Recently, a discussion of the “size of the moon” illusion has once again surfaced (see http://nautil.us/issue/24/error/your-brain-cant-handle-the-moon-rp).

(Caution: snarkiness ahead) There has been a lot of drivel written on this common phenomenon, mostly by people who don’t know what they are talking about. At the risk of adding even more drivel, I’m going to explain the effect so nobody else need ever write about it again.

First, some definitions and comments, so we all know what is being discussed.

1. The moon looks larger when it is on the horizon, rising or setting, than it does when it is higher in the sky.

2. It’s not just the moon, of course: the sun provides the same effect, but with the moon you are less likely to go blind staring at it.

3. The effect can be seen by people with only one eye (that is, it has nothing to do with binocular vision).

4. The effect can be seen even if you are on a ship in the middle of the ocean, with no trees, mountains, or buildings at the horizon for comparison.

Now for the explanation: it’s due to perspective.

That’s it. No need for fancy psychological/physiological theories.

“But, wait! Isn’t there more? Don’t statements numbers three and four completely rule out the possibility of perspective as the controlling factor?”

Um, no. No, they don’t. Humans perceive distance in a couple of ways. One is, to be sure, by using binocular vision. When we look at something nearby with both eyes, things farther away can’t be seen clearly because the retinal images of the distant objects can’t be fused, and vice versa when looking at distant objects. But the moon at the horizon, as well as the horizon itself, are effectively at infinite distance as far as our eyes are concerned. Binocular vision is irrelevant when considering the moon illusion.

Another way we judge distance is by the vanishing point. There is a well-known optical illusion of two lines that converge in the “distance,” and one object at the front of these lines, and the same object at the farther end. Even though the objects are identical, the one at the far end looks larger. This is the Ponzo illusion (see http://en.wikipedia.org/wiki/Ponzo_illusion). This is the one, essentially, that produces the illusion of the changing size of the moon. We compare the moon with other things at the horizon, and they look really, really small like the lines in the distance of the Ponzo illusion. The moon looks very big by comparison. The vanishing point causes us to estimate the size of the moon as much larger than anything we see on the Earth. When the moon is higher, there is no vanishing point to compare it with, and instead we compare it with the width of the sky. The sky is very wide, so the moon looks smaller.

“Ah,” comes the reply, “but I’ve got you now. Statement number four completely contradicts what you just said. There are no buildings, mountains, or trees on the ocean! You totally overlooked that small detail.”

Well, no, I totally didn’t. While it is true that there are no objects on the horizon at sea, there is still a vanishing point. On the ocean, the vanishing point is made of ocean waves and the reflections of the moon from those waves. The reflections form an isosceles triangle with you at the bottom, the short side, and the other two long sides pointing toward the moon, at the vanishing point, just as in the Ponzo illusion. It isn’t necessary to have mountains, trees, or buildings at the horizon, just a vanishing point. The ocean waves also look smaller in the distance, of course.

Even on “a featureless plain on a dark night” there is enough light furnished by the moon to reflect off surfaces and provide you with a vanishing point.

One more thing. It is true that the moon looks large at the horizon in comparison with the vanishing point, and smaller when it is high in the sky when there is no vanishing point. But the moon really is very large compared with any object on Earth. So maybe the real illusion is the fact that it appears so much smaller when it is higher in the sky.

You’re welcome.