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Mathematics and the Paris Fashion Week

“Charm is a way of getting the answer Yes without asking a clear question.”

Albert Camus

In September, the most anticipated fashion week in the world happens: Paris. But what is the relation with mathematics?

We will see.

Mathematics is like a Swiss knife: it can be employed for everything.

The first evidence of its use is the Lebombo's bone, a monkey's fibula with 29 notches, probably dating to 35,000 BC. Since then, and certainly from here on further, mathematics only continues to evolve. Based on the interpretation of axioms and the most rigorous logic, mathematics has shown to be an incredible tool with evolutionary powers accompanying our development. 

But as per Einstein, could we consider geometry -to deal with almost rigid bodies- the ancestral basis of physics? That is, more than a map, could it be part of the territory?

If we assume that a tool embraces the spirit that originated it, we must return to Heraclitus, who attributed fire to the origin of everything, manifesting itself as matter and movement. For Parmenides, the origin of everything would be the mind because since it would not be possible to know the unknowable, he understood that only what we can conceive in our mind can exist.

Empedocles defines four elements generating existence: earth, fire, air, and water. These elements would combine infinite forms because of two larger forces: love and hatred. Similar to Parmenides, for Anaxagoras, what creates reality is Nous, or our minds tuned in the same range of emanations.

All these centuries of philosophical speculation about what reality is, led to the beginnings of mathematics, with Leucippus and Democritus reaching the conceptualization of the atom.

For Democritus, the atom would be the elementary particle that would allow existence. There would be several types of atoms that could combine and be capable of movement. And this mobility, coupled with the possibilities of grouping, would originate the matter.

Pythagoras was so fascinated and in love with mathematics that he even mixed it with religion, influencing our thinking. So much so, that Plato borrowed from Empedocles the four elements and combined them with the Pythagorean solids. The cube represents the earth; the octahedron, the air; water, the icosahedron, and the tetrahedron, fire. 

Instead of love and hatred, Plato assumed the existence of a fifth element used by God in the formation of the universe. For him, the mathematical condition of polyhedrons, with their three-dimensionality, allowed the formation of matter. The squares mean nothing in reality until they unite in a cube that occupies their place in space, and forms the Earth element. And then, Plato defined quintessence.

Through unusual paths, Plato's places reached Einstein, whose theory of relativity ensured that space is defined by the distribution of matter: geometry originates from matter or becomes created by it.

The physicists and mathematicians who participated in the Interpretation of Copenhagen of quantum mechanics concluded that matter, in the form of elementary particles, is no more than a probability function. That is, if the General Theory of Relativity proves that matter and energy are two manifestations of the same concept, then the elementary particle is much more in the mechanics of the matrices than ever before. Which can only lead us to conclude that one elementary particle is no more elementary than another!

Paris Fashion Week is the event of the year, for a $3 trillion per year industry, or 2% of the world GDP. As in my new book State of Vogue, fashion is directly linked to the needs of the Reptilian portion of our brains, where being beautiful and strong guarantees sex, food, and shelter.

Each of the most sophisticated fashion houses reflects its creator. Although I have an overwhelming passion for Yves Saint Laurent, I put Givenchy on the sill of the sublime.

Tall, handsome, aristocratic, and elegant, Hubert de Givenchy is the quintessence of fashion. Mysterious, philosophical, and provocative, mathematics is the quintessence of nature.

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