Date: 6 Dec 1980 14:16 PST
From: McKeeman.PA at PARC-MAXC
In-reply-to: Greenberg's message of 6 December 1980 1644-est
Plummer.SIPBADMIN at MIT-Multics
I do not follow the reasoning. It seems quite possible that there is a
non-symmetric local maximum. In any case, it is not a definition, but rather a
proof that needs doing. It is certainly true that a move from a non-symmetric
configuration will either
a. get closer to home
b. stay the same distance from home
c. get further from home.
Furthermore, it is obvious that there are usually both (a) and (c) cases. What I
don't see is the argument that there must always be a (c) case.
Except from solved, there always exists a move taking you closer
to home. Always: There is NEVER (by the QTW metric) a move that
keeps you the same distance, and from the maximally distant state
it is IMPOSSIBLE to get further from home. Notice I have said
nothing about symmetry.