The Kenning Game: An Introduction

This essay presupposes a familiarity with Hermann Hesse's novel Das Glasperlenspiel (The Glass Bead Game). My own glass bead game, my approach to the Eternal GBG, which of course exists only in the novel and as a Platonic archetype, is called the Kenning Game, and is described below. This is really only a bare outline of the Kenning Game and its possibilities; as a result of my explorations with the Bamboo Garden group here in Seattle, I have elaborated the basic structure below considerably. Look for a paper on more advanced Kenning Games here soon.

What are Kennings?

Kennings are an old Norse poetic device based on the analogy. They're similar to Homeric epithets. Where the Greeks might say "the wine-dark sea" in their epic poetry, the Norse would say "whale road." This of course comes from the analogy "sea is to whale as road is to horse" or something like it. To use the standard shorthand, this becomes

sea : whale :: road : horse

You can also diagram it as

   sea      road
  ----- :: ------
  whale     horse

The key to the Kenning Game is realising that such an analogy provides four kennings possible (or at least permissible). In this case, we have

  sea   = whale road
  whale = sea horse
  road  = horse sea
  horse = road whale

You get these kennings by going "vertically" then "diagonally" from the word in question in Figure 2. With a valid analogy, you can always get a kenning by going vertically then diagonally. Try it and see.

Some of these seem a little strange, but we might make sense of them by positing that "road whale" for "horse" is the product of a culture of aquatic intelligent beings that ride whales the way we ride horses. Some kennings do come out strangely, but one thing we are after in art is the novel viewpoint.

Now, the interesting part of the Kenning Game happens when you "nest" kennings. I'll demonstrate below with a small Kenning Game.

Example Kenning Game

Let's take several analogies and ponder them for a little bit to see what we come up with. First, an easy one:

(A1)  telescope : far :: microscope : small

So a from the above analogy A1, we get kenning K1:

(K1) a telescope is a "far microscope," or "microscope for the far."

Simple enough. Now for a harder one:

(A2)  Eris : Chaos :: Logos : Harmony

Eris is the Greek goddess of Discord. In contemporary times She has come to be worshipped by a coterie of weirdoes who think Chaos is an interesting concept. It's often said of Discordianism, "Is it a joke disguised as a religion, or a religion disguised as a joke?" Eris fulfills the same role vis-a-vis Chaos (close to "disorder") that the Logos (Christ for Christians) does vis-a-vis the concept of Harmony (close to "order"). So we might say

(K2) that Eris is the Chaos Logos.

Now, Discordians are a free-wheeling bunch, and they often tend to be associated with that segment of the population who call psychedelics "entheogens," who regard them as sacred. Discordianism could even be called a psychedelic religion. Art Kleps, a "solipsistic nihilist," calls LSD the Supreme Sacrament of his religion, the Neo-American Church, just as peyote is the sacrament of the Native American Church. The drug used by the Christians in one of their sacraments is wine. Given all this, we might say

(A3) psychedelic : Eris :: wine : Logos

... which gives us

(K3) psychedelic = Eris wine

Here's another simple one:

(A4) psychology : mind :: biology : body

... so

(K4) psychology = mind biology.

Now, Terence McKenna, another major figure in psychedelic religion, says that psychedelics enable humans to examine features of their own minds that would otherwise be inaccessible, just as telescopes enable astronomers to examine galaxies invisible to the naked eye. Thus:

(A5) psychedelic : psychology :: telescope : astronomy

... so

(K5) a psychedelic is a psychology telescope.

The next kenning requires a little contemplation. "Sacrament" is defined as "the outward and visible sign of an inward and spiritual grace." So we might say that a sacrament has an outer, physical part (the bread and wine) and an inner, spiritual part (God's grace) -- just as a human being has an outer, physical part (the body) and an inner, spiritual part (the mind or soul and spirit). Putting this together, we get

(A6) wine : sacrament :: body : human

... or

(K6) wine = sacrament body

You may have noticed that we re-used some of these terms, such as "wine," "Eris," and "telescope." This was intentional. The re-use makes it possible to nest the kennings, to create a "recursive analogy." Let's start with an equation:

(E1) psychedelic = psychedelic

A "tautology," more or less, right? In English: "A psychedelic is a psychedelic." (To which one might reply, if one were speaking to an advocate of the War on Drugs, "Well, there are psychedelics and psychedelics.")

