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)
It seems a good inspiration for Picasso, better than Poincaré's Science and Hypothesis, like Miller thinks. But Picasso would not necessarily know the work of Poincaré to receive inspiration. This source could be arrived from another protagonist of the birth of the cubism. Indeed, following Maurice Vlaminck, the secret origins of the new artistic "language" had three father: a painter, a poet, and a mathematichian.
I witnessed the birth of cubism, its growth, its decline. Picasso was the obstetrician, Guillaume Apollinaire the midwife, Princet the godfather.(1, 3)Also Jean Metzinger seemed confirm the importance of Princet in the first steps of the cubism:
Maurice Princet joined us often. Although quite young, thanks to his knowledge of mathematics he had an important job in an insurance company. But, beyond his profession, it was as an artist that he conceptualized mathematics, as an aesthetician that he invoked n-dimensional continuums. He loved to get the artists interested in the new views on space that had been opened up by Schlegel and some others. He succeeded at that.(1, 3)And Princet was interested in advanced mathematics, in particular in Poincaré's work and, in general, in non-Euclidean geometries.
It also seems that Princet has made known to the Spanish painter Elémentaire Traité de géométrie à quatre dimensions (1902) by Esprit Jouffret, which were described the hypercubes and other complex polyhedra in four dimensions and it was shown how to play on a two-dimensional plane objects with more than three dimensions.(1)And
Listening to Princet, Picasso realised that geometry offered the language to express the deep meaning of primitive Iberian art, which he was working on at the time. In Les Demoiselles d'Avignon, he depicts one of the demoiselles simultaneously full face and in profile, two perspectives at once, a projection from the fourth dimension. He had gone beyond Poincaré.(6)
The oscillation of planes suggests, but does not represent, a psace that trascends the threedimensional; in other words the forms appear to be space-time symbols. The link between the new painting and concurrent scientific developments was emphasized by the mathematician Maurice Princet.(5)At the other hand, Louis Vauxcelles describes the creation of the cubism like a Goldberg machine!
M. Princet has studied at length non-Euclidean geometry and the theorems of Riemann, of which Gleizes and Metzinger speak rather carelessly. Now then, M. Princet one day met M. Max Jacob and confided him one or two of his discoveries relating to the fourth dimension. M. Jacob informed the ingenious M. Picasso of it, and M. Picasso saw there a possibility of new ornamental schemes. M. Picasso explained his intentions to M. Apollinaire, who hastened to write them up in formularies and codify them. The thing spread and propagated. Cubism, the child of M. Princet, was born.(1, 3)Probably Einstein and Poincaré didn't have a direct importance in the birth of cubism. The Einstein's revolution is simply a natural development of science, starting from the observation that the Maxwell's equations aren't invariant under the action of the Galilei's group (the symmetry group of Schroedinger equation).
Poincaré's work is the natural consequences of Reimann's work, and Jouffret's paper is a son of this research subject.
Princet could have been the role of the nerd: when the friends met in some cafe, Princet simply started to tell about mathematics, the non-euclidean geometry, and the space with four and more dimensions. And this conversations may have sown the cubism in the mind of the artists.
In this sense Miller could be right after all, but the most probably solution of the quest is that Poincaré, Einstein and Picasso (and also Princet!) are simply children of time.
(1) Marco Fulvio Barozzi, Einstein e Picasso, con qualche dubbio (Einstein and Picasso, with some doubts)
(2) Photography school: The birth of cubism
(3) Wikipedia: Maurice Princet
(4) Cubism: A New Vision - The Birth of Cubism
(5) Paul M. Laporte, Cubism and Relativity (pdf) via Stagesof discovery)
(6) Arthur I. Miller Henri Poincaré: the unlikely link between Einstein and Picasso