"The most beautiful thing we can experience is the mysterious. It is the source of all true art and all science. He to whom this emotion is a stranger, who can no longer pause to wonder and stand rapt in awe, is as good as dead: his eyes are closed."

Albert Einstein

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Saturday, 7 February 2015

The "fourth dimension" in Arts and Sciences

The "fourth dimension" in Arts 

 Cubism

FROM: 

A phrase coined by Guillaume Apollinaire to describe the particular style of the cubists.

At the start of the 20th century there were two popular interpretations of the fourth dimension. One was that it is time. This is fairly easy to imagine, and remains a common meaning for the term today. The second is that the fourth dimension is another spatial dimension. This is much harder, if not impossible, to visualize. Nevertheless, several illustrators attempted to. One of the most popular illustrations of this was the four-dimensional hypercube. Just as we can form a cube by folding a cross-shaped piece of paper consisting of six squares, so it was believed one could form a four-dimensional "hypercube" by folding a similar arrangement of seven cubes. (see Crucifixion, Dali, 1954) A mathematician, E. Jouffret, attempted to depict four-dimensional objects by drawing their projections on a two-dimensional plane.

These representations were fairly well established when Picasso and Braque invented cubism. While it would be incorrect to claim that they formed the basis of cubism, it would be equally incorrect to say they had no influence on it. In the years before he started cubism, Picasso met regularly with a group of friends who called themselves la bande à Picasso. Guillaume Apollinaire, a member of la bande describes the influence of the fourth dimension on cubism in his book Les Peintres Cubistes.
"Until now, the three dimensions of Euclid's geometry were sufficient to the restiveness felt by great artists yearning for the infinite... The new painters do not propose, any more than did their predecessors, to be geometers. But it may be said that geometry is to the plastic arts what grammar is to the art of the writer. Today, scholars no longer limit themselves to the three dimensions of Euclid. The painters have been led quite naturally, one my say byintuition, to preoccupy themselves with the new possibilities of spatial measurement which, in the language of modern studios, are designated by the term fourth dimension."1
In this statement, he recognizes the graphical representation of the fourth dimension in cubist art, and also the mental influence. The fourth dimension is representative of the infinite possibilities that the cubists sought. Apollinaire reaffirms this in La Peinture nouvelle: "The art of the new painters takes the infinite universe as its ideal, and it is to the fourth dimension alone that we owe this new norm of the perfect..."2Another member, Maurice Princet had extensively studied Poincaré's writings and is widely recognized as having exposed the cubists to his work. Poincaré's book l'Science et l'Hyposthese, written in 1902, popularized four-dimensional geometry and is often linked to the cubists work through Princet. First hand accounts tell of Princet discussing problems of perspective and simultaneously representing objects from multiple viewpoints. This would be a consequence of the fourth dimension being a spatial one which acts as an "astral plane", from which an object of the usual three dimensions can be viewed from all sides simultaneously. (Just as in our three dimensional world we can see the entirety of a two dimensional object at once).

We can see this effect quite clearly in Picasso's paintings. In Les Demoiselles d'Avignon, 1907, the crouchingwoman's body is seen from behind while her head is seen from the front. Similarly, the two central standing figures are shown in a frontal view, but their noses are painted in profile. The painting also shows influences of Jouffret's projections of a four-dimensional ikosatetrahedroid on a plane. The rightmost woman's upper body fits into a diamond grid that is extremely similar to Jouffret's projections of 1903. (This is more clearly seen in Standing Nude with Joined Hands (Study of Proportions), 1907.) The faceting which has become synonymous with Picasso's name is also very similar to Jouffret's drawings, in which he superimposes his projections on top of each other in an attempt to display multiple sides of a polyhedron simultaneously. Though this may have been more a similarity in appearance than a direct depiction of the fourth dimension, it was certainly a rejection of three-dimensional perspective.

Later cubists, particularly Metzinger and Gleize show an even greater influence from Princet's lectures. Unlike Jouffret, who conceded to project his four-dimensional figures into two dimensions, Metzinger believed that the mind was capable of perceiving all four at once. In a style similar to Picasso's he shows figures from various perspectives in the same painting, though often with less fragmentation than Picasso used. In Le Gouter (1911), he varies perspectives as the viewer looks from one side of the woman's face to the other. The left side of her face is seen in a frontal view, her nose in a three-quarters view, and her right eye in profile. Of even greater interest is the bowl from which she eats. The left side of it is seen from the side, while the right side is seen from above. This is almost exactly the same problem posed by Princet in 1910:

"You represent by means of a trapezoid a table, just as you see it, distorted by perspective, but what would happen if you decided to express the table as a type? You would have to straighten it up onto the picture plane, and from the trapezoid return to a true rectangle. If that table is covered with objects equally distorted by perspective, the same straightening up process would have to take place with each of them. Thus the oval of a glass would become a perfect circle."3
Princet, in turn, took this from Poincaré, who writes, "We can even take of the same four-dimensionalfigure several perspectives from several different points of view. We can easily represent to ourselves these perspectives, since they are only three dimensions. Imagine that the various perspectives... succeed one another..."4 In 1880, a mathematician, W.I. Stringham, attempted to illustrate such perspectives. In 1910, two painters also made use of Stringham's work. The vase in Gleizes's Woman with the Phlox and the fruit in Le Fauconnier's Abundance bear a striking resemblance to Stringham's figures.

