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Perceptual psychologists have found that binocular vision has mostly second- and third-order effects. For example, it's necessary (but, as my own sad experience attests, not sufficient) for finding hidden pictures in magic eye images.

We get most of our ability to reconstruct 3D scenes from perceptual cues like relative motion and texture gradients. This takes enough mathematical mojo -- real-time 2D Fourier analysis for the latter, mapping between projective 2-space and euclidean 3-space for the former -- that they probably belong on The List in their own right...