Re: Comp: Geometry Is A Zombie

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On 03 Mar 2013, at 01:46, meekerdb wrote:```
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```On 3/2/2013 1:37 AM, Bruno Marchal wrote:
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On 01 Mar 2013, at 21:02, meekerdb wrote:

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```On 3/1/2013 9:20 AM, Bruno Marchal wrote:
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In physics we sometimes get big numbers, like 10^88 or 10^120, but we never need 10^120 + 1.
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But physics is no more assumed in the TOE derived from comp.
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I'll bet you've never needed to calculate 10^120 + 1 in the world whose TOE is derived from comp either. :-)
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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!

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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).
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I'll be you haven't added 1 to it. :-)

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I did :)

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But I don't want to get us involve in a two easy infinite conversation. So I kept is for myself :)
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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.
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Exactly why almost all chess, go games, and string theories are uninteresting.
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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?
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No, it makes almost all (in the technical sense) brain states uninteresting - they correspond to insanities.
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Our task is the open task of delimiting sanities from insanities. and helping a flow from the second to the first. The number of sane brain is also very huge, I mean that type of numbers, but also, they are exquisitely complex, in the theoretical computer science hierachies, even starting from elementary beliefs in arithmetic.
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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.
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No, many interesting theories assume that - but I wonder how essential it is. It certainly produces antinonmies like Hilbert's hotel and Godel's incompleteness.
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But that is solved in ZF, and first order arithmetic has never led to any antinomies. On the contrary it is part of the finitist part Hilbert wanted to solved the antinomies in set theory.
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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.
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Frankly, for a logician, 10^100 looks really like an infinitesimal :)
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And to mathematicians too, almost all numbers are infinitesimal.
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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.
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And 10^-122 was a surprisingly big number to physicists measuring the vacuum energy density - because they expected it to be zero.
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Indeed. Compared to 1/(omega+[omega]+omega), the number 10^-122 is an incredible giant.
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Bruno

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Brent

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

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