The futurists also used the term fourth dimension, but not in the same way the cubists did. While the cubist fourth dimension was spatial, the futurists' was temporal. Boccioni describes this in his Plastic Dynamism (1913).
"...Instead of the old-fashioned concept of sharp differentiation of bodies, instead of the modern concept of the Impressionists with their subdivision, their repetition, their rough indications of images, we would substitute a concept of dynamic continuity as unique form. And it is not by accident that I say form and not line, since dynamic form is a species of fourth dimension in painting and sculpture, which cannot exist perfectly without the complete affirmation of the three dimensions that determine volume: height, width, depth."5
This "dynamic form" he writes about is easily seen in his work. In The City Rises, 1910, the elongatedbrushstrokes create a blurred motion that is similar to the kind created when a photograph is taken of a moving object. His sculpture Unique Forms of Continuity in Space, 1913 perfectly captures the essence of motion, as the figure seems to liquefy and move forward through itself. Later futurist works, most notablyBalla's "dynamisms" show a scene over the course of a period of time with much less distortion, and clearly demonstrate the idea of the fourth dimension being time. The futurist method was so effective that even Picasso reconsidered the possibilities of the fourth dimension. Around the same time as Balla's paintings, it was reported by Kahnweiler that Picasso "considered setting his pictures in motion using a clockwork mechanism or producing a series of works which could be shown in rapid succession."6

Marcel Duchamp also used the Fourth Dimension (and other topics from Poincaré's books). In 1911 he began meeting regularly with Princet, who, as mentioned above was a leading proponent of art of the "new geometries". A good example of the fourth dimension in his work is The Bride Stripped Bare by Her Bachelors, Even, 1915-1923 (often called Large Glass) In this work, Duchamp's goal was to depict the bride as four-dimensional, and the bachelors in three dimensions. The shapes which make up the bachelors' machine are textbook examples of geometric solids seen in one-point perspective. The bride, however, is composed of parabolic and hyperbolic forms which Duchamp considered idealized and typical of a four dimensional object's projection in three dimensions. Duchamp arrived at the fairly logical conclusion that because a three-dimensional object has a two-dimensional shadow, a four-dimensional object must have a three-dimensional shadow. This is the same reasoning that Jouffret used in his projections, and these were certainly Duchamp's inspiration. Although it is not readily apparent in Large Glass, Duchamp did extensive research into four-dimensional perspective. He likens the three-dimensional projection to "the method by which architects depict the plan of each story of a house"7 and continues to discuss how the four-dimensional object is constructed: "A 4-dim'l figure is perceived (?) through an ∞ of 3-dim'l sides which are the sections of this 4-dim'l figure by the infinite number of spaces (3-dim'l) which envelope this figure."8Though these methods cannot be practically applied, they show the devotion which Duchamp gave to this idea. Some scholars have even gone as far as to claim that Duchamp's famous "ready-mades" have their roots in Poincaré's work. In an essay on mathematical thought, Poincaré describes how the unconscious mind cannot supply "ready-mades", but that it does constantly sift through ideas which the conscious mind can then select from. A related suggestion is that the photos he took of these ready-made objects from various perspectives were the result of his fascination with projecting higher-dimensional objects intolower-dimensional spaces.

The spread of the fourth dimension continued, and the depiction of it became more abstract as art did. Thede stijl artists in Holland interpreted the fourth dimension as negative space. Van Doesburg used shades of gray to represent negative space, and the primary colors as positive space. This interpretation differs from earlier ones because it does not try to represent the fourth dimension a as a physical reality, but conceptually. Mondrian's appreciation for mathematics led him to his unique style of representing the fourth dimension. He believed that his use of colored planes "by both their dimensions (line) and values (color), can express space without the use of visual perspective."9 By eliminating perspective while maintaining the appearance of a three dimensional space, Mondrian has indirectly represented the fourth dimension. In a sense, color was Mondrian's fourth dimension. Van Doesburg continued using the fourth dimension after Mondrian abandoned it. He did this in a sort of natural continuation of Mondrian's work, by combining colored planes in three dimensional compositions. In Color Construction in the Fourth Dimension of Space-Time, 1924 he draws colored planes in perspective to create the four dimensional view which Mondrian denounced in 1918. Around this time, Van Doesburg also began experimenting with the fourth dimension as it was interpreted in Einstein's relativity theory, which was confirmed in 1919 and quickly gained popularity. Van Doesburg also applied the fourth dimension to architecture. In a plan for a house which he drew in 1923, he combined his three-dimensional colored planes with the idea of a hypercube. In this way he combined Mondrian's abstract notion of the fourth-dimension with the original, concrete notion of it. Van Doesburg explains:
"The new architecture is anticubic, in other words, its different spaces are not contained within a close cube. On the contrary, the different cells of space (balcony volumes, etc., included) develop excentrically, from the center to the periphery of the cube, so that the dimensions of height, width, depth, and time receive a new plastic expression. Thus, themodern house will give the impression of floating, suspended in air, in opposition to the natural force of gravity... The new architecture takes account not only of space but also of time as an architectural value. The unity of space and time gives architectural vision a more complete aspect."10
By eliminating gravity, Van Doesburg eliminated the idea of an absolute coordinate system in architecture. No longer was one direction defined as "down" and opposed by "up", nor did the words "left" or "right" have meaning. All directions were equal, and only their relative orientation to each other mattered. The complex shape of his buildings also required motion in time to view. Van Doesburg was also the only majorartist of the time to embrace Einstein's relativity theory. While it may seem natural the popularization of relativity theory would lead to a popularization of the fourth-dimension in art, the actual result was just the opposite.

