x. Then you need only to study the details of how to manage composition f programs, and recursion, in pure arithmetic. That is done in all textbooks. The details are tedious, as it consists in programming in a very low level programming language. But I did show it in all details for the combinatory algebra (which also do not assume anything about a physical reality). > > > and have the power to change things in the physical world > > As I've been saying for years stop telling me about how to do it and just do > it, DO IT AND BECOME GOD! Each time you ask me this you are in the start man fallacy. You ask something impossible. The point is that it is already done … in arithmetic. > > > A number cannot change something in the physical world. > > I see, a number has "the power to change things in the physical world" but "a > number cannot change something in the physical world". No, I take that back, > I don't see. > > > But the relation between the numbers can make relative numbers experience > > change. > > When does 4+3=7 and when does it not? The program x gives 7 on input 4 and 3 when M satisfies T(z, 4, 3, y) & U(y) = 7, with T the Kleene’s predicate (with one argument more) and U the result extracting function. > > >>> To you agree with Euclid’s proof that there is no biggest prime number? > > >> That is a physical question. It depends on if the expanding accelerating > >> universe has the capacity to perform a infinite (and not just > >> astronomical) number of calculations and I don't know the answer to that > >> but I have reasons to be somewhat skeptical. > > > So you don’t agree with Euclid? His proof of the infinity of prime number > > is orthogonal to physics. It says nothing in physics, and it uses nothing > > in physics. > > Euclid's proof contains no error but it starts with a INVALID ASSUMPTION and > you just pointed out exactly what that assumption is; from the first line of > the proof to the last Euclid assumes that numbers have nothing to do with > physics. Wrong in you materialist metaphysics, but that is only the nth times you beg the question. You cannot invoke you metaphysical commitment to refute a proof (of inconsistency). If you believe in matter, you need to elaborate on what it is and how it makes a computation more real/conscious for the entities being emulated. But the reasoning I have given shows that it is impossible. Mechanism and materialism are logically incompatible. 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/CAJPayv15PKZ8%3DgdAWf20sf-m7cPwGSJG1NX_oq4gK2go9mk5Pw%40mail.gmail.com > > <https://groups.google.com/d/msgid/everything-list/CAJPayv15PKZ8%3DgdAWf20sf-m7cPwGSJG1NX_oq4gK2go9mk5Pw%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/A0F70349-42AC-477B-9608-A227B3F62D10%40ulb.ac.be.
