On Tue, Mar 05, 2019 at 10:42:00AM +1100, Bruce Kellett wrote: > On Tue, Mar 5, 2019 at 10:25 AM Russell Standish <li...@hpcoders.com.au> > wrote: > > On Mon, Mar 04, 2019 at 05:31:00PM -0500, John Clark wrote: > > On Mon, Mar 4, 2019 at 11:04 AM Bruno Marchal <marc...@ulb.ac.be> wrote: > > > > > > >> I don't follow you. If the 8000th BB number is unknowable > then > it is > > certainly uncomputable > > > > > > > That is not true. All natural number n are computable. The program > is > > “output n”. > > > > > > I think you're being silly. You're saying if you already know that the > answer > > to a problem is n then you can write a program that will "compute" the > answer > > with just a "print n" command. But that's not computing that's just > printing. > > OK, so what about the program "print X+1", where X is the expansion of > the number BB(8000)-1? > > If that's not computing something, then I'm sure I can cook up > something more complicated to compute. > > > I think the trouble with that, or with variations of that idea, is that they > render the notion of 'computability' vacuous. In order to write such a > program, > or concoct such an algorithm, you need to know the answer in advance. That is > fine, if you just want a program to compute the number 'n', 'n' being given in > advance. But that is no help in computing a number that can be defined, but is > not known in advance. > > So what people are really looking for here is a constructive notion of > computability -- anything else has a tendency to render the notion of > 'computability' trivial. >
Not really, as it makes a distinction with respect to real numbers. All integers are computable, but no real numbers are except for a set of measure zero. And then there are well defined numbers that aren't computable, such as Chaitin's Omega. -- ---------------------------------------------------------------------------- Dr Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Senior Research Fellow hpco...@hpcoders.com.au Economics, Kingston University 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. 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.
