Ballon and Gravitation

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Einstein’s theory of general relativity revolutionized the idea of ​​gravitation: gravitation is no longer thought of as a force but as a curvature of space-time. One afternoon in May 1907, Albert Einstein in a semi-awakened reverie had what he called the happiest idea of ​​his life:

The ballon is a term used in classical dance to designate a quality of the jump. It is said that a dancer has a ballon if, during the jump, his body gives the impression of being free in the air. We find this impression in nature when we admire the jump of a doe or an impala. We will consider the ballon as a natural phenomenon and look for its secrets.

The fall of the bodies on earth is due to the fact that the matter which constitutes the earth attracts all matter by a phenomenon called gravitation. The body of the dancer being made of material does not escape the universal law described by Issac Newton, hence the mystery the paradox of the ballon: during the jump, a dancer who has ballon seems to overcome the constraints of the nature while subject to gravitation. Solving this paradox will consist of identifying the nature of the ballon phenomenon without denying the laws that make it possible to understand our universe.

Gravitation structures our universe. It is so fundamental that Albert Einstein described it in his magnificent theory of General Relativity by the curvature of space, thus extending Newton’s theory: "Gravitation is no longer based on the notion of acting force. on the subject but on the notion of displacement in a space curved by matter; for example, the orbit of the moon in the curvature of space by the earth, the fall of the bodies on earth ... Gravitation can be considered as an acceleration. This is formulated by the equivalence principle of Einstein: in a local experiment, gravitation and acceleration are indistinguishable. Gravitation accelerates the same way the motion of all matter. We will not enter the mathematics of this important property of gravitation, but we will study an experiment to familiarize ourselves with it. In a place like a dance scene, gravitation alters the motion of all parts of the body in the same way. Consequently gravitation acts only on the overall motion of the body, acting neither on the shape given to the body, nor on the evolution of this shape. Gravitation does not acts on the coordination of the body. The body does not feel gravitation. The body is free from gravitation.

Our sensations are objective. Let stand barefoot and close your eyes to feel them at best. What do we feel about our environment? We feel the upward push of the ground under our feet causing the pushing of the legs under our bust, causing vertebra after vertebra a push of the bust under our head and a pull of the arms at the level of the shoulders ... In other words standing we feel the weight of the parts of our body. The initial push of the ground under our feet results in a compression of the successive superimposed parts of our body, and a stretching of the suspended parts. This compression and stretching can be explained by considering that the ground under our feet accelerates us upward exactly as the floor of an elevator would do. This acceleration corresponds to the annulation by ground support of the overall gravitational motion of our body; motion that we can call gravitational free fall. In other words, the ground support stabilizes our position, it supports us. The support of the body by the ground has a price: it creates the corporal constraints mentioned above: weight, compression, stretching which acts on the shape of the body and its evolution.

Commonly in our intuition gravitation always has effects because we are most often supported by the ground thus subject to a compression of the body. Yet gravitation alone, without ground support has no effect on the shape and its evolution by motion. To express this, we will say that without support, gravitation is perfectly transparent for the shape and its evolution by the motion: as pure water allows light to pass through it freely, gravitation lets shape and its evolution free. A lack of effect is difficult to highlight among the complexity of our environment and our motions. To reveal this transparency, fundamental property of gravitation and thus correcting our intuition, it is necessary to purify the environment from the other phenomena acting on matter and to simplify the motion. For example, we can get rid of the effects of the atmosphere by going to the moon to let go (as during an Apollo mission) a hammer and a feather simultaneously from the same height and notice that the lunar gravity animates the two objects with the same speed so that they reach the ground at the same time. The two objects create a shape that is characterized by the distance that separates them, and this distance, therefore this shape, is perfectly preserved by gravitation. We can realize in Earth gravity an equivalent experiment by building a vacuum chamber, to observe the perfectly synchronous motion of a bowling ballon and a feather and thus observe the perfect transparency of the gravitation on the shape. This very nice experimentation that can be watched on the internet strongly evokes the ballon of the dancer https://www.youtube.com/watch?v=NOTQN9o8nQA. The twso objects are free from any constraint until they reach the ground: until a support arizes. The result is surprising and revealing because our intuition of the gravitation is taken in default: one expected that the feather would have been much slower and thus that the shape created by the two objects would have been strongly modified. This error of prediction is due to the fact that our intuition was built in the ordinary environment on Earth where another phenomenon hides the pure effect of gravitation; the phenomenon being the resistance of the air which slows down the feather. Our intuition will have amalgamated support on the air with gravitation. This experimentation shows that the absence of support results in an absence of effect of gravitation on the motion..

