From: Eliezer Yudkowsky (sentience@pobox.com)
Date: Tue Aug 24 2004 - 15:25:59 MDT
Tomaz Kristan wrote:
>
> Yes, but I would go further than that. I can sketch an antinomy inside
> a countable infinite set. Shake the set of all naturals! Shake it
> well, infinitely many times. Now, what do you expect you will see at
> the first 1000 places? What their average is going to be?
>
> On one hand, it should be greater than any N. N much has already been
> after only a finite number of shakes. Later on, this first 1000
> places' average only increases.
>
> On the other hand, every average of all finite naturals is a finite number.
>
> A paradox. Therefore I don't see a possibility for any kind of infinity.
>
> p.s.
>
> I could formulate this paradox in a strict math language, but it's
> enough for a glimpse.
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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