22 Jul 2009

Deleuze’s Dance, III. Wonders of Phenomena: The Infinite Grace of Bergson and Kleist; or the Nietzschean Dance of Deleuzean Dice

by Corry Shores
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Deleuze’s Dance, III

Wonders of Phenomena:

The Infinite Grace of Bergson and Kleist;

or the Nietzschean Dance of Deleuzean Dice

Kvond's recent posting – The Bear with the Rapier: Kleist on Leibniz and Microscopic Infinities – discusses Heinrich von Kleist’s marvelous tale, “On the Marionette Theatre,” translated by Idris Parry. (Robert Lonoke’s translation can be found here.) Kleist recounts a conversation with a dancer-friend who explains his understanding of grace. He uses a geometrical example. What it refers-to is very unclear. Fortunately, kvond figured it out. He does so by making use of Leibniz’ vanishing triangle illustration of infinitesimal magnitudes.

Kvond’s insightful commentary on Kleist’s depiction of grace will help us

1) to elaborate Bergson’s notion of grace, and

2) to gain a grasp of Deleuze’s phenomenological critique of graceful continuities.

All this will enable us to begin articulating Deleuze’s Nietzschean phenomenology.

So Kleist is talking to an old friend. He’s a dancer. He tells Kleist that puppets are more graceful than even the most skilled dancers. For, their mechanisms are designed to move in accordance with centers of gravity and other natural physical forces.

Each movement, he told me, has its centre of gravity; it is enough to control this within the puppet. The limbs, which are only pendulums, then follow mechanically of their own accord, without further help. He added that this movement is very simple. When the centre of gravity is moved in a straight line, the limbs describe curves. Often shaken in a purely haphazard way, the puppet falls into a kind of rhythmic movement which resembles dance.

In a way, the puppets’ motions are largely automatic and fluidly mechanical. [Soon we will see this is a sort of Bergsonian grace.] The puppeteer needs merely to start the physical mechanics in motion, and the puppets exhibit natural, fluid, graceful motions, almost as though they move on their own.

A second advantage puppets have over dancers is this: dancers must exert much effort merely to break gravity so to lift-up but a little bit into the air. Puppets, however, are light, and are pulled-up from above.

Puppets need the ground only to glance against lightly, like elves, and through this momentary check to renew the swing of their limbs. We humans must have it to rest on, to recover from the effort of the dance. This moment of rest is clearly no part of the dance. The best we can do is make it as inconspicuous as possible..."

Another advantage of puppets is that their mechanics allow them to maintain their center of gravity. Usually dancers fall victim to “affections,” which cause their centers of gravity to move outward to their lower backs or elbows for example.

For affectation is seen, as you know, when the soul, or moving force, appears at some point other than the centre of gravity of the movement. Because the operator controls with his wire or thread only this centre, the attached limbs are just what they should be.… lifeless, pure pendulums, governed only by the law of gravity.

The dancer then evokes the metaphor of the fall from paradise, and as well our long human journey back to it. He wants to illustrate the point that there is a naïve form of grace, and it will become corrupted by self-consciousness. But we may regain this pure form of grace by attaining to a hyperbolic form of consciousness. Paradise may be regained.

"we've eaten of the tree of knowledge. But Paradise is locked and bolted, and the cherubim stands behind us. We have to go on and make the journey round the world to see if it is perhaps open somewhere at the back."

Kleist agrees that self-consciousness ruins grace. He relates a story about a graceful young man. Once he tried imitating the statue, Boy with Thorn.

But he only succeeded at making a comical fool of himself.

I laughed [...] He blushed. He lifted his foot a second time, to show me, but the effort was a failure, as anybody could have foreseen. He tried it again a third time, a fourth time, he must have lifted his foot ten times, but it was in vain. [...] The movements he made were so comical that I was hard put to it not to laugh.

From that day, from that very moment, an extraordinary change came over this boy. [...] An invisible and incomprehensible power seemed to settle like a steel net over the free play of his gestures. A year later nothing remained of the lovely grace.

The dancer relates a similar story. He visited Russian noblemen. The sons were expert fencers, especially the eldest one. This young nobleman challenged his guest to a match. But the dancer’s finesse allowed him to outmaneuver the trained fighter. This frustrated the son, but he had a surprise for the dancer.

he said, half in anger and half in jest, that he had met his master but that there is a master for everyone and everything – and now he proposed to lead me to mine.

He takes the dancer to a shed. In it is a bear who is undergoing some sort of training.

