> On 15 Jul 2019, at 23:02, John Clark <[email protected]> wrote: > > On Mon, Jul 15, 2019 at 8:25 AM Bruno Marchal <[email protected] > <mailto:[email protected]>> wrote: > > > physics, indeed, can clearly do something that mathematics cannot do > > Correct. > > > but that does not mean that such a something is not explainable by > > mathematics. > > Correct again. The English language can be used to explain how the sun > produces vast amounts of energy but no language including mathematics can > produce vast amounts of energy, to do that you need 2*10^30 kg of Hydrogen. > > > The ambiguous term is “do” here. > > Nothing ambiguous about it. If INTEL wishes calculations to *do* something, > like make money for example, then only matter can *do* those calculations. > > > I recall the definition of a Turing machine: it is a set of quadruples. > > There is no tape needed, except as a pedagogical tool. There is no > > assumption about atoms, or time, space, etc. > > As I said in my previous post, it's easy to translate Turing's idea into > mathematics that is just as abstract as Church's lambda calculus and just as > incapable of actually *doing* anything; however unlike Church Turing can do > more than that, Turing's idea can also be incorporated into physics and then > and only then can you *do" something with the calculation . A "Lambda > Machine" is just as fictitious as a "Löbian machine", but Turing Machines are > real, I'm using one right now.
Do is ambiguous, and a Truing machine is as much mathematical than a lambda expression. Imagine that you are in a video game. In that game you have to build a city and *do* many things, like collecting taxes, or doing some work to earn money, which is of course virtual by construction here. Yet, you do money, despite the environment is virtual. When you manage the money, it seems material, but you know that this is not the case. Now, the whole video game is executed through pure number relation (indeed sigma_1 one) in the arithmetical reality (in the tiny part that you need to assume to give sense to the word “digital machine”). And if Mechanism is assumes on the top of this, your own activity in the video game is emulated also in virtue of some (sigma_1) relations. In that case you can see that although you need to do work, and manipulate some apparent matter to do apparent money, it does not need to exist. Unless … you tell me that we need some matter to make that happening accompany by genuine consciousness, but then you need to add some non Turing emulable for your consciousness, not emulable by the number relations and thus by any Turing machine (the number relation are Turing complete), and this means that you can no more say “yes” to the digitalist doctor. > > > >> Godel always maintained that Turing's accomplishment was greater than that > >> of Alonzo Church for the very reason's I've been talking about. > > > Not at all. Gödel already knew that his own notion of computability was > > arithmetical. But he thought it was not *universal*? After reading Turing’s > > paper, he got that his own definition of computable was universal, but then > > he can be said that Gödel is the first to get the idea that computation and > > computability are purely arithmetical notion. > > Godel said Church's idea of what a calculation is was: > > "thoroughly unsatisfactory while Turing's was most satisfactory and correct > beyond any doubt. We had not perceived the sharp concept of mechanical > procedures sharply before Turing, who brought us to the right perspective. > The resulting definition of the concept of mechanical by the sharp concept of > performable by a Turing machine is both correct and unique. Moreover it is > absolutely impossible that anybody who understands the question and knows > Turing’s definition should decide for a different concept." > > Even Alonzo Church admitted Turing's way was superior: > > "Computability by a Turing machine has the advantage of making the > identification with effectiveness in the ordinary (not explicitly defined) > sense evident immediately." > > The Church-Turing Thesis <https://plato.stanford.edu/entries/church-turing/> > > > > The Church’s lambda expressions can emulate any Turing machine, and vice > > versa. > > Incorrect. A Turing Machine can do Lambda Calculus but Lambda Calculus can't > even add 2+2 without the help of a Turing Machine. See the combinator thread for a precise disproof of this. All what a Turing machine can do (computation and processes), can be done by a combinator, and thus by a lambda expression. I have shown, in all details how we can compute any partial computable function with the combinators S and K, and S and K are trivially emulate by the the two lambda expression [x][y]x and [x][y][z]xz(yz). So, just those 2 lambda expressions are Turing universal. Church would not have claimed that his lambda calculus defined all computable functions if they were unable to compute all partial computable functions. By the compilation theorem, you can build a recursive bijection between all lambda expressions and all Turing machines. By the interpreter theorem, you can build a lambda expression emulating a universal Turing machine, and vice versa. They are recursively isomorphic, with resect to computability and emulability. > > > That is how programming language works. > > A language can't *do* anything unless someone or something can hear and > understand the language, but a Turing machine is not a language, as the name > implies it is a machine. You can see it as a language, as you can see a programming language as a means to define digital machine, always in their original mathematical sense. You assume that there is an irreducible (and of course Turing universal) material reality. I do not. Invoking an ontological commitment in science is not valid, and begs the question. > > >You can implement lambda calculus directly into a Suze- von Neumann register > >machine > > Sure, As I said, a Turing Machine can do Lambda Calculus and a Von Neumann > computer is a Turing Machine, Strictly speaking, no. A von Neumann computer is better seen as a boolean graph, with a delay and splitting instructions. By the complier theorem, they are recursively isomorphic, with the Turing formalism, but as much than with lambda expression, post production system, Conway’s game of life, etc. All such system determine what I call a universal machinery, that is: a computable enumeration of all partial computable functions, which is noted by phi_i (i = 0, 1, 2, …). > but without that Turing Machine the Lambda Calculus will *do* precisely > nothing. They do exactly the same computations, and they emulate exactly the same digital processes. They are both purely mathematical concept, and both can be implemented in any Turing universal subpart of the physical reality. > > >> Sorry, I just can't keep up with the changing meaning of "Aristotle > >> theology”. > > > Come on John. I have use that expression always with the same meaning. It > > is the belief in the second God, > > Bruno I can honestly say if you've mentioned a "second God" before I do not > recall it. And please don't tell me what that is because I've given up, I > just can't keep up with the changing meaning of "Aristotle theology” Just find one post where I would have said something different about Aristotle theology, which, since day one on this list, is the doctrine which assumes some irreducible (to math for example) substance/matter (called Primary matter by Aristotle). 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/CAJPayv05oBP-%3D6EfMahuHesw%2B%3DmjLgKo1E_REx_PKB_0TRvNLw%40mail.gmail.com > > <https://groups.google.com/d/msgid/everything-list/CAJPayv05oBP-%3D6EfMahuHesw%2B%3DmjLgKo1E_REx_PKB_0TRvNLw%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/AA22B338-957F-4421-A04B-FC4AC20B7C40%40ulb.ac.be.
