Definition. Let be given the mental construction rules, by which the human consciousness reconstructs a spatial scenario from a two-dimensional picture. Then per definitionem those two-dimensional figures (or objects) are impossible whose reconstruction is no object of the three-dimensional world.
Existence. Impossible figures do exist, the simplest of which is the tribar, invented 1934.
Cause. Essentially, the paradox of an impossible figure is caused by the existence of multiple optical fixed points or areas. Focusing on one region of the figure, an observer then sees the reconstructed object in a completely different spatial alignment than focusing on another region. That's the trick: The construction rules applied by the mind work excellently in the small, the observer thinks to recognize an object in space - but in the large the informations do not make sense: a contradiction local versus global informations.
Mathematical consequences. Because an impossible figure locally is representable in the space without any contradiction, it is - up to the edges - a well-defined manifold, i.e., a (curved) closed surface or an open subset of the three-dimensional space (if one considers the interior of the object).
Seeing as data and information processing. Obviously, optical data at first are processed locally. Only this way it can be explained, why an impossible figure is interpreted as a spatial object at all, and not directly as a senseless agglomeration of lines. Not until now the mind tries identify the object as a whole, what fails completely. But instead of unmasking the scribble of lines at least by now, suddenly the local view again prevails, and the consciousness concludes: There is a spatial object... This state of tension (“superposition”) keeps on remaining as long as the impossible figure is observed. It seems as if there are two mechanisms of recognition (at different parts in the brain?) that wrestle each other permanently.
