[FOM] Potgieter on hypercomputation
Robbie Lindauer
robblin at thetip.org
Thu Dec 16 22:00:51 EST 2004
On Dec 15, 2004, at 9:31 AM, Apostolos Syropoulos wrote:
>> Anyway, this is more than enough to consider
>> that this is infinity for practical (say, contemporary digital)
>> computations, and this is the only physical "fact" of such kind
>> that I need to rely on when I say that 2^1000 is infinity.
>
> Well, if your run on your machine the following simple Perl script:
>
> use bigint;
> print 2**1000;
>
> you will get almost immediately the following output on your screen:
>
> 1071508607186267320948425049060001810561404811705533607443750388370351
> 0511249361224931983788156958581275946729175531468251871452856923140435
> 9845775746985748039345677748242309854210746050623711418779541821530464
> 7498358194126739876755916554394607706291457119647768654216766042983165
> 2624386837205668069376
>
> So, is this infinity?
try:
use bigint;
print 2**(2**(2**1000)));
If you have a REALLY BIG computer, try:
print 2**(2**(2**(2**(2**(2**(2**10000)))));
Call that number JEB.
The solution to the problem "JEB has how many prime roots?" is
unfeasible in Sazonov's sense.
Of course, no number is "infinity". Perhaps if Sazonov had counted
instead of particles, relations between particles and relations between
relations between particles and relations between relations between
relations between particles we would have reached a high enough number
to be a useful measuring stick for "infinity".
Robbie Lindauer
More information about the FOM
mailing list