Toward the Glass Bead Game - a rhetorical invention

by Joshua Fost

Copyright (c) 2003-2004 Joshua Fost, All Rights Reserved

Update (2008-Feb-07): One of the central attractions of the Glass Bead Game is the promise it offers of a medium in which we might express the many beautiful symmetries which connect ideas and disciplines. The desire to do this is, I believe, a deep and identifying trait of the human mind. My book If Not God, Then What? Neuroscience, Aesthetics, and the Origins of the Transcendent, proposes a model for the evolutionary and neuropsychological forces underlying both this quest and its ultimate destination.


A realization of Hesse's Glass Bead Game is presented. By associating small images ("beads" and "tiles") with ideas described in ordinary prose, a new vocabulary of glyphs is developed; these glyphs are later assembled in special ways, such that their spatial arrangement asserts symbolic relationships between the corresponding ideas. In particular, arrangements take the form bead-tile-bead, signifying subject-predicate-object assertions. Arranging and connecting multiple bead phrases on a two-dimensional grid allows large groups of related assertions to be made in a compact and appealing visual space, and the communication of rich symbolic connectivity less lengthy and cumbersome than it would be with prose. The entire structure, including narrative, bead phrases, and imagery is represented in the technical forms of the Semantic Web; all beads and tiles are labeled with URIs, and bead phrases become reified RDF.

Keywords: Semantic Web, hypermedia, Magister Ludi, cognitive maps

1. Introduction

What follows is an attempt to realize the vision of Herman Hesse as expressed in his 1943 novel Das Glasperlenspeil, or The Glass Bead Game (Hesse, 1943). In that work, Hesse described the Game as

...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 property -- on all this immense body of 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. ...On the other hand, within this fixed structure, or to abide by our image, within the complicated mechanism of this giant organ, a whole universe of possibilities and combinations is available to the individual player. For even two out of a thousand stringently played games to resemble each other more than superficially is hardly possible. Even if it should so happen that two players by chance were to choose precisely the same small assortment of themes for the content of their Game, those two Games could present an entirely different appearance and run an entirely different course, depending on the qualities of mind, character, mood, and virtuosity of the players. (Hesse, 1943, p.15)

Unfortunately, Hesse was not explicit enough in his writing to provide unambiguous instructions for how to go about actually creating or playing the Game. This has vexed many (Line, 1997; Cameron, 1995; Cohen, 1998; Aitkens, 2000). It is possible Hesse himself did not have a clear vision of the Game, but instead a more or less aesthetic and intellectual hope that something better than narrative language should be possible. That hope is the basis for the present work, which attempts to be more explicit in laying out how such a game might actually be played.

At its core, this attempt becomes an effort to represent patterns of relationships. To do this, we propose borrowing some features from several different writing systems, including the alphabetic script familiar to most westerners, the logographic script familiar to most easterners, and some new elements, such as the dynamic creation of new symbols and the addition of a second dimension for composition. The reasons for these choices will become clear later, but we present here a short preface.

Consider how one would write about a large set of subtlely interrelated ideas. Regardless of the language, one would presumably write some kind of narrative essay, developing each idea in turn, assembling the structure slowly over the course of many pages. What interests us here is the amount of space required to represent the interrelationships. In general, the more numerous and complex they are, the longer the text. The longer the text, the more material a reader must pack into short term memory, and the harder it is to see the whole structure represented in one place. One of our goals here is to condense the expression of our idea so that a grand synthesis need not require a large volume. This is quite explicitly a goal in other fields; in science, theories explaining a lot with a little are not only parsimonious but aesthetically appealing (Dirac, 1963; Feynman, 1965; McAllister, 1996). In poetry, too, there is an elegance to the perfectly chosen word. What of narrative? Can we introduce new techniques into the more everyday forms of communication to convey more with less?

One obstacle is the fact that most writing systems are simply visual representations of things we say, and in general, we do take longer to say things that are complicated. Thus, even given the differences between alphabetic and logographic scripts, there is an upper limit to the amount of meaning embodied in an single word. Of course, there is a reason for this: there are an infinite number of ideas; inventing a new word for every idea becomes overwhelming. But there is another way of thinking about this. Taking a cue from mathematics, we might say this: Narrative lacks variables. In mathematical writing, authors assign labels to quantities to allow for clearer expression. Arbitrarily complex quantities can be given the compact labels ('x', 'y', etc.), making it easy to make ever higher-order statements without increasing the length of a "sentence." Unfortunately, there is no such mechanism in narrative, but this is precisely our aim here: To devise a mode of narrative composition in which we can define new narrative symbols on the fly, i.e. at "run-time," and then assemble those symbols into compact representations of symbolic interrelationships.

2. Summary of the technique

In this section we describe in more detail our approach to the construction of a Glass Bead Game and provide instructions and rationale for those wishing to create their own. In the following two sections, we present an example that embodies the technique shown.

Step 1. Because we have no pre-built vocabulary for the game, our first step will be to write a narrative. From this adjunct text, sections will be bracketed out, labeled with small images (not words -- this is the borrowing from logographic writing systems), and used to develop our first Glass Bead Game vocabulary. The narrative itself will be an ordinary English essay, expressing the assertions that we wish to assemble into some structure later on. The essay should ideally be written in such a way that the assertions are contiguous blocks of text; this will make bracketing and labeling easier.

