00100		This is partly a reaction to A. J. Thomas' experimental proposal
00200	of December 6, 1971 and the proposed experiment of Roger Shepard included
00300	with it an partly an attempt to formulate some ideas of my own concerning
00400	mental images.
00500	
00600		The general problem arises from the fact that people have some
00700	kind of mental image of 3-d objects and scenes and
00800	can perform some kinds of computations with these images.  It seems
00900	to me that I have more than one kind of mental image so the problem
01000	may not be as simple as finding the image.  The general problem of
01100	interest to psychology and also to AI people who hope to gets some
01200	hints from psychological studies is to get some idea of what these
01300	human mental image capabilities are in order to imitate them by
01400	programs.  Whether the programs actually work and how well they work
01500	may in turn help the psychologist.
01600	
01700		Here are some possible experiments:
01800	
01900		1. Ask S to create an object mentally, perform various operations
02000	with it and then answer questions about it.  An example that I have made
02100	informal experiments with is the the following:  S is told,
02200	"Consider a one by two rectangle with the long dimension horizontal
02300	divided into two one by one squares.  Mentally draw the diagonals of
02400	the squares and also draw the diagonal of the rectangle going from
02500	the upper right to the lower left.  What lines does it cross?  Now
02600	erase the horizontal and vertical lines in the figure.  Note that
02700	the long diagonal crosses the left upper arm of the rightmost X.
02800	Does it cross this X closer to the upper left end of this arm or
02900	closer to the center of the X?  Determine the answer by visualizing the
03000	figure.  Do not draw the figure, and do not do mathematics."
03100	
03200		This problem is rather difficult, and most people don't get it.
03300	However, in my preliminary presentations, it seemed that people
03400	who asserted that they were reasonably sure of the answer almost all
03500	correct.
03600	The distance from the intersection point to the end of the arm is
03700	actually twice the distance to the center of the X.
03800	
03900		Another Euclidean experiment would be to ask a naive subject
04000	to estimate the ratio of the diagonal of a square to a side.
04100	
04200		These were metric 2-d questions.  3-d questions are possible
04300	and so are topological questions e.g. about knots.
04400