Relations, analogies, correspondences

in Hermann Hesse's Glass Bead Game and attempts to design playable variants

This piece discusses the nature of analogy and other "linking" relations in Hermann Hesse's Castalian Glass Bead Game and attempts to design playable variants. It was written in four parts for the Magister-L mailing list, and I have left the segues intact.

Charles Cameron

Relations, analogies, correspondences


As we think about the structure of moves in our various Games, what kinds of links we see as permissible between items, and what a Game Archive would look like, it seems to me that the nature of metaphor or analogy naturally becomes an important consideration -- even more so, to the extent that we wish our Games to accord with Hesse's words:

I suddenly realized that in the language, or at any rate in the spirit of the Glass Bead Game, everything actually was all-meaningful, that every symbol and combination of symbols led not hither and yon, not to single examples, experiments, and proofs, but into the center, the mystery and innermost heart of the world, into primal knowledge. Every transition from major to minor in a sonata, every transformation of a myth or a religious cult, every classical or artistic formulation was, I realized in that flashing moment, if seen with a truly meditative mind, nothing but a direct route into the interior of the cosmic mystery, where in the alternation between inhaling and exhaling, between heaven and earth, between Yin and Yang, holiness is forever being created.
At one point, Hesse described the "links" (my word) in his Game offering us a number of different words and phrases:
Thereafter more and more new relations, analogies, and correspondences were discovered among the abstract formulas obtained in this way. Each discipline which seized upon the Game created its own language of formulas, abbreviations, and possible combinations. Everywhere, the elite intellectual youth developed a passion for these Games, with their dialogues and progressions of formulas.
The terms "abstract formulas" and "abbreviations" seem to describe what the Game is woven of, ie the equivalent of "moves" in the HipBone sense, and I think both terms relate to the compressed language of hieroglyphs (Game language as mathematization in the sense in which Gail and others have been discussing it).

The phrase "dialogues and processions of formulas" seems to describe the overall structure of the Castalian Games, and it's interesting to me that "processions of formulas" suggests, so to speak, one mind developing one line of thought at some length, while "dialogues" suggests something closer to the interprlay of two minds or strands of thought -- whether the two minds in dialogue are themselves the work of one mind (cf dialogue in theater), or two (cf dialogue in conversation).

And that leaves us with "relations" "analogies" and "correspondences" as terms for the linkages between moves, between voices, between ideas.


I don't want this to turn into a monologue -- or to put it more accurately, I am about the business of writing a longish piece on this topic, but I also hope to stir some discussion here -- so I'm going to break off at this point, and solicit your comments, course corrections, and feedback. I will post the other segments on list as I write them...


In my previous post, I pointed out that "relations" "analogies" and "correspondences" are terms Hesse uses to describe the linkages between moves, between voices, between ideas within the Castalian Game.

I see "relations" is a catch-all term which includes "analogies" and "correspondences" -- and also I would assume such things as kinship (in the anthropolgical sense), and cause and effect. What I want to do in this section of my piece is to separate other types of "relations" from "analogies" and "correspondences", and to do this I'd like to introduce three distinctions -- between "causal" and "acausal" linkages, between "mundane" and "magical" linkages, and between "contagious" and "homeopathic" forms of magic.


I think Jung is probably the person who introduced the distinction between "causal" and "acausal" linkages into contemporary western discourse. Our "scientific" worldview tends to emphasize "causal" linkages -- cause and effect -- to the exclusion of "acausal" ones, while the traditional Chinese culture (at least as presented by Jung in his Foreword to the Wilhelm I Ching) seems to have placed greater emphasis on "acausal" links. And it was Jung who developed the idea, in his essay "Synchronicity: An Acausal Connecting Principle".

Cause and effect linkages seem fairly straightforward, in the sense that one thing follows from another. I suppose we can use the terms "cause and effect" more or less strictly (gravitational pull of earth's mass on apple's mass causes apple to separate from twig and fall to earth, vs falling apples lead to Newton's theory and / or the Fall of Man idea in Genesis), and there are "levels" of causality, proximate and final causes, etc -- but I think we basically "get" causality, and that for that reason it doesn't often make for interesting Game moves, though as a form of "relations" it would be admissible.

