Hermann Hesse's Glass Bead Game:

A Game Designer's Holy Grail...


In this piece, I want to lay out the essence of the game genre called Glass Bead Games, and to suggest why I consider the development of successful, playable Games in this genre to be something approaching a "Holy Grail" for game designers.

I intend to do this -- paradoxically -- without quoting from Hermann Hesse's book Magister Ludi / The Glass Bead Game, which is the inspiration for the GBG genre.

This should permit game designers who are unfamiliar with Hesse's work to grasp the essence of Hesse's Game in a "Hesse-free" context -- thus perhaps freeing up the imagination from some of the specifics of the Game as Hesse described them for his own novelistic purposes -- and also allow those who are already familiar with his work to see the Game in a fresh perspective.

Charles Cameron



Preamble:

My rationale for describing the Glass Bead Game without referring to Hesse's work -- the paradox at the heart of this essay -- is simple.

Hesse himself calls the GBG "an eternal idea", and tells us:

This same eternal idea, which for us has been embodied in the Glass Bead Game, has underlain every movement of Mind toward the ideal goal of a universitatis litterarum, every Platonic academy, every league of an intellectual elite, every rapprochement between the exact and the more liberal disciplines, every effort toward reconciliation between science and art or science and religion.
Hesse's game, then, is a formalization of something that poets, artists and philosophers have been working towards for many centuries and in a wide variety of cultures.

It is not my intention here merely to catalogue those attempts -- which Hesse himself does in his pre-history of the GBG -- but rather to present contemporary and historical examples of the same phenomenon, in a way which will outline the main features of the Game itself.

Before we really get under way, though, I would like to make one important distinction clear.

Among the games described in the Brahmalaja Sutta of Hinayana Buddhism are "atthapada" and "dasapada", games played on eight and ten-row chess boards respectively, and "akasa", games of the same sort "played by imagining a board in the air". One and the same game, then, can in certain circumstances -- chess would be a good example -- be played with physical counters, or mentally.

And there is perhaps no game of which this is as true as a Glass Bead Game, for the very stuff of which it is woven is the stuff of ideas.

With this in mind, we can proceed...


The Glass Bead Game can be played in two modes:

The Game as described by Hesse can in fact be played two ways: one of these is far more informal than the other.


The informal mode of play:

The informal mode is a play of genius with genius across time: in other words, to play the Game in the informal manner is to juxtapose thinkers rather than thoughts -- though the thoughts in question will naturally interact with one another, and that interaction is the basis of the informal Game -- as also of the more formal version which we shall consider next.

Herman Melville described the exact process beautifully in his novel, Mardi:

In me, many worthies recline, and converse. I list to St. Paul who argues the doubts of Montaigne; Julian the Apostate cross- questions Augustine: and Thomas-a-Kempis unrolls his old black letters for all to decipher. Zeno murmurs maxims beneath the hoarse shout of Democritus; and though Democritus laugh loud and long, and the sneer of Pyrrho be seen; yet, divine Plato, and Proclus, and Verulam are of my counsel; and Zoroaster whispered me before I was born... My memory is a life beyond birth; my memory, my library of the Vatican, its alcoves all endless perspectives, eve-tinted by cross-lights from Middle-Age oriels...
To live in life beyond birth, that memory, that Vatican library, to perceive those worthies, and to witness and join their colloquy is to play the Glass Bead Game in the informal mode.

The philosopher AN Whitehead has been playing it, as we can tell from the following passage in his Aims of Education:

The communion of saints is a great and inspiring assemblage, but it has only one possible hall of meeting, and that is the present; and the mere lapse of time through which any particular group of saints must travel to reach that meeting-place, makes very little difference.
Is there a higher Game than this, that the novelist, the philosopher, sits at the feet of the "worthies" and "saints" -- the figures of genius and sanctity -- assembled across time, and speaks with them?

The novelist Hesse played this very Game while raking and burning leaves in his garden...


