On 23 Oct 2014, at 03:41, John Clark wrote:
On Wed, Oct 22, 2014 Bruno Marchal <[email protected]> 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.
I don't see your point, nor if there is a point.
Bruno
John K Clark
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