Steven Pinker -- How the Mind Works - Hampshire High Italian ...

282 | HOW THE MIND WORKSIt wasn't a mirror-image test, like the Cooper and Shepard experiments;people were told to treat the two versions the same, just as they use thesame word for a left and a right glove. This, of course, is just people'snatural tendency. But somehow our subjects were treating them differently.For the standard versions (top row), people took longer when theshape was tilted farther: every picture in the top row took a bit longerthan the one before. But for the reflected versions (bottom row), tiltmade no difference: every orientation took the same time. It looked as ifpeople mentally rotated the standard shapes but not their mirrorimages. Tarr and I glumly wrote up a paper begging the reader to believethat people use a different strategy to recognize mirror images. (In psychology,invoking "strategies" to explain funny data is the last refuge ofthe clueless.) But just as we were touching up the final draft for publication,an idea hit.We remembered a theorem of the geometry of motion: a 2-D shapecan always be aligned with its mirror image by a rotation of no more than180 degrees, as long as the rotation can be in the third dimension aroundan optimal axis. In principle, any of our mirror-reversed shapes could beflipped in depth to match the standard upright shape, and the flip wouldtake the same amount of time. The mirror image at 0 degrees would simplyswivel around a vertical axis like a revolving door. The upside-downshape at 180 degrees could turn like a chicken on a rotisserie. The sidewaysshape could pivot around a diagonal axis, like this: look at the backof your right hand, fingertips up; now look at your palm, fingertips left.Different tilted axes could serve as the hinge for the other misorientedshapes; in every case, the rotation would be exactly 180 degrees. Itwould fit the data perfectly: people may have been mentally rotating allthe shapes but were optimal rotators, dialing the standard shapes in thepicture plane and flipping the mirror-reversed shapes in depth aroundthe best axis.We could scarcely believe it. Could people have found the optimalaxis before even knowing what the shape was? We knew it was mathematicallypossible: by identifying just three non-collinear landmarks ineach of two views of a shape, one can calculate the axis of rotation thatwould align one with the other. But can people really do this calculation?We convinced ourselves with a bit of computer animation. Roger Shepardonce showed that if people see a shape alternating with a tilted copy,they see it rock back and forth. So we showed ourselves the standardupright shape alternating with one of its mirror images, back and forth