I was astounded to see the bear standing upright on his hind legs, his back against the post to which he was chained, his right paw raised ready for battle. He looked me straight in the eye. This was his fighting posture.

They give the dancer a rapier and tell him to attack the bear. The dancer lunges with all his skill and finesse. The bear, almost like a statue, merely flicks his paw slightly to deflect the attack, as though it required no effort at all. The dancer even tries making fake attacks to throw-off the bear. But the beast could easily discern the true attacks from the false ones.

In one sense, it seems the bear is acting purely on its nature. It’s not likely he was trained to fence. But on the other hand, the dancer portrays him as having intense awareness and concentration. Yet his focus is so profound that it seems he need not pay any attention at all.

Let’s consider our own example. Someone with absolutely no intent to make good music might pick up a guitar and play upon it as would a child, and do things that practiced musicians might find original or interesting. The musicians say to this person, “you have a natural ability. You should try guitar.” Then the novice begins formal lessons. His instructor encourages him to be intently aware of what his fingers are doing, so that he can learn to control them. At this stage, he no longer can play naturally or make anything musical. He sees his left hand but neglects his right. He notices his posture, but forgets his fingers. A person walks in on his drills, and his focus falters. But the more he practices, the more he becomes familiar with all these details. In one sense, he need no longer attend to them after practicing enough. He will know already how his fingers will move, so he can instead look-out at his audience, for example. But in another sense, this is only possible because he has developed a tacit awareness of all these infinite details popping-up simultaneously around him. So now while performing on stage, someone could erupt into the room, and he might blend his strum into a pointing motion toward her, as though it were already a practiced part of his solo. And after the show, he might be able to relate every detail that was going on around him, even though the whole time he was ‘in the zone.’ So when he first toyed-around with the guitar long ago, he was explicitly unaware of what was going on, and so he played gracefully and naturally. But then he became explicitly aware of all the infinite details that go into a good performance. Slowly he became familiar with each detail, and he could place them in the back of his awareness. In this way, he becomes implicitly aware of all the infinity of details, which has the same appearance as back when he was explicitly unaware of them all. In paradise he had grace. Falling, his self-awareness corrupts it. But by increasing his awareness to the infinite, he regained what is virtually the same as that original innocent unconscious grace.

So the dancer concludes his tale with this observation: our grace increases as our consciousness decreases. But paradoxically, consciousness decreases only after first increasing to infinity. The dancer explains:

grace itself returns when knowledge has as it were gone through an infinity. Grace appears most purely in that human form which either has no consciousness or an infinite consciousness.

He offers two illustrations. The first is the one kvond figured out [again, at this entry]. The dancer says specifically that our minds pass through infinity

just as a section drawn through two lines suddenly reappears on the other side after passing through infinity.

I could not comprehend what Kleist means here. So I worked with the other translation:

Consider how the intersection of two lines, which begins on one side of a point and after passing through infinity, completes itself on the other side.

I would offer this explanation. Lines have length but not breadth. That means we could never see them, because they have no form. So when we draw or imagine them, we have to give them a little width, all while supposing that really they have none. Hence we might depict the intersection of two lines this way:

Now we will increase our microscope power, and zoom-in on where the lines meet. But in this case, we will not adjust the width of the lines. So the lines will become thicker as we zoom in.

What we discover is that the two lines touch before they intersect. This is because we have given our lines breadth, which means their outer edges intersect before the internal ideal lines actually cross. But really lines do not touch before they cross. They intersect at a point, which is also invisible even to the most powerful microscope. This is because points have neither length nor width.

But we could also use a program like GeoGebra. When we zoom-in on the intersection, it readjusts the line-width so that it always remains about the same width, no matter how far we zoom-in. So here it is at one scale.

Now we zoom in much further, and find still the same representation. We could keep zooming to infinity, and we will never close-in on where the lines ‘touch’.

Yet even though the lines never ‘touch’ in the way we can imagine lines to cross, they still pop-out on the other side. But first they must pass through an infinity of not-touching.

So if Kleist’s dancer is saying something along these lines, then we can appreciate kvond’s remarkably insightful connection to Leibniz’ triangle demonstration of the differential. We are to imagine the diagonal line moving to the right until crossing through to the other side.

And we are to imagine the horizontal line e moving toward intersection point A, until there is only an infinitely small distance between the line and the point. As infinitesimal, there is no extensive distance between them. The same holds for line c. However, there is an intensive magnitude that is the ratio of the infinitely small length of c compared to the infinitely small length e.

