Oh and GrayMare, if you performed your experiments with just the square or the single sided square (as in what a wall or window are 90% likely to be) please see the other posts here, they show that the light doesn't see these props at all but only recongizes 3d objects, that is objects with values of more than zero on all three axis. Note the different results between the square and the cube shown above. Also the fact that the cube went from casting a shadow to casting no shadow when I scaled iot to zero on the y axis.

"Your work is to keep cranking the flywheel that turns the gears that spin the belt in the engine of belief that keeps you and your desk in midair."

Annie Dillard