Why when the moon is above the horizon line does it seem bigger to us than when it is in the sky
Yanai Ofran
This phenomenon is familiar to anyone who pays attention to the moon. When the moon shines and is above the horizon it looks huge, but when it reaches the dome of the sky it shrinks in a mysterious way, and looks much smaller. If you try to investigate the phenomenon, the mystery only increases. You can, for example, take a shekel coin and hold it in front of your eye so that it almost exactly covers the big moon on the horizon. If indeed the moon "shrinks" when it is in the middle of the sky, it is reasonable to expect that if we hold the coin in front of it, at the same distance from the eye, it will cover the moon. But whoever performs this simple experiment will prove that the size of the moon has not changed at all. Even now the coin will almost cover the moon.
This riddle was nicknamed the "moon illusion", and it has been preoccupying astronomers and researchers for hundreds of years. Dozens of books, articles and studies have tried to explain what causes us to err in estimating the size of the moon. But every time an explanation was proposed, researchers immediately arose who found it absurd. To date, no convincing explanation has been found that is supported by conclusive evidence.
Last Tuesday, an article was published in the Journal of the American National Academy of Sciences (PNAS), in which a neuroscientist from New York University claims to have solved the mystery. Prof. Lloyd Kaufman is already retired, but continues to research the moon illusion. His son James, a physicist at IBM Laboratories, helped him design an experiment that could decide the debate.
The moon illusion, and this is clear to everyone, is caused by a mistake of the brain in interpreting what the eye perceives. Its old explanation suggests that the horizon is perceived by the brain as farther than the sky. If the horizon is further away, the mind assumes, the moon should appear smaller when it is there. But despite the expectation of a smaller moon, the actual size of the moon does not change so it appears larger than the mind expects. According to this explanation, the size of objects is determined in the brain by their approximate distance from the viewer.
Another explanation suggests that the difference is due to the difference in the way we look at the moon when it is on the horizon and the way we look at it when it is in the center of the sky. When the moon is above us, we have to raise our head and this angle of view causes the brain to interpret the information coming from the eyes differently. Therefore, proponents of this explanation suggest, when the moon is at the edge of the horizon it appears closer. According to this model, the distance of objects is estimated by their estimated size.
On top of these basic explanations, over the years the researchers added more models and explanations. Some have suggested, for example, that when the moon is at the edge of the horizon it can be compared to familiar objects, such as houses or trees, and then it appears very large. When he is high in the sky there is nothing to compare him to.
Kaufman supported the first and oldest explanation, but for years could not find proof of it. The experiment he planned with our help provided this proof. With the help of a laptop, the two built a display system, which projected images of two moons onto semi-transparent glass. They climbed a high mountain near New York, with the laptop and a group of volunteers. When the volunteers looked through the semi-transparent glass, they saw the view from the top of the mountain, with the two moons above it. The glass could be placed in such a way that the moons would appear as if they were standing on the horizon line, or alternatively as if they were at an angle of 45 degrees above it. One of the moons remained fixed in its place, and the other moon could be moved with the help of the computer so that it would appear closer. In both situations, the volunteers were asked to move the mobile moon until it was half the distance between the volunteer and the fixed moon. This way the researchers could measure what the volunteers think is the distance between them and the moon when it is on the horizon, and what is the distance to it when it is higher in the sky.
If the first theory is correct, and the reason the moon is perceived as larger is that it is perceived as further away, the subjects will estimate that the horizon is farther than the sky. The second theory states that the moon is perceived as larger because of the difference in the angle of the eyes when looking at the horizon and when looking up, and therefore the horizon appears closer. If it is correct, the subjects will estimate that the horizon is closer.
It turned out that when the artificial moon is at the edge of the horizon, the volunteers estimated that the distance to it is much greater than when it is in the dome of the sky. We expect that the farther away an object is, the smaller it appears, and since we perceive the horizon as farther than the firmament, we expect a smaller moon on the horizon. But the moon stays the same size even when it's on the horizon, so it looks bigger.
Time will tell, if the old mystery of the moon illusion has been solved, or if scientists will be found again this time who will reject the Kaufmans' proof. In the meantime, you can play demos of the experiment on the journal's website - http://www.pnas.org.
{Appeared in Haaretz newspaper, 12/1/2000}
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