Leap Worlds: my 3QD attempt

Hesse gives us an insight into how the game is played at the level of moves and themes when he says a given game might have explored “the rhythmic structure of Julius Caesar’s Latin and discovered the most striking congruences with the results of well-known studies of the intervals in Byzantine hymns” — but he could hardly have known, back in the 1940s, that in 1978 the University of Wisconsin Press would publish Jane-Marie Luecke OSB’s monograph, Measuring Old English Rhythm: an Application of the Principles of Gregorian Chant Rhythm to the Meter of Beowulf. Intentionally or unintentionally, his game is played by all whose minds play with meanings. And there’s a game move right there, in the conviviality between the fictional move of Hesse himself, and the monograph, years later, of a Benedictine nun.

Tiny, you say, a tiny move — but a move in what Hesse termed the “hundred-gated Cathedral of Mind.”

And the scope of that cathedral, in its gradual entirety, is vast — encompassing all the vast quantities of the sciences, with the qualitative depths and heights of the arts and humanities too:

The Glass Bead Game is thus a mode of playing with the total contents and values of our culture; it plays with them as, say, in the great age of the arts a painter might have played with the colors on his palette. All the insights, noble thoughts, and works of art that the human race has produced in its creative eras, all that subsequent periods of scholarly study have reduced to concepts and converted into intellectual values the Glass Bead Game player plays like the organist on an organ. And this organ has attained an almost unimaginable perfection; its manuals and pedals range over the entire intellectual cosmos; its stops are almost beyond number. Theoretically this instrument is capable of reproducing in the Game the entire intellectual content of the universe.

We are drawing close, in a humanly possible way and without making any predications of the being or non-being of such a supposed entity, to the very mind of god.

**

And with immediate real world application, as when Maxwell sees the commonality between electricity and magnetism, Kekulé the serpent-biting-it’s-tail like form of the benzene ring — or Taniyama‘s 1955 “surmise” as Barry Mazur puts it, that “every elliptic equation is associated with a modular form” — an insight that was to bear rich fruit forty years later, in Andrew Wiles‘ proof of Fermat’s Last Theorem.

Hesse’s vision of the game was lucid, elegant, intellectual — but lacked real world application. Viewed as a method of scoring the music of ideas, it offers illuminations from the most abstract and theoretical of mathematics to the most complex of opposed political intrangencies — from Tamiyama to Edward Said, and from Christopher Alexander‘s Pattern Language to John Holland‘s “genetic algorithms“. Alexander and Holland each indicate their debt to Hesse’s fictional game in their own respective works.

How, then, to notate this game, these moves that leap side-wise, pattern-wise, semblance-wise across boundaries and boxes, limitations and disciplines — for it is these leaps, as Arthur Koestler notes in his The Act of Creation, that give us the surprised aha! of discovery, the unexpected ha! of laughter, the gut-wrenching wail aiiyeee! when tragedy strikes.

My own inclinations favor play — solo or with a friend — at a coffee house, with pencil and paper napkin, with a small graph for a board, ideas played at its nodes, connections and resonances represented by its edges. I’m thinking of network mapping on a human scale, between seven and a dozen nodes, each one rich in meaning, anecdote, quote, statistic, image, snatch of song…

But the essence is the single move, the single resemblance. And for this I have a form which I would like to offer you, downloadable, for your own experiments:

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