In what should come as a pleasant surprise to most high school students, scientists have found that people are innately expert at trigonometry. A new study demonstrates that the brain can judge distance based on how far below the horizon an object appears, using the angle between eye level and the object to determine how far off it is.
There are many ways to tell distance. Trees close to a speeding car seem to fly by faster than the far away mountains, a phenomenon known as motion parallax. Equally familiar is linear perspective, the classic example being the way railroad tracks converge in the distance. Another distance cue, called angular declination, relies on the vertical position of an object in the visual field. For example, more distant boats seem closer to the horizon than boats nearer to the viewer. Despite their hunches, researchers have been unable to prove that the visual system measures distance with angles because they couldn't separate angular declination from other visual cues.
So vision scientist Teng Leng Ooi at the Southern College of Optometry in Memphis, Tennessee, and colleagues had volunteers wear prism glasses, which makes everything appear lower in the field of view. To figure out how far away an object seemed to the subjects, the researchers blindfolded the subjects and asked them to walk and point to it. No matter how far they walked, the subjects always stopped short when wearing the glasses, and went too far after they took the prisms off, the team reports in the 8 November issue of Nature, indicating that their brains had been using the distorted vertical position to gauge distance.
Because the only visual cue changed by the prisms was the subjects' viewing angle, the eyes must be comparing the object's position to some constant spot in the field of view, somewhere the eye can always line up with, the researchers say. The brain does this by forming an angle with two imaginary lines: One stretches between the eye and the object, and the second stretches between the eye and the constant spot. Applying trigonometry to the angle formed between these two lines determines distance. The researchers suspected that the horizon, which normally appears to be at eye level, is the constant spot. To check, they measured the position of eye level relative to the horizon after the subjects had worn the prism glasses. The researchers found that these volunteers viewed the horizon as if it were several degrees lower, indicating that the brain tries to keep the horizon as a constant reference point. Additionally, the subjects perceived distances off by the same degree.
Calling Ooi's experiment "incredibly elegant," psychologist Jack Loomis of the University of California, Santa Barbara, says, "it is a fairly pure measurement of perception," adding that the prism test can be applied widely in perception studies, including virtual reality research.