Why? Well it's hard to say. The driving goal of using the fourth dimension had always been to make an art form that was somehow more ideal, more perfected than previous works. With the realization of the fourth dimension, this idea had in some ways been confirmed, but the thrill of pursuing it was lost. Another thing that should be mentioned is the frequent interpretation of relativity as the basis for cubism. Picasso denied any scientific roots to cubism but his recollections often contradict history as well as each other. Einstein, however, flat out states, "This new artistic ‘language' (of cubism) has nothing in common with the Theory of Relativity."11 He seems to reject any connection between science and art, stating, "In science, the principle of order which creates units is achieved through logical connection while, in art, the principle of order is anchored in the unconscious."12

Works Cited:
1 Apollinaire, Les Peintres Cubistes, 1912, p. 15. Cited in Henderson, The Fourth Dimension and Non-Euclidean Geometry in Modern Art, 1983, p. 75
2 Apollinaire, La Peinture Nouvelle. Cited in Henderson, The Fourth Dimension and Non-Euclidean Geometry in Modern Art, 1983, p. 75.
3 Delaunay, 1957, p. 146. Cited in Miller, Einstein Picasso, 2001, p. 114.
4 Poincaré, La Science et l'Hypothese, 1902, p. 89
5 Boccioni, "Plastic Dynamism", 1913. in, Futurist Manifestos, ed. Apollonio, trans. Brain, Flint, Higgitt, Tisdall, p. 93
6 Wolter-Abele, "How Science and technology changed art", History Today vol.46 no.11 , November 1996, p. 64
7 Duchamp, A l'infinitif, 1966. Cited in Henderson, The Fourth Dimension and Non-Euclidean Geometry in Modern Art,1983, p. 139.
8 Ibid.
9 Mondrian, "The New Plastic Painting", 1917. In The New Art – The New Life: The Collected Writings of Piet Mondrian, 1986, ed., trans. Holtzman, James, p.38
10 Van Doesburg, "L'Evolution de l'architecture moderne". Cited in Henderson, The Fourth Dimension and Non-Euclidean Geometry in Modern Art,1983, p. 325
11 Einstein, letter to Paul Laporte, in Laporte, "Cubism and Relativity with a Letter of Albert Einstein", from Leonardo, vol.21 no. 3, 1988, p. 313.
12 Ibid. 

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From The Popular Culture of Modern Art: Picasso, Duchamp, and Avant-Gardism by Mr. Jeffrey Weiss (Yale University Press - 1994) 
FROM:

Within the cubist or hermetic triangle of geometrical science, esoteric science and symbolism, lies the article "Qu'est-ce que... le 'Cubisme'.V* published in December 1913, by initie Maurice Raynal. Raynal explains cubism to the general audience of the magazine Comoedia illustrc by comparing cubists to pnmitifs such as Giotto, whose "mysticism" influenced them to "think painting rather than see it" - to paint following "that remarkable idea of conception that the Cubists have revived for a different
p 81:
purpose... The Cubists, no longer having the need to paint the mysticism of the primitifs* have received from rhcir century a sort of mysticism of logic, of science and of reason," which has been "amplified and rigorously codified under the well-known name of the fourth dimension*1*9

Theories of the fourth dimension had been applied to cubism by critics and artists since 1911, when Apollinaire publicized the term in his speech for the Exposition d'Art Contemporain, first published in 1912. Similarly, Raynal's dichotomy of perceptual and conceptual painting was, as we have seen, a commonplace of popular, often negative, cubist criticism; it too had been disseminated most recently within the community by Apollinaire. who invented the label "Cubisme Scientifique" for one of his four major categories of cubist painting.'51

By 1913, the fourth dimension was well-integrated into the specialist and popular literature on cubism. It is significant that, four months after Raynal's article, Roger Allard denounced elaborate theorizing, that "dreadful scientifico-esthetic vocabulary," as a plague of avant-garde group painting. In particular, he singled out the fourth dimension, describing it as a product of symbolist and cubist discussions at the Closerie des Lilas, the café which Allard himself attended:
Since the time when painters frequented the Closerie des Lilas and some other highly literary popincs* they have been afraid of not appearing cultivated enough. [As a justification for] the slightest plastic initiative, often quite timid in its audacity… it was necessary to call mathematics and geometry to the rescue. It became good form ro speak familiarly of the geometry of Lobachinsky or the theories of Virchow, and from Montmartre to Montparnasse, there was a desperate dance of logomachy on the wire of the fourth dimension.1″
The most developed treatment of fourth dimensional mathematics during the period was Gaston de Pawlowski’s fantasy “Voyage au pays de la quatrième dimension,” published as a serial and a book in 1912.1″ As a contributor to Comoedia of which he was editor-in-chief, Pawlowski had several occasions between 1911 and 1914 in which to address cubist art directly, both as painting at the salons and as the subject of two books, Du Cubisme and Les Peintres cuhistes. As Linda Henderson has shown, Pawlowski appears to make no connection in his writings between the fourth dimension and cubist pictorial space (even after Apollinaire explicitly discussed the fourth dimension in Les Peintres cubistes). Not especially impressed with cubist pictures themselves, he calls cubism ridicule and incompréhcesible. None the less, he approves of cubists as originates* recognizable by a family resemblance of style; and he admits that the works might at least prove ro be a catalyst for positive change in the pictorial arts. 1M


