Beauty, Esthetics and Proportion.

The profound relationship that mathematics and art share as instruments to explain the world goes back to the dawn of humanity. Ancient philosophers and artists were convinced that mathematics was the true essence of the physical cosmos and that the entire universe, including the arts, could be explained in geometrical terms through numbers. In this way, mathematics appears in all the arts and is related in different ways, and its presence can be found in painting, music, architecture and sculpture throughout history.

For the Greeks, the measure of beauty was based on the harmony of proportions, in addition to a search for symmetries. Polyclitus introduces a mathematical approach to sculpting the human body in his "Canon", a treatise he wrote to document the "perfect proportions" of the anatomy of the male nude. From then on, the belief in beauty, which considered the circle, the golden number (PHI) and other entities as divine, ideal and perfect figures, began to become dogma and to conflict with scientific objectivity.

Kepler used the Platonic solids to design a model to explain the observations and thus calculate, in his heliocentric system inherited from Copernicus, the orbits of the wandering stars in the firmament, which meant a new conflict between aesthetic ideals and facts. Later Newton and his elegant formula of attraction of bodies, with the idealized vision of a universe with linear, periodic and gradual phenomena with simple curves, reduced Nature to laws and inert masses. A reduced and idealized world, full of laws, but alien to interactions, singularities, turbulences and bifurcations. A system full of regular solids that reflected in their sections prefigured linear trajectories and in which the Earth definitively ceased to be the center of the universe; a paradigm that would remain in force until the beginning of the 20th century, until Einstein's Theory of Relativity. This conception of the cosmos would have enormous repercussions on the human understanding of himself and the universe.

Chaos y Order.

The understanding of the universe was molded and reduced to the search for beauty in scientific formulas that induced science to error. Without knowledge from experiments, and without observation to confirm theories, scientists developed laws based on aesthetic criteria; faith in beauty and the obsession to find it became the guide to discover Truth. These old aesthetic ideals had been formalized and science and the ideal of beauty showed us a mechanical universe that worked like a perfect clockwork mechanism.

But our senses continued to find proportions and beauty in Nature; in the turbulence of the waters of the rivers, in the clouds, mountains, lightning, branches of plants and trees... that seemed not to obey any order or non-casual model, a beauty full of chaos and irregularity, disorder and randomness in harmony with other proportions, dynamic processes that gave rise to physical forms with a coexistence between order and disorder.

The idea of Chaos was very old, since ancient Egypt it was well defined. The Greek philosopher Epicurus, influenced by Democritus, already formulated a theory by which he understood that every atom tends spontaneously to deviate from equilibrium (repose) and expounded a theory on the genesis of turbulence (whirlwind). But for a complete understanding of a chaotic Nature, with self-organized non-linear dynamics and processes, it would take many centuries.

Nature was left out because of its complexity, its chaos, and progress began to be based on scientific conjectures, with endless tension between models and theories, predictive capacity and rational understanding. Throughout history, this systematic confrontation in the mathematical and scientific world has motivated the progress of thought and knowledge, but it has also been an enormous burden. Euclid's axioms were in force for almost 2,000 years until new models of an alternative, coherent and stable geometry began to emerge in the 18th century. And one of the major breakthroughs came when Poincaré applied his method to the three-body problem (the dynamical system formed by the Earth, the Moon and the Sun) of ancient Greece, and demonstrated that in the stationary model of the universe, the simplest event in the initial state can bring the system to a chaotic "order", what we would later come to know as a strange attractor.

Fractals.

From then on and with the development of infinitesimal calculus, irrational numbers began to appear in unsuspected places; Cantor's set theory gave rise to an expansion in mathematics that shaped new concepts and a new handling of mathematical infinity. All this provoked considerable progress and original schemes of thought in the mathematical, scientific and intellectual world.

The discovery of these chaotic systems and Fractal Geometry comes to revise what in the last millennia we have called Order, and the traditional idea we had of Chaos. With the help of Fractal Geometry, chaos can be described, determined and formalized, and as a result shows us geometries similar to the physical world, with synergies akin to those arising from Nature and random loops that feed back into each other, a dynamic system in constant motion full of infinite bifurcations and a rich inter-connected internal structure.Apparent chaotic movements with dynamics far from precise cycles and linear processes, systems far from equilibrium where, in an exchange with the environment, they are reconducted to generate new forms of order. A new paradigm that harmonizes human knowledge with Nature and with its own essence.

The great paradox of this long journey, of this our history as a "mathematical" civilization, where Order was bounded and Chaos banished, demonstrates both the solidity of hundreds of mathematical and scientific laws for centuries, and also reveals us about the firmness of what we call "reality", but above all it teaches us about absolute truths and about what can never be deciphered by logic or reason.The finding and the final evidence of what is hidden under the appearance of Chaos is surprising and fascinating; the very seed of the Fractals, the dynamic traces of Chaos, contains and envelops in its most intimate part the PI Number and the Golden Number. Beautiful and deep contradictions.