In French :

Le monde de la nature est ultra fractal
Whatever the scale at which they are considered, fractals have the same degree of complexity. This is for example the case of the coast of Brittany: whatever the scale of the map, it is shredded. Magnify the detail of a fractal reveals a pattern similar to that of the entire drawing.

Examination of a natural object - whether the whole universe or a speck of dust - let appears, when the scale is changed, a series of views of the same complexity - but unlike Fractals they are not similar.

Consider the universe. Its geometry is non-Euclidean (space is curved). At the level of everyday experience the geometry is Euclidean. We find clusters of molecules in the grain dust examined by electron microscopy. Later we will encounter atoms, then the probability waves of quantum mechanics. Farther particles appear. We could go on, we could also select other scales ...

In the thinnest detail of nature lies, as in a fractal, a complexity which is equivalent to that of the whole. However each of the scales follows a peculiar geometry. This adds another kind of complexity to the complexity of the fractal. Nature, being essentially complex, is "ultra-fractal."

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The examination of any physical object - your hand, a pencil, a speck of dust - can never achieve a detailed and complete description. This despairs those whose only absolute knowledge can satisfy the thirst for knowledge, but "absolute knowledge" is a mirage consisting of words that should not be juxtaposed.

The destiny of every human being is the both comic and tragic theater of the dialectic between the ultra-fractal world of physical, human and social nature and the world of values that animate his intentions. . This dialectic is

*the action*.

To act he doesn't need an absolute knowledge: he needs only a

*relevant* knowledge, that is to say a knowledge that is adequate to the action he intends to achieve. This knowledge, being expressed in a finite number of concepts, will always be

*simple* compared to the complexity of nature.

The concepts that are necessary to driving - identifying obstacles and signals, anticipating the behavior of other drivers - select for example, in the complexity of the visual spectacle, a finite number of events. It is the same for all our actions: explicit thought is always simple and it is best to reserve to nature the qualifier "complex" ("complex thought", expression dear to Edgar Morin, is an oxymoron) even if a thought can be

*complicated* in the sense that its acquisition requires a long apprenticeship. By cons the process of elaboration of thought is complex because the brain belongs to the world of nature.

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The contrast between the simplicity of thought and the complexity of nature invites to postulate that this complexity is

*unlimited* (that is to say not only infinite as a right line, but

*without limit*). This hypothesis is an axiom because we can neither prove it nor demonstrate the opposite.

This axiom has the consequence that any mathematical theory, that is to say any logical structure based on a non-contradictory battery of axioms, is the model of a phenomenon belonging to the world of nature: thus the non-Euclidean geometries, created as an exercise in pure logic, provided subsequently a model for the geometry of the cosmos). If this was not the case, this theory would be a limit to the complexity of nature.

A mathematical theory can wait a long time or even never encounter the phenomenon it models because, being not revealed by experiment has revealed, this phenomenon remains is buried in the complexity of nature: but we are sure it exists. This confers to the math a radical realism, with an obvious caveat: if any mathematical theory models a phenomenon, it does not model all phenomena. It follows that the ambition of a "Theory of Everything" in physics is a mirage.