Another potential route for the interface of this game is in the abacus. The book describes how a modified abacus was one of the first iterations of what was to become the glass bead game.
The concept behind this is to transcode math into music, and music into math; this process of transcoding one field into another is essentially the game.
There are only two issues I see in this strategy: one is that no one around here probably knows how to use an abacus, and two is that no solution on how to turn an abacus into music notation leaps to mind.
I'll pose this question later in the q/a folder to see if anyone has an idea.
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