> On 25 May 2019, at 12:12, 'Cosmin Visan' via Everything List > <[email protected]> wrote: > > I told you: The definition of a number is: 1, 2, 3, 4, 5, 6, etc. If you > start seeing number as being alive, then you have a problem.
Yes, number are not alive, nor machine, nor brains, no piece of matter, nor anything finite, actually. But number can be involved in relation making computations definable in arithmetic. In fact, very elementary arithmetic has been shown to be Turing universal. So, whatever you can do with a computer (a digital universal machine, implemented in a physical reality) can be done, and *is* done, in the arithmetical reality. You can see the arithmetical reality as a block mindscape: it emulates all the dreams (including the waking experiences), which explains why we have to recover the physical reality appearance from the statistics on all computations (which are purely arithmetic object, even when implemented in a continuum or in a physical reality). The first proof that Arithmetic is Turing Universal is already in Gödel’s paper of 1931. Gödel did not understood this, because he remained skeptical that his definition of computation was general enough to define all computations possible, but eventually he will be convinced on this when reading the 1936 paper by Kleene. The fact that the notion of computation is purely arithmetical is typically “very well known” by mathematical logicians, but basically not understood by non-logicians. Yet, it is not difficult to prove, although it is rather tiedous, as it is like programming with a very low level assembly language. Such facts are prove in all details in good textbook, like Eliot Mendelson’s introduction to Mathematical Logic, or the classical 1952 book by Kleene “Introduction to Metamathematics”. But see also the Dover book “computability and unsolvablity” by Martin Davis, which is a cheap dover book, with an appendix proving Matiyasevitch proof that not only computation is arithmetic, but it is even polynomial (with diopahnatine polynomial were we search the integer or natural number solution, and the coefficient of the polynomials are integers). Ask any question for more explanation, Bruno > > On Thursday, 23 May 2019 19:39:42 UTC+3, Bruno Marchal wrote: > > Cosmin, ask question, it is simpler that way. You can read the papers also. > > Bruno > > > -- > 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/c8cb7d4c-d7fb-4551-bb97-90fd9734d983%40googlegroups.com > > <https://groups.google.com/d/msgid/everything-list/c8cb7d4c-d7fb-4551-bb97-90fd9734d983%40googlegroups.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/70D9D0E4-0F6D-4C86-B624-578DABDD8885%40ulb.ac.be.