Thus in some of our Games (and the HipBone Games would be a case in point), it would be quite legitimate to link two "items" on the ground that they followed one another causally. A valid move might, say, see a link between conclusion Wittgenstein reached at the end of his 1921 Tractatus ("What we cannot speak about we must pass over in silence"), and his subsequent "silence" of many years in matters of philosophy (the next book he wrote was a spelling dictionary for use in elementary schools, 1925). There's nothing particularly strange or magical about this: Wittgenstein sees the futility of certain types of discourse, and decides to work at something else.


But what about acausal relationships -- such as those which Jung describes as "synchronistic"? What about the connections -- always more interesting -- which verge on the magical?

Jung's notion of synchronicity has to do with a perceived similarity between an exterior event and an interior state of being: he suggests that there is a "patterning" of events which we recognize at times when the exterior and interior "coincidentally" reflect one another, and that this "patterning" is strong enough to "direct" apparently haphazard or chace effects such as a throw of the dice or yarrow stalks -- the implication being that "random" events of this sort can be used to "read" the pattern of the moment, eg by consulting the I Ching.

Chance events, events which seem "random" in terms of causality, will thus tend to display the "acausal connecting principle" of synchronicity.

I certainly believe that synchronicities have a great deal to do with our Game -- in the sense that synchronicities may themselves provide "links" between moves, but also and more generally in the sense that the playing of our Games may help us develop a sense for synchronicity, by (i) offering us with unexpected / coincidental moves while we are playing, and (ii) getting us into the habit of associative thinking, so that we become more likely to recognize synchronicities in our lives outside the Game...

But all these things have to do with "analogies" and "correspondences" -- and I want to come back to them in my next post.


It may seem as though synchronicity is a "magical" phenomenon, by contrast with causality, and I initially thought I might find "causal" and "acausal" mapped pretty exactly onto "mundane" and "magical" -- but I don't think that's the case.

The distinction between the "mundane" and the "magical" is a pretty simple one, again, at least on the surface... I tend to think of "mundane" connections as connections that are fairly obvious to the common sense observer -- which would certainly include "cause and effect" connections, but also such things as kinship.

Kinship -- and I'm taking the term literally -- is another form of "relation" which doesn't require a magical agency. A valid move might link Wittgenstein the philosopher of the Tractatus with his brother, the one-handed pianist for whom Saint-Saens wrote a one-handed piano concerto.

And at this point I'd like to ask anyone else who can think of other "non-magical" ways in which ideas might be linked to suggest them.


Magic, it seems to me, brings us a whole lot closer to Hesse's notion of links which provide us with "a direct route into the interior of the cosmic mystery"... But what sorts of links are in fact "magical"? And do any other list members share my feeling that an understanding of the "magical" tradition is in some way central to GBG design?

Anthropology recognizes two forms of magic cross-culturally, and terms them "contagious" and "homeopathic".

Roughly speaking, "contagious" magic works on the principle that whatever has been in contact with something else at one time continues to influence that something else long after the two things have been separated: actions performed on one will influence the other. That's why many magical operations involve eg the use of fingernail parings or hair clippings from the person they are intended to influence.

By the same token, "homeopathic" magic works on the principle that similar things influence one another: actions performed on one will influence the other. That's why many magical operations involve eg the pouring of water to procure rain, and why homeopathic remedies for instance work on the principle that "like cures like" (similia similibus curantur).

I think we can say that "contagious" magic would be covered by Hesse's term "relations", while "homeopathic" magic is a matter of "analogies" and "correspondences"...


The light is beginning to dawn for me at this point, I am beginning to perceive that there are in fact two categories of "linkage" possible in our games... "contact" linkages, which would include cause and effect, kinship, contagious magic, and any other kind of linkage based on proximity, and "similarity" linkages, which depend on the structural similarities between two ideas, and would include metaphor, analogy, homeopathic effects...