The formal mode of play:

There is, however, a more stringent Game, and it is this more formal Game which Hesse describes in some detail in his novel. In it, the persons of the "worthies" and "saints" fall away, while their ideas remain "in play" -- and that play of ideas is given pattern.


A Game played with ideas as pieces:

In formal mode, the Glass Bead Game is a Game played with ideas for game pieces -- markers, counters -- and it is played across the entire gamut of ideas...

The figure of Pierre Sogol in Rene Daumal's novel Mount Analogue lives in an attic studio in Paris -- accessible by a little mountaineering over the rooftops! -- and a pebbled path leads through shrubs and bushes and cactus plants around his studio:

Along the path, glued to the windowpanes or hung on the bushes or dangling from the ceiling, so that all free space was put to maximum use, hundreds of little placards were displayed. Each one carried a drawing, a photograph, or an inscription, and the whole constituted a veritable encyclopedia of what we call 'human knowledge.' A diagram of a plant cell, Mendeleieff's periodic table of the elements, a key to Chinese writing, a cross-section of the human heart, Lorentz's transformation formulae, each planet and its characteristics, fossil remains of the horse species in series, Mayan hieroglyphics, economic and demographic statistics, musical phrases, samples of the principal plant and animal families, crystal specimens, the ground plan of the Great Pyramid, brain diagrams, logistic equations, phonetic charts of the sounds employed in all languages, maps, genealogies -- everything in short which would fill the brain of a twentieth-century Pico della Mirandola...
Pierre Sogol is clearly a Glass Bead Game Player to my way of thinking, and these ideas -- the sum total of ideas which constitute our world cultural inheritance, in fact -- are the "glass beads" with which the GBG is played.

A Glass Bead Game is a Game played with ideas for pieces -- and while the whole wealth of human discourse is at the player's disposal, the ideas in question are juxtaposed in such a way that the connections between them become the player's focus...


The ideas can be of any sort:

It may not be necessary to mention this in view of the paragraph above, but the ideas with which the Glass Bead Game is played may not only be drawn from any discipline, art or science -- they can also be expressed in musical, mathematical, textual, visual or choreographic form. The Game is not a Game of words only, but of ideas of all sorts, musical, verbal, numerical, visual, kinaesthetic...

And this breadth of ideation, this willingness to include pictorial, sculptural, architectural and even choreographic ideas within the scope of the game is important, in my view, because it returns the Game itself to the body -- or, better, perhaps, heals the Cartesian split between body and mind and returns us to an earlier unity. For as Elizabeth Sewell points out in her book The Orphic Voice, ideas of all these kinds, viewed in this light, are not merely mental but also bodily pleasures and delights:

such constructions as logic, syntax, fugue, algebra, are enjoyed by the body as its own kith and kin. ...
The very fact that Sewell juxtaposes "logic, syntax, fugue, algebra" here is enough to tell us that she, too, is a Game player -- if we had not already deduced it from an earlier statement in the same book:
Every poem and recounted myth and scientific myth and theological statement and theory of politics or history and every philosophy become records of happenings at particular times, all of which, if they have any life in them at all, have the capacity to be taken further, in varying degrees, by other minds present and to come.
where, once again, she insists on infusing the "abstract" realm of ideas with life...

Note:

It is not part of my main argument here -- which has to do with outlining the Glass Bead Game in words drawn from other writers than Hesse -- but it is central to my sense of the Game's inherent possibility as a vehicle for human understanding, that this infusion with life, this embodiment of thought, which Sewell explores with impressive biological and poetic rigor in her book, is itself a necessary counterpoise to the "abstractive" tendency engendered when, as I put it above, "the persons of the 'worthies' and 'saints' fall away" in the passage from Hesse's informal Game in the garden to the formal "Castalian" Game of the novel itself.