[Here we see something similar to Spinoza’s different sizes of infinity, but in this case, different sizes of the infinitely small.]

But even though the diagonal line must pass through an infinity before reaching the limit at point A, it still magically pops-out on the other side. We could imagine the movement of the diagonal as being equivalent to the increase in our GeoGebra zoom. Hence kvond’s remarkable insight into this geometrical example.

Kleist’s dancer offers another illustration: the concave mirror.

or as the image in a concave mirror turns up again right in front of us after dwindling into the distance. (Parry transl.)

Or, consider how the image in a concave mirror is first seen, then vanishes to infinity, and then reappears right before us. (Robert Lonoke transl.)

I am not qualified to explain this example, so I ask that those who can, please correct my errors (or just re-explain it properly). I will work with basic descriptions from the internet.

To conceive of a concave mirror, we first imagine a large sphere. On the inside surface is the mirror part. We cut a circular section from the sphere, and then we have a concave mirror. Where the sphere’s center is, relative to the mirror curvature, is called the center of curvature (C). [The image below was obtained gratefully from http://www.phys.ttu.edu. I take the terminological definitions from: http://www.physicsclassroom.com]

Half-way between the center of the sphere, and the center of the mirror, is the focal point (F). We see above that if parallel rays reflect from the mirror, they converge at the focal point.

When the object is outside the center, it is inverted and smaller.

When it is at the center, it is inverted although showing the same size.

When it is between the center and the focal point, it is inverted and larger.

Then when it is between the focal point and the mirror, it will become upright and larger.

So we see that as the image moves inward toward the focal point, it gets larger-and-larger. And at the focal point, it will invert and become infinitely large. Then it continues on the other side of the focal point, upright, and it is larger than the original (but not infinitely large like it is right at the focal point.) But how does it make that transition from down to upright at the focal point?

For an instant, it will disappear. This is because the reflected rays will only converge at infinity. Look below at the way the rays converge, and how at the focal point (fourth image below), they become (nearly) parallel and hence converge only at infinity.

Focal Point Infinity:

I honestly do not know what these lines mean. But let’s look first at some animations, then an actual demonstration.

We might go to this site, and click on the play icon for the “concave mirror image” animation. We can slide the object location and height around the space in front-of the mirror. Notice that as we near the focal point, the reflecting rays become more-and-more parallel until they reach the point where they seem unlikely ever to converge. In a sense, they converge at infinity (see the table in the middle of this wikipedia entry). Also notice how the mirrored image’s height is determined by how far the reflecting rays converge from the axis. But if the rays at the focal point only converge at infinity, then the image will grow to be infinity large, which might be why it disappears. On the one hand, we are looking at something whose image is infinitely large. But on the other hand, the mirror only displays one very tiny part of that infinitely large image. As the object nears the focal point, we are zooming-in on that small part. So as the reflection grows outward to infinity, we zoom inward into an infinitely small part of the image. All at once, we see something both infinitely large and infinitely small, and as well, something that is both upright and upside-down, simultaneously. Somehow these polar opposites contract together.

Now let’s watch a video of a girl filming herself move from behind the focal point to in front of it. So we will see her image flip. [May I thank the creators of this video for their wonderful site on optics: http://www.wfu.edu/physics/]

I wish we could isolate the point where the image expands to infinity while at the same time flipping-over. But there is a series of temporally-spaced frames, so of course that magical moment lies between two frames. But let’s look anyway for something to notice. Right around the time that the image flips, we see this here.

Before this point in time, the yellow started from the top, but then pops out at the bottom below the blue. At the same time, the blue started from the bottom, but pops out near the top. See how there is the blue-band enveloping the bottom, and how this lower blue-band is mirrored by the yellow-band enveloping the top. Similarly and inversely, the yellow top band envelops a blue region, and the bottom blue band envelops a yellow region. We see something like the yin yang symbol, where the top is in the bottom, and the bottom is in the top. This screen frame does not depict the moment of infinity. But it helps us understand how such a polar inversion can occur.

So what we miss of course is the instant when the image stretches to infinity, leaving us to peer into the infinite. This is equivalent to taking an infinitely powerful microscope to the object's part lying right upon the focal point. So indeed, like Kleist’s dancer suggests, to move through the focal point of the concave mirror is to pass through infinity. Before that we are a recognizable image of our self. So too after. But we are inverted. It’s we, but on the other side of the looking glass. Hence our metaphor for grace. The practicing guitarist must also pass through an infinity of consciousness before he can again be gracefully unconconscious of the infinity of details around him, (and inverting from explicit unawareness to implicit awareness).