Now, let's substitute one of our kennings for "psychedelic" on the right:

(E2) psychedelic = (psychology telescope)

I will use parentheses to group the two terms of a kenning together. This makes it easier to see which term is the "modifier" and which is the "modificand," and this will be important as we start to nest.

The Crucial Point

Both "psychology" and "telescope" have their own kennings. Let's go one step further and substitute a kenning for one of the two terms on the right:

(E3) psychedelic = ( (mind biology) telescope)

It's getting more interesting (I hope). Let's try "telescope":

(E4) psychedelic = ( (mind biology) (far microscope) )

So a psychedelic can be called (in grammatical if strained English) "mind-biology's microscope of the far."

Let's try another multi-level kenning for "psychedelic." This time I'll minimise the play-by-play:

(E5) psychedelic = (Eris wine)
(E6) psychedelic = ( (Chaos Logos) wine)
(E7) psychedelic = ( (Chaos Logos) (sacrament body) )

So a psychedelic is also "the sacramental body of the Logos of Chaos."

Put it all together, and we get

(E8) ((Chaos Logos) (sacrament body)) = ((mind biology) (farmicroscope))

In English: "The sacramental body of the Logos of Chaos is mind-biology's microscope of the far."

This is a very crude Kenning Game, but I have tried to introduce a certain aesthetic. Notice that our game is symmetric structurally: both sides are of the form

((a b) (c d))

Also, on one side we have a religious conception of psychedelics and on the other a scientific conception. While I think it would be going a little far to call this "the Union of Science and Religion" or something else equally highfalutin', it may be similar in a simple way to what Hesse was aiming at.

Now imagine we try a proposition that is not a tautology, like "individual = society" (a very Castalian theme and one that Hesse says the Castalians explored). Would it be possible to expand each side with kennings so that at some point in the expansion both sides said the same thing, thereby "harmonising" the two or "proving" their equivalence?

The Game Archive

Obviously a kenning must be vivid to succeed. Must it also be self-evident? The classical Norse kenning "sword liquid" for "blood" may be; "Chaos Logos" may not be. To some degree, this can be taken care of by a Game Archive of allowable symbols and analogies, just as the Castalians had. The Norse, too, had a de facto Game Archive with the kennings that everyone in their culture recognised, like "sea = whale road." The Kenning Game needs a definite library of symbols that can be agreed upon by everyone. Do these symbols have to be objective, then? No. No symbol is objective. But the symbols must be objectivated, which is a term from the sociology of knowledge referring to the quality of a concept that has become a concrete cultural fixture and can no longer be altered by an individual. A Kenning Game Board could scour art, science, math, music, and literature for "objectivated" analogies.

The Game Language

The GBG as portrayed in Hesse used a strict and formal language to represent concepts in the Game. The language used is described as something resembling mathematical notation with a glyphic or ideographic and calligraphic slant. How can we faithfully represent this aspect of the GBG in the Kenning gbg?

There is a "conlang" or "constructed language" called Lojban that could serve very well as the foundation of a formal language for the GBG. You can learn more about it off my Planlingvoj Links Page.

Lojban has some interesting properties:

I should point out that something very similar to the kenning is fundamental to the way Lojban makes new words and phrases, called lujvo and tanru, from root words, or gismu.

What about the hieroglyphs? Well, I believe it is possible to create a graphical equivalent for each "brivla" or content word. Let's look at this hypothetical Lojban kenning, but in English:

sun : moon :: gold : silver

sun = gold moon
moon = silver sun
gold = sun silver
silver = moon gold

Now imagine we substitute the astrological signs for "sun" and "moon" for the written words. "Sun" is represented by a circle with a dot in the center, "moon" by a crescent. Anyway, just remember that in the book, one Magister Ludi (the young Thomas von der Trave, if I recall) has his signs eventually incorporated into the Game Archive, and they are based on the alchemical significances of the planets.

