Essay 6.3 The Moon Illusion

We should start with one basic fact. Measured in units of visual angle, the moon is the same size at its zenith as on the horizon (0.52°, to be precise), even if your well-meaning elementary school teacher told you that the atmosphere somehow magnifies the moon. If you do not believe this, measure it yourself. You will find that your thumbnail at arm’s length roughly covers the moon in all positions (depending a bit on your thumb size and arm length). This result may be hard to believe at first because the moon looks much bigger on the horizon than it does when it is overhead.

Why does it look bigger? We will offer one account, though it must be noted that there is still no universal consensus on the details of the illusion (in spite of literally thousands of years of speculation on the subject; for details, you can consult whole books on the topic). The first part of the story is that the visual system has no real idea how far it is to the moon. Even if you know at some level that it is about a quarter of a million miles away, distances this great are more than you can really fathom. So the visual system makes a wild guess about the perceived distance to the moon.

When you look at the moon on the horizon (A), you have some estimate of its distance and that makes it look a certain size. When it is high in the sky (B), it is the same physical distance and the same size on your retina, but if some part of you thinks it is closer (C), then it will appear to be smaller.

The strange thing is that the visual system appears to estimate this distance to be greater when the moon is on the horizon than when it is up in the sky, possibly because when the moon is low there are other objects along the ground plane to compare it to. It is as if the visual system assumes that the vault of heaven is an oval and not a sphere (see figure at right).

Now, here’s the critical step that leads to the illusion. If it is farther to the horizon than to the sky overhead, then a half-degree object on the horizon (e.g., the moon) must be physically bigger than a half-degree object high in the sky.

This is an old story. It can be traced back to the great Arabic scholar Alhazen (as he was known to Europeans; his real name was Abu Ali Hasan ibn Al Haitham), who wrote about it in the early Middle Ages. For just about that long, it has been known that there is a problem with this story. The difficulty is that the moon does not appear to be farther away when it is on the horizon. If anything, it appears to be closer. Why? Well, because it is bigger. Therefore, this story does not seem to add up. The moon looks bigger because it is perceived to be farther away—and because it looks bigger, it appears to be closer. Which is it—farther or closer?

The answer seems to be “both.” In one sense, this is just another example of the visual system tolerating contradiction as in the Escher pictures we saw in the text and in Essay 6.1 (Making the Implicit Explicit). This case is a bit different and seems to have something to do with the distinction between visual processes that are hidden to the observer and those that give rise to perception. Think of this as a three-step process (Boring, 1943):

• First, you have the image of the moon. Boring called this “the basic sensory excitation that identifies the perception.”
• Second, you have what Boring called the “context,” which are “all the other forms of sensory data that modify or correct the data of the core.” In this case, that context consists of the various depth cues that assign a size to the moon.
• Third and finally, the moon, with its apparent size, now becomes a depth cue in its own right.

You don’t really know how far it is to the sky or to the horizon. All you have are a collection of depth cues. Now you have one more: the known size of the moon. You are most familiar with the appearance of the moon when it is high in the sky. When you see the moon on the horizon, it looks bigger. One reasonable guess about things that look bigger than usual is that they are closer than usual. Thus, you can have a horizon moon that appears both bigger and closer than the moon high in the sky.

By the way, the illusion is reduced if you view the moon through your legs with your head upside down. Why might that be? We will leave that as an activity for the reader.

Reference

Boring, E. G. (1943). The moon illusion. American Journal of Physics 11: 55–60.