Tag Archives: games

The Tangram

Further Reading:





The Glass Bead Game

No permanence is ours; we are a wave
That flows to fit whatever form it finds:
Through night or day, cathedral or the cave
We pass forever, craving form that binds.

― Hermann Hesse, The Glass Bead Game

“The Glass Bead Game”, also known as “Magister Ludi”, is the last full length book by German author Hermann Hesse. His works include many thoughtful and interesting stories, detailing the main character’s personal development and spiritual growth. Hesse won the Nobel Prize in Literature in 1946, and his books saw a resurgence of popularity in the 1960’s and 1970’s in the US.

“The Glass Bead Game” is special to me because it describes, although vaguely, a fictional game that is cultivated and played in a future idyllic setting of intellectual devotion, although the larger world is certainly a post-apocalyptic one. All human knowledge is the subject of the game, and the play somehow links mathematics, music, science, cosmology, history, poetry and literature and everything else accepted as higher learning for the imagined cultural time and place.

Is the book sexist because it describes the cloistered society of the game as being restricted to boys and men because of ability, or the idea that men are less distracted from intellectual pursuits without women around? The book is either a product of its time, or perhaps of the political setting in its fictional future. Interestingly, the main character, along with three other character’s lives shown in short stories said to be written by the main character himself, are easily associated with Carl Jung’s theory of psychological types. This is the meaning of the figure above.

Several individuals and groups have tried to imagine how the actual game or any “glass bead game” (GBG) could be played, and there are scattered links on the web, many broken over time and neglect. I agree that analogy and metaphorical thinking are key points to any GBG, as well as the other pillars of attributes nicely discussed in links below.

  • Analogy
  • Connection (or Affinity)
  • Cogitation (or Contemplation, Thought)
  • Formalism (or Rules)
  • Iconicity (or Representation)
  • Syncretism (or Objectivation, of Culture or Civilization)

(Some attributes have been substituted by thesaurus for word length.)

Further Reading:

Hermann Hesse / The Glass Bead Game










… For although in a certain sense and for light-minded persons non-existent things can be more easily and irresponsibly represented in words than existing things, for the serious and conscientious historian it is just the reverse. Nothing is harder, yet nothing is more necessary, than to speak of certain things whose existence is neither demonstrable nor probable. The very fact that serious and conscientious men treat them as existing things brings them a step closer to existence and to the possibility of being born.

[*8.138, *10.82]


A Game of Fourfolds, Part 5

In this fifth installment of our ongoing series, I propose that a game could be played by making a set of equally sized and shaped triangular tiles with simple words or phrases on them. The triangles are all isosceles right triangles, also called monoboloes, so that two of them joined along their long edge would be a square, and four of them joined at their right angles would be a larger square. Figures of two tiles joined along any edge of equal length are called diaboloes, three are called triaboloes, four are called tetraboloes, and in general the figures are called polyboloes (or also polytans, after the Chinese tangram puzzle).

The words or short phrases on the monoboloes would need to be chosen judiciously so that each word has a matching opposite. (A list of such pairs of opposites or duals can be found at my previous fourfold game post.) This is so that a square diabolo could be formed from opposites, and a square tetrabolo could be formed that makes some conceptual sense. In fact, the game play would require that tiles should only be played and joined if there was a rational or explainable reason for their combination.

For example, “Water” and “Fire” could be aligned along their long edge as well as a short edge, whereas “Earth” and “Below”, not being opposites, could only be aligned along a short edge. Opposites could also be aligned “corner” to “corner” (where corner is the 90 degree angle), if there is a supporting tile between them.

During game play, the players alternate playing tiles from their hand onto the table, or pick tiles up from the table and place them back in different positions. Obviously the rules of play would need to be specified in more detail, as well as a method for scoring so that a player could “win”. Or, as a game of solitaire, perhaps winning is just maximizing the number of tiles played onto the table, or the illumination of concepts brought about by the play.

I might also consider that the flip-side of a monobolo is the same word but perhaps having white letters on a black background or colored differently to distinguish it from the “front”. And would the flip-sides all be of the same color? As I have shown various fourfolds on this blog, I have tried to orient them in a common conceptual “direction”, although that is often not clear to me or agreed upon by others of similar temperament. Perhaps they could be the same color if they metaphorically point this same way.

