Path: utzoo!utgpu!watmath!clyde!att!osu-cis!tut.cis.ohio-state.edu!bloom-beacon!bu-cs!buengc!bph
From: bph@buengc.BU.EDU (Blair P. Houghton)
Newsgroups: comp.ai
Subject: Re: The nine-nodes puzzle and AI
Message-ID: <1701@buengc.BU.EDU>
Date: 17 Dec 88 17:47:33 GMT
References: <43353@aero.ARPA>
Reply-To: bph@buengc.bu.edu (Blair P. Houghton)
Followup-To: comp.ai
Organization: Boston Univ. Col. of Eng.
Lines: 34

In article <43353@aero.ARPA> abbott@aero.UUCP (Russell J. Abbott) writes:
>An alternate formulation is to present the problem as 9 nodes in terms
>of which one is supposed to define arcs for some yet-to-be-defined
>graph.  In these terms there is no solution (as the naive problem solver
>suspects)--unless one adds additional nodes, which is the insight.  This
>second approach also requires that one define the notion of "colinear"
>arcs.  But if colinear arcs are defined only in terms of the given 9
>nodes, there is no way to add new nodes that are colinear with any of
>the existing nodes.  So a more general notion of colinear is needed,
>e.g., in terms of the nodes as embedded in a plane.

If I may, this sort of situation came up at the Pub the other day.  We
settled on it's being the distinction between the mathematical fields
of Topology and Geometry.  I.e., the nodal description is strictly
topological, and the solution requires a geometrical formulation,
to wit, your statement "embedded in a plane".

It took a half-drunk MS candidate, a near-sober Ph.D., and an easily
sloshed Ph.D. to get the distinction straight.

>A natural question at this point is whether anyone knows of a system
>that could deal with such a problem--on the level on which it is
>intended.

Sorry, but I don't.  It seems from your posting that even overeducated
humans have trouble with it, so an artificial system that could solve
it would be a curious bird, indeed.

				--Blair
				  "Is Usenet therefore topological
				   or geometric, taking economics
				   (costs) into account? And does
				   it affect the cost of Harpoon
				   Winter Ale?"