posted by @ulaulaman about #cubism #PabloPicasso #AlbertEinstein #HenriPoincaré #mathematics #art #relativity

*A great thanks to ***Marco Fulvio Barozzi**: his post^{(1)} *about Miller's book is the main inspiration of my post.*
Yesterday,

on the Guardian,

**Arthur I. Miller**, the author of the book

*Einstein, Picasso: Space, Time and the Beauty that Causes Havoc*, wrote a briefly article in which he resumed his thesis about the connections between

**Poincaré and Einstein**, between

**Poincaré and Picasso** and, for translation, between

**Einstein and Picasso**.

**Henri Poincaré** was one of the most important mathematician of the early XX century: his most important contributions, that have a great impact also in physics, are in group theory and representation theory. His work was indeed important for the birth of the ray representations (the theory was developed in particular by

**Valentine Bargmann** starting from

**Weyl** and

**Wigner**'s works) and basic for special relativity and in particular for general relativity. Poincaré was the first to propose the symmetrical form of the Lorentz transformations, and his work was important for the creation of the Poincaré group, the symmetry group of the general relativity. In particular about the relativity, Poincaré written on his book

*Science and Hypothesis* (1902)

Our Euclidean geometry is itself a sort of linguistic convention; we may state the facts of mechanics in relation to a non-Euclidean space, but this would be a less convenient reference, although legitimate like our ordinary space.^{(1)}

He also defined the

*principle of relative motion* like

the physical impossibility of observing absolute motion.^{(1)}

Two years later he named it

*Principle of Relativity*.

At the other hand, Einstein did not cite Poincaré's works in his paper published in 1905 by

*Annalen der Physik* and only in a conference in 1921 Einstein confirmed his debt to the french mathematician, but only about general relativity and non-euclidean geometry. And this is the only documented connection between Einstein and Poincaré: we must suppose that the two scientists worked indipendetly and also after his first paper Einstein used Poincaré's discoveries in order to develop the mathematical formalism of the general relativity.

Some years later the first Einstein's paper, the cubism was born in France:

A circle of poets and critics, and followers of the philosopher **Bergson**, stood up for cubism in the visual arts. This group became known as the Cubists. The poet and publicist **G. Apollinaire** became the undisputed leader of this movement.^{(2)}

It seems that relativity played a relevant role in the phylosophy of the artistic movement

Like the scientists, the artists has come to recognize thatclassic conceptions of space and volume are limited and one-sided. (...) The presentation of objects from several point of view introduces a principle which is intimately bound up with modern life - simultaenity. It is a temporal coincidence that Einstein should havebegan his famous work (...) with a careful definition of simultaneity.^{(5)}

In this quotation by

**Sigfried Giedion**, the connection was simply casual, only a

*temporal coincidence*, but a lot of art historians think that the connection is not so casual. One of this is

**Paul M. Laporte**, who published two paper about cubism and relativity, and submitted them to Albert Einstein. The great physicist reply with a long letter, in which he concludes:

This new artistic "language" has nothing in common with the Theory of Relativity.^{(5)}

And probably it is so. Indeed in 1903 the

*Introduction to Metaphysics* by

**Henri Bergson** was published. In the book Bergson argued that

human consciousness experiences space and time as ever-changing and heterogeneous. With the passage of time, an observer accumulates in his memory a store of perceptual information about a given object in the external visible world, and this accumulated experience becomes the basis for the observer’s conceptual knowledge of that object. By contrast, the intellect or reasoning faculty always represents time and space as homogenous. Bergson argued that intellectual perception led to a fundamentally false representation of the nature of things, that in nature nothing is ever absolutely still. Instead the universe is in a constant state of change or flux. An observer views an object and its surrounding environment as a continuum, fusing into one another. The task of metaphysics, according to Bergson, is to find ways to capture this flux, especially as it is expressed in consciousness. To represent this flux of reality, Picasso began to make references to the fourth dimension by "sticking together" several three-dimensional spaces in a row.^{(4)}