Also, by design and by construction, the monoboloes could be considered “Words”, diaboloes could be considered “Thoughts”, triaboloes could be considered “Actions”, and tetraboloes could be considered “Things”. This would be more in line with the hierarchy given by Richard McKeon’s 1972 lectures on Aristotle’s “Topics”. Words, thoughts, actions, and things are called “commonplaces” by McKeon, or a “place within which inquiry about meanings that are about things that are covered by that meaning can take place”.

The association of these tiles with tangrams is an interesting one. The standard tangram set consists of two small tans (unitans?), three bitans (square, midtan?, and paratan?), and two tetratans that form larger tans (bigtans?). I wonder if there is a standard nomenclature for these pieces, because mine seems rather silly.

I used to have a tangram set when I was a child and even still have an old Dover book by Ronald C. Reed “Tangrams: 330 puzzles”. It’s nice to see that it’s still available on Amazon. Of course the arrangement of the pieces in tangrams is much more flexible than what I’m proposing here for my game so really they are very little alike.

Further Reading:




Richard McKeon / Disciplines, Arts, and Faculties: Invention and Justification: Topics, Lectures given at University of Chicago 1972. (Taped, Transcribed and Edited by Patrick F. Crosby, by private communication)


Possible names for tile combinations:

  • Unit, Solitary, Unitary, Simple, Singular, Singleton
  • Binary, Duplex, Dual, Twofold, Bipartite
  • Triple, Threefold, Ternary, Trinity, Tripartite
  • Quaternary, Quadruple, Tetrad, Fourfold, Quadripartite



Snakes and Ladders


My propositions are elucidatory in this way: he who understands me finally recognizes them as senseless, when he has climbed out through them, on them, over them. (He must so to speak throw away the ladder, after he has climbed up on it.) He must surmount these propositions; then he sees the world rightly.

— Ludwig Wittgenstein, from Tractatus Logico-Philosophicus 6.54

Consider the children’s game of “Snakes and Ladders”.

The object of the game is to traverse a sequence of locations on a game board, numbered from one (the beginning) to some maximum goal (the end), with the numbers increasing from the bottom of the board to the top. The player usually competes with other players to win the goal first, because otherwise why do it. Ladders join lower numbers at their base with higher numbers at their top. Snakes join higher numbers at their head with lower numbers at their tail.

The players take turns and each move forward a number of locations determined with a roll of a die. If a player lands on the bottom of a ladder, she can immediately climb to the top of it, skipping the locations in between. However if she lands on the head of a snake, she must slide down the snake to its tail, essentially losing her recent gains of several turns.

The game progresses by chance, and indeed the winner is completely chosen by luck. There are no choices that players can make to increase their chance of winning the game, and so it is completely random. It is evidently an ancient game and older versions often portrayed the ladders as virtues and the snakes as vices. What can this game teach us about morality and life in general?

Unfortunately the player cannot gain knowledge or experience along their journey to help them. There is no way to increase one’s chance to land on a ladder’s bottom or decrease one’s chance to land on a snake’s head. The game is on the other end of the spectrum from a choice driven game such as tic-tac-toe, or even chess. I’m also reminded of the card game “War”, which is another random game played by children. Such completely random games equalize chances of winning among different ages, I imagine.

From Wikipedia: The game (Snakes and Ladders) is a central metaphor of Salman Rushdie’s Midnight’s Children. The narrator describes the game as follows:

All games have morals; and the game of Snakes and Ladders captures, as no other activity can hope to do, the eternal truth that for every ladder you hope to climb, a snake is waiting just around the corner, and for every snake a ladder will compensate. But it’s more than that; no mere carrot-and-stick affair; because implicit in the game is unchanging twoness of things, the duality of up against down, good against evil; the solid rationality of ladders balances the occult sinuosities of the serpent; in the opposition of staircase and cobra we can see, metaphorically, all conceivable oppositions, Alpha against Omega, father against mother.


Actually, it reveals the fourness of things. The snake tails and ladder tops are different in kind from the snake heads and ladder bases, because landing on the former the player doesn’t change position. She can instead contemplate possibly backsliding and revisiting this location via snake or the experiences of having taken the long way instead of just climbing to this location via  ladder.

A more modern version could replace the snakes and ladders with one entity, perhaps wormholes, which would deliver one instantly to the opposite end, either forward or backward. The name could be revised to “Shortcuts and Backtracks”, perhaps. Or maybe it would be too confusing.




[*8.144, *9.102]