Because gravitation inevitably brings the dancer’s body back to the ground, it is futile for the dancer to act in the air against gravity. Because gravitation preserves the shape and its evolution, it is not necessary for the dancer to act against gravity when he is in the air because he can momentarily hold a posture in the air exactly as if the gravitation did not exist. Because it is in contact with the ground, the body undergoes constraints related to gravitation and can and must act against them. A glass in free fall does not momentarily undergo any gravitational constraint: placed on a table it does. The shape is kept by the interaction of the molecules that constitute the glass. Moreover by a sufficient heat, these interactions weakening, the glass will settle, lose its shape, because of the pushing of the table in the gravitation terrestrial. In the same way, a bodruche filled with water can not rest on a table to maintain a free shape, because the support modifies the free shape by creating a flat part at the contact of the table. On the contrary in free fall by neglecting the resistance of the air, the shape of the bodruche is free of effects related to gravitation. However, if at the moment when it is released in the air its shape is not well defined and stablized, that is to say if its motions are not well synchronized, the bodruche will deform during its fall in a more or less oscillating way . Then the neutrality of the gravitation on the shape although always true will be concealed by its motions. Similarly for the ballon, a good synchronization is necessary to highlight the freedom of shape in the air. Initial synchronization is a very important condition for the ballon to manifest itself clearly. Musicality plays a very important role for synchronization and therefore for the ballon; especially accentuation, phrasing, musical breathing. Conversely, the freedom of the ballon can be used to present the music.

Here is another intuition that must now be corrected. In flight, the bird does not abstract gravitational constraints because it is supported on the air by its wings so that free motion is prevented by local action. The wings of the bird have the same role as our feet. This is what the Greek statuary seems to tell us: with wings at his feet, Hermes evolves as well in support on earth as on the air making him the messenger of the gods. The proximity of the wings with the feet reinforces the idea that the support is necessary to maintain in the air. From this proximity also follows that the same postures are plausible both in the air and on the ground, so that the god have little to worry about the transitions between the two environments. We can probably see there a form of humor. As a result of its wing support the bird in flight feels effects related to gravitation as we feel on the ground as a result of our pedestrian support. The parts of the bird’s body in flight have a weight like the body parts on earth. The bird in flight does not maintain its shape freely in the air. The bird in flight should be compared to the dancer on the ground rather than to the dancer in the air. The air acts on the posture of the bird as the ground on the posture of the dancer. The bird compensates the very weak cohesion of the air compared to that of the ground by a very large surface of support, the camel compensates the weak cohesion of the sand by the width of its foot.

Unlike flying, the dive is close to the ballon. The dive of the pilgrim falcon minimizes air resistance, which is equivalent to saying that it minimizes its support. Thus the effect of gravitation on its shape is minimized while its acceleration becomes that of gravitation, and one could as well say that it falls like a stone or that it falls like the feather in the void. In this situation without taking into account the resistance of the air, the body of the bird does not feel the effects related to the gravitation. This constitutes for the hawk’s mind a simplification which could explain its extreme precision at the gliding of its prey; without this precision, instead of a spectacular predation, it would be a horrible crash. In the same way, the constitutive freedom of shape of the ballon brings a simplification which could explain the art with which the dancer receives himself; without this art, the soil would damage the body of the dancer.

