[FOM] Potgieter on hypercomputation

[Robbie Lindauer]

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