Instead of this [academic] spatial model, Cubists turned to new models of geometry and the 'fourth dimension' as inspiration for the works like Gleizes's Passy (Ponts de Paris) of 1912, which he and Metzinger reproduced in their tract Du Cubisme as exemplary of art expressing their ideas. This urban landscape synthesized the river, trees, clouds, buildings, steel bridges and smoke of the modern city. Partially geometrized forms—such as the green arc of tree on the upper left or arched doors and windows on the rectangular buildings in the center—are subjectively evoked through limited colour range; shifting perspectives, signified by long vertical and diagonal bands cutting off the edges of objects contained within them; and shifting relative scales of objects, such as the two steel bridge spans. [...] the Cubists justified this novel approach to pictorial space in part on the basis of the mathematician Henri Poincaré's theory of 'conventionalism'.