p 154:
Princet’s influence, at least according to Duchamp’s account, was similarly conditioned by this fascination for the kind of erudition that falls somewhere between positivistic bourgeois sincerity and outrageous hoax. “We weren’t mathematicians at all,” Duchamp explained, “but we really did believe in Princet. He gave the illusion of knowing a lot of things.”

p158:
critic Jacques Rivière on cubist science in May 1912:
There is nothing for which one should be more cruelly punished than having taken for granted the intelligence of a painter. As soon as you think you’ve confirmed his position by explaining the sense of his research, he inflicts upon you an explosive denial and makes everyone know that you’ve understood nothing of his business… What good does it do to critique their works? I would only like to describe their state of spirit. They pretend to think; they would have you believe that they are theoreticians; for them intelligence dominates sensibility. They feel that in order to be new, they must pose as intellectuals… But in their brain there is nothing; consequently, an idea dilates there like the gas in the cylinder of a motor, expanding to fill the available space, inflating and carrying them forward.
Among the repertory of cubist pseudo-ideas, Rivière includes “representing objects in the ‘four dimensions of esoteric space*.”250
————–

DUCHAMP: [...] Paris was very divided then, and Braque’s and Picasso’s neighborhood, Montmartre, was very much separated from the others. I had the chance to visit it a little at the time, with Princet. Princet was an extraordinary being. He was an ordinary mathematics teacher in a public school, or something like that, but he played at  being a man who knew the fourth dimension by heart. So people listened. Metzinger, who was intelligent, used him a lot. The fourth dimension became a thing you talked about, without knowing what it meant. In fact, it’s still done.
(Note: cfr Apollinaire on 4th dimension!!!)
from “Dialogues with Marcel Duchamp” By Pierre Cabanne
Maurice PRINCET : Autoportrait - encre et aquarelle - 1928
Maurice Princet (1875 – October 23, 1973) was a French mathematician and actuary who played a role in the birth of cubism. He was an associate of Pablo Picasso, Guillaume Apollinaire, Max Jacob, Jean Metzinger, and Marcel DUCHAMP. He is known as “le mathématicien du cubisme” (“the mathematician of cubism”). Princet is credited with introducing the work of Henri Poincaré and the concept of the “fourth dimension” to the cubists at the Bateau-Lavoir. 

Princet brought to Picasso’s attention a book by Esprit Jouffret, Traité élémentaire de géométrie à quatre dimensions (Elementary Treatise on the Geometry of Four Dimensions, 1903),[5] a popularization of Poincaré’s Science and Hypothesis in which Jouffret described hypercubes and other complex polyhedra in four dimensions and projected them onto the two-dimensional page. Picasso’s sketchbooks for Les Demoiselles d’Avignon illustrate Jouffret’s influence on the artist’s work.

From Princet (french wiki)
The contribution of Princet to the adventure of Cubism was also raised by Louis Vauxcelles and André Salmon, who made him the initiator of the fourth dimension with painters. Yet, as noted by Jacob, "there is very little math in Cubism. Obviously, we could apply the arithmetic parabols but assuming that the Princet had known them, Picasso would had been at pain in applying them." (Letter from Jacob to Salmon, in "Max Jacob et Picasso").

Located in Montmartre, Princet organizes with his wife Alice evenings where Apollinaire, Picasso and Jacob share various thoughts and indulge in the pleasure of opium and hashish . He became close to Jean Metzinger , and then took part in the meetings of Puteaux . By his knowledge of mathematics , he is certainly a useful intellectual support to painters who, by destroying perspective, materialize space subject to incomprehension. He is probably the cause of rapprochement of their works with Einstein 's Theory of Relativity, which causes Apollinaire to speak of "fourth dimension ." It is likely that by sharing his knowledge to painters , he narrows their research , including those of Picasso who, from 1912 , make to cohabit several spaces (both Cubist and perspective ) . But Princet certainly has more affinity with the group of the Golden Section , then enthusiast about sciences and which feels the need to justify scientifically the directives of Cubism.
+ Maurice Princet , le mathematicien du Cubisme  (amazon) "Maurice Princet. le mathématicien du cubisme"
by Marc Décimo- Published by Echoppe, 2007
——————-

 >< Einstein’s general relativity (same time!)


"Just as a non-Euclidean world, one can imagine a four-dimensional world,"  Henri Poincaré wrote in his 1902 La Science et l’Hypothèse.
Culture and sensitivity of Poincaré allowed him to bring the exact sciences research to a lay audience without 'popularizing', but in expressive and visual poetic terms. His conception of space as a joint representative experience of visual space, tactile and motor has call to the artists. 
Even though, as such, the curved non-Euclidean space  hardly appears in Cubist painting, the new geometries have been at the heart of the intellectual concerns of artists of the early twentieth century in France and Russia.
Painting and new geometries

The painter " brings his body ," said Valery [ quoted by Merleau-Ponty in L'Œil et l'esprit] , it is by "offering his body that the painter changes the world in painting." Friend of Alfred Jarry (La pataphysique, Ubu) , and readre of  Herbert George Wells (The Time Machine), Valéry was a passionate admirer of Poincaré. He had even started studying mathematics in 1890 and his notebooks between 1894 and 1900 were filled with equations.