The notion of support is essential to the existence of a gravitational effect. The ballon that assumes liberty in relation to gravitation is therefore in no way a flight. However, the start and the reception of the dancer’s jump can be compared to the flight and the landing of the bird: dancer and bird taking support.

Indeed to achieve a stable shape from a moving body we must be able to synchronize the main parts of the body: the shape is obtained if all parties reach the same speed at the same time. For example the feather with the bowling ballon are synchronous and therefore constitute a stable shape because the two objects were released with the same speed at the same time. Due to the simplicity of this binary system, this shape is here entirely defined by the distance that separates the two objects. An evolution of the shape of the binary system would therefore consist in modifying the separation distance. Gravity makes both objects evolve at the same speed, so distance thus shape are preserved. By the initial synchronization we highlight - and it is the same for the dance with ballon - the property of gravitation not to alter shape and its evolution; a gift of nature to dance, a spectacle for the eyes.

The synchronization necessary for the ballon brings clarity to the dance: in the way that by a subtle alchemy a drop of a mysterious substance would lighten a murky water, the synchronization that leads to a classic position brings clarity to the motion.

A material is transparent if the light passes through it freely, in other words if this material does not interact with the light. The term diaphanous, transparent in Greek, was dear to Theophile Gauthier to write about the romantic ballet. It is not only the romantic tutu, but also the ballerina dance and the ballet dance that is diaphanous and, especially by extension of the notion of transparency, the ballon; the diaphanous term becoming the extension of the notion of transparency to phenomena that coexist without interacting. With the ballon the phenomenon of gravitation coexists without interacting with the shape and its evolution by the motion. Thus the ballon which gives freedom in the jump to the dancer can be considered as an extended form of transparency: the ballon makes the jump diaphanous.

This instantaneous disappearance of the gravitational stresses does not systematically result in the freedom expressed with the ballon because new constraints can appear with the jump.

Gravitation acts in a universal way to bring the dancer’s body back to the ground in an overall motion. The duration of the suspension is therefore governed by nature. The ballon takes place during this time. The duration of the ballon is the time during which the dancer can achieve a shape free from external constraints and their possible consequences in the air. The longer is the ballon duration, the more the effect is apparent. But the ballon can be manifested as well in the little battery where the suspension time is much shorter. The effect therefore does not simply depend on the suspension time.

Our reflection has focused particularly on the effect of gravity on shape and its changes; in other words, the effect on the relative motion of the parts of the body. Now let’s look at the whole body motion. Unlike the relative motions which are free from gravity, the overall motion is described by a single point, the center of the masses, which, without support of the body, follows a parabolic curve. This trajectory is entirely governed by gravity, unlike internal motions that are independent of gravity.

Newton’s theory tells us that in an environment of pure homogeneous gravitation the objects describe parabolic trajectories as a function of time. At the top of such a trajectory, the object remains suspended for a moment, which is in accord with our intuition built by playing stones throwing for example. This suspension would therefore be a priori a good candidate to explain the ballon. However this natural behavior is not enough to explain the ballon because then any dancer would have ballon, we need in addition the gravitational freedom of the shape.

A half descending parabola will rather express the idea of ​​a fall than that of freedom in the air. Thus the ballon does not appear when a ballerina carried is released to be received in position fish near the ground as is done in the ballet Don Quixote, the impression of falling predominates over that of being free in the air. The emphasis is on the reception near the ground where the ballerina has a weight because the dancer resting on the ground supports her; the gravitational forces are thus in evidence and the ballon is hidden.

In the Specter of the Rose of Michel Fokine, Nijinsky’s exit through the window in a grand jete marked the history of ballet. The end of this legendary ballon jump is not visible to the public, so the ballon is both an apogee of ballet and the last image of the Spectre. The impression of falling is avoided by hidding the second part of the parabola which enhance the ballon.

