initiatory prelude

links to:  Val Camonica   Bohuslän   Parthénon   Rose gothique   Niemeyer   Matisse   Brancusi   Magritte   Arman

straight to the sketches of this example

Model of the link used to display the Venus in the right frame: venus
Model of the link used to display the English version of the text in the left frame:
text opposite
If your screen does'nt display 2 frames, clink on this link.
Except when mentioned, the underlined links load a text or an image into the right frame. If you wish, a right clic of the mouse loads them into a separated window, but each time it will be a different one
Remark: this text with its links is similar to the French one, what involves that several links are leadind to French texts

[French version français  of this text]
[English version of this text for printing.]

A further analysis : the back side of the Venus (in French)

The Venus of Lespugue

Strangely enough, historians occasionally suggest that the rounded shapes of many prehistoric Venuses indicate the cellulite of the women of this epoch. Do they suppose that Picasso's models had both eyes on the same side of the face?
Strangely enough, art historians present the distortions of Picasso as a radical and unheard-of turning point, an incredible audacity without precedent, which innovates and definitively changes the practice and the meaning of art. Did they ever look at a prehistoric Venus? Did they think that prehistoric artists were stupid ancestors who only tried to represent the fat shapes of their females with their awkward fingers and with their very poor intellect?
Prehistoric artists had too complex preoccupations to deal with the trivial reproduction of reality. We had to wait for millennia before art degenerates so much that it identifies with the ability to reproduce convincingly the reality.

venus  The Venus of Lespugue, from the so called gravettien period, is thought to date to approximately 23,000 B.C. So, she is even older than the Lascaux cave.
In fact, this statuette was broken at the time of discovery, and the figurine we will analyse is a restored reproduction which is part of the catalogue of the "Musées de France" (internet site: where you can buy it - keyword: lespugue). On the site of Christopher Witcombe, which kindly links to this analyse to point out its restored state, you can look at its broken state under several angles.

If you wish a better understanding of the stage this Venus represents in art history, and also for going to the other analysed works from the very same stage, you can use the link that leads to all the studies about the paleolithic.
This link is available from the content of the "art" section (1- accès chronologique), or from the specialised home page called "A history of art" (les analyses d'oeuvres : de - 40 000 à - 2 000). The stage corresponding to the Venus of Lespugue is the third one, and it's conventionally numbered B0-13.
[By the way, if my hypothesis is correct, the famous paintings of the Chauvet Cave are not from the 1st stage of the history of art, but from the second one. This means that we can hope to find painted caves even older than Chauvet, and we can anticipate that they will have a different style than Chauvet. We can even say, before they are discovered, what are the characteristic visual effects of their style]
From the very same pages, you can also open the table that sums up all the stages of art history. This table describes all the successive combinations of the paradoxes. As it loads a bit slowly, it systematically opens up into its special window so that it can always be at your disposal.

The one after the other, we will consider the paradoxical (ie contradictory) visual effects the shapes of the Venus of Lespugue produce.
We begin with an effect that we will name "homogeneous/heterogeneous".

The First Paradoxical Effect: "homogeneous/heterogeneous"

An analytic expression from the  a3p6  type for the paradox homogeneous/heterogeneous:

venus   Two features are obvious: this sculpture has perfectly smooth surfaces, evenly polished; to the other side, these surfaces formed dramatic, clean folds, without any transition, tearing apart each other.
A smooth surface is a surface with a homogeneous aspect, and folds breaking the continuity of the surfaces form as many dramatic heterogeneities. So, this sculpture makes simultaneously two things that are clearly in contradiction with each other: homogeneity with its usual surfaces, and heterogeneity at the place of its folds.

Homogeneous here and heterogeneous there: we observe that the statuette uses different places for each of these two options.
Often, when a paradox expresses itself in this way, dividing its two aspects in very distinct places, we will say that it's an "analytic" expression, for the paradox is then broken down and its two separated aspects don't really fight each other.

There are many ways to make analytic homogeneous/heterogeneous, and to differentiate them, each of them got numbering. The paradox that we have just considered is numbered "a36". Of course, there is no use to remember this numbering. You just have to notice that "a" means "analytic". "3" is the numbering of another paradox which is connected to this effect and which doesn't matter for the moment. 6  is the graphic symbol for the paradox homogeneous/heterogeneous. A page indicates how the different symbols were chosen.
As a rule when this type of numbering appears, you also have a link that leads to the "library" of the whole set of paradoxical effects. For instance, if you follow this a36 link, you will have other examples of works in which some part is homogeneously made and the other one is heterogeneously made. Although on the same principle, you will see that the means are different: as here, sometimes it would be homogeneous surfaces contrasting with the heterogeneity of the intersections between these surfaces, but sometimes it would be the homogeneity of a simple line in its usual part contrasting with the sharp folds of its local inflections, or it would be the homogeneity of a texture of lines contrasting with completely irregular, then heterogeneous textures.
From any of these examples, a link allows you to go back to the complete analysis that it comes from, and to reach then its detailed explanation.
You can also go to the whole plastic effect's library, from a table (in English) with links to the list of effects for any of the 16 paradoxes.
For instance, you can go to the complete list of effects making homogeneity/heterogeneity.

