Chasing Moonlight

Dear Tin,

            I’m a hopeless romantic and I’ve just finished watching the movie adaptation of Nicholas Sparks’ Dear John. No, I’m not going to talk about romance or anything war-related. But there were two lines which struck me as I was watching the film, and the conversation went this way,

Savannah: Did you ever notice how big the moon is when it’s rising, and how little it is when it’s up in the sky?

John: Yeah, but it’s only perspective. It doesn’t matter where it is in the sky, or where you are in the world… it’s never bigger than your thumb.

            Yup, he’s probably right but I still can’t understand why. Can you help me?

Senserely yours,

Thinking-of-the-moon

Dear Thinking-of-the-moon,

           

          Hello there! As I am writing to you now, I can’t help but also notice how the moon seems to be far up in the sky (and yes, my thumb can also cover it when I stretch my arm). Just like you, I have also wondered how the moon plays these tricks until I came across certain theories which answered the questions I had in mind. Savannah’s question could be explained by elaborating on the moon illusion while John’s reply could be understood further by introducing the concept of visual angles--- which is also somehow related to the moon illusion, as we would see later on.

      

         The phenomenon when the horizon moon seems to be larger than the elevated moon is known as the moon illusion (Goldstein, 2010). Rock and Kaufman (1962) rejects the eye-elevation hypothesis proposed by Boring and his colleagues. According to this hypothesis, the horizon moon appears larger since it is viewed directly at eye level while the zenith moon appears smaller since the observer must look up. Rock and Kaufman (1962) offers an alternative view in which they tested the effect of the absence or presence of terrain through the apparent distance theory. The horizon moon is accompanied by a terrain which involves a number of depth cues as opposed to the overhead moon which has no terrain. Thus, this creates a perception of greater distance for the horizon moon. To further understand this, let’s bring in the concept of visual angles. Visual angle refers to the angle created by an object relative to the observer’s eye, and it depends on both the stimulus size and the distance from the observer (Goldstein, 2010). Thus, although the moon’s size and distance remains constant as viewed here on Earth, there is an apparent change in distance that results from the additional depth information provided by the terrain. This is why the horizon moon seems farther than the overhead moon. Despite this, observers may not be consciously aware that they are perceiving the horizon moon with a greater distance. Some even report that the horizon moon is nearer, and this may be due to the concept of relative size (Rock & Kaufman, 1962). Relative size states that when two objects are of the same size, the one that is farther away takes up less of the visual field than the closer one (Goldstein, 2010). Thus, observers may reason out that the horizon moon is nearer since it appears to be bigger, but this is not what the apparent distance theory seeks to explain. 

        Rock and Kaufman (1962) claim that the terrain is crucial in forming the moon illusion, and the varying magnitude of the illusion is influenced by terrain and sky conditions. They also found that obstructing the observer’s view of the terrain leads to the disappearance of the illusion and inverting the terrain that comes with the horizon moon lessens the said illusion. Moreover, they acknowledged that another factor might play a role and cited the effect of framing or relational effect which is the case when the horizon moon is viewed between buildings or other land objects. This brings us to the next theory, the angular size contrast theory which states that surrounding the moon with larger objects makes it appear smaller, as what happens when the overhead moon is surrounded by the whole stretch of the sky (Goldstein, 2010). According to Plug and Ross (1994), there is an increase in the perceived angular size of horizon objects by about a factor of 1.5-2.0 in diameter. No wonder that the moon seems bigger when viewed in the horizon. This illusion is likewise affected by scene details. (Note that we keep on using terms like apparent and seem because we are analyzing things based on how perceive them and not on what is actually out there)

          Now that we have addressed your first concern, we move on to the next one. John said that wherever you are in the world, the moon would never be bigger than your thumb. How could this be when we know for a fact that the moon has a diameter of about 2200 miles as compared to the very small width of your thumb? Literally speaking, the moon is way much bigger than our thumb, but if we put things into perspective, what John said was right. Considering that the moon is 245,000 miles away from Earth, the resulting visual angle (which we talked about earlier) becomes very small, and measures at around 0.5°. The thumb held at arm’s length, on the other hand, compensates for its small size with its much closer distance to the eye. Thus, it has a visual angle of 2° when held at arm’s length. Since the moon’s visual angle is only ¼ of that of our thumb, we do not have trouble covering the moon. 

         It's amazing, right? I hope you got something from here. If you want to explore more about visual angles, why not try covering the moon with your pinky finger? PS: Tell me if it also works that way. :D

Senserely yours,

Tin

References:

Dear John. [Photograph]. Retrieved on February 5, 2014, from: http://wakeups.livejournal.com/868.html

Goldstein, E.B. (2010). Sensation and Perception. Belmont, California: Wadsworth Cengage Learning

Rock, I., & Kaufman, L. (1962). The moon illusion, II. Science, 136(3521), 1023-1031.

Plug, C., & Ross, H. E. (1994). The natural moon illusion: a multifactor angular account. Perception, 23, 321-333.