Towards a glass bead game (The Structure of Human Knowledge as Game I)

Herman Hesse’s glass bead game is an intriguing intellectual thought experiment. He describes it in detail in his eponymous last novel:

“Under the shifting hegemony of now this, now that science or art, the Game of games had developed into a kind of universal language through which the players could express values and set these in relation to one another. Throughout its history the Game was closely allied with music, and usually proceeded according to musical and mathematical rules. One theme, two themes, or three themes were stated, elaborated, varied, and underwent a development quite similar to that of the theme in a Bach fugue or a concerto movement. A Game, for example, might start from a given astronomical configuration, or from the actual theme of a Bach fugue, or from a sentence out of Leibniz or the Upanishads, and from this theme, depending on the intentions and talents of the player, it could either further explore and elaborate the initial motif or else enrich its expressiveness by allusions to kindred concepts. Beginners learned how to establish parallels, by means of the Game’s symbols, between a piece of classical music and the formula for some law of nature. Experts and Masters of the Game freely wove the initial theme into unlimited combinations.”

The idea of a the unity of human knowledge, the thin threads that spread across different domains, the ability to connect seemingly disparate intellectual accomplishments — can it work? What does it mean for it to work?

On one level we could say that is simple – it is a game of analogy, and we only need to feel that there is a valid analogy between two different themes or things to assert them as “moves” in the game. We could say that the proof of the existence of an infinitude of primes is related to Escher’s paintings and argue that the infinite is present in both. The game – at its absolute lower boundary – is nothing else than an inspiring intellectual, collaborative essay. A game, then, consists of first stating the theme you wish to explore and then each player makes moves by suggesting knowledge that can be associated by analogy in sequence to the theme. This in itself can be quite interesting, I imagine, but it really is a lower boundary. The idea of the glass bead game being a game suggests that there is a way to judge progress in it, to juxtapose one game against another and argue that it is more masterful than the other.

Think about chess – it is possible to argue that one game in a Game (capital G Game being the particular variant of gaming, like chess, go or a boardgame) is more exciting and valuable than another, is it not? On what basis do we actually do that? Is it the complexity of the game? The beauty of the moves? How unusual it is? The lack of obvious mistakes? Why is a a game between Kasparov and Karpov more valuable in some sense than a game between me and a computer? (If we ignore, for a moment, the idea that a game between humans would have an intrinsically higher value than one between computers, something that seems dubious at best)? How do we ascribe value in the domain of games?

The aesthetic answer is only half-satisfying, it seems to me. I feel that there is also a point to be made about complexity, or about the game revealing aspects of the Game that were previously not clearly known. Maybe we could even state a partial answer by saying that any game that is unusual is more valuable than one that closely resembles already played games. Doing this suggests assigning a value to freshness or newness or simply variational richness. If we imagine the game space of a Game we could argue that there is greater value to a game that comes from an unexplored part of the game space. This idea, that the difference between a game and the corpus of played games could be a value in itself is not a bad one, and has actually been suggested as an alternative ground for intellectual property protection in the guise of originality (there always has to be an originality threshold, but beyond that). A piece that is significantly different from another (by mining the patterns of the corpus and producing a differential, say) could then be protected for longer or with broader scope, than one that is just like every other work in the corpus.

So, we could ascribe value through originality through analysis of the differential between the game and the corpus of played games (something like this seems to be going on in the admiration for AlphaGo’s games in the game community — there is a recognition that they represent an original – almost alien – way of playing go).

But originality only gets you so far in the glass bead game. I am sure noone has argued that Nietzsches theory of eternal recurrence can be linked to Joanna Newsom’s song Peach Plum Pear – but the originality of that association almost _lessens_ the value of the move in a glass bead game. There is an originality value function, but it exists within the boundaries of something else, of a common recognition of the validity of the move that we are trying to make within the theme we are exploring. So there has to be consistency with the theme as well as originality within that consistency.

Let’s examine an imaginary example game and see if we can reconstruct some ideas from that. Let us state that the theme is broad, the interplay between black and white in human knowledge. That theme is incredibly broad, but also specific enough to provide the _frame_ that we need in order to start working out possible moves that could suit and give us an idea. A valid move could be things like associating Rachmaninov’s piece Isle of the dead with Eisenstein’s principle of the use of color in movies (“Hence, the first condition for the use of color in a film is that it must be, first and foremost, a dramatic factor. In this respect color is like music. Music in films is good when it is necessary. Color, too, is good when it is necessary.”) By noting that Rachmaninov wrote his piece after having seen Böcklin’s painting The Isle of the Dead – but only in a black and white replica – and adding that he then was disappointed with the color of the original, we could device the notion of the use of black and white in non visual arts and science and then start to look for other examples of art and knowledge that seem to be inspired by or connected to the same binary ideas – testing ideas around two-dimensional Penrose tiling, I Ching, the piano keys, understanding the relationship to chess and exploring the general architecture and design of other games like go and backgammon, and othello…There exists a consistency here, and you could argue the moves are more or less orginal. The move from go to othello is less original than the move from Isle of the Dead to the I Ching (and then we could go back to other attempts to compose with the I Ching in a return move to the domain of music, after which we could land with leibnizian ideas inspired by that same book. It would seem that the binary nature of the I Ching then could be an anchor point in such a game).

It quickly becomes messy. But interesting. So the first two proto-rules of the game seem to be that we need originality within consistency. As we continue to explore possible rules and ideas we will at some point have to look at if there is an underlying structure that connects them. I would be remiss if I did not also reveal that I am interested in that because I wonder if there is something akin to a deep semiotic network of symbols that could be revealed by expanding machine translation to the domain of human knowledge over all. As has been documented, machine learning now can use deep structure of language to translate between two languages through an “interlingua”. At the heart of the idea of the glass bead game is the deceptively simple idea that there is such an interlingua between all domains of human knowledge – but can that be true?

The glass bead game – and the attempt to construct one – is a powerful play thing to use to start exploring that question.