An analytic expression from the  a14p6  type for the paradox homogeneous/heterogeneous:

venus  The Venus's overall form is generated by the homogeneous repetition of the same type of shape: the repetition of curved surfaces, in almost oval-shaped ball.
As a counterpoint to this homogeneous repetition of the shape, the reading directions (or the reading types) bring some heterogeneity for they often are clearly different.
Thus, we read legs as a series of volumes which follow on, going up from the feet to the buttocks.
On the contrary, breasts certainly read as going down volumes. Like the breasts, arms rather read going down, with hands following, crossing the breasts' direction. But even the going down arms do not read as the breasts do, because the breasts read as twin volumes which swell up while going down, whereas every arm reads in isolation by the thin drawing that its edge outline.
The head reads as a small ball strictly closed on itself, quite the opposite of the legs following on several volumes the ones after the other, and quite the opposite of the breasts extending well continuously the reversed hollow of the neck and the arms.
The stomach also reads as an autonomous volume, rather horizontal however in its development.

We call the previous example an analytic one, for the homogeneous places (the usual surfaces) were physically separated from the heterogeneous ones (the folds between the surfaces).With this new example, we enter a more general definition of what is an "analytic" effect: the split in two contradictory aspects can result effectively from a physical separation of the places concerned by each of the two aspects, but what fundamentally matters is the separation in two separate times of the two aspects in our perception.
Thus, in this new example, in a quick look we can note the visual effect of the repetition of the oval-shaped ball regularly combining to form together a large lozenge. However, to closely follow the detail of these shapes reading differently (by volume or by line - by pair or one by one - side by side or one after the other) and that also read following very different directions (from the bottom - or from the top - or in closed loop - or horizontally), we have to give up the overall homogeneous vision to look, the ones after the others, at these shapes' generations mutually heterogeneous.
We need a time to experience the homogeneous unity of the type of shape which is used, and we need another time to explore the whole variety of the evolutions of the different shapes.

Analytic paradoxes and synthetic paradoxes

Obviously, if we spook of analytic effects, that is because there is another kind of effects. This other kind, we call it "synthetics" effects.
Unlike the analytic ones, these synthetic effects don't break their two paradoxical aspects down, displaying them separately in two distinct moments of our perception, but they superimpose them in the same perception and in a global way that cannot be untangled, using a set of shapes whose reading inseparably sparks off these two aspects.
If you need to see again the difference between an analytic expression and a synthetic one, you can go to the small glossary at the end of the contents of the "art" section.
Now, we will see a synthetic effect that reads s10p6. Clicking on the link of this numbering, you can then discover its use in other works of art. Of course, "s" is a reminder for "synthetic".

Three synthetic expressions from the  s10p6  type for the paradox homogeneous/heterogeneous:

The principle of this effect is to repeat the same kind of shape systematically: they are always balls, or they are always rectangles, or they are always lines, etc. All the shapes are then alike, they are of a similar type, and therefore they are homogeneous the ones for the others. But, in addition, these shapes differ in another aspect: for instance, they are of a different size, or they are of a different color, or they are differently oriented in space, and therefore they are heterogeneous the ones for the others by this second aspect.

venus  In the Venus of Lespugue, we find this effect three times.
As already mentioned, its global shape is generated by the homogeneous repetition of the same kind of shape: the repetition of curved surfaces, in quite oval-shaped balls.
However, these oval shapes are heterogeneous the ones for the others by their sizes: there is a small tight ball to make the head, there are ample curves to make the arms and the breasts, and, from the feet to the buttocks, there are curves of different lengths.
The intensity of their curves is also very heterogeneous: there are very stretched ovals (the arms, the breasts, the thighs), there are almost spherical ovals (the buttocks), and there is an oval of medium proportion (the head).
So, the Venus is made by the homogeneous repetition of the same oval shape, and these ovals have sizes and curves that are heterogeneous the ones for the others.

venus  Then, we saw the first use of the  s10p6   expression in the Venus.
The second one is about the curve's direction of the oval surfaces: sometimes they are concave surfaces (the arms), and sometimes they are convex surfaces (the whole rest of the form).
Being always rounded, the shapes are always homogeneous the ones for the others, but the opposite directions of their curves force to feel that they are heterogeneous.

venus  The third utilisation of the  s10p6   expression is about the diamond shape that we find in the exterior contour of the Venus as well as in the very distinct central volume consisting of the breasts and the stomach: these two lozenges are homogeneous with regard to their shapes since they are identical, but they are heterogeneous with regard to their sizes which are clearly different. They are also heterogeneous in position, since one is an exterior contour and the other is in internal position.

Plastic paradoxes and physical paradoxes

As far as the homogeneous/heterogeneous analysis is concerned, we have done it with this Venus, and you can go right away to the next effect that will be named "to assemble/to separate".
But, before that, you can wonder about the presence of "homogeneity/heterogeneity" in a gravetien sculpture. And why do the other examples found by the a36 and the s106 links reveal the return of this effect in other periods of art history? And why not in the whole periods?
The presented hypothesis has two aspects: for one part, we want to show that the whole works of art can be broken in paradoxical plastic effects; for the other part, we want to show that these effects are not due to chance or due to the artist's whims. They would be linked to the state of complexity of the society the artist lives in, and to which he confronts. To build oneself, and then to hold out as an independent personality, this confrontation would force him to construct in himself an internal complexity which can be of a sufficient level with regard to the complexity gained by the society of his time.
To simplify, but also caricaturing, we can say that every historical period is characterized by a certain "social dynamic", and that this homogeneous/heterogeneous paradox corresponds to one aspect of the functioning of this dynamic. Its return in art history would point out that, at least by this aspect, the same kind of social dynamic occurs in a new stage of the development of humanity.
In the series of analyses making the "initiation prelude" we won't try to understand the reason why a specific paradox appears in a specific era, but we will try to show how, by some aspects, the social dynamic behave in a way that evokes a physical dynamic.
Of course, it's not appropriate to identify the human society with a mere physical phenomenon. If you are interested about this point, you can go to the developments called "the core of the theory", more particularly to the chapter "the four dimensions of the human society" (les quatre dimensions de la société humaine).

