PARADOXES—IN WHICH THE SAME information may lead to two contradictory conclusions—give us pleasure and torment at the same time. They are a source of endless fascination and frustration, whether they involve philosophy (consider Russell's paradox, “This statement is false”), science—or perception. The Nobel Prize winner Peter Medawar once said that such puzzles have the same effect on a scientist or philosopher as the smell of burning rubber on an engineer: they create an irresistible urge to find the cause. As neuroscientists who study perception, we feel compelled to study the nature of visual paradoxes.
Let us take the simplest case. If different sources of information are not consistent with one another, what happens? Typically the brain will heed the one that is statistically more reliable and simply ignore the other source. For example, if you view the inside of a hollow mask from a distance, you will see the face as normal—that is, convex—even though your stereovision correctly signals that the mask is actually a hollow, concave face. In this case, your brain's cumulative experience with convex faces overrides and vetoes perception of the unusual occurrence of a hollow face.
Most tantalizing are the situations in which perception contradicts logic, leading to “impossible figures.” British painter and printmaker William Hogarth created perhaps the earliest such figure in the 18th century (a). A brief view of this image suggests nothing abnormal. Yet closer inspection reveals that it is logically impossible. Another example is the “devil's pitchfork,” or Schuster's conundrum (b). Such impossible figures raise profound questions about the relation between perception and rationality.
In modern times, interest in such effects was partly revived by Swedish artist Oscar Reutersvärd. Known as the father of impossible figures, he devised numerous geometric paradoxes, including the “endless staircase” and the “impossible triangle.” These two were also independently developed by Lionel and Roger Penrose, the famous father-and-son scientists; c, on the next page, shows their version of what is now commonly called the Penrose triangle.
Dutch artist M. C. Escher playfully embedded such figures in his engravings exploring space and geometry. Consider Escher's staircase (d, on next page): no single part of the staircase is impossible or ambiguous, but the entire ensemble is logically impossible. You could be climbing the staircase upward forever and yet keep going in circles, never reaching the top. It epitomizes the human condition: we perpetually reach for perfection, never quite getting there!
Is this staircase truly a perceptual paradox? That is, is the brain unable to construct a coherent percept (or token of perception) because it has to simultaneously entertain two contradictory perceptions? We think not. Perception, almost by definition, has to be unified and stable at any given instant because its whole purpose is to lead to an appropriate goal-directed action on our part. Indeed, some philosophers have referred to perception as “conditional readiness to act,” which may seem like a bit of an overstatement.
Despite the common view that “we see what we believe,” the perceptual mechanisms are really on autopilot as they compute and signal various aspects of the visual environment. You cannot choose to see what you want to see. (If I show you a blue lion, you see it as blue. You cannot say, “I will choose to see it as gold because it ought to be.”) On the contrary, the paradox in d arises precisely because the perceptual mechanism performs a strictly local computation that signals “ascending stairs,” whereas your conceptual/intellectual mechanism deduces that it is impossible logically for such an ascending staircase to form a closed loop. The goal of perception is to compute rapidly the approximate answers that are good enough for immediate survival; you cannot ruminate over whether the lion is near or far. The goal of rational conception—of logic—is to take time to produce a more accurate appraisal.