Step 2. Step two will be to assemble a library of two types of images. The first type, which we will call "beads," are round and have a small amount (a few characters at most) of writing or imagery on them. To create a bead yourself, choose a design that will be mnemonically easy to associate with an element from your assertions. For example, if the white whale from Moby Dick is such an element, you might create a white bead with the characters "WW" or "MD" on it, or perhaps an iconic representation of the white whale itself. Any design or device that facilitates association of the image with the idea is permissible. The second type of image, called "tiles," will represent the relationships asserted to exist between the elements of the narrative. These images will be square, and again, have a small amount of writing or imagery on their faces. If you assert that the white whale is the destroyer of Ahab, you might choose for the tile any image evocative of destruction: a mushroom cloud, a null sign, a skull and crossbones.

Step 3. The third step will be to arrange the beads and tiles into groups of three, with the interpretation that bead-tile-bead signifies a subject-predicate-object assertion. Thus, for each symbolic assertion we make, we will have one bead-tile-bead phrase. In the white whale example above, the assertion "the whale is the destroyer of Ahab" would be conceptually reduced to "whale-destroyerOf-Ahab," and represented with the destroyer tile interposed between the whale and Ahab beads. We will place each bead-tile-bead trio ("bead phrase") near the narrative in which the assertion appears, and provide a mechanism allowing the reader to establish the relationship between the image of the elements and the text that defines them.

Step 4. The fourth and final step will be to arrange all the bead phrases onto a two-dimensional grid in a way that makes larger-scale symbolic patterns more readily apparent. This activity will not follow a script at all; it will be one of the central opportunities for creativity and criticism by the Glass Bead Game player. The player's goal will be to guide the reader up out of the atoms of discourse and into a plane where larger-scale structures emerge. There will be no limit to the size of the grid upon which you place the beads and tiles. Assertions can be repeated, groups of assertions can be separated from other groups into islands, or densely meshed webs of symbolism can be laid down. A player with insight into a rich subject matter and a keen sense of parsimony should be able to assemble an attractive and semantically meaningful grid.

Once these steps are complete, the Game's creative demands will have been met, but there is a remaining technical effort that can add great depth and scholarship to the work: To encode the entire content of the game in the languages of The Semantic Web, which makes it possible for other players, and even computers, to reference and understand the ideas and imagery. At first sight, connecting one Game to another seems to be just a Link -- i.e. that form of connectivity shared by all hypertexts. But in the Semantic Web, links can be labeled; entities can have relationships; the focus is on meaning more than it is on data. This kind of connectivity is much richer than in HTML, which says the same thing about every single link, i.e. "the link target has some unknown relevance to the link origin." Another way of saying it is that publishing a Glass Bead Game on the Semantic Web makes the connections not so much about navigation as about discovery. Explaining the details of this technology here would take us too far afield, so it appears instead as Appendix A; reading it can be postponed.

3. Foreward to an example

Having explained the basic technique, we now introduce an example Glass Bead Game. This particular game concerns a web of symbolism centering on the 1994 Tarantino film "Pulp Fiction" (Tarantino and Avery, 1993) and involving ideas and characters from other works. Among the design choices are the use of English letters on the beads and Chinese kanji on the tiles. These choices are not meant to constrain other players. In general, all that is needed is that all participants and spectators of a game agree that a particular symbol signifies a particular idea; the choices of symbol are arbitrary. This is no different than agreeing that the word 'apple' signifies a particular kind of fruit. Indeed, the kanji used here do not in general carry the full meaning of the relationships they are meant to signify, but they are usually as close as I, a non-Chinese speaker, could come. Often they are radicals for words that might naturally be associated with the relationship.

Other visual aspects of the beads were not meant to carry explicit representational load. The patterns of the beads themselves, their colors, and the fonts and styles of the imprinted characters, are all intended here as matters for personal and creative expression, perhaps of subtext or evocative of the sense of an idea (with a nod to Frege), but not of strong denotative significance. In other words, what appears here as a black/aquamarine bead with a light blue "bg" on it, could just as easily appear as a stainless steel bead with a white "bg" on it, and still denote the same idea, for example, "the burger shared by Mia and Vincent in Pulp Fiction."

To establish the association between images and ideas, I have used several dynamic effects in the example below. Before each paragraph, a set of images appears -- these are the bead phrases, and in some cases isolated beads, with references in the associated text. As the user hovers the mouse over the image of a bead or tile, a section of text in the following paragraph lights up. With beads, the meaning is straightforward: the highlighted text is what the bead denotes. With tiles, two sections of text are highlighted, with the following interpretation: The tile denotes the relationship between the first idea (highlighted in blue) and the second idea (in pink). In addition to these effects, hovering over a bead or a tile will display a label. For beads (the subjects and objects of assertions) this is often a noun. For tiles (the predicates) the label is often a verb phrase or a simile. These techniques are not the only way to establish image/idea associations and are not meant to be proscriptive; again, this is a matter for refinement and individual choice.

