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 theGlass) with One Eye, Close to, for Almost an Hour, shows ahyper-pyramid to be placed on each face of the hyper-cube formed bythe 3-dimensional cube with runners in The Large Glass, thus forminga 24-cell that can be used to tile spacetimeafter spacetime has been reduced to 4 dimensions.

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

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

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

The D5 Lie algebra is a 45-dimensional subalgebra of the78-dimensional E6 Lie algebra. Physically D5 contains bosons andspacetime only, while E6 contains bosons, spacetime, and fermions.Therefore the Small Glass is concerned with spacetime, andparticularly its 24-cell tiling after reduction to 4 dimensions.

The lower Small Glass oculist witness (corresponding to the bottomoculist witness of The Large Glass which has 60 radial rays) omitssome of the 60 rays, leaving only the 45 that represent the45-dimensional Lie algebra D5.

From the center of the lower Small Glass oculist witness anobelisk 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 anoctahedron floating over the ocean.

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

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