Regarding "matter", for Poincaré , one of the most amazing discoveries physicists have announced in recent years is that the matter does not exist.

This statement puzzled painter Matisse who wrote to Derain in 1916 about "Science and Hypothesis " : "Have you read this book ? There are some assumptions in a breathtaking audacity, in particluar about the destruction of matter. Movement exists only by the fact of the destruction and reconstruction of matter. "

But it is especially the idea of ​​the "fourth dimension", a possible mode of theoretical understanding of the new Cubist painting, which will fascinate the art world.

What we have to to remember is the highly social aspectof Cubism. Everyone knows each other, ideas circulate and take mathematical, literary, pictorial forms. However, these ideas must be centered around those of Poincaré's. It is he who gives for the first time this distinction between a geometric space and representational space. This may explain not only the birth of Cubism in France , but also a minimum of public ready to receive it.

However, Einstein's theories are unlikely to have influenced cubism as they are known in France relatively late . The development of the theory of relativity itself spans over a fairly long period.
The fourth dimension and Cubism

"They say Matisse was the first to use this expression ("fourth dimension", note) before Picasso's first Cubist researches. "
That is what Italian Futurist painter Gino Severini wrote in 1917 about the fourth dimension in the Mercure de France. Matisse, who read a treatise entitled Essai sur l’Hyperespace would have shouted: "Oh! but this is but a popular book! ". (This is Metzinger who quotes this anecdote in Le cubisme était né  and he so concludes: "Ultimately, it demonstrated that for large tan (fauve), the time when the ignorant painter was running, carried by the wind, looking for a beautiful pattern, was over for good.")

****

En 1909, Charles Camoin écrit à Matisse à propos de son art :
« Quelle profession honteuse à une époque de si grandes spéculations et après la découverte de la 4e dimension. »
Si Matisse peut, dès les premières années du siècle, estimer à sa juste valeur un ouvrage sur les nouvelles géométries et s’entretenir de la 4e dimension, c’est en effet certainement parce qu’il connaît les publications scientifiques qui font autorité dans le Paris d’avant-guerre à savoir, celles d’Henri Poincaré.

Notamment La Science et l’Hypothèse, parue en 1902, dont les deux chapitres Les géométries non-euclidiennes etL’espace et la géométrie décrivent de façon simple et précise quelques notions essentielles sur les géométries non-euclidiennes, les géométries à n-dimensions, et la quatrième dimension. Mais la force de cet ouvrage réside dans sa description de la différence entre l’espace géométrique qui est une convention (la géométrie n’est pas vraie, elle est avantageuse), et l’espace représentatif à composantes visuelle, tactile, motrice.

C’est le mathématicien Maurice Princet, qui fréquentait les cercles cubistes, qui le premier établit une analogie formelle entre l’effet de facettes obtenues dans les perspectives cavalières des seize Octahédrons d’un Icosatetrahédroide de Jouffret et le Portrait cubiste d’Ambroise Vollard par Picasso (1910). Mais Picasso a toujours énergiquement nié avoir jamais discuté mathématique avec Princet (interview à Alfred Barr, 1945). Le collectionneur et marchand d’art Daniel-Henry Kahnweiler, dans son livre sur Juan Gris, 1947, précise à propos de Princet “qu’il n’ajamais eu la moindre influence sur Picasso ou Braque, pas plus que sur Gris, qui avait suivi ses propres études de mathématiques.”
Mais l’idée de la quatrième dimension dans le cubisme a incontestablement une origine mathématique, celle de Poincaré. Comment s’est-elle transmise ?

