
The study of mathematics is thought have begun in ancient India and China. "Zero" and
"infinity" were not so much discoveries as human inventions. The notion of length with no
width is very curious indeed, the pencil line I draw being only an approximation of an
invisible mathematical line. Endeavors in art are also mere approximations, efforts to
render visible unseen realms.
Among the notes Marcel Duchamp left in his Green Box are various mathematical
notations. The Large Glass attempted to throw projections of the unseen fourth
dimension onto our threedimensional experience, much in the same way that three
dimensional objects cast shadows onto twodimensional surfaces.
While not wholly subscribing to the postRenaissance grationalh scientific regard on the
natural world, I especially appreciate those eighteenth and nineteenthcentury optical
devices and experimental implements that gave visible form to unseen hypotheses. I
have photographed suites of "stereometric exemplars" purchased from the West during
the Meiji era (18681911), now preserved by the University of Tokyo. The mathematical
models are sculptural renderings of trigonometric functions; the mechanical models were
teaching aids for showing the dynamics of Industrial Revolutionage machinery. Art
resides even in things with no artistic intentions.
 Hiroshi Sugimoto