For now, preserving the spirit of a mere initiation, we consider what the "homogeneous/heterogeneous" notion means for a purely physical dynamic.
We can observe this in a water flow, provided that the current is not strong enough to generate some whirlpools:
    - it's water everywhere indeed, then the same water, the same kind of molecules. In this aspect, the current's matter is therefore perfectly homogeneous.
    - in the same time however, the current carries aways some parts of the water faster than the others: a segregation forms between the liquid's layers slowed down by the banks, and the liquid's layers with a faster wake in the middle of the current. Scientist call "laminar layers", the layers flowing smoothly the ones over the others in the same fluid. Although made of the same water, the different layers of the liquid are autonomous the ones for the others to the extent that they slip the ones over the others. Then, the liquid which is homogeneous in its substance, is simultaneously heterogeneous because of the autonomous layers in which it cleaves.

Laminar layers don't only form in liquids: they also form in the air; for example when a source of heat makes an air stream going up.
This phenomenon also occurs near an aeroplane's wing or near a boat's sail: the difference between the speed of air near the wing (or near the sail) and the speed of air quite away cleaves the air into several layers whose speeds progressively increase.
As an illustration of this physical effect, we display the image of laminar layers forming near the sail of a boat whose tension is well-adjusted so that its does not make backwash.
Every time we will deal with a plastic effect of a homogeneous/heterogeneous type, we could feel it by recalling this principle of a homogeneous fluid cleaving itself into laminar slices that are heterogeneous the ones for the others.

Second Paradoxical Effect. We will call it: "to assemble/to separate"

Except for a case on which we will come back, we need to remember that the plastic effects in the same work of art always correspond to strictly successive rungs of the dynamic.
This means that if a homogeneous/heterogeneous effect can be illustrated by the dynamic of the laminar layers that cleave a fluid, the next paradoxical effect can be illustrated by what happens to the laminar layers when the dynamic of the fluid becomes "a rung" more raging. Further again, we will get the new following paradoxical effect by observing what happens when the dynamic becomes "a new rung" more raging again. Then, this deductive reasoning allows us to lean on the physical phenomena, most of them being well known and well understand. As they throw light on what is going on in the very mysterious history of art of the very mysterious human beings, it would be shame if we don't use it.
Then we use it, and even before examining forwards the shapes of the Venus, we wonder what happens to the fluid split in laminar layers when the difference of speeds between its various layers increases too far.
To illustrate the homogeneity/heterogeneity, we gave the example of the sail of a boat which was loose enough so that it does not cause backwash. Now, we will stretch the sail a little more (the sailors say they "take up the slack") to increase the difference of speeds between the air well protected behind the sail and the air which violently flows in each of its ends. At some point, the difference of speeds became too big for the laminar layers to remain behind the sail: they don't bear any more this gradient getting excessive, and they break, they shear in all directions.
We will turn our attention to what happens at the boundary between the two laminar layers when their differential of speed becomes too high so that they cannot go on slipping the one over the other without tearing: what happens is that they locally interpenetrate, that they built together a succession of mixing zones going at an intermediate speed. On the whole, these repeated mixings allow the differential of speed between the two layers to remain bearable.

In these zones which follow one another intermittently, the two layers assemble; but these assemblages can only be local, on their boundaries, and due to the fact that a part of their fringes separates out of their initial layer.
So, at this state of the fluid, at the boundary between different layers, that assembles and separates in the same time, and that assembles precisely because that can separate: a fringe separates because it is driven by the opposite layer, and because this drive is so big that it cannot remain within its layer going at too different a speed.
Then, after the time of the "homogeneity/heterogeneity" comes the time of "to assemble/to separate", and when we mention the "to assemble/to separate" paradox in an analysis of a work of art, you could remind this sketch; you could remind the principle of the laminar layers which locally interpenetrate when their differential of speed becomes unbearable: successive zones in their fringes separate out, assembling with local zones of the opposite layer.

Now it's time to go back to our Venus to examine its various effects of "to assemble/to separate".
As for the previous paradox, first we will see the analytic kind before seeing the synthetic one. But you don't have to worry about this division that only concerns the order in which the effects are presented. Don't worry nether about the numbering, and for each of the effects you could follow the link (such as a157 ) which will lead you to other examples of works using similar effects.

Two analytic expressions from the  a15p7  type for the paradox to assemble/to separate:

This kind of expression, numbered  a15p7   consists in assembling small shapes in a bigger one which is clearly legible for its own, whereas these small shapes remain well distinct, well different, or well separated the ones from the others.
venus  In the Venus, we first find this in the overall shape: all its parts assemble in a large, well legible lozenge, but this assembling does not manage to melt together groups of shapes that read well separately:
    - the head forms a small ball completely aside;
    - the arms form a hollow that stands out with the rest of the shapes;
    - the stomach and the breasts form a central compact packet in a diamond shape that is clearly distinguishable from its neighbourhood;
    - and the legs make a V whose branches diverge, developing in a plane that clearly stands back of the protuberance formed by the stomach and the breasts.

venus  We can find another use of this effect on a smaller scale.
As we just mentioned, the centre of the body also has a diamond shape, and this lozenge assembles in the same well compact packet the balls forming the breasts and the bottom of the stomach. In the same time though, all these shapes remain clearly separated, clearly cut the one from the other by the deep furrows that mark their respective boundaries.

