On 01 Mar 2013, at 21:02, meekerdb wrote:

On 3/1/2013 9:20 AM, Bruno Marchal wrote:

In physics we sometimes get big numbers, like 10^88 or 10^120, but we never need 10^120 + 1.

But physics is no more assumed in the TOE derived from comp.

I'll bet you've never needed to calculate 10^120 + 1 in the world whose TOE is derived from comp either. :-)

False. because now I need to calculate it to make my point:

10^120 + 1 =
10000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000001

I told you, an infinitesimal!

Nothing compare to the finite, but really huge, number that I described some years ago, to illustrate some use of diagonalization, on this list (omega + [omega] + omega, if you remember).





The number of chess games is about 10^120. The number of GO games is far bigger.
And string theory points on 10^500 theories.

Exactly why almost all chess, go games, and string theories are uninteresting.

The number of possible brain connection, and thus possible subjective state is about equal to 60,000 ^ 1000000000.
Does that makes all brains non interesting?

Look, if you argue seriously that comp is not interesting because it uses that for all x we have x ≠ x + 1, I think most people will conclude that comp is winning.




And my friends the Roses have never seen a gardener dying. Some rare Roses have heard rumors that can happen, but all rational Roses knows that belong to fiction.

Frankly, for a logician, 10^100 looks really like an infinitesimal :)

And to mathematicians too, almost all numbers are infinitesimal.

Hmm... It depends of the context. The cardinal of the monstrous finite simple group is usually considered as a big number, as nobody expected such a big number to occur there.



Except instead of seeing this as a bizarre problem indicating something is awry about their theories, they happily invent transfinite numbers.


You might read paper by P. Dehornoy, who solved a problem in braid theory, with application is physics, by using large cardinal in set theory. Then later it is has been possible to prove Dehornoy's result without using those cardinals, but the result has still be found through them.

Comp is ontologically finitist, though, but not ultrafinitist, indeed.

Bruno

http://iridia.ulb.ac.be/~marchal/



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