Plato was the first person to challenge his readers to contemplate seriously the dimensionality of shadows. He appealed for dimensional empathy to great effect in the seventh book of the Republic in his allegory of the cave. In that allegory he proposed an unrealistic scenario: a race of individuals are from birth so constrained in all their movements that they can only see shadows cast on the wall of a cave. They never experience color or shade, and they are never able to touch the objects that cast the shadows. Yet they could obtain quite a bit of information about all sorts of objects from the lower-dimensional representations projected on the wall of their cave. In the allegory, the observers are shown the shadows of different kinds of objects, for example various urns. They could appreciate the shape of an urn, especially if it were turned around so that its symmetry became evident. A tall urn could be distinguished from a short one, and the more discriminating observers of shadows could put together an entire catalog of urns. We who are gifted with sight and freedom of movement can only pity the limitation of these poor creatures. We can imagine the amazement of a prisoner suddenly brought into the open to view the true solid appearance of the objects casting the shadows. The incredible disorientation could well drive the prisoner back to the safe world of the cave. Once the fear was overcome, however. the newly enlightened individual might have a great desire to share his insights with those still constrained. Plato fully realized the difficulty such a seer would face. The contented cave dwellers would scorn the suggestion that all their hard-earned lore of shadows was inferior to another kind of vision. The prophet could expect only rejection and even persecution, as was the fate of Plato's master, Socrates, described in the Apology.

			Drawing Shadows
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