An analytic expression from the  a6p7   type for the paradox to assemble/to separate:

In the effects we just saw, the gathering was provided by the external contour of the shape, whereas the splitting was provided by its internal divisions, let well affirmed.
In the  a6p7 type of expression we do not find this relation in the global arrangement of the shapes, but we find it in the internal relation of the different shapes: in a place the shapes gather together, whereas they move away from each other in another place.
venus  Mainly, we find this in the way the legs of the Venus are made: at the bottom, the legs firmly stick together, they firmly assemble. In the tip of the feet, they are even completely continuous the one with the other.
On the contrary, the two legs separate in their upper part, then they move more and more away the one from the other.

venus  We can also find this effect in the breasts, assembling at the top in the chest, and separating toward the bottom.

A synthetic expressions from the  s12p7  type for the paradox to assemble/to separate:

venus  The legs and the buttocks made curves that follow on the one after the other: first the curve is moderate at the shinbones' level; then, it becomes more strengthened at the thighs' level; then at last, it becomes very tight, rounding off the very sharply bulging buttocks.
If we read in that way the roundnesses from the bottom to the top, we feel that the curve assembles - squeezes - the shape in a packet which is more and more tight; and we feel that, simultaneously, it separates more and more every shape from the previous one:
         - the bottom of the legs are barely hunched up; they are still relatively continuous with the thighs. The feet of the two legs are even completely merged.
         - to the opposite, the buttocks round off to the maximum in a compact ball, and doing this they separate very clearly from the thighs.

So, from a curve to the next one, the increase of the tightening which assembles in a more and more compact shape, causes the simultaneous increase of the effect of separation between each curve and the previous one.
Due to the fact that the separation is directly suggested by the force of the tightening, the two contradictory aspects of separation and compact squeeze are here inseparable from each other, and that is precisely what makes this effect a "synthetic" one.

Third Paradoxical Effect. We will call it: "synchronized/incommensurable"

The notions of homogeneity and heterogeneity, then the notions of assemblage and separation, were not very complicated.
For this third paradox it's a bit more difficult.
Its very name is somewhat abstruse: synchronized/incommensurable. However, to make it simple, we can say that it refers to something "that works as if by magic": indeed we see that several motions are well-coordinated, indeed we see that they are marvellously well-adjusted the ones with the others, nevertheless however, to achieve this adjustment they don't seem to rely on any common reference or on any common rhythm. In short, it's incredible but it works: it's magical!

Don't wait for any passes of a conjurer: it's geometry only.
The characteristic figure of this effect will be the spiral.
To generate a spiral turning without losing its shape, its distant parts have to perfectly coordinate with its more central ones when moving:
    - and yet they have nothing in common, since they are completely cut off the ones from the others by a great number of spiral turns;
    - and yet their motions are very different, since they don't go at all at the same speed: the more a point is away from the centre, the more it has to go faster to make a complete revolution in the same time than the central parts having less movement to make;
    - and yet their motions don't even follow the same way: the more the curve is external, the less it is tight.
Then, the figure of a rotating spiral does correspond to the surprising coordination, somewhat magical, among separated movements that follow different curves at completely different speeds.

This figure of geometry is all the more significant here because it is directly suggested by "the next rung" of the dynamic that we have used as a physical illustration for our two first paradoxes.
We first saw what happens in a fluid when laminar layers form because some of its parts have to go faster than its neighbours. Then, we saw what happens when the differential of speed between two layers increases until they cannot bear the sliding of their neighbour over their surface, and when the layers breaks consequently and locally interpenetrate in a repeated way.
Now, if we increase anew the differential of speed in the fluid, so that local and intermittent interpenetrations are not enough any more to cope with these differences, then a spiral does form in this fluid.
In this new image of the flow of the air behind the sail of a boat, again we find the two regimes already seen: ahead, the laminar flow of the air is not disturbed by the sail, then, just behind the sail, we see the shearing caused by the slowing down of some parts of the air. Now, if we look even more away behind the sail, we discover the splendid spiral made by the regular arrangement of the speeds, between a cental part where the air turns very slowly and the external ones where the air whirls in full speed.

Anew, we go back to our Venus to see a first effect of synchronized/incommensurable.

An analytic expression from the  a3p8  type for the paradox synchronized/incommensurable:

venus  The Venus too owns a global shape with remarkable geometry.
Of course, it's not a spiral: it's a lozenge. What is astonishing though, is that the regularity of this figure is obtained by the gathering of shapes dispersing in the whole directions, with rhythms and with motions that are completely different the ones from the others. A priori, such independent shapes have no reason at all to form together a regular shape:
    - for no reason at all, the movement that goes from the head to the arms, then to the buttocks, finds itself in the symmetrical movement that goes from the joints feet to the shinbone, then anew to the buttocks;
    - for no reason at all, the curves of the breasts and the opposite curves of the arms exactly coordinate so that they remain in this regular figure;
    - for no reason at all, the top of the breasts and the bottom of the stomach exactly coordinate so that they form together another diamond-shaped figure inside the big diamond shape of the Venus.
All this geometry is all the more surprising that it suggests the look of a woman, and that we don't expect this very kind of regularity in a woman's body . . . whatever our opinion on cellulite in the prehistoric era!

