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From: gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>)
Newsgroups: net.math
Subject: Re: Dot Town, U.S.A.
Message-ID: <4319@brl-tgr.ARPA>
Date: Wed, 29-Aug-84 12:59:29 EDT
Article-I.D.: brl-tgr.4319
Posted: Wed Aug 29 12:59:29 1984
Date-Received: Fri, 31-Aug-84 03:21:27 EDT
References: <2479@hplabsb.UUCP>, <940@houxz.UUCP>
Organization: Ballistics Research Lab
Lines: 16

Ed Davisson & I discussed the Dot Town puzzle under the assumption that
everyone believed the stranger (assume it was God speaking or some such).
Under this condition, the puzzle turns into a "prisoner's dilemma".  One
can reason that the town suicides no matter how many blue dots there
are (must be at least one, God has spoken), under additional reasonable
assumptions about how long it takes the logicians to reason etc.  The
dilemma is that in the case of several blue dots no one has received any
additional information from God's speech, and it is possible to reason
that the town was stable and alive before the speech.

If the stranger is not known to be trustworthy, then also there is no
new information added, so if the town was stably alive it remains so.

Can such a town exist (be self-consistent and stably alive)?  Apparently
not, since its existence leads to the dilemma.  Is there some way to
determine that the town cannot exist without invoking the dilemma??