> On 1 Jun 2020, at 19:31, Jason Resch <jasonre...@gmail.com> wrote: > > Speaking of large but finite numbers, I think sometimes we forget just how > big some finite numbers can be: > > This article really stretched my brain/hurt my head: > https://waitbutwhy.com/2014/11/1000000-grahams-number.html > <https://waitbutwhy.com/2014/11/1000000-grahams-number.html> Numbers can be > so big they become scary.
And I have explained how such graham numbers are infinitesimal, compared to what logicians can do. I did this to illustrate the transendental power of diagonalsiation, on this list, some years ago. I did this to better explain why Gödel is right to call the CT thesis a “miracle”. It makes “all computations” an explanatively close theory/realm, even close for the most transcendental mathematical operation (diagonalisation). It tools a long time for me to believe in CT, but I knew since long that if CT is true, physics cannot be the fundamental science, and has to be reduced to arithmetic, or to any universal machinery. Arithmetic seen from inside is inconceivably bigger than the physical observable universe, in fact it is bigger than the set-theoretical universe … yes, it can be scary … Bruno > > Jason > > On Sat, May 23, 2020 at 6:37 PM Russell Standish <li...@hpcoders.com.au > <mailto:li...@hpcoders.com.au>> wrote: > On Sat, May 23, 2020 at 12:05:08PM -0700, 'Brent Meeker' via Everything List > wrote: > > > > > > On 5/23/2020 4:42 AM, Bruno Marchal wrote: > > > > > > Well, those are theorem provable in very weak theories. It is more a > > > question of grasping the proof than subscribing to a philosophical idea. > > > That arithmetic executes all programs is a theorem similar to Euclid’s > > > theorem that there is no biggest prima numbers. It is more a fact, than > > > an idea which could be debated. I insist on this as I realise this is > > > less known by the general scientists than 20 years ago. We knew this > > > implicitly since Gödel 1931, and explicitly since Church, Turing and > > > Kleene 1936. > > > > Recently you have said that your theory is consistent with finitism, even > > ultrafinitism. But the idea that arithemtic exectues all programs certainly > > requires infinities. > > Only potential infinities, not actual infinities. For the UD (a finite > object) to execute any given program, one only needs to wait a finite > amount of time. > > However, I would think that ultrafinitism would change COMP's > predictions, and in a sense be incompatibe with it. Some programs will > not exist, because one would need to wait too long for them to be > executed by the UD. In fact, the choice of reference universal machine > would be significant in ultrafinitism, IIUC. > > > -- > > ---------------------------------------------------------------------------- > Dr Russell Standish Phone 0425 253119 (mobile) > Principal, High Performance Coders hpco...@hpcoders.com.au > <mailto:hpco...@hpcoders.com.au> > http://www.hpcoders.com.au <http://www.hpcoders.com.au/> > ---------------------------------------------------------------------------- > > -- > 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 everything-list+unsubscr...@googlegroups.com > <mailto:everything-list%2bunsubscr...@googlegroups.com>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/20200523233705.GC27696%40zen > > <https://groups.google.com/d/msgid/everything-list/20200523233705.GC27696%40zen>. > > -- > 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 everything-list+unsubscr...@googlegroups.com > <mailto:everything-list+unsubscr...@googlegroups.com>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/CA%2BBCJUgRf%2BTqhT-nXF8s5vGFQo%2BHrD55fFObFLESRKDL32PSyQ%40mail.gmail.com > > <https://groups.google.com/d/msgid/everything-list/CA%2BBCJUgRf%2BTqhT-nXF8s5vGFQo%2BHrD55fFObFLESRKDL32PSyQ%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 everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/62C99513-C593-43AD-84BF-3B360C5D5E8B%40ulb.ac.be.