So, to sum up, everything synchronizes in a figure with regular geometry, and yet everything disperses in directions that are incommensurable the ones for the others.
Here, "incommensurable" means that they go away in directions which are too much unrelated the ones to the others so that we cannot assess the rhythm of the progress of the ones in relation to the rhythm of the progress of the others.
To cut short: together the shapes are forming a lozenge, but we cannot grasp how they manage to do so.

A synthetic expression from the  s6p8  type for the paradox synchronized/incommensurable:

Often the incommensurability is expressed by the mean of two perceptions that we cannot keep inside us at the same time, preventing us to measure or to assess the relation between them easily.
A way to prevent us from keeping these two perceptions inside us at the same time is to produce shapes that read from places that are as much apart as possible and going the one toward the other. As it happens, to read a movement going in a direction, our perception installs in our body the imaginary direction of this movement. Therefore, to read the movement going in reverse, we necessarily have to "uninstall" the perception of the first direction in order to install the perception of the reverse one in our body.

venus  So, in the Venus the legs read from the feet, progressively going upwards along the curves of the legs separating on each side of the stomach. In reverse, the top of the body reads from the neck toward the stomach, following the reliefs of the breasts.
Not only these two visual paths do not meet, but above all they leave from opposite points and they go in reverse. Because our perception does not allow us to easily follow at the same time two such paths going the one toward the other, necessarily we give up one of them when we want to follow the other; we stop reading the path going from the feet toward the buttocks when beginning reading the path going from the neck toward the breasts.
As we cannot read them at the same time, we cannot confront them easily, what prevent us grasping how they manage to coordinate. We cannot follow every detail of their progressive coordination, we cannot assess its rhythm and accompany this coordination as it goes along; but the fact is, and we can see it clearly: they manage to synchronize to form finally the very shape of a lozenge.

A synthetic expression from the  s12p8  type for the paradox synchronized/incommensurable:

Another way to prevent us "holding" two perceptions at the same time in our sensation, is to use a contrast between concave shapes and convex ones. As it happens, our perception does not allow us to experience these two kinds of shapes at the same time: we perceive a concave hollow by arching in imagination our body in a hollow, then, this time to perceive a convex bump, we have first to uninstall this hollow in us, in order to curve in imagination our body in the reverse direction.

venus  In the Venus, the surface of the arms forces us to read a concave hollow.
On the contrary, all the balls forming the body - and particularly these of the breasts which are directly confronted with the hollows of the arms - force us to read them as convex bumps.
In order to read the hollow of the arms, we have to stop reading the bumps formed by the rest of the body, we have to "uninstall" their perception in us. In reverse, to read the balls of the body, we have to uninstall the perception of the arms in us. And yet, we clearly see that all these shapes we cannot visually grasp at the same time, manage to synchronize as needed to build together the very shape of a lozenge.

Analytic and synthetic expressions in the case of incommensurability

Before finishing with this paradox, we have to give a detail which can be left out for a simple initiation.
We just explained that incommensurability often expresses oneself by preventing us holding two perceptions at the same time, so that we cannot grasp the way by which the synchronization of the shapes manages to do.
And yet, earlier we said that the essence of an analytic expression is also to force the perception in two separated times.
So, how can we speak of synthetic expressions in the two previous examples?

In the case of the previous analytic example, it was by means of two very different readings that we saw, firstly the over-all diamond shape, and secondly the stampede in the whole directions of the shapes building this lozenge: there is no way following the complex movements of the internal shapes, and in the same time managing the reading of the external diamond-shaped perimeter in which they stand.
By turns, our perception makes theses two observations, then it draws the conclusion: it comes as a surprise that all this internal complexity manages to form a lozenge in the whole.

In the last synthetic example, our perception is driven, by means of the regular repetition of ball-shapes and by means of the suggested arrangement in a lozenge, to read this diamond-shaped gathering "as if it was perfect", as if the synchronisation in this regular shape was successful. And it is at the very same time when our perception is driven to read the perfect shape of a lozenge, that it is hampered by the presence of volumes in reverse curve refusing to be grasped in this perception.
In the case of an analytic expression, the two times of the perception are "a way of reading", whereas in the synthetic expression of incommensurability it is rather what we could call "a way of failure of the reading": because the overwhelming suggestion of the other shapes, we are poised to read a completely synchronized shape, and at the very same moment we are doing this reading, it fails because there is no way for doing it. So, simultaneously we read the synchronized shape which is suggested and we note the impossibility of this reading. The failed reading and the admission of failure are simultaneous, as suited for a synthetic expression.
In the same way, in the first synthetic example, reading the regular lozenge of the shape we expect it to have a central symmetry so that it can be read from its center; and it is then that we are disturbed to note that it must be read from the two ends: we are driven to read it from the center, but as soon as we try this reading its impossibility reveals, and separated readings from two poles establish themselves as indispensable. In fact, in this effect we do not really read from the bottom and from the top: we just notice that we have to, and this is enough to spoil the central reading of a central symmetry that did seem here.