As supporting material for the thesis of the essay and of the Game, I have included "simple" links, i.e. HTML-like links, in the text. Most often the link targets are sections of the works in question: the Pulp Fiction screenplay, the Holy Bible, and Bram Stoker's Dracula. The links can be skipped completely; they are only there to allow readers to see for themselves whether the assertions have a reasonable basis in the source works.

4. Pulp Fiction essay

Marsellus Wallace is a gangster, a king in the deteriorating society of inner-city LA. Like a rising tide, an inevitable swell of sin surrounds him. He is respected and feared, yet interested in something mysterious and noble: the contents of the holy briefcase. His involvement with this object signifies that he is an enigma: a sinner, a king among sinners, but also the bearer of God's grace. When we first see Wallace, it is from behind. He has a finely shaved head with a band-aid at the sacrum -- perhaps he is recently shaved, or with a coarse utensil?
In the first of the biblical parallels, consider Ezekiel, the son of a priest, who also lives in a deteriorating society. The Israelites have turned away from the Lord and his ways, and Ezekiel receives God's call to deliver His message of warning to them: They must turn away from their evil ways or they will die. God commands Ezekiel to shave his own head with a sword and to go amongst the sinners in Jerusalem and deliver God's warning. It is clear from the book of Ezekiel that the delivery of this message will be with words first and steel later.

Vincent, one of Marsellus' thugs, takes Marsellus' wife Mia out on the town as a favor. For dinner, they go to Jackrabbit Slim's, where each orders a burger. Their waiter, taking their order, asks their preferences: "How d'ya want it, burnt to a crisp, or bloody as hell?" Both Mia and Vincent order their burgers bloody. Vincent orders an unremarkable vanilla coke, but Mia orders a five-dollar milkshake. Tarantino goes to some effort to emphasize the shake. When it's delivered, its container, a stainless steel mixer, is center frame. Mia and Vincent are just visible on either side. As the camera looks past the milkshake onto the empty dance floor, we listen to Mia make a big deal out of how delicious the shake is. Vincent can't believe she paid $5 for a simple milkshake, so he has to try a sip. To his surprise ("Godamn! That's a pretty fuckin' good milk shake!"), it is outstanding. In this unlikely environment of resurrected 50's stars, Vincent and Mia have shared the communion.
One of the central events of the New Testament, and one of the correspondingly most symbolic and powerful rituals of modern Christianity, concerns the Last Supper that Jesus had with his apostles before his crucifixion. At this event, Jesus gave bread and wine to his followers, instructing them that they were his flesh (the bread) and blood (the wine), and that by eating them the disciples were entering into a covenant with him. The modern symbolic recreation of this covenant is done with communion wafers and wine, and is intended to signify that that recipient accepts Jesus' death as atonement for his (the recipient's) own sins.

Throughout the film, Wallace's henchmen Vincent, Jules, and The Wolf each display the same ambiguous morality as Wallace. Vincent offers us one of the more explicit examples. On one hand, he is a gangster's hit man and a heroin addict. On the other, he is philosophical and loyal. While out with Mia, he gives himself a pep talk in the bathroom mirror, trying to suppress his attraction to Mia. When he finally gets control of his hormones, he exits the bathroom to find Mia, overdosed on his drugs, convulsing, and possibly dying, on the living room floor. In a panic, he throws Mia in the car and races to his drug-dealer friend's (Lance's) house, where Lance gives medical tutelage more reminiscent of vampire assassination than emergency healthcare. At this point, Mia has shown no sign of life for 15 minutes and is presumed dead. In a hilarious but high-tension moment, Vincent stabs Mia as instructed with the enormous syringe, whereupon Mia shoots immediately bolt upright, needle sticking out of her chest, screaming like a banshee, but alive and well. She has been resurrected.
Now consider Bram Stoker's Dracula. Arthur's fiancee, Lucy, is bitten by the vampire. After a long period of misdiagnosis, she is finally treated correctly by Dr. Van Helsing, but too late and with too little supervision. She "dies" but subsequently rises from death and is transformed unto one of the undead, becoming an extreme danger and liability to her loved ones and all those around her. Once Van Helsing becomes convinced of what must be done, he leads Arthur down into her tomb, where they find her in a state between life and death, and supernaturally seductive. Van Helsing, though the expert, insists that naïve Arthur must be the one to drive a stake into her heart. In a gory, violent scene, he does so, whereupon Lucy flails and writhes but ultimately settles into a more peaceful sleep -- that of natural death.

It was precisely the symbolism of a holy communion through blood, and of a resurrection after death, that Bram Stoker and Francis Ford Coppola mocked in Dracula, and which Tarantino mocks here. In Coppola's rendition of Dracula, a mortal man has been betrayed by men and God. While he was away at war defending Christianity, his Muslim enemies sent false news of his death to his wife. In despair and devotion to her husband, she committed suicide, but thus became doomed to Hell in her orthodox Catholic faith. Raging with anger against both men and God, Dracula the man impales the altar crucifix with his sword. Blood comes streaming out, flooding the floor of the church and terrifying the local priests. The man bitterly and spitefully offers a cup of the blood to God, then drinks it himself. By reversing the ritual of the communion and drinking the blood of man, he turns the tables on Christ, becoming Dracula, a vampire, an Antichrist -- immortal through the consumption of man's blood (not Christ's), but doomed to Hell. Indeed, Mia seems equally connected to both sides through her resurrection.

