On Mon, Jul 15, 2019 at 8:25 AM Bruno Marchal <[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. > >> 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. * > 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 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, but without that Turing Machine the Lambda Calculus will *do* precisely nothing. >> 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” 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]. 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.
