# The Small Glass, To Be Looked at (from the other side of the Glass) with One Eye, Close to, for Almost an Hour, by Marcel Duchamp (1887-1968):

Sources and References:

Marcel Duchamp, Moure, Rizzoli (1988); and

Marcel Duchamp, MIT Press (1993).

Duchamp's Small Glass, To Be Looked at (from the other side of the Glass) with One Eye, Close to, for Almost an Hour, shows a hyper-pyramid to be placed on each face of the hyper-cube formed by the 3-dimensional cube with runners in The Large Glass, thus forming a 24-cell that can be used to tile spacetime after spacetime has been reduced to 4 dimensions.

Two lines of the Small Glass represent the scissors of The Large Glass and therefore lead the pyramid to its proper place on a face of the cube with runners.

The Small Glass contains two oculist witnesses, corresponding to the middle and bottom oculist witnesses of The Large Glass.

The higher Small Glass oculist witness (corresponding to the middle oculist witness of The Large Glass with 6 circles) has 5 circles. The 5 circles correspond to the 5-torus, the maximal torus of the D5 Cartan subalgebra of the D5 Lie algebra.

The D5 Lie algebra is a 45-dimensional subalgebra of the 78-dimensional E6 Lie algebra. Physically D5 contains bosons and spacetime only, while E6 contains bosons, spacetime, and fermions. Therefore the Small Glass is concerned with spacetime, and particularly its 24-cell tiling after reduction to 4 dimensions.

The lower Small Glass oculist witness (corresponding to the bottom oculist witness of The Large Glass which has 60 radial rays) omits some of the 60 rays, leaving only the 45 that represent the 45-dimensional Lie algebra D5.

From the center of the lower Small Glass oculist witness an obelisk rises, representing the cube topped by the pyramid.

The 4-dimensional 24-cell has 24 faces, each of which is a 3-dimensional octahedron.

Duchamp's Handmade Stereopticon Slides show an octahedron floating over the ocean.

The Small Glass contains two lenses, which together form a telescope with which to view The Large Glass, behind which the Small Glass should be viewed. So long as the Small Glass is in New York, and The Large Glass is in Philadelphia, a proper viewing is difficult.