> On 4 Jun 2020, at 22:33, Philip Thrift <[email protected]> wrote: > > > > On Thursday, June 4, 2020 at 6:30:51 AM UTC-5, Bruno Marchal wrote: > >> On 4 Jun 2020, at 07:19, Philip Thrift <[email protected] <javascript:>> >> wrote: >> >> >> >> On Wednesday, June 3, 2020 at 1:03:58 PM UTC-5, Lawrence Crowell wrote: >> On Wednesday, June 3, 2020 at 8:35:34 AM UTC-5, Philip Thrift wrote: >> >> >> On Wednesday, June 3, 2020 at 5:26:08 AM UTC-5, Lawrence Crowell wrote: >> >> >> For the most part computers are meant to run various algorithms that solve >> some restricted set of problems, say business applications. We use them >> largely as tools. >> >> LC >> >> >> >> >> >> >> All of the (usable) theories of physics invented to date can be (and are) >> implemented on supercomputers (like those in the Dept. Of Energy national >> labs). >> >> Some physicists though talk as if there is a Church they must go to -- where >> their minds are elevated into a Platonic realm where Physics is revealed to >> them. >> >> @philipthrift >> >> I guess one might say that is what experiments do. >> >> LC >> >> As I say, >> >> Physics = Math + Witchcraft. >> >> (Computational Physics though is a programming domain.) > > That is correct. But computational physics, like physics, cannot be the last > word, and the physical reality, nor the psychological reality can be > “entirely” computable. The universal machine is already not something totally > computable, only partially. > > Any theory rich enough to define what is a computer has a non computable > semantics. > > Bruno > > > > Years ago I wrote about the Zetans > > > http://poesophicalbits.blogspot.com/2012/04/persons-without-infinities.html > <http://poesophicalbits.blogspot.com/2012/04/persons-without-infinities.html> > > who never imagined infinities, nor found any reason to either think of them, > or invent them. > > They have a fine definition of computers and computing, and have found no > need for anything more than finite mechanism in any of their theory of > computing. > > That we came to think "infinity" plays a role in computing (or in computing > theory, or in mathematics in general) is just an aspect of our own peculiar > psychology and history, but it is not needed.
That makes some sense. You can compute without axiom of infinity, and indeed you can define what is a computer just by using the two axioms Kxy = x, and Sxyz = xz(yz), as I have explicitly shown on this list. Similarly you can define a computer using only elementary arithmetic, like Gödel did implicitly and Kleene did explicitly. But to prove anything non trivial, you need induction, and to get semantics treated mathematically, you need actual infinity axioms, like with the notion of real numbers, etc. To *understand* Kxy = x …, you need an axiom of infinity at the meta-level, and this is required by all scientist-numbers in arithmetic, so “infinity” is more than welcome to define the notion of observer, and for the notion of physical *laws*. Bruno > > > @philipthrift > > -- > 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/46bfade6-2376-4bb1-abaa-d15a7d08061do%40googlegroups.com > > <https://groups.google.com/d/msgid/everything-list/46bfade6-2376-4bb1-abaa-d15a7d08061do%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/A153CD38-C6CB-44C8-A595-41773F6ABA40%40ulb.ac.be.