Though there are many biblically symbolic links for Pulp Fiction characters, Jules is one of the few for characters whom the links are explicit. When he and Vincent visit Bret's apartment to retrieve the briefcase, we hear for the first time Jules' rendition of Ezekiel 25:17. Immediately upon quoting scripture, Jules fires the first shot in a hail of bullets. When the smoke clears, three are dead but Jules and Vincent are miraculously unscathed. Jules becomes convinced that their escape is an act of God. God got involved, gracing them by moving the bullets. Jules interprets the event as a message to mend his ways. This defining moment convinces him to leave behind his life as a sinner and killer and begin to "walk the earth until God puts [him]...where he wants [him]." Later, in the coffee shop, he begins to manifest this newfound faith by expressing a disdain for pork and chastising Vincent for blaspheming. This moral introspection recapitulates earlier conversations with Vincent, including the Antwan Rockamora foot massage issue and Vincent's respectful treatment of Mia.
Other than the explicit citation (and Tarantino's deliberate paraphrasing / mis-quoting of Ezekiel) of Biblical verse, Jules' behavior is directly guided by scripture. This is in some ways a chronological reversal of the path of the Israelites', who in Exodus wandered the earth until led by God into their holy land. Throughout, they followed God's law as given by Moses. These rules become more detailed in Leviticus, when God tells the Israelites not to eat pork, for example, because it is unclean. Later, through the prophet Isaiah, God goes further, threatening those who eat pork with his fury and flame. Christ said that those who blaspheme against the Holy Spirit are condemned as sinners. So while Jules turned away from sin and went toward God and was saved, the Israelites did the opposite and were punished.

If the vampire is one manifestation of the Antichrist symbolism in the film, then the wolf is another, and we meet two. The first is Esmerelda Villalobos, "Esmerelda of the wolves," Butch's sultry Columbian taxi driver. After Butch refuses to throw the fight for Marsellus, and killing the man who was supposed to beat him, he needs to make a getaway. Still in his boxing gear, he gets into Esmerelda's cab and speeds away. Esmerelda has been listening to the fight on the radio, so has heard news of the death in the ring. Once she makes the connection, she wants to know what it feels like to kill someone with bare hands. In her thick accent -- which could be Transylvanian as easily as Columbian -- she pesters Butch to tell her. Finally, Butch admits that he is indifferent or even slightly pleased by his deed. His ease with manslaughter places him in the morally gray zone occupied by almost every Pulp Fiction character.
The second lupine character, Winston Wolf, an associate of Marsellus, is introduced when Vincent accidentally (but too casually) shoots and kills Marvin, one of the clean-cut briefcase thieves. Just as Vincent is expressing scepticism about God's involvement in Jules' "miracle," his gun mysteriously goes off, hitting the cherubic Marvin in the face and killing him instantly. After a cellphone call, Marsellus' Wolf comes to the rescue. In contrast to Esmerelda's fire, this wolf is cool, efficient, totally unflappable. He directs the mop-up of skull fragments, brain tissue, and pools of blood with ease and nonchalance. And yet, he is likeable. The whole cleanup process exudes domestic tranquility and happiness.
Throughout the film, there is a seeming backwardness, or at least a tangled ambiguity, of who is good and who is bad, of who is in God's favor and who is not. This tangle, and the consequences for those on the wrong side, mirrors themes of Ezekiel: The Israelites, once God's favored people, have descended into sin and are threatened with destruction.

After his betrayal of Marsellus, Butch and Fabian need to make a speedy getaway. Fabian has packed the apartment and is waiting for Butch at a motel. When he gets there and is preparing to go, he realizes that Fabian has forgotten the only thing that he cared about: the family heirloom watch passed down to him by his father. He can scarcely contain his fury, realizing that he must now return to his apartment to retrieve it -- at enormous risk. But he does so, gets lucky, and kills Vincent in the process. He thinks he is scot-free...until surprised by a chance encounter with Marsellus (who says "I'll be damned!" during their chance meeting at a stop sign.) In the ensuing fight, Butch and Marsellus stumble into the Mason-Dixie Pawnshop, where they are captured by the proprietor, Maynard. Maynard gags and binds them in his basement dungeon as we sickeningly await the arrival of Maynard's sadistic brother Zed. Zed has come from work, which apparently is some kind of pseudo-law-enforcement / security officer occupation. While Zed rapes Marsellus, Butch escapes, and though he seriously considers leaving Marsellus to torture and certain death, his ethics ultimately get the best of him. He finds a weapon and returns cautiously downstairs. The weapon he has chosen is not a hammer, a chainsaw, or a baseball bat -- all considered and passed over -- but a magnificent Samurai sword, a katana. He impales Maynard, rescuing Marsellus. Once freed, Butch and Marsellus strike a live-and-let-live deal, but Butch has to promise to leave immediately, going into permanent exile from LA. Zed's fate is left in the hands of a wrathful Marsellus. Butch leaves, taking Zed's keychain (with a big "Z" on it) and, fortuitously, Zed's Big Chrome Chopper with "Grace" emblazoned on the side.
The central theme in Ezekiel is that the Israelites have rebelled from the way of the Lord, and Ezekiel is being sent as a messenger to tell them to mend their ways. The Lord's message is that those who have become wicked, even if they were righteous at one time, shall die. But those who are righteous, even if they were wicked at one time, shall live. Zed, as a uniformed law enforcement officer in public but a murderous and sodomizing rapist in private, epitomizes God's condemned classes. In the basement dungeon, surrounded by corruption and demons (the masked "thing"), he and Maynard represent the Satanic.
The flashing sword Butch uses to bring Zed and Maynard's abuse to an end is used repeatedly in Ezekiel as a symbol of the Lord's deliverance of justice to sinners. But once again emphasizing the moral ambiguity of Pulp Fiction characters are the Biblical statements that in addition to sinners, the God of Ezekiel condemns those who set up idols in their heart -- as Butch's superstitious attachment to his lucky wristwatch separates him from God.