En 1918, Louis Vauxcelles se moquait de Princet et de la façon dont s’était répandue l’idée de la quatrième dimension en art :
«Il est de notoriété publique dans les ateliers de Montparnasse, et partout ailleurs, que l’inventeur du cubisme était Max Jacob. Nous le croyions nous-mêmes. Mais il est nécessaire de rendre son honneur à César, et César, dans ce cas précis, s’appelle M. Princet. C’est, nous le pensons, la première fois que ce nom est imprimé dans les annales du cubisme. M. Princet est un “agent d’assurance” et très fort en mathématiques. M. Princet calcule comme Inaudi. M. Poincet (sic) lit Henri Poincaré dans le texte. M. Princet a étudié à fond la géométrie non-euclidienne et les théorèmes de Rieman, desquels Gleizes et Metzinger ont parlé si négligemment. Ainsi, un jour, M. Princet rencontra M. Max Jacob et lui confia une ou deux de ses découvertes sur la quatrième dimension. M. Jacob en informa l’ingénieux M. Picasso, et M. Picasso y vit la possibilité de nouveaux schémas ornementaux. M.Picasso expliqua ses intentions à M. Appollinaire qui se hâta de les mettre en formules et de les codifier. La chose proliféra et se propagea. Le cubisme, enfant de M. Princet était né. »
En fait Max Jacob fait mention dans un article fin 1915 pour un périodique américain “291″ de sa rencontre avec Galani dont la tentative d’expliquer la quatrième dimension fut convertie par Max Jacob le religieux en une explication des apparitions et disparitions du Christ ressuscité.
Matisse, dans une lettre à Derain en 1916, parle de Galani qui vient juste de lire La Science et l’Hypothèse, livre dans lequel il a trouvé l’origine du cubisme (Matisse ajoute trois points d’exclamations entre parenthèses).
Gleizes et Metzinger avaient probablement étudié l’œuvre de Poincaré d’assez près. Mais, d’une part, les discussions avec Princet, et d’autres part des lecture possibles de théosophes citant Poincaré comme Revel dans “L’esprit et l’espace: La Quatrième dimension” ont pu amener une certaine confusion dans la façon dont le lien entre les nouvelles géométries et le cubisme s’établissait.
Pour Gleizes et Metzinger il existe deux sortes d’espaces géométriques, l’espace euclidien et l’espace non-euclidien. L’espace euclidien pose l’indéformabilité des figures en mouvement. L’espace non-euclidien est celui auquel il convient de rattacher l’espace des peintres. Gleizes et Metzinger préconisent à ce propos d’étudier les nouvelles géométries :
« Si nous devions rattacher l’espace pictural à une géométrie particulière, nous devrions nous référer aux savants non-euclidiens; il nous faudrait étudier, en fin de compte, certains des théorèmes de Rieman (sic). »
En fait, malgré les préoccupations intellectuelles des artistes au sujet des nouvelles géométries, l’espace courbe non-euclidien apparaît rarement dans la peinture cubiste sauf dans des œuvres comme l’Estaque, par Braque et Dufy (1908), les Tours Eiffel de Delaunay (1910-1911), ou le Paysage cubiste de Metzinger (1911), où il semblerait que celui-ci se soit appliqué à mettre en pratique consciencieusement les principes de déformation de l’espace courbe non-euclidien.
Duchamp a déclaré à Pierre Cabanne : « C’est Roussel qui, fondamentalement, fut responsable de mon Verre, La Mariée mise à nu [...], ce furent ses Impressions d’Afrique qui m’indiquèrent dans ses grandes lignes la démarche à adopter » et qu’ayant lu les « choses de ce Povolowski » (sic), il a simplement « pensé à l’idée d’une projection, d’une quatrième dimension invisible [...], autrement dit que tout objet de trois dimensions, que nous voyons froidement, est une projection d’une chose à quatre dimensions, que nous ne connaissons pas ».
Visual Space. — First of all let us consider a purely visual impression, due to an image formed on the back of the retina. A cursory analysis shows us this image as continuous, but as possessing only two dimensions, which already distinguishes purely visual from what may be called geometrical space. On the other hand, the image is enclosed within a limited framework; and there is a no less important difference: this pure visual space is not homogeneous. All the points on the retina, apart from the images which may be formed, do not play the same role. The yellow spot can in no way be regarded as identical with a point on the edge of the retina. Not only does the same object produce on it much brighter impressions, but in the whole of the limited framework the point which occupies the centre will not appear identical with a point near one of the edges. Closer analysis no doubt would show us that this continuity of visual space and its two dimensions are but an illusion. It would make visual space even more different than before from geometrical space, but we may treat this remark as incidental. However, sight enables us to appreciate distance, and therefore to perceive a third dimension. But every one knows that this perception of the third dimension reduces to a sense of the effort of accommodation which must be made, and to a sense of the convergence of the two eyes, that must take place in order to perceive an object distinctly. These are muscular sensations quite different from the visual sensations which have given us the concept of the two first dimensions. The third dimension will therefore not appear to us as playing the same role as the two others. What may be called complete visual space is not therefore an isotropic space. It has, it is true, exactly three dimensions; which means that the elements of our visual sensations (those at least which concur in forming the concept of extension) will be completely defined if we know three of them; or, in mathematical language, they will be functions of three independent variables. But let us look at the matter a little closer. The third  dimension is revealed to us in two different ways by the effort of accommodation, and by the convergence of the eyes. No doubt these two indications are always in harmony; there is between them a constant relation; or, in mathematical language, the two variables which measure these two muscular sensations do not appear to us as independent. Or, again, to avoid an appeal to mathematical ideas which are already rather too refined, we may go back to the language of the preceding chapter and enunciate the same fact as follows: — If two sensations of convergence A and B are indistinguishable, the two sensations of accommodation A’ and B’ which accompany them respectively will also be indistinguishable. But that is, so to speak, an experimental fact. Nothing prevents us is priori from assuming the contrary, and if the contrary takes place, if these two muscular sensations both vary independently, we must take into account one more independent variable, and complete visual space will appear to us as a physical continuum of four dimensions. And so in this there is also a fact of external experiment. Nothing prevents us from assuming that a being with a mind like ours, with the same sense-organs as ourselves, may be placed in a world in which light would only reach him after being passed through refracting media of complicated form. The two indications which enable us to appreciate distances would cease to tie connected by a constant relation. A being educating his senses in such a world would no doubt attribute four dimensions to complete visual space.
Poincare is wrong: this “illusion” does NOT come from our senses but our BRAIN!!!
  • // same error as Descartes! Yes, our perceptions come via our senses BUT this the brain which makes sense of it all! Besides eyes don’t need to be two to see. They already see in perspective! Stereoscopic vision adds the depth info to this projection.
  • Nietzsche: time = chaos (Heraclitus) and dominates eveything (so >< images, order, Apollo)
  • Hegel: time = sequential, logical/ rational (zeitgeist), order -> historic determinism (Marx/Engels)