And my sense is that "contact" linkages -- whether magical or mundane -- are inherently far less interesting than "similarity" linkages.


When Hesse writes of "relations" "analogies" and "correspondences", then, it seems that the word "relations" is wide anough to permit what I am calling "contact" linkages, but that "analogies" and "correspondences" are where the meat of the matter lies, and that making a stab at classifying and listing the different types of metaphor, analogy, and symbol may be an important first step in clarifying this business of moves and links.

In my next post, I shall begin the exploration of "analogies" "correspondences" and other forms of similarity from my own perspective, which is that of a poet -- but again, I'm also hoping for input, challenges, and discussion from a variety of other angles and points of view.


Going back to my earlier point that Hesse's "relations" "analogies" and "correspondences" should presumably offer "a direct route into the interior of the cosmic mystery", I'd like to do some of my thinking out loud here about "analogies"...


I suppose there's general agreement that any analogy contains two elements and implies a common third:

1. a Jaguar [car]
2. is like a jaguar [cat]
3. in that it is sleek and speedy, etc.
But the third is not always articulated, and seldom dwelt upon. The person who first named the car might have thought, she'll be fast, and has beautiful lines, let's call her a Jaguar! -- without reflecting on speed and beauty as such. And still less do we necessarily dwell on the effect that glimpsing that underlying "third" has.

What I'm getting at is that analogies doesn't on the face of it seem to be particularly mystical, and that it's in no way obvious that analogies as such will lead us into the cosmic mystery.

And yet they can: and Hesse seems to say that in the Castalian Game, they do...

It may be that this is simply because meditation is applied to them in the course of the Game -- or it may be that this has something to do with the nature of analogy itself.


I suggested that "synchronicities" have by nature to do with the perception of analogies between the external and interior worlds, and I think it's fair to say that people who observe synchronicities in their lives (i) are witnessing a pattern of sorts, which they perceive as underlying both the external event and their own interior state, and that (ii) this comes pretty close to the definition usually given of a sacrament -- "an outward and visible sign of an inward and spiritual grace"...

I'm not sure that all synchronicities are experienced in this way, mainly because there seem to be some synchronicities which are more paranoid than gracious -- but my point here is that at least some synchronicities seem to go along with a basically "sacramental" view of life: and I think here of Archbishop Temple, who said "When I pray, coincidences happen, and when I don't, they don't."

With synchronicity, it seems that reflecting on the "meaning" of the conjunction of two likes can hardly be avoided -- we may decide the universe is out to get us (paranoid worldview), or to bless us (sacramental worldview), or even just to tease us (though who knows what that would be called), but in any case we feel woven into a greater fabric, and the world seems qualitatively different as a result.

What I'm getting at is that synchronicities don't just show us an intriguing "third" or common ground between interior and external, they shock us with it: they partake of the numinous. Like koans in zen, they catapult us into a new awareness.


As some of you know, I feel that one of the things the structure of my TenStones and WaterBird Games can facilitate is a type of insight which I call "stereophanic". Holding two structurally similar ideas in the mind's eye, I maintain, has an effect that's not unlike stereoscopic vision or stereophonic sound -- it procures a kind of "third dimension" of vision. And because the added dimension is in the realm of ideas, I find it akin to epiphany / theophany.

And here again, it is the nature of analogy which gives rise to the insight.

I don't think this would work with all "relations" -- in fact I think it specifically wouldn't work with what I described in my last post as "contact" relations: kinship, cause and effect, and even contagious magic. But it can work -- it is implicit in -- all relations of an analogical sort.


Which is where "correspondences" come in.

When Hesse speaks of "relations" "analogies" and "correspondences", it seems to me that he is using the word "correspondences" in what is effectively a technical sense: to refer to the analogies which mediaeval and renaissance natural science would say were built into creation. Once again, we are dealing here with a type of analogy which has an explicit link with meditation.

