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From: gwyn@brl-smoke.ARPA (Doug Gwyn )
Newsgroups: sci.math
Subject: Re: angels and devils
Message-ID: <5023@brl-smoke.ARPA>
Date: Wed, 29-Oct-86 19:27:15 EST
Article-I.D.: brl-smok.5023
Posted: Wed Oct 29 19:27:15 1986
Date-Received: Thu, 30-Oct-86 07:25:43 EST
References: <2056@princeton.UUCP> <514@aurora.UUCP> <126@fortune.UUCP> <188@mck-csc.UUCP>
Reply-To: gwyn@brl.arpa (Doug Gwyn (VLD/VMB) <gwyn>)
Organization: Ballistic Research Lab (BRL), APG, MD.
Lines: 20

In article <188@mck-csc.UUCP> bmg@mck-csc.UUCP (Bernard M. Gunther) writes:
>Therefore: since a two dimensional field is in reality just equivalent to
>the case where the number of rows (N) goes to infinity, the blocks must
>be built an infinite distance from each other and therefore, the angel
>cannot be trapped.  

The fallacy in this reasoning can be schematized as:
	Method "A" works in the 1-dimensional case.
	One possible way of extending method "A" to the 2-dimensional case
	doesn't work.
	Therefore no method will work for the 2-dimensional case.
For the conclusion to be valid, additional lemmas would be needed:
	No method other than "A" works in the 1-dimensional case.
	The way of extending method "A" to the 2-dimensional case is
	essentially unique.
But these points weren't demonstrated and they're not obvious.

I think this is a really hard problem, and intuitive approaches aren't
likely to solve it.  I suggest having a local mathematician check any
proposed solution before posting it, to avoid wasting people's time.