[ by Charles Cameron — wishing I was fluent in music, and might as well ad mathematics, Hebrew, Arabic, classical Persian, you know the drill, Sanskrit, Tibetan, Japanese.. and their courtly modes and rituals, and could play badminton, chess, dharma combat, go, eh? ]
Here’s a wonderful description of a game in which the rules — in this case, mathematical languages — change from move to move:
It happens again and again that, when there are many possible descriptions of a physical situation—all making equivalent predictions, yet all wildly different in premise—one will turn out to be preferable, because it extends to an underlying reality, seeming to account for more of the universe at once. And yet this new description might, in turn, have multiple formulations—and one of those alternatives may apply even more broadly. It’s as though physicists are playing a modified telephone game in which, with each whisper, the message is translated into a different language. The languages describe different scales or domains of the same reality but aren’t always related etymologically. In this modified game, the objective isn’t—or isn’t only—to seek a bedrock equation governing reality’s smallest bits. The existence of this branching, interconnected web of mathematical languages, each with its own associated picture of the world, is what needs to be understood.
That’s from A Different Kind of Theory of Everything in The New Yorker, an intriguing rerad, though as a non-physicist, seeing an equivalence with Calvinball — a game in which the game in play constantly changes — is about as far as I can go.
When I was talking with Ali Minai, I said that both music and math were languages I didn’t speak, and that cut me off from much by way of discourse with mathematicians (Ali himself) and musicians (my nephew the conductor Daniel Harding), and Ali commented that music is at least an embodied abstraction, whereas math is a pure abstraction with no embodied component. I hope I’ve understood and expressed that well enough. Anyway, it was a striking comment, and not one that had ever crossed my mind, on a topic of considerable interest and real regret.
Richard Feynman would have enjoyed a Calvinball reference, methinks — but for any sober-sided physicists who don’t play bongos, here’s the philsopher Alasdair MacIntyre to much the same effect:
Not one game is being played, but several, and, if the game metaphor may be stretched further, the problem about real life is that moving one’s knight to QB3 may always be replied to by a lob over the net.
I’d hoped to have more intriguing math or game quotes to offer here, but no luck so far, so I’m gonna post anyway.