Fourth Paradoxical Effect. We will call it: "continuous/cut"

If something is perfectly continuous, then it is not divided in stages that we can set apart. Conversely, if it is cut up into separated stages, it cannot be continuous: this paradox "continuous/cut in stages" is easier to explain than the previous one. To simplify matters, we will call it "continuous/cut".
Until now, we explained the successive paradoxes by showing how every of them corresponds to a real physical effect, effect that we observe while increasing the internal differential of speeds of a fluid. Well, we will go on exactly in the same way, and we will find our new paradox functioning in a fluid whose motion speeds up again, beyond the conditions that generate a whirl in a spiral.
It's just one rung more in the dynamic: still, the fluid cannot do more than to absorb its differential of speeds with a spiral, but one spiral only is not enough any more: as soon as one spiral has exhausted all it can do to help matters, it gives up, and, immediately, it gives way to a new spiral. We see this at the right of the boat in the top of the previous figure, but we can also consider a situation where this effect is forming in a more regular way, so that we can see it clearly. Physicists labelled this organisation a "von Karman Vortex Street" (I find the French name more poetic. It approximately reads: a "swirling path of von Karman" - une "allée tourbillonaire de von Karman"). Von Karman was a greet Hungarian "Fluid Mechanical" who found in 1911 a mathematical expression about this phenomena.
In this photograph of a laboratory vortex street, very clearly we can see the initiation of a spiral that every whirl forms: a spiral forms, it tries to contain in itself the differential of speeds, it grows as much as it can to achieve this, then, when it fails to grow large enough, it moors to a new spiral, which tries in its turn to organize the fluid. In its turn it fails in the same way, however without ever breaking the continuity of the fluid.
The spirals of a von Karman Vortex Street are clearly cut the one from the other, because each of them separates from the previous one, and even goes in the opposite direction. Just as clearly as that, they form a continuous strip which is never broken off. So, it's a dynamic which by one aspect is cut up in successive stages, and, by another aspect, appears uninterrupted, because every spiral belongs a bit to the previous one, and it also belongs a bit to the next one. Although each spiral forms a distinct stage clearly separated from the other ones, nowhere we can find a boundary which would separate, on one side a complete spiral, and on the other side a complete second spiral.
The impossibility to point out the very place of a separation between the successive spirals whereas we "very well see" that they are cut off the one from the other, is an excellent example of a really paradoxical situation, because the spiral are really and inextricably simultaneously continuous the one with the other and separated the one from the other.

Two analytic expressions from the  a10p9  type for the paradox continuous/cut:

venus  If we want to see a woman in this Venus, one of its most striking "improbability" is the atrophy of the forearms and of the hands, which only mark a notch in the continuous curve sliding down from the neck to the bottom of the breasts.
Continuity of the curved surface going down the neck, and simultaneous cut of this continuity by the stroke of the hands: that's it! It's then continuous/cut.

All the curves building the Venus' shape follow on and link together in a well continuous way.
The small ball of the head resumes and carries on this effect of chained curves; but, because it is separated from the other ball-shapes by the opposite hollow of the arms' curve, it is also felt completely cut from the compact packet that the other balls are forming.

A synthetic expressions from the  s11p9  type for the paradox continuous/cut:

venus  Very clearly, the volume of the Venus is generated by the repeated (continuous) bounce of a curved surface, which each time breaks (cuts oneself) before going farther away: so, the cut of the curve is repeated in a continuous way.
As the notion of a break and that of continuity here are intrinsically tied and inseparable, this is an effect of a synthetic kind.

State Paradoxes And Transformation Paradoxes

We successively studied four paradoxes borne by the shapes of the Venus; at the same time, we saw that these paradoxes follow on the one after the other in the same way as the effects of a more and more energetic dynamic do.
For the Venus of Lespugue, these four chained paradoxes make what we will call "the four state paradoxes".
"State" paradoxes, simply means they describe "the state" of the internal complexity the artist had to built in, in order to hold out as an independent personality in the social dynamic of its time and to which he confronted. We saw four paradoxes, and there always will be four: no more, no less. Four, because each of them describes where things are in one of the four dimensions of every human complexity; dimensions which follow on and progressively consolidate as four stages of a successive complexity.
Why "four" chained stages? This does not matter to follow the proposed analyses of works, and this point will not be developed in this introduction. Of course, it matters on a theoretical point of view, and if we have to get the bottom of things we have to say that "four" is because the four dimensions of space-time. Each complexity developing in our four dimensional universe has to submit to such a decomposition, four rungs by four rungs, and it has to fold up in cycles more and more complexe which themselves follow on, four by four.
For a less cursory explanation you can go to the text "the 4 successive stages of every complexity - les 4 stades successifs de toute complexité ", where this point is developed in a manner I believe easy to understand.

To describe the state of a physical dynamic, one paradoxical effect was enough. For example, to describe the dynamic of a fluid splitting up into laminar layers, it was enough to mention the simultaneous homogeneous and heterogeneous aspect of this fluid. In the case of the dynamic of a human society, this time we saw that we have to combine four paradoxical effects, and that is only to describe its state.
Then, a human being which is plunged into its society, that's a little more complex to understand than a drop of water mixed to the water forming a river.
And in fact, that's still more complicated, because four state paradoxes are not enough to exhaust all the aspects of the situation: we still have to add several paradoxes, which we will call this time "transformation paradoxes".
As it suits, by difference with the state paradoxes which indicate "the state" of what it is, the transformation paradoxes describe the way things are transforming. For example, if we say that a car is at a precise place, we only describe the state of its position at a given moment: at a given moment, it is right here. An information about the transformation of its position would be, for example, to say that it is stationary, or that it is moving forward at a regular speed, or that it is accelerating, or still that it is sharply braking. Then, completing the information on the momentary state of its position - its state at a given moment - this type of information allows us to know how the position of the car will transform, it describes its state at the next moment.
For now there is no use understanding the difference between "state paradoxes" and "transformation paradoxes", and in the analyses this decomposition will be mainly used to decide on the order of presentation of the paradoxes.
Incidentally, let'us make a remark: if the human complexity has to be enlighten on the way it is transforming, simultaneously with the knowing of its state at a given moment, that's because, in reverse of a pure physical phenomenon, a human being has a memory, and always thinks himself with regard to the long-term. Besides, he relates himself to the past of humanity as well as to its future: we are living in the present, but we are living with the nostalgia or the repulsion for some past eras, and with hope or fear for the future of humanity if it goes on in the way we know in the present.
The way we imagine the past and the future of humankind changes the way we behave in the present. Consequently, the past and the future don't only enlighten the present; they transform it really.

