We shall now attempt to sketch the further steps in the history of the Glass Bead Game. Having passed from the musical to the mathematical seminaries (a change which took place in France and England somewhat sooner than in Germany), the Game was so far developed that it was capable of expressing mathematical processes by special symbols and abbreviations. The players, mutually elaborating these processes, threw these abstract formulas at one another, displaying the sequences and possibilities of their science. This mathematical and astronomical game of formulas required great attentiveness, keenness, and concentration. Among mathematicians, even in those days, the reputation of being a good Glass Bead Game player meant a great deal; it was equivalent to being a very good mathematician.
Within the world in which we live -- and by we I mean the author of this present work and the reader -- Joseph Knecht reached the summit and achieved the maximum. As Magister Ludi he became the leader and prototype of all those who strive toward and cultivate the things of the mind. He administered and increased the cultural heritage that had been handed down to him, for he was high priest of a temple that is sacred to each and every one of us. But he did more than attain the realm of a Master, did more than fill the office at the very summit of our hierarchy. He moved on beyond it; he grew out of it into a dimension whose nature we can only reverently guess at. (p38)
The feuilletons...seem to have formed an uncommonly popular section of the daily newspapers, were produced by the millions, and were a major source of mental pablum for the reader in want of culture. They reported on, or rather "chatted" about, a thousand-and-one items of knowledge. It would seem, moreover, that the cleverer among the writers of them poked fun at their own work. p11
In that feuilleton world they had constructed of paper, people postulated the total capitulation of Mind, the bankruptcy of ideas, and pretended to be looking on with cynical calm or bacchantic rapture as not only art, culture, morality, and honesty, but also Europe and "the world" proceeded to their doom. Among the good there prevailed a quietly resigned gloom, among the wicked a malicious pessimism (p15)
But never forget what I have told you so often: our mission is to recognize contraries for what they are: first of all as contraries, but then as opposite poles of a unity. Such is the nature of the Glass Bead Game....
The whole of both physical and mental life is a dynamic phenomenon, of which the Glass Bead Game basically comprehends only the aesthetic side, and does so predominantly as an image of rhythmic processes. (p95)
I imagine," Knecht wrote to his patron, "that one can be an excellent Glass Bead Game player, even a virtuoso, and perhaps even a thoroughly competent Magister Ludi, without having any inkling of the real mystery of the Game and its ultimate meaning. It might even be that one who does guess or know the truth might prove a greater danger to the Game, were he to become a specialist in the Game, or a Game leader. For the dark interior, the esoterics of the Game, points down into the One and All, into those depths where the eternal Atman eternally breathes in and out, sufficient unto itself. One who had experienced the ultimate meaning of the Game within himself would by that fact no longer be a player; he would no longer dwell in the world of multiplicity and would no longer be able to delight in invention, construction, and combination, since he would know altogether different joys and raptures. (p107)
Every active Glass Bead Game player naturally dreams of a constant expansion of the fields of the Game until they include the entire universe. Or rather, he constantly performs such expansions in his imagination and his private Games, and cherishes the secret desire for the ones which seem to prove their viability to be crowned by official acceptance. The true and ultimate finesse in the private Games of advanced players consists, of course, in their developing such mastery over the expressive, nomenclatural, and formative factors of the Game that they can inject individual and original ideas into any given Game played with objective historical materials. A distinguished botanist once whimsically expressed the idea in an aphorism: "The Glass Bead Game should admit of everything, even that a single plant should chat in Latin with Linnaeus. (p124)
Llull’s Ars magna (or “ultimate general art”) from 1308 outlines a form of analysis and argumentation based on working with different permutations of a small number of fundamental attributes.