So substitute the alchemical signs for "gold" and "silver," and we have a completely graphical kenning! One, moreover, which can be pronounced in a liturgical presentation, if we maintain the isomorphism with Lojban.

Charles Cameron has pointed out to me that the alchemical signs for "sun" and "gold" were identical, as were those for "moon" and "silver." To the alchemists, gold and the sun were one and the same, so our last kenning is a tautology when expressed graphically. However, for purposes of the Kenning Game, it may be possible to differentiate between them simply by composing new kennings. Suppose you had glyphs for "metal" and "planet":

gold : metal :: sun : planet


gold = metallic sun
sun = planetary gold

silver = metallic moon
moon = planetary silver

Simple enough, if it's in the Archives. I think it would be.

IMHO, there would need to be at least a small number of abstract glyphs, for representing prepositions, articles, particles, and so on. However, my own approach is to take the most traditional sign for the concept wherever possible. If we were playing a game based on feng shui like Joseph Knecht's first game as Magister Ludi, we'd want to use the Chinese ideograms. If we were doing a (European) alchemical game, we'd use the signs we mentioned above. And after all, if you look at the Chinese "five elements" and compare them to the European four, you'll find that Chinese earth is not the same as European earth, for example, so you'd want to have a way to distinguish them (all the better to relate them).

It's also possible to use substantial sentences rather than simple equations like "psychedelic = psychedelic" or "individual = society." Try, for example, that very Castalian sentiment from Ecclesiastes, "There is nothing new under the sun." Step one might be to expand it to "There is nothing new under the gold moon."

Note that a parenthesis-structure like the ones above can also be represented by a "tree." This brings in the possibility of manipulating the structure with graph theory, or representing the game as a structure in LISP.


Kenning Riddles and Musical Games

Having just returned from Music City, i.e. Nashville, Tennessee (in Summer 1996), I have a few thoughts on music and its relation to the GBG, my Kenning Game, and Charles's (pro)posed Game problem.

Just before I left for Nashville, I bought a copy of Douglas Hofstadter's book Fluid Concepts and Creative Analogies. Hofstadter wrote the Pulitzer Prize-winning book Goedel, Escher, Bach, itself a sort of gbg (and I do not say that lightly) and is now an artificial intelligence researcher and cognitive scientist who is developing software that can create its own analogies. His software can find the correct answer for an analogy in the domain of Roman alphabet letter sequences. That is, if you ask it "What is to 'ghi' as 'abd' is to 'abc'?" it will answer 'ghj' 99% of the time.

This in itself is interesting, but the salient fact here for the Kenning Game is that this analogy is a sort of kenning that can be used as the basis for a musical gbg.

The analogy here is [abc : abd :: ghi : ghj]. This is simple for any human with a basic knowledge of the Roman alphabet, or rather the English one. Now what if we replace these strings of English letters with sequences of musical notes? Then, say, when you take the simple melody puzzle in the key of C, [CDE : CDF :: FGA : ? ], you are likely to come up with the simple melodic answer 'FGB'.

Two points here:

  1. This presents a new way of playing the Kenning Game, that of "kenning puzzles" where the listener must supply the missing term.
  2. Musical "kenning puzzles" of this sort, but more complex, of course, may have been what Hesse was thinking of when he wrote,

The Game was at first nothing more than a witty method for developing memory and ingenuity among students and musicians.... pupils at the Cologne Seminary had a rather elaborate game they used to play. One would call out, in the standardized abbreviations of their science, motifs or initial bars of classical compositions, whereupon the other had to respond with the continuation of the piece, or better yet with a higher or lower voice, a contrasting theme, and so forth. It was an exercise in memory and improvisation quite similar to the sort of thing probably in vogue among ardent pupils of counterpoint in the days of Schuetz, Pachelbel, and Bach...

Of course, melodic sequences are not the only kind of musical kenning possible. I'm sure there are many others. I would just like to note here that transposition of a melody from one key to another involves a sort of kenning, to wit:

melody : key :: melody' : key'

If you regard an exercise in transposition a music teacher might give a pupil in this way, then very simple musical Kenning Games are already being played by such.

