**From:** Eliezer Yudkowsky (*sentience@pobox.com*)

**Date:** Tue Aug 24 2004 - 15:25:59 MDT

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Tomaz Kristan wrote:

*>
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*> Yes, but I would go further than that. I can sketch an antinomy inside
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*> a countable infinite set. Shake the set of all naturals! Shake it
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*> well, infinitely many times. Now, what do you expect you will see at
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*> the first 1000 places? What their average is going to be?
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*>
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*> On one hand, it should be greater than any N. N much has already been
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*> after only a finite number of shakes. Later on, this first 1000
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*> places' average only increases.
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*>
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*> On the other hand, every average of all finite naturals is a finite number.
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*>
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*> A paradox. Therefore I don't see a possibility for any kind of infinity.
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*>
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*> p.s.
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*>
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*> I could formulate this paradox in a strict math language, but it's
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*> enough for a glimpse.
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I don't see how you could formulate this paradox in strict math language.

There is no concept of a "random shake" in set theory that I'm aware of,

and Jaynes has made an excellent case that "randomness" is strictly a

property of maps rather than territories.

-- Eliezer S. Yudkowsky http://intelligence.org/ Research Fellow, Singularity Institute for Artificial Intelligence

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