When we do use our minds, we can see how Penroses' visual ambiguity is created (see Illustration 1 ). The far corners of the cube rise and push away. Further analysis reveals impossible "overlaps" and corner joinings of the bars compared with an actual cube in three-dimensional space. Visual clues lead to conscious expectations. Whether or not these clues conflict, our unconscious minds process them and apparently make a best guess of prediction for interpreting what we are seeing. The confusion introduced by illogical depth signals (between two and three dimensions) is artificial, because the brain does not normally have to deal with this kind of ambiguous object in the everyday world. Based both on apparent "rules" of how the world works and our prior experience of objects and representations, our unconscious guesses are generally so good that, for the most part, our expectations match reality. But impossible figures (and visual illusions in general) prove that perception is less a direct translation of reality than a complex interaction between the eyes and brain, creating only a limited representation of a reality that we believe to be true based on our experiences (Gregory, 1979).

Much mischief can be created by someone aware of how vulnerable we are to mixed depth clues in representations, and, more broadly, to the wide gap between the seduction of the obvious  ("seeing is believing...if it looks like a duck...then it's a duck") and critical thinking ("but is it a duck?").

Scholars have documented many cases wherein artists have been influenced by science. Escher (1986, p. 78), most famously, made extensive use of Lionel and Roger Penrose's concept of the impossible figure in numerous prints and credited their 1958 article as the source of his inspiration.¹ Yet, what about instances of scientists being influenced by artists? Examples from art history are difficult to locate. The development by artists of a Renaissance perspective immediately comes to mind-and this discovery did lead to scientific innovations in navigation and technology. However, perspective is not a fair example, because art and science were not as yet recognized as separate categories in the Renaissance, and, in the case of perspective, the new geometry was developed by people who were considered to be both artists and scientists.

Let us consider Marcel Duchamp's famous "rectified" readymade Apolinère Enameled, created in 1916-1917 (see Illustration 2). Duchamp tells us that this work is an enamel paint display sign that he acquired and for which he then changed the text at the top and bottom. Duchamp also claims that he added the "missing" reflection of the back of the girl's head in the mirror above the dresser. He does not indicate the significance of the piece; nor does he say much else beyond expressing disappointment that the poet Apollinaire (who, we assume, was the "namesake" of this piece and who died in 1918) had not seen it.

Several scholars have noted that something is "wrong" with the bed, the best analysis being that of Andre Gervais (1984). Despite observations that the bed was "out of whack," no scholar has considered the historical relationship between this fact and the Penrose discovery.² Duchamp's bed is, in fact, a classic example of an impossible object done in 1916-1917, yet the Penroses' paper was published in 1958! Duchamp's example predates the Penrose discovery by forty years.

One must ask: could the Penroses have been influenced by Duchamp's bed? My research, although not conclusive, offers strong circumstantial evidence that the answer may be "yes." If such is the case, we have located an unusual example of an artist's influence on scientists. Until now, Duchamp has only been credited with having been influenced by scientists and mathematicians-namely, Poincaré and various texts on perspective (Adcock, 1984; Henderson, 1983).