Butch returns to the motel on Chopper Grace to retrieve Fabian. He is in a huge hurry to leave, pursued, he thinks, by Marsellus' henchmen or the law, but all Fabian can do is chatter about her disappointment at not being able to find a "big plate of blueberry pancakes with maple syrup, eggs over easy, and five sausages." Butch tries to care as she pouts over the substandard buttermilk pancakes she was forced to eat instead. They load up the Grace chopper and leave town, Fabian's craving unsatisfied.
As the Israelites depart Egypt to wander the desert, in exile from both their native lands and places of servitude, God promises them that he will deliver them into the land of milk and honey. Though they are accustomed to bread with yeast, they have to leave in such a hurry that they can bring only unleavened loaves. The Egyptians and Israelites existed unhappily in a master-slave relationship. Eventually Moses convinced Pharaoh to free his people from bondage, and so the Israelites left hastily from Egypt, which had been their home for 430 years. They took unleavened bread on their backs and walked, with whatever belongings they could carry, out of Egypt.

Any essay on Pulp Fiction needs to address the briefcase question, i.e. What is in it? This may be a loaded question. There may not need to be anything in the briefcase. For the purposes of the present work, however, simply say that the briefcase symbolizes the triumph of good over evil, of the graceful over the crude, of God over Satan. To do this, however, it is caught in the middle, acting as a rope in the tug-of-war between the battling symbolisms of the Pulp Fiction characters.
In the first place, the combination to the briefcase is 666, the number of the Devil. We learn this watching Vincent inspect its contents upon reposession at Bret's apartment. Secondly, its association with Marsellus gives it something of a nefarious sheen. But thirdly, and much more importantly, is the reaction it produces in Honey Bunny during the cafe robbery. Jules, expressing his newfound faith by restraining himself with Honey Bunny, opens the briefcase in an attempt to defuse a tense situation. A peaceful golden light shines out from the briefcase, and a tear comes to the eye of Honey Bunny. An aggressive, testosterone-saturated moment has been transformed into a humble recognition of sincere tranquility.
The briefcase is an icon for most of the characters of Pulp Fiction, stretched tight in the battle between good and evil. Its dual nature reflects the bivalence of Marsellus (connoisseur / gangster), Zed (officer / rapist), Butch (lover / killer), Jules (prophet / hitman), and Vincent (loyalist / murderer).

5. Pulp Fiction Glass Bead Game

The semi-serious Game below contains two "islands," each with its own subset of content. As should be clear, this is by no means the only or the best arrangement, even given the small number of assertions above. The purpose is simply to give a concrete example of what one Game might look like. As above, hovering over a bead or tile yields a description label.

6. Discussion

It should be emphasized that this work claims no special access to Hesse's intentions for a realization of The Glass Bead Game. Indeed, it is possible that Hesse himself thought of his work as a joke or ironic metaphor (Ziolkowski, 1969). Even if true, however, this is not disruptive to our effort -- e.g. Einstein's renunciation of the quantum theory he began did not prevent other physicists from pursuing it productively. Certainly others have taken the vision seriously and brought different interpretations to it (Cameron, 1995; Cohen, 1998; Aitkens, 2000), achieving different things with different formulations. The work of Line stands out as a particularly piquing example, integrating the invention of an artificially constructed language (a "conlang") and a one-to-one correspondence between statments in that language and symbolic / ontological statements in the Game (Line, 1997). Cohen's approach also includes a connected network of images symbolizing ideas, but there are significant differences with the methods introduced here. First, the lack of systematic structure in the underlying representation makes Cohen's games essentially a free-form hypertext, difficult to integrate with other games. Second, the graphical picture of the network is only circumstantially connected to the ideas it connects; there is no methodical association between the images of the network and the ideas, no new writing system. The narrative text, which here develops and supports the assertions, is not present in the CoreWave mode. Finally, it is not clear that one could play Cohen's game anywhere other than in a hypermedium. In our formulation, a game could be played with physical beads and tiles, so long as the denotation of each was clear to the players and audience.

