Why is the moon so much bigger when it's rising and setting, compared with its size when it's high in the sky?

Practically everybody has noticed this oddity at one time or another. When the moon is low, near the horizon, it looks huge compared with how it looks a few hours later when it is higher overhead. The effect is especially noticeable when it is a big, beautiful, full disk—a full moon. But you can notice the effect at any phase. People have been wondering about this curiosity for at least two thousand years, since long before they even knew what the moon was or how it moves around Earth. (But you know, don't you? Any doubts?) Now would you believe that in today's so-called space age we can play hop-scotch on the moon, but we still don't know the answer to the puzzle about its apparent size? As you can imagine, people have come up with dozens of “explanations” over the years. But all save a few of them can easily be shown to be wrong.