Unlike state paradoxes, there are not always four transformation paradoxes.
At the stage of the Venus of Lespugue, they are only two.
By the end of the paleolithic, the analysis of art works reveals that a third one is added on, then a fourth one is still added on around the beginning of our era. To be comprehensive, we can state that their number falls back to two in the contemporary period.
Why does this number vary when that of state paradoxes remains always four? This can be understood with the analogy we gave previously with the description of the state of the position of the car:
    - if it is stationary, then there is only one thing to indicate: the place where it is;
    - if it is running at a constant speed, then there are two things that we can tell: the place where it is now, and its speed;
    - if it is accelerating, this time there are three things to be said: the place where it is now, its present speed, and the speed of change of its speed.
Nearly the same thing applies for the dynamic of the human society: depending on its rate, the way it transforms is more or less complex to describe, and then it requires more or less paradoxical effects to be expressed with plastic shapes.

There is another difference with the state paradoxes: although transformation paradoxes strictly follow on as the state paradoxes do, there is an exception for the last one.
This last one evolves along the history of society with a rhythm of its own. We can caricature this, saying that as long as we are in a fundamentally stationary society, then a specific family of paradoxes is standing at the last rank of the transformation paradoxes, and, by means of its special nature, it "sums up" the precise fact that the society is fundamentally stationary. Then, when the society is moving on, a new family sums up this, a family which is precisely specialized to express the movement. And when the society is accelerating, again a new family of paradoxes sums up this kind of transformation, a family which is then specialized to describe an effect of acceleration.

At any time, to see again the notion of state paradox and that of transformation paradox, you can go to the small glossary at the end of the contents of the "art" section.
For more details, but then it will be a little hard if you are not a fervent enthusiast for the theoretical abstraction, you can go to the texts about state paradoxes and the one about transformation paradoxes.

The First Transformation Paradox: "coordinated effect/autonomy"

Now, back to the Venus of Lespugue. We already said that, as for the whole works of its time, there are only two transformation paradoxes to consider. As it happens, matters will be even simplier because the second paradox is the paradox 'homogeneous/heterogeneous" we already studied as the 1st state paradox.
The 1st transformation paradox is: coordinated effect/autonomy.
As this paradox is not "a rung of complexity" up or down the paradoxes already considered, for the moment we will not try to show the physical phenomenon it can be associated with. This will not prejudice at all the comprehension of its plastic effects.
However, if you want to see this point, I give some links you can use. Besides, you can use these principles for any of the 16 paradoxical effects:
    - for a summarized explanation of the 16 effects: the text "how the physical phenomena become more complex"(comment se complexifient les phénomènes physiques) which belongs to "the core of the theory" (le noyau de la théorie) in the contents of the French "art" section.
    - for an explanation of this effect only, always summarized, but this time with lights on its social, plastic and musical aspects: its "summary card" (fiche de synthèse). All such cards can be reached from the "more in-depth study of each of the 16 paradoxes" (l'étude plus approfondie de chacun des 16 paradoxes) which belongs to the "theoretical enlightenments" (éclairages théoriques) in the contents of the French "art" section.
    - finally, for a more comprehensive explanation of the physical phenomenon: the text "near the melting point" (approche du point de fusion) accessible from the "table of the 16 paradoxes with their 4 cycles" (le tableau des 16 paradoxes et de leurs 4 cycles) which also belongs to the "more in-depth study of each of the 16 paradoxes" (l'étude plus approfondie de chacun des 16 paradoxes) in the "theoretical enlightenments" (éclairages théoriques).
For whatever purpose it may serve, I specify that the paradox "coordinated effect/autonomy" is the third one in the 1st cycle of the paradoxes.

An analytic expression from the  a7p3  type for the paradox coordinated effect/autonomy:

venus  The surfaces of the balls are developing towards very diverse directions, and with very various rhythms.
Though, all these completely independent movements (then, autonomous) generate a common shape: a lozenge. We find this lozenge in the external contour of the Venus, but also we find it in the internal shape made by the breasts and the bottom of the stomach. The "diamond-shaped effect" is here the coordinated effect produced by autonomous movements which, in addition, are dispersing in the whole directions.

We can notice that this expression closely pairs with the a146 expression of the paradox homogeneous/heterogeneous (second transformation paradox) used in the Venus.

A synthetic expression from the  s7p3  type for the paradox coordinated effect/autonomy:

venus  All the surfaces are forming the same effect: that of a separated oval-shaped ball.
And yet, each separated ball is noticed as such, only because a sharp and distinct fold, or a deep furrow, cuts it from the rest of the volume, and allows it to be read as an autonomous swelling.
So, all these swellings are making together the same effect of a separated oval-shaped ball, and this coordinated effect happens to be the very effect allowing each of the oval balls to assert its individual autonomy.
Coordinated effect and the assertion of autonomy are perfecty inseparable here: then, we do have an effect of the synthetic type.

