The mental construction rules often admit to a given two-dimensional figure various three-dimensional situations. We speak of stereographic ambiguities. The figure on the left hand illustrates this phenomenon: The red line AB of figure a enables the consciousness at least three interpretations. Depending on the context, the position of the end-points A and B are determined differently. Correspondingly, the length of the line diverses.
The mental construction rules, especially the culturally given ones based on the prevalence of the right angle, can be applied easily to delude the human consciousness. Look at the figure on the right hand side. It shows a gate on a tiled floor. A simple shortening of the right post generates an impossible object, see left below. Our consciousness constructs a gate which extends simultaneously into two different spatial directions. However, would animals - or human beings of different culturs without right angles - construct an impossible object at all? Would not they perceive rather a Greek Gamma constructed of bars, whose shorter leg only is situated over one of the tiling squares just casually, due to the special perspective?
A wonderful example of delusion by contradictory interpretation of planes is Oscar Reutersvärd's picture Perspective japonaise no. 274dda (detail):
