On Apr 11, 8:54 am, Quadibloc wrote:
On Apr 11, 4:36 am, Guy Macon http://www.guymacon.com/ wrote:



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Quadibloc wrote:
Also, I'm thinking in terms of digital games like Chess. If one thinks
of an analog game like Billiards, the number of board positions is
infinite.

Unless, of course, the Planck Length (1.61609735×10^-35 meters) is
the quantum of distance and the Planck Time (5.3907205×10^-44 Seconds)
is the quantum of time. If they are, then the number of positions in
Billiards is finite. The smallest difference in starting billiard ball
position that can lead to a difference in ending billiard ball position
that is larger than the resolution of the human eye is far larger than
the Planck Length.

As for a game with infinite variations, the human brain has a large
but finite number of possible states, and thus such a game would
have to map multiple variations to one brain state, and thus the
brain would see those multiple variations as being the same variation.

Yes, I am oversimplifying. After all, a game like PONG by Atari,
although it mapped a game played with idealized physical objects to a
digital system with a finite number of states, was adequate.

A game that is finite, but not in a well-defined way, whose boundaries
are not obvious like those of my Random Variant Chess, that has,
instead of 10^5 sets of rules, 10^1000 sets of rules, of which
somewhere around 10^100 are distinguishable but one can't really put a
finger on the exact number... would be perhaps as close to Heraclitean
Chess as one might get in the real world, but it might be close
enough.

John Savard

I believe to get at the answer to this question, there either has to
be an infinite number of specific rule categories with a set number of
states, or a single rule category that has an infinite number of
rules. Outside of an infinite sized board, or varying the amount of
time people have to play (or make their turns), the question then
becomes, whether or not there is either an infinite number of rules
categories, or a given category (such as pieces) that is infinite.

- Rich