The rather elegant woman wearing only a pearl necklace and the horse are immersed in a landscape with trees and a window (in the 'background'), a vase, with fruits and vegetation (in the 'foreground') clearly taken from the natural world.

[4] David Cottington wrote: In the absence of more evidence than such brief snatches of commentary in wide-ranging salon reviews can provide, we can only speculate as to whether Metzinger intended, or its initial audience read, the provocative juxtaposition in this painting of a naked woman with horse, and of natural with cosmetic adornment, as a follow-up to Tea Time's essay on sensation and the viewer's apprehension of it.

Through its fussy geometry we can discern a nude woman, her limbs and upper torso picked out in sensuous chiaroscuro, perched side-saddle on a studio prop-horse and stroking its mane (visible top right) .

As others have pointed out (Antliff and Leighten),[5] and as emerges upon close examination, the nude woman is seated on what appears to be a rectangular block or cube, perhaps a model's pedestal (visible to the left).

"[6] The nude figure sitting to the left, the horse standing to the right, along with other elements of the painting, are depicted in a faceted manner, based to some extent on non-Euclidean geometry.

Denying the illusion of Renaissance perspective the artist breaks down the figures and background into facets and planes, presenting multiple aspects of the subject all at once.

[7] Where the dialectic nature of Paul Cézanne's work had been influential between 1908 and 1910 during the expressionistic phase of Cubism, the flat, linear structures of Georges Seurat would capture the attention of the Cubists from 1911.

The Chronophotography of Eadweard Muybridge and Étienne-Jules Marey that directly influenced Marcel Duchamp's 1912 Nu descendant un escalier n° 2[9] could also be read into Metzinger's work of 1911–12, though here, rather than simultaneously superimposing successive images to depict the motion of the horse, Metzinger represents a horse at rest viewed from multiple angles; the dynamic role is played by the artist.

Because the horse's movement was too fast for the human eye to register, there was a scientific debate in the 1870s questioning (Marey's hypothesis originally) whether all four hooves ever left the ground simultaneously.

[16] The anti-Hellenic concept of representing a subject from multiple view-points was a central idea of Jean Metzinger's Note sur la Peinture, 1910.

In that article, Metzinger writes about the works of Robert Delaunay, Henri Le Fauconnier, Georges Braque and Pablo Picasso, noting that they "discarded traditional perspective and granted themselves the liberty of moving around objects."

[20] The idea exemplified in La Femme au Cheval of moving around an object in order to see it from different view-points was elaborated upon in Du "Cubisme" (1912),[21] written in collaboration with Albert Gleizes.

In addition to being illustrated in Du "Cubisme", Metzinger's La Femme au Cheval is also reproduced in Les Peintres Cubistes by Guillaume Apollinaire, 1913.

At the same time, Metzinger new full well that to varying degrees a barrier would remain, insurmountable, between the exclusive intellectual geometric deliberations of Cubism practiced by the Section d'Or group and popular culture.

This 'reciprocity' between artist and public is perhaps one of the reasons Metzinger felt the need to include elements of the real world into his paintings of the period, untouched by the wrath of mobile perspective.

"The reminiscence of natural forms cannot be absolutely banished; not yet, at all events" wrote Metzinger and Gleizes, for art, to them, could not "be raised to the level of a pure effusion at the first step.

The radical new concept based on non-conventional precepts of space and time transformed the canvas from something quasi-static to something that possessed dynamic evolutionary characteristics.

No longer governed by Euclidean geometry (or classical Renaissance perspective), Metzinger's Woman with a Horse is composed of a series of ellipses, curvilinear and rectilinear structures and planes juxtaposed and distributed throughout the canvas in complex myriad combinations of abstract volumetric forms that suggest rather than define the underlying subject.

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 with the present, and its progression into the future that most intrigued Metzinger:[23] "If we wished to relate the space of the [Cubist] painters to geometry, we should have to refer it to the non-Euclidean mathematicians; we should have to study, at some length, certain of Riemann's theorems.

"[21]The concept of observing a subject from different points in space and time simultaneously (multiple or mobile perspective) "to seize it from several successive appearances, which fused into a single image, reconstitute in time" developed by Metzinger (in his article, Cubisme et tradition, Paris Journal, 16 August 1911) and observed in La Femme au Cheval was not derived from Albert Einstein's theory of relativity, though it was certainly influenced in a similar way, through the work of Jules Henri Poincaré (particularly Science and Hypothesis).

Princet brought to attention of these artists a book entitled Traité élémentaire de géométrie à quatre dimensions by Esprit Jouffret (1903) a popularization of Poincaré's Science and Hypothesis.

Princet was close to Metzinger and participated in meetings of the Section d'Or in Puteaux, giving informal lectures to the artists, many of whom were passionate about mathematical order.

[17] The similarity of Metzinger's own work of 1910 to that of Picasso is exemplified in his Nu à la cheminée (Nude), exhibited at the 1910 Salon d'Automne.

[5] Reviewing the 1910 Salon d'Automne Roger Allard wrote of the 'new innovators': "Metzinger's nude and his landscape are ruled by an equal striving for fragmentary synthesis.

He penetrates to its intellectual core: an art capable of synthesizing a reality in the mind of the observer..."[24] Arthur I. Miller, author of Einstein, Picasso: Space, Time and the Beauty that Causes Havoc (2002), writes: "Cubism directly helped Niels Bohr discover the principle of complementarity in quantum theory, which says that something can be a particle and a wave at the same time, but it will always be measured to be either one or the other.

"[25] Niels Bohr (1885–1962), the Danish physicist and one of the principal founders of quantum mechanics, moved into a mansion owned by the Carlsberg Foundation (where he and his family resided after 1932)[26] and was given unconditional authority to furnish it.

Bohr, vitally interested in the rapid changes taking place in modern art, took great pleasure talking about La Femme au Cheval and in giving "form to thoughts to an audience at first unable to see anything in Metzinger's painting—They came with a preconceived idea", according to the Danish artist and writer Mogens Andersen.

[...] Consequently, evidence obtained under different experimental conditions cannot be comprehended within a single picture, but must be regarded as complementary in the sense that only the totality of the phenomena exhausts the possible information about the objects.

This massive exhibition occurred exactly one year after Metzinger, Gleizes, Le Fauconnier, Delaunay, Léger and Laurencin were shown together in Room 41 of the 1911 Salon des Indépendants, which provoked the scandal out of which Cubism emerged and spread throughout Paris with wide-ranging repercussions in Germany, the Netherlands, Italy, Russia, Spain and elsewhere (influencing Futurism, Suprematism, Constructivism, De Stijl and so on).