In spite of some unresolved issues, the close match we have found between mental rotation and their counterparts in the physical world leads inevitab… - Roger Shepard

Most studies employing three-dimensional objects as stimuli have used simultaneous presentation whereas most studies employing two-dimensional objects have used comparison of a single visual stimulus with a memory presentation. We suspect that it is this procedural difference rather than the difference in dimensionality that is the principal determiner of rate of mental rotation.

A psychological space is established for any set of stimuli by determining metric distances between the stimuli such that the probability that a response learned to any stimulus will generalize to any other is an invariant monotonic function of the distance between them. To a good approximation, this probability of generalization (i) decays exponentially with this distance, and (ii) does so in accordance with one of two metrics, depending on the relation between the dimensions along which the stimuli vary. These empirical regularities are mathematically derivable from universal principles of natural kinds and probabilistic geometry that may, through evolutionary internalization, tend to govern the behaviors of all sentient organisms.

I suggest that the psychophysical function that maps physical parameter space into a species' psychological space has been shaped over evolutionary history so that consequential regions for that species, although variously shaped, are not consistently elongated or flattened in particular directions.