Gracing Bergson

In §9 of Time and Free Will, Bergson explains his theory of grace. We consider someone’s motion to be graceful if at every moment the movement calls-forth the following changes of direction.

If jerky movements are wanting in grace, the reason is that each of them is self-sufficient and does not announce those which are to follow. If curves are more graceful than broken lines, the reason is that, while a curved line changes its direction at every moment, every new direction is indicated in the preceding one. Thus the perception of ease in motion passes over into the pleasure of mastering the flow of time and of holding the future in the present. (Bergson, Time and Free Will, 12b)

Si les mouvements saccadés manquent de grâce, c'est parce que chacun d'eux se suffit à lui-même et n'annonce pas ceux qui vont le suivre. Si la grâce préfère les courbes aux lignes brisées, c'est que la ligne courbe change de direction à tout moment, mais que chaque direction nouvelle était indiquée dans celle qui la précédait. La perception d'une facilité à se mouvoir vient donc se fondre ici dans le plaisir d'arrêter en quelque sorte la marche du temps, et de tenir l'avenir dans le présent. (9bc)

In Mind and Matter, Bergson speaks again of fluid continuous motions that result from motional habits built-up through familiarities. But before we become familiar with our surroundings, our motions are ungraceful and discontinuous.

For instance, I take a walk in a town seen then for the first time. At every street corner I hesitate, uncertain where I am going. I am in doubt; and I mean by this that alternatives are offered to my body, that my movement as a whole is discontinuous, that there is nothing in one attitude which foretells and prepares future attitudes. (Bergson, Matter and Memory, 110a.b, emphasis mine)

Je me promène dans une ville, par exemple, pour la première fois. A chaque tournant de rue, j’hésite, ne sachant où je vais. Je suis dans l’incertitude, et j’entends par là que des alternatives se posent à mon corps, que mon mouvement est discontinu dans son ensemble, qu’il n’y a rien, dans une des attitudes, qui annonce et prépare les attitudes à venir. (93a)

Consider if we are visiting the wilderness in another part of the world, Australia, Brazil, Africa, wherever. We hear some noises that are made by harmless creatures. Others by deadly predators. But we don’t know which is which. Every thing around us is a sign overflowing with meaning. All that appears to us might mean something. Because we don’t know which things indicate important information, and which do not, everything around us then appears and shines-forth with weight or significance to us, popping-up like firework flashes going-off at unexpected places and times.

Soon our bodies learn the proper ways to react to things. Some sounds tell us to duck and hide. Others call us to enjoy a beautiful mating song. Bergson explains that we slowly come to develop recognitions for the things around us. We recognize something when this happens: we perceive it, and our bodies automatically undergo a fluidly-mechanical automated-reaction.

So at first in new situations, we are ungraceful, because our attention is tossed-about from detail-to-detail. Slowly, we develop tacit awarenesses of these details, which are exhibited in our habitual reactions to them as familiar recognizable things. We become graceful, but also mindless in a way. In one sense, we are completely aware of everything around us, but in another sense, we don’t notice a thing that is happening. When driving our familiar daily route to work, we might arrive at our destination and have the feeling that we were not aware of anything on the way over.

Co-contributor Scott Wollschleger asked long ago to this entry on Bergson’s grace:

...what about the "flash" that occurs in communication? wouldn't this be viewed as an interruption of some sort? can grace even be gracefully communicated?

I was not able to answer the question at that time. But because kvond introduced me to the Kleist writing, I think we might reply.

The “flash” that Scott refers-to I presume is the “phenomenal flash” that Deleuze describes in Difference & Repetition. [See this entry for an aesthetics discussion of this flash.]

