From: scotts@math.orst.edu (Scott Settlemier)
Subject: The Glass Plate Game
Organization: Oregon State University Math Department
Date: Wed, 14 Oct 1992 01:41:51 GMT

I've a friend, Dunbar, here in Corvallis who has created a game in the spirit
of the Glass Bead Game as described in Hermann Hesse's novel by the same name.
He's asked me to prepare a math deck for the game so I'm asking all of you for
help. The game's primary feature is sets of cards (decks) representing ideas
in the deck's field; one side of the card briefly describes the idea and the
other side features some visual mnemonic for the idea. Play in the game
consists mostly of building up interrelations amongst the ideas. What you
could do to really help me is give me more or better ideas for cards than I've
got right now. Below are some examples of cards and a first attempt at some
sort of grouping for them:

    Theorems:
        Goedel's theorem, Weierstrass approximation theorem, fundamental
        theorem of calculus, theorema egregrium, Heine-Borel theorem, inverse
        function theorem, Kronecker's extension theorem, etc.

    Proofs:
        epsilon/3 proof, proof of the Weierstrass approx. theorem, etc.
        (it's hard for me to think of proofs that you could relate to other
        things.)

    Axioms:
        Axiom of choice, Euclid's fifth axiom, principle of the excluded
        contradiction, Peano's axioms, completeness axiom, principle of
        induction (just what is this? I believe it on intuition. is it an
        axiom?), etc.

    Problems:
        Halting problem, Brachystochrone problem, Zeno's paradox (I've heard
        there're others.), etc.

    Fields of study:
        Set theory, predicate calculus, propositional calculus, algebra,
        calculus, Galois theory, ergodic theory (Can anyone give me an
        inspired definition for this one?), topology, geometry, etc.

    Definite objects:
        Unit circle, Fibonacci numbers, Koch snowflake, Mandelbrot set,
        Cantor set, Platonic solids, etc.

    Object classes:
        Galois group, Hilbert space, Metric space, Markov process, Borel
        field, Geodesic, function, set, theorem, point, locus, kernal, image,
        algorithm, sequence, neighborhood, derivative, etc.

    Operations:
        Closure, differentiation, addition, counting, projection, recursion,
        induction, permutation, rotation, composition, etc.

    Measures:
        cardinality, dimension, magnitude, multiplicity, curl, torsion, etc.

    Properties:
        continuous, transcendental, algebraic, real, Cauchy, open, connected,
        convergent, periodic, congruent, reflexive, commutative, bijective,
        tangent, dense, etc.

If you have any ideas for cards please send it to me at scotts@math.orst.edu
and include the idea for the card, which category to place it under, a
description of the idea and perhaps what would make a good visual mnemonic.
If you have any good ideas about how to categorize the cards other than how
I've done it above, please also tell me about it. And if you are interested in
the final deck, please wait a couple of weeks before writing. If however you
wish to talk to Dunbar, you can write him about the game at
caploc@jacobs.cs.orst.edu. Thanks a lot folks.