The essence of the Game is patterning:

Thomas Mann inscribed a presentation copy of his novel Doctor Faustus to Herman Hesse with the words:
To Hermann Hesse, this glass bead game with black beads, from his friend Thomas Mann, Pacific Palisades, January 15, 1948.
and indeed figures in Hesse's novel as the Magister Ludi Thomas von der Trave -- so we can take it that he has some insight into the Game itself. I find in my own reading that there are at least two points in Mann's novel Doctor Faustus where he describes the very style of thinking on which the formal Game itself is based. First, he writes:
Creatively dreaming Nature dreamed here and there the same dream.
This is the basic insight on which the formal Glass Bead Game is posited: that there are certain patterns which underlie the diversity of natural phenomena... and of human thought. Thus Gyorgy Kepes, in his New Landscapes of Art & Science, writes:
Seen together, aerial maps of river estuaries and road systems, feathers, fern leaves, branching blood vessels, nerve ganglia, electron micrographs of crystals and the tree-like patterns of electrical discharge-figures are connected, although they are vastly different in place, origin, and scale. Their similarity of form is by no means accidental.
and Richard Grossinger, in his book, Planet Medicine:
When the surf echoes and crashes out to the horizon, its whorls repeat in similar ratios inside our flesh... We are extremely complicated, but our blood and hormones are fundamentally seawater and volcanic ash, congealed and refined. Our skin shares its chemistry with the maple leaf and moth wing. The currents our bodies regulate share a molecular flow with raw sun. Nerves and flashes of lightning are related events woven into nature at different levels.
The patterns Kepes and Grossinger mention are patterns in nature, however, and it is important to note that the same patterns also figure in human thought. Or to put it another way, the forms of nature, and the forms which arise in the human mind in dreams, in reverie, and in thought, are frequently homologous.

Thus, for instance, the logarithmic spirals of the florets in a sunflower are homologous with the Fibonacci series -- and though mathematical philosophers debate the relations between mathematics and form, this isomorphism between a natural form and a mathematical idea serves as an example of the way in which the two realms can be juxtaposed, just as the form of the sunflower and the chambered nautilus can be compared.

The Glass Bead Game, then, is "played" specifically with the analogies and isomorphisms between ideas...


The relations between ideas are of the essence:

Mann's second remark in Doctor Faustus which strikes me as eerily exact in its premonition of the Glass Bead Game reads as follows:
To look at the relations between things must be the best thing after all.
It is not individual ideas -- or forms in nature -- which preoccupy the Glass Bead Game player, but the relations between them.

Gregory Bateson's "the pattern that connects" is the essence of the Glass Bead Game, and EM Forster's "Only connect..." the player's imperative...


A Game played in a language...

These ideas -- which as we have seen may take the form of musical or mathematical or visual or textual or even choreographic utterances -- may or may not be presented in play in terms of an as yet undetermined common language which underlies and underlines their homologies...

Galileo wrote:

Philosophy is written in this grand book, the Universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the letters in which it is composed. It is written in the language of Mathematics, and its characters are triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it; without these, one wanders about in a dark Labyrinth.
Galileo's universal language is mathematics -- but the Game is not similarly limited. The language in which the isomorphisms between ideas are presented in the Game could be logical or mathematical, biological or theological or musical -- or entirely other!

It is an open matter how the ideas are juxtaposed and related -- and one of the possible benefits of the Game is precisely the generation of a new language for representing formal correspondences between heretofore "widely separated" areas of knowledge.


The aesthetics of play...

The aesthetics of play nevertheless calls for the connections posited between ideas to be as concise as possible.

The architectural theorist Christopher Alexander, in the essay on "The Poetry of the Language" which serves as an introduction to his brilliant book, A Pattern Language, describes the need for concision:

It is essential then, once you have learned to use the language, that you pay attention to the possibility of compressing the many patterns which you put together, in the smallest possible space.
and its rationale:
It is... the only way of using a pattern language to make buildings which are poems.
Alexander is talking about the uses of pattern in architectural structures, just as Galileo was talking about the uses of mathematics in the sciences -- but it is fundamentally a Glass Bead Game that they are each describing.


A board constructed of connections:

We have seen that the Game demands a juxtaposition of ideas, but it may be helpful to consider the possibility of there being a board of some kind on which the juxtaposition can take place.