In Section 1 and Appendix A, we describe how various technologies and languages from the Semantic Web are used in this formulation. Other authors are also using semantic web technologies and languages to represent networks of ideas -- though none have applied this to Hesse's work. Ayers (2004) is developing IdeaGraph, a Java-based software tool for creating conceptual graphs, and Pietriga (2003) provides IsaViz, a similar but more general authoring tool. The underlying representation of both tools is the same as that used here (RDF -- see Appendix A); while there are many tools that support this format, the fact that these tools are both visual editors and explicitly about knowledge representation make them relevant to our efforts. Although all the assertions developed in this document were encoded manually, tools like these could speed the creation of Glass Bead Games.

The small bead size used here raises the question of how one could possibly create sufficiently many visually distinct beads to map onto the infinity of ideas. Context may solve this problem. If the Pulp Fiction theme had been previously established in a particular Game, the laying of a bead with "bg" on it might be understood as referring to the burger. But if another context were in play -- astronomy, for instance -- the same bead might be interpreted as the star Betelgeuse. The re-use of symbols would make puns and double-entendres (or, pessimistically, confusion) easier and more common in the Game than outside it. This is a weakness in principle for any variable notation, but in practice it is not a serious hurdle. In physics, "c" is the speed of light; in mathematics it is often an arbitrary (non-physical) constant. Readers use context to decide which is the proper meaning and are rarely confused.

Again, all the beads and tiles shown in this example are of my own devising, but in general my hope is that some ideas would be so often-cited that they would become associated with tokens recognized by everyone. This would constitute the creation a higher-order vocabulary in which certain simple glyphs would stand for more or less complex ideas in their entirety. This is no different than how regular language creates words for common references. The greater familiarity a reader had with the symbols, the easier it would be to parse and understand a Glass Bead Game, just as familiarity with the vocabulary of a language makes it easier to read prose.

One facet of the present work is its presentation of a new writing system, i.e. as a modification and extension of the ways we write today. As such, it is worthwhile to consider any purported novelty. Here we will consider three types of common modern writing systems: logographic, logophonetic, and alphabetic, and, briefly, two more rare or extinct systems: proto-writing and syllabic. Logographic systems, like Chinese and Nushu, have a large number of signs, where each sign denotes a morpheme, or unit of meaning. Altogether new signs are rarely created, but new meanings can be expressed via sign compounding. For example, the Chinese character for "cabinet" contains the signs for "wood-in-the-kitchen." The Glass Bead Game shares the morphemic approach -- this is why kanji seemed like a natural choice for the tiles -- but whereas real logographic systems have a fixed set of characters, the GBG allows and even depends upon the creation of new symbols on the fly. Logophonetic systems, like Sumerian, Japanese, and Egyptian hieroglyphics contain elements of logographic systems and of syllabic or alphabetic systems, so their signs are either morphemes or syllables. The novelty here rests with the syllabic and alphabetic approaches, which denote units of speech, not of meaning. The signs of proto-writing systems like Aztec and Naxi are neither logographic (units of meaning) nor phonetic (units of sound) but rather are more or less pictograms, literally drawing the thing they represent. In this respect they are perhaps the most original and rudimentary writing systems, though more modern and effective logographic systems can be seen as abstract line drawings of the very same pictograms. What all of these systems share is a limitation that the repertoire of symbols is more or less fixed. The Glass Bead Game approach presented here dissolves that limitation, borrowing the practice of defining new symbols at use-time, in much the same way as variables are used in mathematical writing systems.

A possible objection to the use of beads as tokens for ideas is that words are already such tokens: Why not use them? The answer is that the Glass Bead Game is as much an aesthetic effort as an intellectual one. The alphabetic script used by English makes it extremely powerful, as opposed to the ideographic scripts used by several modern and ancient languages, but it also makes it "stringy," i.e. visually unconstrained. Alphabetic script often becomes too small when entire words -- let alone entire ideas -- are written to fit in a constrained space. In other words, alphabetic script is powerful precisely for its combinatorial power, but longer combinations of symbols take up more visual space: a problem for the Glass Bead Game. In our formulation, alphabetic script is used sparingly -- just one or two representative letters for a word. There is nothing special or preferred about my choices, however. The point is simply to associate an idea with an image.

When played on a two-dimensional grid, there is a limit to the density of connections that can be expressed. On a rectangular grid the upper limit is 8 links per node, though in practice this would rarely be achievable for more than a few nodes. To overcome this limit, one can simply copy a node to other more-or-less distant squares and start a new web of relationships. In the Pulp Fiction example above, the known set of relationships was shuffled significantly to achieve a balance of relationship density and overall game attractiveness, and the 2D limit was ameliorated by creating spatially separate islands of content. A second technique to increase the number of neighbors per node is to play in more than two dimensions. This would be very interesting, but likely much harder to produce and understand. Then there is the possibility of dissolving the grid completely. This would open the door to cognitive maps and semantic networks which, in comparison with the Glass Bead Game, are more general but perhaps less approachable. On the other hand, one of the noteworthy features of these other forms of conceptual diagrams that might be profitably introduced to the Glass Bead Game is the feature of directionality on a relationship arc, i.e. the ability to visually distinguish whether xPy or yPx is being asserted. One can envision several ways such polarity might be visually represented in this context.

