But how could readymades
be third-dimension shadows of his fourth-dimension
Large Glass machine? For an answer we can look to the great mathematician
of the late-nineteenth and early-twentieth century, Henri Poincaré,
who continues to be regarded as one of history's great mathematicians, was also
a famous popularizer of scientific ideas. Many artists, at the beginning of modern art
in the early-twentieth century, knew and discussed Poincaré's works
(Henderson, 1983). Poincaré had developed a specific geometric technique
(see Illustration 5),
where two-dimensional shadows could be used to express
the existence of a three-dimensional sphere without the observer ever actually
seeing the three-dimensional object (Davis, 1993, pp.
138-139).^{13}
From a two-dimensional creature's perspective, by mentally putting together
(in a series) the relations of two-dimensional shadows projected
from the sphere, we can, through logic, extrapolate and therefore "know"
or see in our minds the higher dimensional
object.^{14}
Duchamp had also said that he wanted the titles of his readymades
"to carry the mind of the spectator towards other regions
more verbal" (Sanouillet & Peterson, 1973,
pp. 141-142). For Duchamp, one cannot physically see the fourth
dimension (Sanouillet & Peterson, p. 98). For
two-dimensional creatures, Poincaré's 2-D shadows would lead to
the 3-D sphere
Let us return to what Duchamp called his "rectified readymade,"
Gervais (1984, p. 115) has made the general observation that
the bed is an "impossible object." One assumes, since he does not
cite "impossible figure or object" as a psychological category of
optical illusions, that he uses this term as a vernacular description of
the perspective problems in the bed without linking them to the Penroses'
formal idea and term. Gervais cites three problems: (1) the
right foot of the headboard is attached to the front mattress rail;
(2) the back mattress rail cuts diagonally from the mattress rail;
and (3) the painted rungs, four in the footboard and five in the headboard,
should be equal in number, but are not (p. 115). I had to make a
three-dimensional model of the Art & Academe (ISSN: 1020-7812), Vol. 10, No. 1 (Fall 1997): 26-62. Copyright © 1997 Visual Arts Press Ltd. |

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