Science
References to Dalí in the context of science are made in terms of his fascination with the paradigm shift that accompanied the birth of quantum mechanics in the twentieth century. Inspired by Werner Heisenberg’sUncertainty Principle, in 1958 he wrote in his “Anti-Matter Manifesto“: “In the Surrealist period, I wanted to create the iconography of the interior world and the world of the marvelous, of my father Freud. Today, the exterior world and that of physics has transcended the one of psychology. My father today is Dr.Heisenberg.”[63]
In this respect, The Disintegration of the Persistence of Memory, which appeared in 1954, in hearkening back to The Persistence of Memory, and in portraying that painting in fragmentation and disintegration summarizes Dalí’s acknowledgment of the new science.[63]
Jouffret’s Traité élémentaire de géométrie à quatre dimensions.
The book, which influenced Picasso, was given to him by Princet.
Francis Picabia: Portrait de Poincaré (1927-28); collage.
Pablo Picasso: Ambroise Vollard (1915)

On cubism and pseudo-science 




DUCHAMP

SEQUENTIALITY IN ART

Cinema's influence on Braque and Picasso
When Picasso and Braque Went to the Movies  = also a FILM (2008)
This was rejected and Duchamp went into a war against the art establishment >>> urinal!


Duchamp’s interest in plotting the static phases of a moving subject has often been compared to the work of the Italian Futurists, who were obsessed with notions of velocity. Another precedent for the work can be found in the time-lapse photography of Étienne-Jules Marey in France and Eadweard Muybridge and Thomas Eakins in the United States. Muybridge’s book Animal Locomotion, of 1887, which included a sequence of twenty-four images of a naked woman descending a flight of stairs, possibly served as a source for Duchamp s landmark painting.
————-
1832 Joseph Plateau and sons introduce the Phenakistoscope. Like other toys of its kind, the Phenakistoscope was one of the more successful illusion toys. Pictures on one disc viewed through slots in the other, appeared to move when the two were spun and viewed in a mirror.
1834 Another illusion toy – the Zoetrope was introduced by William George Horner. The Zoetrope used the same principle as Plateau’s Phenakistoscope but instead of discs the pictures and slots are combined in a rotating drum. Zoetrope’s were widely sold after 1867. FROM
Wiki: The earliest known zoetrope was created in China around 180 AD by the inventor Ting Huan. The modern zoetrope was invented in 1833 by British mathematician William George Horner. He called it the “daedalum“, most likely as a reference to the Greek myth of Daedalus, though it was popularly referred to as “the wheel of the devil“. The American developer William F. Lincoln named his toy the “zoetrope”, meaning “wheel of life“. Almost simultaneously, similar inventions were made independently in Belgium by Joseph Antoine Ferdinand Plateau (thephenakistoscope) and in Austria by Simon von Stampfer (the stroboscope).
The praxinoscope was an improvement on the zoetrope that became popular toward the end of the 19th century. The praxinoscope was an animation device, the successor to the zoetrope. It was invented in France in 1877 by Charles-Émile Reynaud. In 1889 Reynaud developed the Théâtre Optique, an improved version capable of projecting images on a screen from a longer roll of pictures. This allowed him to show hand-drawn animated cartoons to larger audiences, but it was soon eclipsed in popularity by the photographic film projector of the Lumière brothers.
NOTE: Picasso et al were fans of MOVIES! (see below)
COULD BE SEEN AS SEQUENTIAL OR ALL AT ONCE… 
  • SO we are (at best) invited to follow a journey passing through all these various perspectives… : = sequentiality!
  • OR attempts (via photos snapshots) from D Hockney
CUBISM: multiple points of perspective (// Nietzsche’s perspectivism?)
N perspectivism -> Cubism as concept of a DECONSTRUCTED space (chaos) through TIME (sequential) 
 <->  Heraclitus!
FILM TECHNOLOGY: See Picasso & Braque Go to the Movies (2008) influence of FILMS in 1906-07 (note: Duchamp nude rejected THEN -> DADA REVOLT!) 
<-> silent films (FRENCH invention -the Lumieres bros) // nude descending stair
The Frenchman Louis Lumiere is sometimes credited as the inventor of the motion picture camera in 1895. Other inventors preceded him, and Lumiere’s achievement should always be considered in the context of this creative period.  Lumiere’s portable, suitcase-sized cinematographe served as a camera, film processing unit, and projector all in one. He could shoot footage in the morning, process it in the afternoon, and then project it to an audience that evening. His first film was the arrival of the express train at Ciotat. Other subjects included workers leaving the factory gates, a child being fed by his parents, people enjoying a picnic along a river. The ease of use and portability of his device soon made it the rage in France. Cinematographes soon were in the hands of Lumiere followers all over the world, and the motion picture era began. The American Thomas Alva Edison was a competitor of Lumiere’s, and his invention predated Lumiere’s. But Edison’s motion picture camera was bulky and not portable. FROM