This time, we could note in passing that this expression is very closed to the a36 expression of the paradox homogeneous/heterogeneous used in the Venus.

Two synthetic expressions from the  s10p3  type for the paradox coordinated effect/autonomy:

venus  All the surfaces are forming the same effect: that of a separated oval-shaped ball.
Simultaneously, these shapes are very different the ones from the others: there are the convex ones and the concave ones, the big ones, the medium ones and the small ones, the ones very well stretched and in reverse the ones completely hunched up in a ball, the ones going straight downwards and the ones going upwards on the bias.
So, the whole shapes coordinate to make the same effect of an oval-shaped ball; and in the same time they are doing so in very autonomous ways the ones for the others.

We notice that this expression uses the same set of shapes than the s106 expression of the paradox homogeneous/heterogeneous, in the first and in the second example we gave of its use in the Venus.

The s103 expression also uses the lozenge shape:
    - the exterior contour of the Venus is a diamond shape;
    - the very distinct central volume consisting of the breasts and the stomach is also diamond-shaped.
Then, the shapes coordinate to repeat twice the same effect of lozenge, and this repetition is made by two volumes of different sizes. Precisely because their sizes are different, and also because one is in the position of an external contour and the other one in an internal position, these two lozenges read very autonomously the one from the other.

This time, this set of shapes is similar to the third example given for the s106 expression of the paradox homogeneous/heterogeneous.

The two transformation paradoxes answer each other

As we went along, we pointed out that the two transformation paradoxes (coordinated effect/autonomy, and homogeneous/heterogeneous) fundamentally use the same set of shapes.
This corresponds to a systematic principle. This principle concerns the two transformation paradoxes, during the whole period of art history where there are only two such paradoxes. This mixture of the two paradoxes on the same set of shapes is linked to the mode of functioning of the paradoxes, that is the way they are mutually interfering inside the combination they form.
You just have to note that this mode of functioning changes as the society becomes more and more complex; when useful in the analysis, then we will give the consequences this has on the way of reading the plastic effects.

Before Leaving The Venus Of Lespugue

So, the analysis of the shapes of the Venus of Lespugue is now finished. We used it to introduce the key notions in passing.
You can use this link to print this analysis with the pictures included inside the text instead of being in a separated frame (it opens into another window).

To continue, if you want texts in English only, some of the analyses have their sketches translated. They correspond to the first links at the top of this page, and they are also listed in the content of the English "Art" section (this link opens into another window).
If you read French, as you are now introduced to the key useful notions, you can go directly to any of the analyses:
    - either by picking through the other analyses forming the initiation prelude whose whole links are at the top of this page. If you wish the chronological order, the next stage will lead you to the neolithic period, in the Valcamonica of the Italian Alps.
    - or through the chronological links of the content of the French "Art" section (this link opens into another window).
If you don't master French vcry well, often sketches will help you.
You have to know that the analyses about the prehistorical period have exhaustive developments. Temporarily, the ones about the medieval period only have the presentation of the effects of the 4 state paradoxes: then the transformation paradoxes are missing. The analyses about architecture history, from the Renaissance to nowadays (accessible through part -3- of the theoretical enlightenments in the content of the French "Art" section, or through the content of the French "Architecture" section - these links open into another window), each time concentrates on one paradox only.
I intend giving similar analyses on other civilization chains. Sorry, but it won't be soon.

This burning sob that rolls from age to age
(Charles Baudelaire - Beacons)

We noticed that the two transformation paradoxes often use the same set of shapes exactly. In fact, for the main part this matches for the whole paradoxes we found in the Venus of Lespugue.
As we said, this partly stems from the special functioning of the interference between the different effects during the prehistorical period. However, apart from this kind of nuance about the functioning of the paradoxes, this remark fundamentally applies for the whole works of art. Because this is due to their role, to their very justification.
Each human being is in search for its internal unity, to provide a meaning and some coherence to its live.
Trying to grasp and to handle the various and complex relations which he strongly feels in him but he cannot say with words, an artist is always looking for a set of shapes which could simultaneously bear these whole relations and their complex mixings. Because he is in search for unity, necessarily he will try condensing these relations in a limited set of shapes, in order to install in his sensation the rich detail of their mixing relations as well as their overall unity he is trying to grasp.

You must not suppose that the sculptor was on its first try when turning the shapes of the Venus out of a mammoth's tusk: to be so synthetic, these shapes are necessarily the result of some slow maturing of trials. Little by little only, he managed to find the right effects and their right interlockings, so that all the details' shape and the overall shape itself can answer each other in an efficient and very limpid way.
Several times he tried, but 23 000 years later the shapes he managed to find have not yet exhausted their effect, then their elusive mystery, on the other human beings.
Silicon chips and the world-wide Internet are now extending the efficiency of this ivory form, so small a form that it holds in one hand only. It came from old times; technology now enables us to carry away its effects. But how many words we need to only approximately near, and by means of many successive touches, what a few bouncing curves can do, in a strong, precise, and perfectly coordinated way!

The verso ot the Venus

A further analysis : the back side of the Venus (in French).

Last update: 29 December 2006 - link to the verso of the Venus added: 12 February 2012 -

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