Kepler wrote (and I'm quoting him here, aptly enough, from the essay which Wolfgang Pauli wrote to accompany Jung's essay on Synchronicity in their joint book, The Interpretation of Nature and the Psyche):

First of all the nature of every thing was bound to represent God its creator as far as it was able to do so within the condition of its being. For when the all-wise Creator sought to make everything as good, beautiful, and excellent as possible, He found nothing that could be better or more beautiful or more excellent than Himself. Therefore when He conceived in His Mind the corporeal world He chose for it a form that was as similar as possible to Himself.
The "nature of of every thing was bound to represent God", according to this line of thinking -- which can be traced back at least as far as Proclus -- because each created thing is by its very nature a living analogy for its Creator. And the consequence is that we can read the natural world as if it were a book.

Indeed St Bernard finds the "book of nature" to be a better teacher in this respect than his fellow theologians:

What I know of the divine sciences and Holy Scripture, I learnt in woods and fields. I have had no other masters than the beeches and the oaks. Listen to a man of experience: thou wilt learn more in the woods than in books. Trees and stones will teach thee more than thou canst acquire from the mouth of a magister.

In theology, the "correspondences" are precisely these natural analogies for the divine, built into the very forms of nature. Proclus gives an example which I have quoted here before, but I think it bears repeating:

Just as in the dialectic of love we start from sensuous beauties to rise until we encounter the unique principle of all beauty and all ideas, so the adepts of hieratic science take as their starting point the things of appearance and the sympathies they manifest among themselves and with the invisible powers. Observing that all things form a whole, they laid the foundations of hieratic science, wondering at the first realities and admiring in them the latest comers as well as the very first among beings; in heaven, terrestrial things according both to a causal and to a celestial mode and on earth heavenly things in a terrestrial state....

What other reason can we give for the fact that the heliotrope follows in its movement the movement of the sun and the selenotrope the movement of the moon, forming a procession within the limits of their power, behind the torches of the universe? For, in truth, each thing prays according to the rank it occupies in nature, and sings the praises of the leader of the divine series to which it belongs, a spiritual or rational or physical or sensuous praise; for the heliotrope moves to the extent that it is free to move, and in its rotation, if we could hear the sound of the air buffeted by its movement, we should be aware that it is a hymn to its king, such as it is within the power of a plant to sing...


Correspondences, then, are analogies built into the nature of things -- and pointing directly to the creator. And once again, we are dealing with analogy in a sense which carries a meditative implication.

What I am trying to show here is that meditation is not simply something which is "introduced" to the Game by the League of Journeyers to the East -- Hesse writes:

The brethren of that League cultivated a spiritual rather than an intellectual discipline. They fostered piety and reverence, and to them we owe important elements in our present form of cultural life and of the Glass Bead Game, in particular the contemplative elements.
-- but which is inherent in the Game itself by its very nature as a Game of analogy.


That seems enough for now, and it contains the main thrust of what I was wanting to say in this piece. In a final post, I hope to explore briefly the question of "like" and "unlike" analogies for things divine, as it was discussed by eg the mystical theologian known as Pseudo-Dionysius -- because when we play the Game we are choosing analogies which have the power to take us "into the interior of the cosmic mystery"... and the choice of analogies which will pre-eminently do this was one which many artists, poets and theologians in the past have also faced -- and upon which they have lavished a great deal of insightful thought.


I hope I have shown to your satisfaction that the Game is fundamentally analogical in structure, and that analogy is in its own nature conducive to meditative effects and spiritual insights. In this post, I would like to explore what poets and theologians have had to say about the nature of analogy, bearing in mind its "sacred" purpose...


And once more, I'd like here to begin by drawing a distinction -- very important to the poets and mystics, though little attended to in our own day -- between "signs" and "symbols". I know, I know, the two words are synonyms in current usage -- but "traditionalists" such as Kathleen Raine and Rene Guenon make a sharp distinction between "signs", which refer to something without embodying it, and "symbols", which in an analogical sense "embody" that which they refer to.