The most profound analogy to a GBG "board" which I have been able to find outside Hesse's work is the Hua-Yen Buddhist concept of the net of Indra (Yin-t'o-lo kang).

Here is Dusan Pajin of Belgrade University's definition of the net, drawn from his article "The Mirror and the Source: Hua-yen Philosophy and Chinese Landscape Design", published in the International Review of Chinese Religion & Philosophy, Vol. 1, March 1996:

In the heavenly abode of Indra there is a net stretching into all directions. In each "eye" of the net is a jewel which reflects all other jewels, and is reflected in all other jewels. It is like many mirrors reflecting in each other, multiplied endlessly, with infinite reflecting.
And Sir Charles Eliot's description:
In the Heaven of Indra, there is said to be a network of pearls, so arranged that if you look at one you see all the others reflected in it. In the same way each object in the world is not merely itself but involves every other object and in fact IS everything else. "In every particle of dust, there are present Buddhas without number."
A Glass Bead Game board, then, might ideally be a stepped-down version of the net of Indra -- a web or network whose "nodes" contained the idea counters, and whose "links" expressed the connections (analogy, metaphor, isomorphism) between them.

To give you a glimpse of what this might look like, both the Sephirotic Tree of classical Kabbalah and the Quincunx which forms the frontispiece to Sir Thomas Browne's The Garden of Cyrus would be possible examples of what I am calling "stepped-down versions" of Indra's Net -- though the "network" in question is purely geometric in the case of Browne's Quincunx, while the geometry is put to semantic and meditative purposes in the case of the Sephirotic Tree.

The point is this: like the Sephirotic Tree -- and like the "semantic networks" of contemporary AI -- the geometry of a Glass Bead Game board should support both the positioning of "meanings" and the notation of the links between them. Furthermore, the net of Indra is fundamentally a net of mirrors: and the emphasis on symmetry between ideas which this implies should be translated over into whatever "stepped-down" board is used.

But in all that I have said above, I am considering "visualizable boards" -- while the possibility also exists that the board may be conceptual rather than visual or geometrical: it is entirely possible for a Glass Bead Game to be played on a board which has no visual component, where it is the logic of the moves ("ideas") themselves which organizes them...


The Game may be played entirely in imagination:

We return here to a point made about the "informal mode" of Glass Bead Game, and extend it to cover the "formal mode" of play.

The Glass Bead Game, being a Game of ideas, can be played on a board, yes -- but it can equally be played "akasa", in pure imagination, "by imagining a board in the air"... To return briefly to the net of Indra and its Chinese context, the mind itself can serve as a mirror -- and thus the board.


The Game is inherently contemplative:

To function in this way, though, the mind must be still: and this, too, is a requirement of Hesse's Game, that it should be played in a meditative manner, and toward meditative ends.

It is this requirement which allows the whole breadth of subject matter with which the Game concerns itself -- the entirety of mathematics and music, theology and literature, the sciences and humanities -- to reach symmetry, balance, proportion, beauty.

As Chuang Tsu puts it -- and he might as well be describing a Game Player after a well-played Game:

The sage's mind in stillness is the mirror of Heaven and earth, the glass of ten thousand things.


By way of summary:

The Glass Bead Game can be played informally, by visualizing the interactions of great thinkers of the past, or more formally, by formalizing the patterned interplay of ideas.

In the more formal Game -- which is the Game most game designers will be concerned with -- ideas are related to one another in terms of analogies and isomorphisms between them, in such a way that those analogies and isomorphisms are of the essence, not the ideas themselves.

The entire range of ideas can thus legitimately be brought into play: and this means not only that ideas from different disciplines can be juxtaposed, but also that ideas expressed in "languages" as diverse as music, painting, sculpture, dance, mathematics, and philosophy can be juxtaposed, without necessarily first being "translated" into a common language -- although the creation of such a common language -- mathematical, logical, or other -- may itself play an important role in the design of a Glass Bead Game.

