On Apr 10, 4:41 pm, Simon Smith wrote:
No, it's trivial to prove that there are infinite possibilities for any rule
system:

Assume a 28 letter alphabet (A-Z plus space and full stop.)

Write down all 28^1 one-character statements A-.
Write down all 28^2 two-character statements AA-..
Write down all 28^3 three-character statements AAA-...
Write down all 28^4 four-character statements AAAA-....

And so on.

This is a countable infinity of 'statements', where each statement consists
of one or more 'sentences'.

Even after you've crossed out all the ungrammatical ones, and all the ones
that do not pertain to Calvinball chess you'll still have a countable
infinity of rules for chess variants remaining. Then there's the infinite
number of different recipes for eggnog, and all the chess/rugby variants
where pawns are allowed to tackle, and so on.

Let's talk about MEANINGFUL rules changes. Changing the colors and
looks of the pieces is irrelevant to the question. While one could
end up having what you state above for letters would show that each
space is a place where a different rule can slide in. While you can
add multiple letters to a statement, this still doesn't show whether
that these amount of spaces are infinite. Of course, in anyone of
those letter spaces, if there can be an infinite range of states
associated with a rule, then that would be infinite. But, outside of
boardsize or time to make a move, what else can have an infinite range
of states for a board? Such as, when it comes to chess, are there an
infinite number of pieces a game of chess, even on an 8x8 board, can
have?

Pretty much, you either have to show that, MEANINGFULLY there are
either an infinite number of MEANINGFUL rules that can be added to a
game, or that one rule can have an infinite number of states, for
Heraclitian/Calvinball to be added.

- Rich

[BTW The number of cross-posted groups for this message is a bit high.
I've removed sci.math and rec.games.design from the followups.

As for this being in sci.math, it does relate to game theory and also
aspects of logic and infinity.

- Rich