That may seem a somewhat clunky distinction, so let me give some examples:

The "Mercedes" logo is a sign. Most of us know that that particular circle with three spokes in it signifies the Mercedes Benz company and the cars it manufactures: but this is pure convention, there's nothing in particular about Benzes (as opposed, say, to Fords) that has to do with threeness of spokes in a wheel -- and indeed, the addition of a fourth spoke is enough to turn the logo into a sign for "peace", despite the fact that peace is not a Benz with an additional spoke... nor a Benz peace with a spoke missing.

Most words are "signs" in this sense. It is pure convention that leads us to associate the word "tether" with tying an animal in place. In another language, another word entirely would be used.

Symbols, by contrast, embody analogically the object they refer to. Coleridge expresses it thus:

A symbol is characterized... above all by the translucence of the Eternal through and in the Temporal. It always partakes of the Reality which it Renders Intelligible; and while it enunciates the whole, abides itself as a living part in that Unity of which it is representative.
The sun is symbolic of the divine radiance because in some measure it embodies that radiance and exemplifies it -- and when Shakespeare uses rain as a symbol of mercy, in Portia's speech:
The quality of mercy is not strain'd,
It droppeth as the gentle rain from heaven
Upon the place beneath:
we can meditatively expand the analogy to include the sense in which rain washes, cleans, freshens and gives new life -- as does mercy. And these two symbols, sun and rain, also illustrate the idea that the divine radiates or showers blessings on all that lives, and not only on "good" people... for both grace and mercy, both sun and rain touch all of us, as Christ says in the gospels [Matt. 5: 45]:
for he maketh his sun to rise on the evil and on the good, and sendeth rain on the just and on the unjust...
The "bread and wine" which become the "body and blood" in the Catholic Mass are symbols in this sense -- they are characterized by the translucence of the Eternal through and in the Temporal, they partake of the reality which they render intelligible, and while enunciating the whole, they abide themselves as a living part in that unity of which they are representative...


What I'm trying to get at here is the sense that a sign doesn't have anything more to reveal to us than the thing which by common agreement ("convention") it points to, while the symbol can be meditated upon -- and like a work of art, has more to teach us each time we contemplate it. In this regard, a sign is like a puzzle, in Heidegger's formulation:

A puzzle is the unknown, to be solved, while a mystery is the unknowable, to be entered into and dwelt within.
and by the same token, a symbol is like a mystery...


I quoted Kepler above to the effect that "the nature of every thing" and of the "corporeal world" as a whole was "as similar as possible" to the Creator. He goes on to say:

Thus originated the entire category of the quantities, and within it the differences of the curved and the straight, and the most excellent figure of all, the spherical surface. For in forming this the most wise Creator created playfully the image of His venerable trinity. Hence the centre point is, as it were, the origin of the spherical body; the outer surface the image of the innermost point, as well as the way to arrive at it; and the outer surface can be understood as coming about by an infinite expansion of the point beyond itself until a certain equality of all the individual acts of expansion is reached. The point spreads itself out over this extension so that point and surface are identical, except for the fact that the ratio of density and extension is reversed. Hence there exists everywhere between point and surface the most absolute equality, the closest unity, the most beautiful harmony [literally: breathing together!], connection, relation, proportion and commensurability. And although Centre, Surface, and Distance are manifestly Three, yet they are One, so that no one of them could be even imagined to be absent without destroying the whole...
Here we see the sphere as an analogy of the divine... and it is not long before Kepler notes also the spherical nature of the cosmos, and of the sun...
Hence the sun is a certain body in which [resides] that faculty of communicating itself to all things which we call light. For this reason alone its rightful place is the middle point and centre of the whole world, so that it may diffuse itself perpetually and uniformly throughout the universe. All other beings that share in light imitate the sun.
Pauli comments on all this:
From this example it can be seen that in Kepler the symbolical picture precedes the conscious formulation of a natural law. The symbolical images and archetypal conceptions are what cause him to seek natural laws. For this reason we also regard Kepler's view of the correspondence between the sun with its surrounding planets and his abstract spherical picture of the Trinity as primary: because he looks at the sun and the planets with this archetypal image in the background he believes with religious fervour in the heliocentric system -- by no means the other way around, as a rationalistic view might cause one erroneously to assume.

