> On 3 Mar 2019, at 03:27, John Clark <johnkcl...@gmail.com> wrote: > > > On Fri, Mar 1, 2019 at 4:23 PM Lawrence Crowell > <goldenfieldquaterni...@gmail.com <mailto:goldenfieldquaterni...@gmail.com>> > wrote: > > > There are numbers that have no description in a practical sense. The > > numbers 10^{10^{10^{10}}} and 10^{10^{10^{10^{10}}}} have a vast number of > > numbers that have no description with any information theoretic sense. > > The 8000th Busy Beaver Number can be named but not calculated even > theoretically,
The busy beaver function is not computable, but on each individual n, it is computable theoretically, of course, not practically, as there is no room in the observable universe to even write the result. The 8000h BB number is well defined, so it is a (finite) number, and so youthere exist a finite program computing it: just “write that numbers”. All initial segment of non computable function are computable with a look-up table. (All finite function are computable). > but most Real Numbers can't even be uniquely named with ASCII characters, not > even with an infinite number of them. Yes, like the Total computable functions. Turing defined a computable real number par the total computable function giving its decimal, or its approximation. That is a good simplifying definition, but it makes, as Turing eventually realise, addition and multiplication not computable. The “modern” definition of computable real numbers add some condition of computable modulus of convergence to remedy. Note that if there is a miraculous “Church’s thesis” for the computable functions on finite objects, there is no equivalent thesis for the reals, although there are relations with the analytical hierarchy. People can Google on elementary, hyperelementary, projective Borel …” to get more information of this. 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 everything-list+unsubscr...@googlegroups.com > <mailto:everything-list+unsubscr...@googlegroups.com>. > To post to this group, send email to everything-list@googlegroups.com > <mailto:everything-list@googlegroups.com>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <https://groups.google.com/d/optout>. -- 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 post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
