The late 19th and early 20th centuries were a vibrant period of significant scientific and technological advances, from the discovery of X rays and the advent of powered flight to Albert Einstein's formulation of the special theory of relativity.

It was also a time of great popular interest in a fourth spatial dimension--a concept that appeared to offer painters and sculptors, in particular, an avenue of escape from conventional representation. Moreover, the development of non-Euclidean geometries, which overturned Euclid's postulate that parallel lines never meet, provoded alternative but perfectly consistent models of reality.

These ideas came together in a fascinating assemblage that Duchamp completed in 1914 and called "3 Stoppages Étalon," or three standard stopping points.

In typically meticulous fashion, Duchamp described how he cut three lengths of thread, each 1 meter long. Holding each thread in turn horizontally between outstretched hands, he dropped them from a height of 1 meter onto canvas strips painted blue. He then used drops of varnish to fix the threads, no longer straight, in their new configuration.

The creation of these contorted lines was "drawing without using your hand," comments philosopher Arthur C. Danto of Columbia University. It aslo exemplified Duchamp's use of chance to create art objects, he says.