On Apr 10, 8:00 pm, Quadibloc wrote:
I was going to note that one way to implement a Calvinball type of
game would be, for example, to have the Pawns be cubes, which you
would roll (not like dice) in the direction of their moves, which
would be one step in any Rook direction. Then use the face-up symbols
to grant an extra power to one of your pieces.

Are literally infinite variations on the rules possible? No, unless it
is possible for people to play a game where the rules might fill every
volume in every library in a city where all the buildings are
libraries. If there is an upper limit to the complexity of the game,
to the length of its description, then the number of possibilities is
finite.

As I see it here, the only way Heraclitian/Calvinball is going to be
infinite, is if you either have one rule with infinite states, or an
infinite number of game rules that can be added, of distinct types.
If they are of the same type, then that is merely another state of a
given rule. And my question comes back to a LITERAL infinite number
of rules existing. That is the original question Heraclitian/
Calvinball poses.

The good news, though, is that the number of possibilities can still
be quite large.

It gets astronomical, as George Duke's 91 1/2 Trillion Falcon Chess
Variants rule show.

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.

Yes, when it comes to analog, you can have an infinite number of
states, assuming that the universe is infinitely small. The digital
equivalent for Chess is the infinitely big chess board. In that, you
can have an infinite number of start positions, so thus Chess on an
infinite chess board is infinite. Of course, one may then argue
despite infinite states, there are universal strategies that can be
applied over all the board configurations.

In terms of games rather than sports, miniatures wargames could be
said to have an infinite number of positions, since pieces can move
arbitrary distances at arbitrary angles.

Yes, in analog, presuming there is an infinite number of different
spot between two points in the universe that are perceived to be
different to the human eye, then it is possible to have an infinite
number of set ups. And I believe this is one of the aspects of the
physical world that Heraclitus touched on with his never the same
river twice. Of course, you bring Zeno in with the paradox, then an
infinite number of spaces between two points sounds absurd, because
one if his is true, then one can always travel half the distance
between two points. And if this is so, then you end up where nothing
should end up reaching is destination.

- Rich