Dear Tout-Fait,

Duchamp, in a communication to Katherine Dreier in Paris, once sent a subtly altered photograph of a seemingly typical bar scene. On examination, spatial relationships were “out of whack” when referred to any rational floor plan. This may anticipate the work of the mathematician Donald Spencer (1912-2001) on systematic distortions of complex assemblages. Duchamp fooled the untutored eye by rearranging the spatial context in such a way that a non-visual logic replaced the logic of perspective (but in a superficially undetectable way). Such an alteration is, of course, reversible. This answers the requirement of reversibility in any complex distortion, which, in effect, is an operation for which an equation can be written. I wonder if any relationship could be traced between Duchamp’s anticipatory work and the later, formal work of Spencer and other geometers.

With best wishes to all,

Timothy Phillips