Kenning Chains

My wife Marty Hale-Evans points out that analogies must be exact in a Kenning Game or one runs the risk of the chemist who must add experimental error while adding measured quantities. (6 +/- 2 plus 4 +/- 3 equals 10 +/- 5.) This "error" can mount up when you're expanding kennings, thereby producing a very sloppy, questionable, or invalid result. This bug has been turned into a feature with her invention of a new form of Kenning Game, the Kenning Chain.

Incidentally, when I was in Nashville, it was to hear Elvis Costello in concert. Opening for him was the Fairfield Four, a gospel quartet. Their music made me think of Charles Cameron's posing of a "game problem" for Gamemasters to translate into their respective games, based on his TenStones game "Hear That Long Snake Moan" about voodoo and jazz. I think I would enjoy attending a voodoo ceremony. I just don't fancy being possessed by Christian entities, as they tend not to leave politely afterwards like loa. Nevertheless, these guys on stage obviously enjoyed being "full of the Spirit," and this triple-kenning occurred to me:

loa : voodoo ceremony :: Holy Spirit : gospel music :: the Muse :jazz

When Marty saw this, she invented the Kenning Chain. One player constructs a kenning; the next constructs a new kenning from half of that kenning and a new half, and so forth. In other words, one must construct intermediary kennings that connect two sets, or create a circular kenning-construct:

Player 1:  Loa : voodoo :: Spirit : Charismatic Christianity
Player 2:  Spirit : Charismatic Christianity :: Keg : Frat party
Player 3:  Keg : Frat party :: Stripper : Voyeur
Player 4:  Stripper : Voyeur :: Fox : Grapes

....and so on.

Marty calls this a kenning version of the "lead-into-gold" game: a round of Word Golf I devised once that assigned a more-or-less traditional alchemical stage of transformation to each word in the following chain:


Telesmatic Images

There is a truism in psychology that human short term memory can only hold "7 +/- 2" items at one time. Does this mean that we cannot understand much more complex games than the above? Not necessarily. For one thing, meditation is crucial to the GBG, and could lay down the entire structure in long term memory for contemplation. For another thing, we can "chunk" -- regard parts of the kenning as a single unit and contemplate their relation to other units. Finally, one does not have to see the whole Bayeux Tapestry at once, hear a whole song in a fraction of a second, or read every word in a novel simultaneously to appreciate their structure and beauty.

Nevertheless, there seems to be a way to represent Kenning Games pictorially for the human mind to contemplate as a whole. The method is based on the magickal concept of "telesmatic images" and the ancient/medieval mnemonic technique of "memory palaces." It is too complex to go into here but will be explored more fully in a later paper.

The Transfinite Aspect

When I was an undergraduate at Yale, my friends and I played a game, or rather metagame, called Nomic. Nomic was invented by Peter Suber, a philosopher of law at Earlham, and changing the rules is itself part of the game. In fact, it might be said in a loose sense that changing the rules is the object of the game. If you are curious about Nomic, you can find a link to some Nomic pages on my Game Links Page.

There are many Nomic games being played over the Net at the moment. Back in the Eighties, though, none of them were yet in existence, so, as I said, my friends and I started a face-to-face game that lasted about two and a half years and even now has not officially ended.

But let us speak theoretically for a moment. James P. Carse, in his marvellous book Finite and Infinite Games, says:

There are at least two kinds of games. One could be called finite, the other infinite.

A finite game is played for the purpose of winning, an infinite game for the purpose of continuing the play....

If the rules of a finite game are unique to that game it is evident that the rules may not change in the course of play -- else a different game is being played.

It is on this point that we find the most critical distinction between finite and infinite play. The rules of an infinite game must change in the course of play. The rules are changed when the players of an infinite game agree that the play is imperiled by a finite outcome -- that is, by the victory of some players and the defeat of others....

For this reason the rules of an infinite game have a different status from those of a finite game. They are like the grammar of a living language, where those of a finite game are like the rules of debate. In the former case we observe rules as a way of continuing discourse with each other, in the latter we observe rules as a way of bringing the speech of another person to an end.

