Another example of the use of spatial interpolation is seen in the man walking down the stairs carrying a large box that obscures the view of his feet. A single glance around the side of the box is enough to mentally map the stairway in sufficient detail to subsequently position the feet for a number of steps. This is really a rather remarkable feat that is difficult to explain without the use of a fully spatial map of the obscured portions of the view. The visual system appears to "fill in" the unseen portion of the stairway from the memory of that single glance, with the help of somatosensory feedback from the feet, as well as the spatial context provided by the surrounding stairwell. This geometrical model must be updated with every motion of the man's body in order to constantly monitor the critical distance between the man's foot and the next step. Again, this distance must be modeled with a high degree of precision, as can be seen by the small deviation in regularity of the stairway which would be sufficient to make the man stumble, especially if that irregularity were introduced after his initial glance at the stairway. Furthermore this example shows that the spatial mapping ability of the brain is not restricted to creating simple planes as in the case of the tennis player, but can map a more complex geometrical structure such as a stairway.
A simple mental exercise will emphasize this point. Imagine holding a geometrical box, shaped either as a cube, or a pyramid, or a truncated cone. It is possible to cup the imaginary form in your hands, and to polish its imaginary faces with your palm oriented at the proper angle, or to follow the imaginary corners between faces, with your fingers bent to the angles of the intersecting faces. The mental representation of the imaginary box, while lacking the vividness of a real percept, nevertheless can posses a high degree of spatial resolution and geometrical detail which is fully spatial in nature, and can be mapped exactly to the configuration of the body, compensating for the variabilities of posture.
The limitations of this spatial imaging ability are as interesting as are its capabilities. I can imagine the spatial arrangement of my living room, and I can imagine the spatial arrangement of the continental United States, but I cannot imagine both of them simultaneously in the proper spatial relation to one another. When at the scale of the United States, my living room is too small to resolve even as a single point, while at the scale of the living room the United States is collapsed into a single horizon line. This limitation is seen more clearly still when considering astronomical scales such as the size of the earth, the solar system, and the galaxy, or microscopic scales such as the cell, the molecule, and the atom. Like a roving eye, the imagination can image at any one of these scales at a time, but there are limits to the amount of spatial detail that can be represented at any single scale. This remarkable ability to automatically re-scale a limited spatial imaging capacity leads to the subjective impression that our mental imag ing capacity has no bounds. Studies by Kosslyn [7] however confirm the existence of such limits as measured by a time delay reported by subjects as they switch from one scale to the next.