> On 26 Aug 2019, at 21:08, John Clark <[email protected]> wrote: > > > On Mon, Aug 26, 2019 at 6:31 AM Bruno Marchal <[email protected] > <mailto:[email protected]>> wrote: > > > A computer is a universal number. > > I agree because my personal idiosyncratic definition of "universal number" is > a chip of Silicon made by the Intel corporation, and that is ever bit as > valid as your personal idiosyncratic definition of "universal number". And > since you quoted every word of my long post without comment I assume you > agree with every word of it. Why else would you repost it?
My definition of “universal machine” or “universal number” is the standard one. A number n is universal in the universal machinery phi_i if phi_n(x,y) = phi_x(y), for all x and y. It is equivalent of Turing’s original definition of a universal Turing machine, which is (the code) of a set of quadruplets which, once having n and m coded on its tape, compute phi_n(m), and find the result of the nth program when applied on the number m. The chip off silicon, when being a general purpose computer, is a physical implementation of universal number. That physical implementation requires the assumption of the existence of some physical things, but the standard definition of a universal number/words/machine requires only elementary arithmetic, or elementary lambda calculus, or the game of life, etc. 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/CAJPayv1bnmc55i2-skNsdyyf0sThPoit9%2Bepz-BcdTK8vCKcTw%40mail.gmail.com > > <https://groups.google.com/d/msgid/everything-list/CAJPayv1bnmc55i2-skNsdyyf0sThPoit9%2Bepz-BcdTK8vCKcTw%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/DB69D191-41EF-459C-B636-8D39D989C6F7%40ulb.ac.be.
