On Wed, Oct 22, 2014 Bruno Marchal <marc...@ulb.ac.be> wrote: > > >> >> Wait? How long should I wait? > > > Well, it depends which programs you want to know if it stops or not. The > disonaur program stopped. In case it is that one. But for the search of a > proof of Goldbach in ZF, you might have to wait a bit long more. You can > bound the running time of the programs with the Busy Beaver function (BB). > The answer to your question is : no more than BB(k) seconds where k is the > number of bit used to describe the program you ask if it stops or not. I > assume a machine doing computational step in one second. >
If the program is to find the smallest even integer greater than 2 that is not the sum of two primes and then stop, and if there are no even integers greater than 2 that are not the sum of two primes then I will be waiting forever for it to stop and forever be uncertain if Goldbach is true or not. Maybe someday it will find such a number and stop or maybe there is no such number and it will never stop; but the Busy Beaver function is only defined for the class of Turing Machines that eventually stop, and nobody knows if the the Goldbach Turing Machine is of that class or not. And even if it is and Busy Beaver has a meaning for it nobody knows what number BB(k) is and nobody has anyway of calculating it so it does me no good whatsoever. >> Do you think real numbers exist or do you not? > > > > What I think is of no concern to you. > Sorry for asking such a personal question. > I work in a theory (computationalism + an infinitesimal use of Occam > Razor, and the classical theory of knowledge). In that theory, the real > numbers do not exist, as what exists is only 0, s(0), s(s(0)), etc. > But the real numbers still exists at the machine epistemological level. > So at the human epistemological level Harry Potter exists. 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. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