All this is clear, no? Nomic, as we played it, would seem to be what Carse calls an infinite game. Nomic was a social activity for us and although there were competitive aspects to it, as when players vied to have their own rule changes adopted, we never wanted to stop playing, and we had a rule that even when someone managed to bring play to an end and "win" the game by making further play impossible, the "metagame" had not ended, and would continue. This is why our single game of Nomic lasted most of the time we were in college.

There is one problem. Carse poses us a poser in the very last sentence of his book. It reads, "There is but one infinite game."

What are we to make of this? Carse is a theologian, a Professor of Religion at New York University. Given that background, I would interpret his remarkable statement to mean that the single Infinite Game is "Lila," the Hindu concept of the Divine Play that produces the Universe: the Game a (lonely?) God plays down through the aeons, pretending that there is and can be anything other than Itself.

So given that there is only one infinite game, and given that the rules of finite games cannot change in the course of play, what should we call Nomic, which by definition cannot be either?

In mathematics, there is a class of numbers that one might think of as "halfway between" finite and infinite. They are called "transfinites." For example, the first transfinite number is Aleph Null. It represents, among other things, the total number of integers: the naive "infinity" of everyday conversation, as when a child says "I bet you can't count from one to infinity!" There can be larger and smaller "infinities" or transfinites. For example, although it is outside the scope of this discussion to prove it, the transfinite representing the number of points on a line is larger than the number of integers, Aleph Null. While both are "infinite," they are "countably infinite," not "absolutely infinite." The countably infinite can be represented mathematically as transfinite numbers; the absolutely infinite transcends all other infinities and all attempts at representation. ("The Tao that can be named is not the true Tao.")

So I propose a clarification: besides finite games and the (Absolutely) Infinite Game, there are "countably infinite games" or "transfinite games" like Nomic, which partake of the nature of both finite and infinite games, by (for example) having rules that change in the course of play, and continuing indefinitely, like the One Infinite Game, and by not being coterminous with the entire Universe, like finite games.

Into which category should our glorious Glass Bead Game fall? Well, the rules of the ideal Glass Bead Game as Hesse described them are indeed "like the grammar of a living language," and we do indeed play the GBG to continue discourse, and not to shut other people up. In fact, Dunbar Aitkens says that his Glass Plate Game was conceived of as a way to enhance conversation.

I propose to "open up" the Kenning Game from finite to transfinite by allowing its rules to change in the course of play, like Nomic. Remember, Hesse said that the Glass Bead Game "comprised technique, science, and social institution" (emphasis mine). Thus I think there should be some sort of Board associated with the Kenning Game that decides the rules.

Besides the possibility of the individual gameforms' opening up, which is entirely up to their creators, may I propose an opening up into the "transfinite" of the grand synthesis of the Glass Bead Game? This idea can be further explored in my paper, "Notes Toward an Inter-GBG Protocol."

The point is to make the procedure of deciding the rules part of the game itself. Otherwise we cannot call the GBG a transfinite game. I suppose we could just change rules haphazardly, but that would hardly be a game, merely, as Gail Sullivan puts it, "a freakin' free-for-all." We want to play the Glass Bead Game, not Calvinball. Right?

We must have impermissible moves, so we need a set of rules to decide how to change the rules. I thought about suggesting Nomic as a basis, since it is tested and ready to go "off the shelf," but after reading Robert's I realised two things: first, Robert's is far more complete as a way of making rules in an assembly -- the Initial Set of Nomic is intentionally only a sketch; and second, Nomic (at least in its Initial Set) is geared toward competition -- players vie for points and try to "crash" the game by creating a paradox. Robert's, on the other hand, is designed from the beginning to make decisions as smooth and fair as possible -- surely more along the lines of what we want.

Ron Hale-Evans
Founder, Center for Ludic Synergy
Gamemaster, Kennexions
Charter Member, Bamboo Garden of Seattle

Kennexions GBG | Center for Ludic Synergy

Ron Hale-Evans

Last modified: 29 June 2000