In the experiment with the feather and the billiard ballon, the expression of the gravitational freedom is improved by the following of the common motion of the two objects by the camera. So the impression that nothing acts on the two objects is enforced. By thus abstracting from the motion of the whole body, we are getting closer to the true nature of gravitation. In the same way, the spectator, captivated by the dancer, will follow his trajectory with his eyes and will then have the impression with the ballon that nothing acts on the dancer, that gravitation does not exist; thus approaching an advanced conception of gravitation.

Suspended with a cable, the Sylphides that rise in the air are subjected to constraints on the shapes because the natural motion of the body in the gravitational environment is prevented: the Sylphides do feel the weight of the parts of their body. While pure gravity exerts no constraint on the shapes because it has the same effect on all the parts of the body, the suspension as the support acts on the shapes because they are exerted on definite parts of the body. Suspension, support, and flight are some of the situations where the body is prevented from falling, and shapes are constrained. On the contrary with the ballon the fall is not prevented and the shapes benefit from the gravitational freedom.

Vaslav Ninjiski answered that it was enough for him to think to stay in the air to get his legendary ballon. The term "sufficed" can be associated with the demonstration of the natural property of gravitation not to act on the shape and its evolution: there is no need, once in the air, to fight against the gravitation. "To think to stay in the air" corresponds to asking one’s body to realize a shape in the air which is done by synchronizing the main part of the body: the presumed spontaneity of Nijinsky’s dance allowing this direct approach to art of the jump, the presumed quality and purity of Nijinsky’s dance to avoid any harmful disturbance to the ballon. The ballon is a natural effect but it requires full possession of the art of jump.

The ballon reveals that one can momentarily keep a shape or make it evolve in the air as if the gravity did not exist. In absence of support, the gravitation no longer produces any constraint on the shape and its changes, and it is this absence of effect on the shape and its evolution by the motion, this freedom, that the ballon shows us. This lack of effect is counter-intuitive because on the ground, and therefore usually, the effects of gravitation are manifested throughout the body. By revealing to us this essential aspect of nature and by thus undoing our intuition, the ballon raises our thought above its trivial habits.

The paradox of the ballon is that of a body that appears free in the air as it falls inexorably. This wonderful impression or sensation that invades us with the ballon is not due to a metaphysical stopping or slowing down of the dancer’s body in the air, it is due to the quality of the dancer’s adaptation to the absence of gravitational effect on his body during the suspension of the jump. Placed on the ground like any other object on earth and like the earth itself, the body of the dancer is "aglutinated" on it by gravitation. The body feels settling and tugging, signals that it tells him that he is in an ordinary situation. In the air these reassuring constraints disappear, the gravitation has more effects on the body which can enjoy a momentary freedom compared to the gravitation. The counterpart of this freedom is the difficulty of the transitions between the usual terrestrial situation where the body feels the gravitation and the extraordinary aerial situation where these effects disappear. The ballon consists in mastering these disconcerting transitions so as to emphasize and highlight the freedom that is attached to it.

The ballon is the expression of the freedom offered by gravitation on shape and its evolution. The dancer who knows how to exploit this fundamental property of gravitation, can more easily maintain a shape or realize a motion in the air because for a moment gravity no longer exists for him; the parts of the body having no more weight since the body has no support on the ground. The ballon reveals this hidden freedom that is linked to the deep nature of gravitation, a phenomenon essential to the understanding of our universe. The ballon is not a transgression of the laws of nature: it is a magnificent illustration that delights us, arising in us a healthy curiosity and leading us to reconsider our intuition of the phenomenon of gravitation, to appricate its strange beauty. By letting us touch the existence of a deeper conception of gravitation than the common intuition suggests, the ballon astonishes us. The ability to amaze is one of the quality of the art: "Etonne moi" asked Diaguilev. In this way, we get away from the ordinary thoughts and its banch of familiar illogicismes, to approach the extraordinary reality with its new and strange questions that can make our thinking evolve towards more coherence.