one of my teaching ideas involves a game that's supposed to teach students about "group theory" (which to me is so all-pervasive in mathematics and in life and the universe in general as to encompass a whole lot of other stuff)...

i'm thinking about this now because of my planned upcoming trip to visit laurens gunnarsen... i'm planning on mainly learning rather than teaching on this particular trip, but since it's all about teaching i'm thinking a lot about teaching ideas in general...

like most of my teaching ideas this is one that i've had almost no chance to put into practice, so it's in very rough form... i think that i have many different variations of the game in my mind, and i'm not sure which would work better for various purposes... it would probably take a lot of experimenting with actual students to figure that out...

i probably don't have a good name for that game yet, but for now i'll call it "the masquerade game"... and the basic idea is pretty simple: to put some of the players in a situation where they have limited information (or limited means of acquiring it) about the "true identity" of some of the other players (or in some variations, of game tokens of some sort), to try to get them to realize how their state of knowledge or "perceptual power" can be measured as a permutation group which controls and shapes their experience within the game; how invariance or covariance wrt the group corresponds to the "observability" or "realness" of a concept from the viewpoint of the player whose perceptual power is being measured.

of course some of the variations of the game are more heavy-handed than others in terms of how explicitly various aspects of group theory are forced upon the players...

it occurs to me at the moment that there might be variations where a change in perceptual power over time more or less explicitly brings out the idea of "symmetry-breaking" ... which is pretty much always implicitly there anyway, though...

perhaps big julie's "dice with no spots" would make a nice silly illustrative example... ??is that from one of the original stories?

??in a somewhat related vein, there's also the "game" where the player is given a pair of n-variable rational functions, one at least as symmetric as the other, and tries to express the more symmetric one as a rational combination of the less symmetric one with completely symmetric ones... for example, express "x" as a rational combination of "x^2" and symmetric rational functions of x and y...