The aesthetics of the Game calls for the connections posited between ideas to be as concise as possible, and these connections or juxtapositions may in some cases be notated on a board, real or imagined. The Buddhist "net of Indra" may serve as an inspiration in thinking about such boards, as may the contemporary exploration of "semantic networks".

Finally, the purpose of the Game itself is contemplative: the glimpsing of some unity of form or structure beneath the bewildering profusion of appearances. And it is precisely this contemplative nature of the Game which allows it, at its best, to be a vehicle for mastery -- and an access point for mystery...


This Game is a natural Grail for game designers:

I began this piece by presenting the Glass Bead Game is a sort of natural Grail for game designers.

I hope that my esteemed colleagues in game design will have gathered something of the nature of the Game as I have presented it, and that those who are interested will also consult Hesse's writings on the topic -- informally, in his poem "Hours in the Garden" from his book of the same name, and more formally in his novel Magister Ludi / The Glass Bead Game itself.

Why do I think of the design of such a Game as a sort of Grail?

Let me approach this question in a somewhat oblique way. Stephan Zweig describes the "royal game" of Chess thus:

I was well aware from my own experience of the mysterious attraction of the royal game, this one among all games contrived by man which rises superior to the tyranny of chance and which bestows its palms only on mental attainment, or rather on a definite form of mental endowment. But is it not an offensively narrow construction to call chess a game? Is it not a science too, a technique, an art, that sways among these categories as Mahomet's coffin does between heaven and earth, at once a union of all contradictory concepts: primeval yet ever new; mechanical in operation yet effective only through the imagination; bounded in geometric space though boundless in its combinations; ever- developing yet sterile; thought that leads to nothing; mathematics that produces no result; art without works; architecture without substance, and nevertheless, as proved by evidence, more lasting in its being and presence than all books and achievements; the only game that belongs to all peoples and all ages and of which none knows the divinity that bestowed it on the world to slay boredom, to sharpen the senses, to exhilarate the spirit. One searches for its beginning and for its end. Children can learn its simple rules, duffers succumb to its temptation, yet within this immutable tight square it creates a particular species of master not to be compared with any other...
This is the most profound praise of any Game that I have come across in the literature, and to my mind, nothing is said here which could not as truly be said of Go, or -- and there are vanishingly few other Games to which such praise could be applied -- of the Glass Bead Game.

Indeed, those who are familiar with Hesse's book will find in certain phrases of this paragraph -- particularly, perhaps, the phrase "ever-developing yet sterile" -- an eerie echo of the way in which Hesse himself distances himself from his magisterial Game in the course of his novel, while also offering it as the topic of a profound and extended metitation.

But there is more.

Chess -- and Go, for that matter, for it is only proper to praise both these great Games at this point -- Chess and Go, though of great formal beauty, are abstractions from human culture.

Go may have originated as an educational tool, a model of warfare or a cosmological device -- the historian Ban Gu (32-92 AD) writes in the "Yi Zhi" [The Essence of Go]:

The board must be square and represents the laws of the earth. The lines must be straight like the divine virtues. There are black and white stones, divided like yin and yang. Their arrangement on the board is like a model of the heavens...
-- and Chess, too, as Chaturanga, may have had its origins in Rajah Balhait's request to a wise Brahmin that he should invent a game to exemplify the virtues of diligence, foresight, prudence, and wisdom...

But whatever properties of cosmology or the display of virtue these Games once possessed has long since evaporated, and even their use as metaphors for war is now tenuous at best... whereas the Glass Bead Game by its nature incorporates meaning, incorporates thought, incorporates all that is finest in human culture, incorporates -- let us hope -- wisdom...


And lastly...

And lastly, the "formal" Glass Bead Game, though described with considerable detail in Hesse's book, is not described in such a way that we can simply play a round or two. We know enough to know a great deal about the Game -- the range of ideas it covers, the ways in which they are juxtaposed, the beauty that can be found in their juxtaposition...

But the Game itself -- and by this I mean the format and rules which alone will transform Hesse's ideal into a playable Game -- the Glass Bead Game remains to be invented...


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