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.