La Quadrature illustre cette métaphore, compliquant encore l’immémorial problème par la construction d’une composition en plusieurs plans, l’insertion du cône inversé et la localisation des éléments dans un espace aux perspectives multiples. L’objet de La Quadrature apparaît par la suite dans Le Beau Temps, œuvre maîtresse de Man Ray de 1939 (Wendy A. Grossman, op. cit., p.192). Dans cette toile monumentale, qui apparaît comme une prémonition de la Seconde Guerre et de l’importance de la science à cette époque, La Quadrature est reproduite en miniature au sein d’un livre ouvert.
Man Ray’s fascination for geometric forms and mathematical problems can be traced back to his work experience as a commercial graphic artist as well as his mechanical works of the Dada period, and remained present throughout his career. In La Quadrature of 1938, Man Ray invented an unprecedented mechanical object, imagined in a dream, and painted it onto a wooden panel. “…he takes on the problem posed by geometers since antiquity of squaring the circle, the unresolvable challenge of constructing a square with the same area as a given circle using a finite number of steps and tools. Questioning the existence of certain axioms of Euclidean geometry, this classic problem – which Man Ray claims came to him in his dream – became a metaphor for the impossible or the fruitless, taken up by writers as diverse as Artistophanes, Dante, Alexander Pope, O. Henry, and James Joyce (Wendy A. Grossman in Man Ray / Human Equations : a journey from mathematics to Shakespeare, Washington, D.C., The Phillips Collection, 2015-16, p. 192). In an interview in 1973, Man Ray described the origin of this work: "I was still in New York; I studied mathematics a lot in order to be able to use the mechanical instruments I needed to express myself. Then, one day I dreamt that I had found the solution for the squaring of a circle. How to transform a circle into a square? I made a circle with a piece of string and then I pulled it with four fingers to make four corners and it became a square. Mathematically, it was not valid. Only, I am not going to justify my dream with logic! It has to remain a bit mysterious. Even for me.” (Irmeline Lebeer, "Man Ray Fautographe", L'Art vivant, no. 44, Paris, November 1973, p. 24)
La Quadrature takes up this metaphor, further complicating the challenge of squaring the circle by constructing the composition across multiple planes, inserting the inverted cone, and situating the elements in a multifaceted perspective space. The central components in the painting first appear alongside other sketches in a preparatory study for Le Beau Temps (Fair Weather), a monumental painting completed a year later (Wendy A. Grossman, op. cit., p. 192). In this monumental canvas, which can arguably be viewed as a premonition to the Second World War and of the importance in the advances of science, La Quadrature is reproduced in miniature, as an illustration in an open book - an emblem of the artist’s fascination for geometry and his respect for science.
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