Whenever something appears to us, it is a phenomenon. So that means we notice it, explicitly or implicitly. But for Deleuze, if there is no change or difference, and everything is familiar, than nothing has appeared. Recall how for Bergson, we are in ‘autopilot’ when we recognize everything around us. However, when we are in new situations, everything around us is its own singularity with its own overflow of significance. A wide variety of unique things surrounding us all at once. In the foreign wilderness, new sounds coincide with unrelated new sights; we find colors placed together in arrangements we do not normally see. Unrecognizable animals move-about in such strange ways they seem like aliens to us. Perhaps we see something that at the same time makes us think it’s a cat, while also just as much it seems like a monkey. All these differences contract together. We cannot place any phenomenal distance between them, because they’re all there together in one instant, one smashed-in with the other. Consider when we force two magnets together, north-end to north-end. Their oppositional differences resonate in each other. They communicate their incompatibility with each other. They are both ‘north’, but they do not assimilate. In fact the closer we contract one towards the other, the more they make each other shudder and shake. If we force them together real fast, we’ll feel a shock-wave through both arms, through our whole bodies. This is a ‘flash’ that contracted differences communicate. [See this entry for the logic behind these contractions.]

The same happens when we see the cat-monkey. It stops us in our tracks, because it is unfamiliar, and because it resists assimilation. We cannot synthesize it into a blend. They are discrete differences forced together despite the oppositional resonances they communicate to each other. So we only experience phenomena when there are these breaks and discontinuities, when our bodies no longer function like fluid organic mechanisms, but rather are push-and-pulled in many directions at once. In other words, grace & phenomena, and as well, grace & consciousness, do not go hand-in-hand for Deleuze.

Something is graceful for Bergson when one motion calls-forth another new and different one, all while that new one is already beginning. Motions are changing. But each one overlaps and thus is somewhat predictable from the previous one. This is continuity of the analog variety. But we can only have the phenomenal flashes if something happens that we did not expect. In the Bergson model, we anticipate something, and thus we assimilate it in advance. But when we are surprised, there is a breach in our associations and assimilations.

Deleuze illustrates this with his notion of Nietzsche’s dice throw. Life is a children’s game. The rules are always changing. A tree at one time is a hide-and-go-seek “base.” Then it might suddenly become a ship-mast riding the open sea. Every time the rules change, the game changes. And every time the game changes, the things in the game change too. Predators and prey become sailors and sea monsters. When children are playing these rule-changing games, they themselves change (as their play-roles shift), and the world around them changes radically from moment-to-moment. This is the reality of the Nietzschean dice-throw. Every instant, chance decides how the rules of reality will change. [See this entry for Deleuze's interpretation of Lewis Carroll's unpredictable rule-change games, and also section 8 of this entry for Gregory Bateson's version of the same idea.] When the change is made, we must recognize that it could not have been otherwise. This is Deleuzean grace, if there would be such a thing. We shudder-and-shake from one moment of life to another, when we realize that the world around us is constantly a new world, and that we repeatedly become new selves. This too is a dance. When we affirm each chance outcome as fate, we appreciate “the heavenly necessity which compelleth even chances to dance star-dances.” (Nietzsche, Thus Spoke Zarathustra, Book III, "The Seven Seals," Common transl.) Deleuzean grace is the ability to be Alice on the other side of the looking glass. In wonderland, one new world and reality is contracted immediately to the next. In each scene, the rules are different, and Alice continually adapts to the new selves she must repeatedly become as a result of each unpredictable rule-change. [It’s like in dreams when an object or scene changes to something totally unrelated and unrealistic, and yet our dream-selves treat it like absolute normality.]

But, is not Alice’s wonderland the most phenomenal of all? And are not dreams made-up of the most phenomenal appearances, strung one-upon-another, each discontinuity affirmed gracefully in full?

Bergson, Henri. Matière et mémoire: Essai sur la relation du corps à l'esprit. Ed. Félix Alcan. Paris: Ancienne Librairie Germer Bailliere et Cie, 1903. Available online at:http://www.archive.org/details/matireetmmoiree01berggoog

Bergson, Henri. Matter and Memory. Transl. Nancy Margaret Paul & W. Scott Palmer. Mineola, New York: Dover Publications, Inc., 2004; originally published by George Allen & Co., Ltd., London, 1912. Available online at:http://www.archive.org/details/mattermemory00berg

Bergson, Henri. Time and Free Will: An Essay on the Immediate Data of Consciousness, Transl. F. L. Pogson, (New York: Dover Publications, Inc., 2001).

Available online at:


French text from:

Bergson, Henri. Essai sur les données immédiates de la conscience. Originally published Paris: Les Presses universitaires de France, 1888.


Nietzsche, Friedrich. Thus Spake Zarathustra. Transl. Thomas

Common. London: T.N. Foulis, 1911. Online text available at: http://www.archive.org/details/thusspakezarath00ludogoog and http://www.gutenberg.org/files/1998/1998-h/1998-h.htm

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