In the Pulp Fiction case above, the "Game" is not really for diversion, but a single-author work that visually collects the symbolic propositions of the essay into one presentation. It should be easy to see how the medium could equally be turned into a form of scholarship or entertainment, however, as two or more authors could contribute to the same board, with arbitrary constraints about the domain of discourse. One Game might limit its subjects to the collection of historical figures and chains of shared characteristics, seriously or whimsically connecting ideas (Franklin - Inventor - Ford - Theater - Lincoln). Another might allow subjects drawn from topological theorems, musical styles, or works of literature. Some Games might be Scrabble(tm)-like, allowing players to draw from a pre-determined set of subjects and predicates, while others might allow players to arrive with their own private collections of beads and tiles. In each case, it would be up to the players and an optional Game Master (Magister Ludi) to determine the pace, the purpose, the rigor, and the domain of discourse.

The Game is not completely art nor is it completely science, but can be molded into shapes that are clearly combinations of the two. At its best, it is a expressive platform and an artistic medium, a way to assert relationships between disparate concepts, and a stimulus to help the audience achieve that blissful state of conceptual unity that so often precedes deep insight. In this version, many of Hesse's more piquing suggestions have been omitted, particularly the Glass Bead Game's intimate ties with music. Such improvements will have to wait for a later version.

Appendix A - Technical notes

Hesse's vision seems to be one in which the Glass Bead Game can express a vast and rich interconnectedness between ideas. To do that, the players of the Game must agree on a vocabulary and notation about what those ideas are, and how they are represented. This is precisely one of the problems posed and addressed by The Semantic Web (Berners-Lee et al., 2001). Accordingly, this presentation of the Glass Bead Game makes use of some of the technologies produced by and related to the Semantic Web Activity of the World Wide Web Consortium (W3C) (Miller et al., 2003).

In the first place, this document and all author-controlled link targets are well-formed eXtensible Markup Language (XML) (Quin, 2003). This structured format ensures machine-processability, presentation-layer flexibility, and availability to automated inference engines, among other things. Second, the XML form of the Resource Description Framework (RDF/XML) is used to identify all ideas and assertions used in the Game (Manola et al., 2003). A detailed description of RDF is beyond the scope of this paper, but a brief summary follows.

At their core, Glass Bead Game assertions are reified RDF/XML triples. For example, the assertion that Marsellus Wallace has a shaved head like Ezekiel, for example, looks like this (in part):

<rdf:Statement rdf:ID="assertion1">
   <rdf:subject rdf:resource=""/>
   <rdf:predicate rdf:resource=""/>
   <rdf:object rdf:resource=""/>

Because each of the resources in this assertion is a URI, other players referencing the same characters (Wallace or Ezekiel) in assertions of their own could use the same URIs. Rather than simply using the same word, this would refer to the same exact entity, eliminating ambiguity caused by multiple meanings and facilitating computer-based processing. As semantically meaningful webs like this grow larger, it is easy to see how an autonomous software agent could scan the Semantic Web for related assertions and assemble much more meaningful search results than are possible today.

Note that the URIs in the assertion above refer not to sections of text in the narrative, but to the characters themselves, which are not on the web. This is what we want; i.e. we assert that the character Wallace has a shaved head like the character Ezekiel, not that the word "Wallace" in this particular XML file has a shaved head like the word "Ezekiel" in the same file. Nevertheless, we also wish to identify sections of text with URIs, not least because the text itself is the only incarnation of the idea it expresses. This is particularly true for subjects and predicates more complex than a single word or short phrase can describe. Indeed, this abbreviation was one of the goals of the Glass Bead Game's use of idea/image association in the first place. To accommodate this need without compromising the integrity of the RDF assertions, we append several custom items to each assertion:

  1. Three image references: one each for the subject, object, and predicate.
  2. Four XPointers to sections of text: one each for the subject, the object, and the two sides of the predicate.
  3. A reference to the person making the assertion, i.e. the Glass Bead Game player.
The logic behind including references to images is obvious, and the implementation is straightforward. Using a GBG-specific namespace, the image references are encoded like this:

<gbg:subjectImage rdf:resource="img/wallace.png"/>
<gbg:predicateImage rdf:resource="img/bald.png"/>
<gbg:objectImage rdf:resource="img/ezekiel.png"/>

...where the RDF resources are relative to a base URL of". The logic behind the XPointers, however, is more subtle. One reference each for the subject and object seems natural:

<gbg:subject rdf:resource="[@number=4]/p[@number=1]/ref[@rdf:ID='wallace'])"/>
<gbg:object rdf:resource="[@number=4]/p[@number=1]/ref[@rdf:ID='ezekiel'])"/>

...where the XPointers refer to fragments of the adjunct narrative text delimited by <ref> tags, e.g.:

<ref rdf:ID="wallace">Marsellus Wallace</ref> is a gangster, a king in the deteriorating society of inner-city LA...

In other words: The raw RDF/XML triples use URIs and assert claims about objects that are not on the web. After the RDF/XML triple, the RDF work is complete. The GBG, however, when it needs to make explicit ties to the narrative that is only on the web, must use URLs and further specify that piece of content to which the beads and tiles refer. To do this, every GBG entity has an associated text that is marked off with <ref> tags and an RDF ID, which is cited in an RDF resource attribute of a GBG-specific tag.