Ex nihilo nihil fit ("Out of nothing comes nothing")

How large is this "instant" between "past" and "future"? How long does this "instant* last?
This "instant" is an imperceptible space of time yet this instant as we have seen it, is not equal to zero (otherwise it leads us to Zeno's paradox) : time (i.e. change, movement) itself would stop from existing which is absurd.
So this "instant" is not "nothing." It is paradoxically an infinitely small yet non-zero entity without which Time itself would cease to exist. Yes as we have seen it: "Out of nothing comes nothing." This sentence was dramatically used in William Shakespeare's King Lear when his dearest daughter Cordelia is unable to put her love for him into words. The King then says, "Nothing will come of nothing", meaning that as long as she says nothing to flatter him, she will receive nothing from him. Later in the play, Lear will repeat this line several times, while plunging into madness. As Lear's, Eckaert Tolle's philosophy is also deeply "nihilistic" (and depressing.)
But this philosophical definition of "nothing," is quite different from that defended by scientists (to which Tolle sometimes refers to.) In the real physical world as studied by them this "philosophical nothing" has no existence since "nothing" can always be defined by certain properties such as space, and is governed by physical laws. Even in today's quantum mechanics, "nothing" refers to a "quantum vacuum." In "quantum field theory," this so called "vacuum" or "Zero-point" field is the quantum state with the lowest possible energy and contains no physical particles. According to quantum mechanics, the "vacuum" is not truly empty but instead contains fleeting electromagnetic waves and particles that pop into and out of existence. This "vacuum model" is a strong argument, by analogy, in favor of a multiverse cosmological model where universes could pop into and out of existence. This is very different from our philosopher’s or theologian’s idealized "nothing" and "creation."
So, in reality there is always "something."
This reality is in itself the answer to this old question : "Why is there something rather than nothing? "
  • Artist Brian Eno's "Long Now" project about "long-term thinking."
  • Time as fourth dimension??? (cubism)

PERSPECTIVE: FROM 3D TO 2D

3D > 2D:

solution = PERSPECTIVE (PROJECTION)
Note: cubism REJECTS such perspective


From my 4th dimension (≠ time!) 

Einstein: spacetime >> time as "fourth dimension" >>> BRANES

Einstein: space-time ("fourth dimension")

Time's arrows as the "fourth dimension"?

Hawking: 
A temporal dimension is a dimension of time. Time is often referred to as the “fourth dimension” for this reason, but that is not to imply that it is a spatial dimension. A temporal dimension is one way to measure physical change. It is perceived differently from the three spatial dimensions in that there is only one of it, and that we cannot move freely in time but subjectively move in one direction.
The equations used in physics to model reality do not treat time in the same way that humans commonly perceive it. The equations of classical mechanics are symmetric with respect to time, and equations of quantum mechanics are typically symmetric if both time and other quantities (such as charge and parity) are reversed. In these models, the perception of time flowing in one direction is an artifact of the laws of thermodynamics (we perceive time as flowing in the direction of increasing entropy).
The best-known treatment of time as a dimension is Poincaré and Einstein’s special relativity (and extended to general relativity), which treats perceived space and time as components of a four-dimensional manifold, known as spacetime, and in the special, flat case as Minkowski space. more and here
= sequentality (“time”) and diff view points = like a de-construction of space via time (// cubism)
Is “time” a “fourth dimension”, ie euclidian space (3d) is a mere projection of a 4d “hyperspace”? in which case time as a “fourth spatial” dimension <—> Riemann
HAWKING AND IMAGINARY TIME AS FOURTH DIMENSION (different from REAL time)

The Beginning of Time

It seems that Quantum theory, on the other hand, can predict how the universe will begin. Quantum theory introduces a new idea, that of imaginary time. Imaginary time may sound like science fiction, and it has been brought into Doctor Who. But nevertheless, it is a genuine scientific concept. One can picture it in the following way. One can think of ordinary, real, time as a horizontal line. On the left, one has the past, and on the right, the future. But there's another kind of time in the vertical direction. This is called imaginary time, because it is not the kind of time we normally experience. But in a sense, it is just as real, as what we call real time.
The three directions in space, and the one direction of imaginary time, make up what is called a Euclidean space-time. I don't think anyone can picture a four dimensional curve space. But it is not too difficult to visualise a two dimensional surface, like a saddle, or the surface of a football.
In fact, James Hartle of the University of California Santa Barbara, and I have proposed that space and imaginary time together, are indeed finite in extent, but without boundary. They would be like the surface of the Earth, but with two more dimensions. The surface of the Earth is finite in extent, but it doesn't have any boundaries or edges. I have been round the world, and I didn't fall off.
If space and imaginary time are indeed like the surface of the Earth, there wouldn't be any singularities in the imaginary time direction, at which the laws of physics would break down. And there wouldn't be any boundaries, to the imaginary time space-time, just as there aren't any boundaries to the surface of the Earth. This absence of boundaries means that the laws of physics would determine the state of the universe uniquely, in imaginary time. But if one knows the state of the universe in imaginary time, one can calculate the state of the universe in real time. One would still expect some sort of Big Bang singularity in real time.

From http://www.hawking.org.uk/the-beginning-of-time.html


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