Shape

137 What’s That or How Many?
figures on paper may alter erratically? The logo is like the five-pointed star. The parts
of faces interact as copiously as the parts of triangles and chevrons, and don’t fall
neatly into independent groups. Try to draw some of the faces without drawing the
others, or to erase one of the faces and keep the others intact. When it comes to
calculating, there’s no more to art—drawing, poetry, etc.—than to business, logic,
mathematics, and science. Simon thinks so, and so do I. But our intuitions run in
opposite directions. In art, there’s no more than meets the eye. This changes what calculating
is.
Of course, this isn’t the whole story. Drawings can be used in myriad ways. In
particular, Simon shows how drawings work ‘‘to resolve syntactic ambiguities’’ in sentences.
This one
I saw the man on the hill with the telescope.
is a good example of what he has in mind. His account of the matter is perfectly
straightforward.
This sentence has at least three acceptable interpretations; a linguist could, no doubt, discover
others. Which of the three obvious ones we pick depends on where we think the telescope is: Do
I have it? Does the man on the hill have it? Or is it simply on the hill, not in his hands?
Now suppose that the sentence is accompanied by [the] figure
The issue is no longer in doubt. Clearly it is I who have the telescope.
The figure has the list structure
SAW ((I, WITH (telescope)), (man, ON (hill)))
which does in fact disambiguate the sentence. But this list structure isn’t the only possible
description of the figure. It might also be
SAW (I, (man, ON (hill), WITH (telescope)))
Who has the telescope isn’t all that has to be decided. The location of the hill is in
doubt. The figure flips like a Necker cube, or Otto Neurath’s picture a-boy-walksthrough-a-door
on page 50 where the boy goes into or out of a house. How does Simon
know that he’s looking up at a hill from its base and not down at a hill across a valley?