So much for the beads (subjects and objects)...but why does (or, more accurately, why can) the GBG predicate have two textual references? Because sometimes the relationship we wish to capture is more delicate than a monolithic block of narrative. For example, the relationship between Wallace and Ezekiel is not just they both have shaved heads, but that they are recently shaved, and each shaved with a coarse instrument. Referring back to the first paragraph in the essay, we see the two sides of the predicate in blue and pink as we hover over the tile connecting Wallace with Ezekiel. The relationship between the characters is exactly the relationship between the ideas expressed by those two sections of highlighted text. Although the label for the relationship is given sometimes as a word, a short verb phrase, or a simile, its full richness is implicit, unstated. We simply give RDF resource labels to the subject- and object-side predicates (here 'sub1' and 'obj1').

<gbg:subjectSidePredicate rdf:resource="[@number=4]/p[@number=1]/ref[@rdf:ID='sub1'])"/>
<gbg:objectSidePredicate rdf:resource="[@number=4]/p[@number=1]/ref[@rdf:ID='obj1'])"/>

...where the references to ID tags would be resolved in the text with <ref> tags, just as before.

Our final element in the assertion is authorship. This closes the loop on reification, taking us from the omniscient assertion "Marsellus Wallace is shaved like Ezekiel" to the more modest and defensible statement "Author jwfost asserts that Marsellus Wallace is shaved like Ezekiel:"

<dc:creator rdf:ID="jwfost"/>

...which makes reference to an identified RDF node previously included in the file, using the the vCard namespace for RDF:

<rdf:Description rdf:nodeID="jwfost">
   <vCard:FN>Joshua Fost</vCard:FN>

With all these pieces in place, we have everything we need to both reference the assertion in another Game and to render it (with the present methods at least). The assertion in its entirety now looks like this:

   <rdf:Statement rdf:ID="assertion1">
      <rdf:subject rdf:resource=""/>
      <rdf:predicate rdf:resource=""/>
      <rdf:object rdf:resource=""/>
      <gbg:subject rdf:resource="[@number=4]/p[@number=1]/ref[@rdf:ID='wallace'])"/>
      <gbg:subjectImage rdf:resource="img/wallace.png"/>
      <gbg:subjectSidePredicate rdf:resource="[@number=4]/p[@number=1]/ref[@rdf:ID='sub1'])"/>
      <gbg:predicateImage rdf:resource="img/bald.png"/>
      <gbg:objectSidePredicate rdf:resource="[@number=4]/p[@number=1]/ref[@rdf:ID='obj1'])"/>
      <gbg:objectImage rdf:resource="img/ezekiel.png"/>
      <gbg:object rdf:resource="[@number=4]/p[@number=1]/ref[@rdf:ID='ezekiel'])"/>
      <dc:creator rdf:nodeID="jwfost"/>

Each document's metadata are in Dublin Core format (Dublin Core Metadata Initative, 1995). All links are XLinks, and references to subsections of link target resources are XPointers (Thomson, 2000). The subjects and objects in this document refer to sections of text in this document or other author-controlled documents, but in general they could refer to anything with a URI -- this is how Semantic Web technologies support Hesse's vision. There are promising other Semantic Web technologies not used by the current document, such as DAML+OIL; the current document should be considered only a starting point.

This presentation depends implicitly on the reading of this document in a suitable browser. DHTML is used interactively: As the user hovers over a particular bead or phrase, sections of the narrative will become highlighted, revealing the association between bead or tile and idea; this is in general not obvious from the appearance of the bead phrase itself. In the case where only a bead (subject or object) is inspected, most often a single section of text will be highlighted. In the case where a tile is inspected, however, either one or two sections may become highlighted. The meaning of two sections being highlighted is this: The relation between subject and object is the same as the relation between the first section of text and the second section of text. In such cases, the explicit formulation of that relation in prose is in general not presented. In the case where only a single section of text is highlighted by inspection of a tile, the meaning should be clear from context.

No current browser supports all the technologies used herein, but Microsoft Internet Explorer 6.0, Netscape 7.01, and Mozilla 1.02 correctly process most document features except the XPointer links.

Some sections of external references such as the Pulp Fiction screenplay, the Bible, and Dracula, have been transcribed by the author and structured as XML. The purpose of this is to show how rich interconnectivity and semantic precision can be achieved as the vision of the Semantic Web becomes more realized. Again, XPointer XLinks are used to reference specific sections of these references, but most current browsers do not correctly process them.

Appendix B - Glossary

  • DAML+OIL (DARPA Agent Markup Language + Ontology Inference Layer) - A W3C framework supporting the development of web-based and web-usable ontologies.
  • RDF (Resource Description Format) - An XML framework allowing anything with a Uniform Resource Identifier (URI) to be described with metadata and placed in relation to other URIs.
  • Reified RDF - A formulation in RDF syntax allowing an RDF statement to be cited.
  • URI (Uniform Resource Identifier) - A unique web-based identifier for objects that may or may not themselves be on the web.
  • XLink - An extension of HTML links to include bidirectionality, one-to-many relationships, and link descriptions with metadata.
  • XML (eXtensible Markup Language) - A subset of Standard Generalized Markup Language (SGML) allowing authors to develop their own sets of elements and attributes.
  • XPointer - A scheme for identifying sections of XML documents.


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