I am going on at some length about this business of the symbol analogically embodying the divine principle to which it refers, because I believe that poetry which uses symbols (in this sense of the word) tends to be more powerful than poetry which lacks this kind of symbolic content, and imagine that the same would be true of our Games -- that Games which are built of symbolic analogies will tend to have a power that Games built on "lesser" forms of analogy will lack.

I want to offer you these distinctions and examples because I think they are important for our Games, then -- and also for our understanding of the Castalian Game. But I also want to suggest that matters of analogy -- and more importantly, of the inherent connection between analogy and the sacred -- have been explored in some detail by others, and that we can only benefit from the study of their conclusions.

My final point -- and it's the point at which I began the wanderings that have resulted in this series of posts -- is that some of those who have thought most intensively about such things feel that analogies are best when they are to all intents and appearances very far-fetched indeed.


Pseudo-Dionysius, in his Celestial Hierarchies, has a chapter entitled "That Divine and Celestial matters are fittingly revealed even through unlike symbols" in which he addresses the issue of analogies for the divine, and concludes that "unlike" symbols may be in some ways more suitable than "like".

His argument, if I've got it right, goes like this.

Holy scripture and the fathers of the church use analogies to describe the divine realm:

sometimes they celebrate Deity itself with lofty symbolism as the Sun of Justice, as the Morning Star rising mystically in the mind, or as Light shining forth unclouded and intelligibly...
Dionysius argues, however, that it is only too easy for mortal minds to get caught up in "lofty" symbols of this sort, and to mistake the symbol for the ineffable / indescribable reality which it is intended to point to.

Thus, he writes, we may read the poetic language of scripture literally, and

imagine that there are some kind of fiery wheels above the heavens, or material thrones upon which the Supreme Deity may recline...
He next points out that some of the wisest of theologians [the apophatics] avoid all images on these grounds, and make whatever statements they wish to make about divinity in the form of negations: God is not good, or wise, or just, or like the sun, or like a sphere, or whatever -- because these are limited human analogies for something which far transcends them.

But just as negations may bring us past our thoughts to an apprehension of the divine, so may imagery that is incongruous and seemingly base:

we may celebrate the Divine Natures through the truest negations and also by the images of the lowest things in contrast with Their own Likeness.
And so it is that there are two ways of choosing analogies which will lead the mind to a state of true contemplation:
the most holy Mysteries are set forth in two modes: one, by means of similar and sacred representations akin to their nature, and the other through unlike forms designed with every possible discordance and difference.
And of these two, it is the representation "through unlike forms ... with every possible discordance and difference" which Dionysius finds paradoxically most appropriate:
If, therefore, the negations in the descriptions of the Divine are true, and the affirmations are inconsistent with it, the exposition of the hidden Mysteries by the use of unlike symbols accords more closely with That Which is ineffable.

It remains only to give some examples of what Dionysius means by "unlike symbols". And remember, the contrast here is with "like" symbols such as the "Sun of Justice" or the "Morning Star rising mystically in the mind"...

The lowest images are also used, such as fragrant ointment, or the corner-stone, and they even give It the forms of wild animals and liken it to the lion and panther, or name It a leopard, or a raging bear bereaved of its young. I will add, furthermore, that which appears most base and unseemly of all, namely that some renowned theologians have represented It as assuming the form of a worm...
I particularly like the idea of "a raging bear bereaved of its young" as a symbol of the divine.


From our point of view as Game designers, "unlike" symbols surely have a peculiar power that comes from the fact that they stretch the mind farther than "like" symbols.

I don't want to take this though any farther at this point, because I'm hoping some of you will be stirred to comment in some way on what I have proposed: but I get a glimpse here of a more general issue in the classification of analogies -- from the Game designer's point of view, what are the strengths and weaknesses of (a) "like" analogies, which contain many subordinate "links" between one thing and another, and (b) "unlike" analogies, which add contrast and chiaroscuro to our Games, and stretch the mind farther...

Friends and Players, what say you?

Charles Cameron

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