Theory
Jean Metzinger and Albert Gleizes wrote with reference to non-Euclidean geometry in their 1912 manifesto, Du "Cubisme". It was argued that Cubism itself was not based on any geometrical theory, but that non-Euclidean geometry corresponded better than classical, or Euclidean geometry, to what the Cubsists were doing. The essential was in the understanding of space other than by the classical method of perspective; an understanding that would include and integrate the fourth dimension with 3-space.
Though the rupture with the past seemed total, there was still within the avant-garde something of the past. Metzinger, for example, writes in a Pan article, two years before the publication of Du "Cubisme" that the greatest challenge to the modern artist is not to 'cancel' tradition, but to accept "it is in us," acquired by living. It was the combination of the past (himself inspired by Ingres and Seurat) with the present, and its progression into the future that most intrigued Metzinger. Observed was the tendency; a "balance between the pursuit of the transient and the mania for the eternal. But the result would be an unstable equilibrium. The domination would no longer be of the external world. The progression was from the specific to the universal, from the special to the general, from the physical to the temporary, towards a complete synthesis of the whole—however unattainable—towards an 'elemental common denominator' (to use the words of Daniel Robbins).
Whereas Cézanne had been influential to the development of Metzinger's Cubism between 1908 and 1911, during its most expressionistic phase, the work of Seurat would once again attract attention from the Cubists and Futurists between 1911 and 1914, when flatter geometric structures were being produced. What the Cubists found attractive, according to Apollinaire, was the manner in which Seurat asserted an absolute "scientific clarity of conception." The Cubists observed in his mathematical harmonies, geometric structuring of motion and form, the primacy of idea over nature (something the Symbolists had recognized). In their eyes, Seurat had "taken a fundamental step toward Cubism by restoring intellect and order to art, after Impressionism had denied them" (to use the words of Herbert). The "Section d'Or" group founded by some of the most prominent Cubists was in effect an homage to Seurat. Within the works by Seurat—of cafés, cabarets and concerts, of which the avant-garde were fond—the Cubists' discovered an underlying mathematical harmony: one that could easily be transformed into mobile, dynamical configurations.
The idea of moving around an object in order to see it from different view-points is treated in Du "Cubisme" (1912). It was also a central idea of Jean Metzinger's Note sur la Peinture, 1910; Indeed, prior to Cubsim painters worked from the limiting factor of a single view-point. And it was Jean Metzinger, for the first time in Note sur la peinture who enunciated the stimulating interest in representing objects as remembered from successive and subjective experiences within the context of both space and time. In that article, Metzinger notes that Braque and Picasso "discarded traditional perspective and granted themselves the liberty of moving around objects." This is the concept of "mobile perspective" that would tend towards the representation of the "total image."
Though at first the idea would shock the public they eventually came to accept it, as they came to accept the 'atomist' representation of the universe as a multitude of dots consisting of primary colors. Just as each color is modified by its relation to adjacent colors within the context of Neo-Impressionist color theory, so too the object is modified by the geometric forms adjacent to it within the context of Cubism. The concept of 'mobile perspective' is essentially an extension of a similar principle stated in Paul Signac's D'Eugène Delacroix au néo-impressionisme, with respect to color. Only now, the idea is extended to deal with questions of form. (See Jean Metzinger, 1912, Danseuse au café ).
Cubism by 1912 had abstracted almost to the point of total non-representation. In Du "Cubisme" Metzinger and Gleizes had realized that figurative aspects of the new art could be abandoned: "we visit an exhibition to contemplate painting, not to enlarge our knowledge of geography, anatomy etc. 'Let the picture imitate nothing; let it nakedly present its motive, and we should indeed be ungrateful were we to deplore the absence of all those things - flowers or landscapes or faces - of which it could never have been anything other than a reflection'. Though Metzinger and Gleizes hesitate to do away with nature entirely: 'Nevertheless, let us admit that the reminiscence of natural forms cannot be absolutely banished; as yet, at all events. An art cannot be raised all at once to the level of a pure effusion.' 'This is understood by the Cubist painters, who tirelessly study pictorial form and the space which it engenders'.
One of the essential arguments of Du "Cubisme", was that knowledge of the world is to be gained through 'sensations' alone. Classical figurative painting offered only one point of view, a restrained 'sensation' of the world, limited to the sensation of a motionless human being who sees only that which is in front of him from a single point in space frozen in a moment of time (time was absolute in the Newtonian sense and separate from the spatial dimensions). But the human being is mobile and dynamic, occupying both space and to time. The observer sees the world from a multitude of angles (not one unique angle) forming a continuum of sensations in constant evolution, i.e., events and natural phenomena are observed in a continuum of constant change. Just as the formulations of Euclidean geometry, classical perspective is only a 'convention' (Henri Poincaré's term), rendering the phenomena of nature more palpable, susceptible to thought and understandable. Yet these classical conventions obscured the truth of our sensations, and consequently, the truth of our own human nature was limited. The world was seen as an abstraction, as Ernst Mach implied. In this sense, it could be argued that classical painting, with its immobile perspective and Euclidean geometry, was an abstraction, not an accurate representation of the real world.
What made Cubism progressive and truly modern, according to Metzinger and Gleizes, was its the new geometric armature; with that it broke free from the immobility of 3-dimensional Euclidean geometry and attained a dynamic representation of the 4-dimensional continuum in which we live, a better representation of reality, of life's experience, something that could be grasped through the senses (not through the eye) and expressed onto a canvas.
In Du "Cubisme" Metzinger and Gleizes write that we can only know our sensations, not because they reject them as a means of inspiration. On the contrary, because understanding our sensations more deeply gave them the primary inspiration for their own work. Their attack on classical painting was leveled precisely because the sensations it offered were poor in comparison with the richness and diversity of the sensations offered by the natural world it wished to imitate. The reason classical painting fell short of its goal, according to Metzinger and Gleizes, is that it attempted to represent the real world as a moment in time, in the belief that it was 3-dimensional and geometrically Euclidean.
Read more about this topic: Jean Metzinger
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