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Articles


R. rO. S. E. Sel. A. Vy

by Roberto Giunti


Marcel's Topology

4a. Recipe for Bottles

We read, in the Green Box, the note:

 

…on the other hand:
the vertical axis considered separately turning on
itself, a generating line at a right
angle will always determine
a circle in the 2 cases 1st turning
in the direction A, 2nd direction B—
Thus, if it were still
possible; in the case of the vertical axis at
rest.,  to consider 2 (contrary) directions for
the generating line, the figure engendered
(whatever it may be.)
can no longer be called left
or right of the axis—

—As there is gradually less differentiation
from axis to axis., i.e. as all the
axes gradually disappear
in a fading verticality the front and the back,
the reverse and the obverse acquire a
circular significance: the right and
the left which are the 4 arms of the front and
back. Melt. Along the verticals.
—————————
The interior and exterior (in a fourth dimension)
can receive a similar identification. But
the axis is no longer vertical and has no longer
a one-dimensional appearance 

Although the note is a little bit obscure, and as always it's reading is arduous, it is possible to hypothesize an interpretative model consistent with its principal parts; furthermore, this model is consistent with some of Duchamp's capital works.

Let's start by imagining a simple rectangle. If we trace a vertical axis across this rectangle, it makes sense to distinguish right and left parts of the figure with respect to that axis. Now, if we are in a 3D space, with a circular motion we close the rectangle to form a cylinder (Fig. 33A).

Fig. 33A

It no longer makes sense to speak about right and left parts with respect to the previous axis, because each point of the cylinder can be reached by turning toward either the left or the right.

If we use the rectangle to represent the cylinder in a 2D space, we must agree upon the simple convention that the two vertical sides of the rectangle represent the same line of the cylinder. Thus, if we walked on the rectangle as if we were on the cylinder, when we went out from the left side we could continue re-entering from the right side, and vice versa, as shown in Fig. 33B and 33C.

Fig. 33B
Fig. 33C

Click to enlarge
Figure 34
Marcel Duchamp, Door: II, rue Larrey, 1927

Duchamp applies this idea to the suggestive Door: II, rue Larrey (1927) (Fig. 34): when the door closed the left room, it opened the right one, and vice versa.

Thus, by means of a simple circular closing we pass from the rectangle to the cylinder, losing the distinction between left and right. Now, if we repeat the same operation of circular closing starting from the cylinder, we obtain a ring-shaped figure which topologists call torus or tore (Fig. 35A). With this operation we lose the distinction between high and low too.

 

 


Fig. 35A

As before, if we use the rectangle to represent the torus in a 2D space, we must agree upon a second simple convention, analogous to the first one: the two horizontal sides of the rectangle represent the same circular line along the torus, and if we walked on the rectangle as if we were on the torus, when we went out from the top side we could continue re-entering from the bottom side, and vice versa, as shown in Figs. 35B and 35C. >>Next

   Fig. 35B 
  Fig. 35C

Fig. 34
©2002 Succession Marcel Duchamp, ARS, N.Y./ADAGP, Paris. All rights reserved.

 

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