From: Robin Hanson (rhanson@gmu.edu)
Date: Tue Jun 03 2003 - 10:23:30 MDT
On 6/3/2003, Eliezer Yudkowsky wrote:
>Suppose that you have two barrels; one barrel contains a billion
>billiards, and the other barrel contains ten billiards. The billiards in
>each barrel are sequentially numbered - in the first barrel, the billiards
>are numbered from one to a billion; in the second barrel, the billiards
>are numbered from one to ten.
>
>Suppose that the billiards are self-aware observers. A billiard numbered
>'5' can look at itself and reason: "Gee, I'm numbered '5'! What a
>surprise! Now how likely is *that*, if I'm not in the second barrel? It's
>got to be virtually certain that I'm in the second barrel! Such a
>tremendous surprise has to be evidence for *something*!"
>
>But we *know* this is wrong. Within the whole physical universe of
>discourse, two billiards reason this way. Two billiards have these
>thoughts. Of these two billiards, one is in the first barrel and one is
>in the second barrel. Whatever line of reasoning they carry out, it
>should end in the conclusion: 50/50. ...
Er, Eliezer, this *is* exactly an example of Doomsday type reasoning. If
you are a billiard who does not know his number, you reason that since only
one in a hundred million balls are in the small barrel, there is only a one
in a hundred million chance that you are in the small barrel. Then you
look at your number and decide that there is now a 50/50 chance you are in
the small barrel. Your estimate of "doom" (living in a small barrel) just
went way way up.
Robin Hanson rhanson@gmu.edu http://hanson.gmu.edu
Assistant Professor of Economics, George Mason University
MSN 1D3, Carow Hall, Fairfax VA 22030-4444
703-993-2326 FAX: 703-993-2323
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