ABSTRACT
A sentiment expressed by J. J. Gibson serves as a guide: If the theories of space perception do not provide an adequate explanation for the visual control of locomotion in animals. The dragonfly’s perceiving modulates its acts and its acts modulate its perceiving in a form of causality that is best expressed not as a cycle of separate events but as the co-occurring events of a temporal Mobius Band. Mathematically speaking, the two distinct classes of parameters, those relating to perception and those relating to action, are duals that together form a duality. The Mobius band and the relation of cube and octahedron are illuminating. In respect to cube and octahedron, although they are pictorially different, they are identical in respect to symmetry operations—intuitively, the ways one can do something to a thing so that having done them the thing looks the same as before.
