Moon Illusion

from Michael’s Visual Phenomena & Optical Illusions

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Moon Illusion

What to do & see

In the above picture the size of the moon varies: it becomes smaller when the mouse hovers over the image (or you tap it). Which size is the correct one, given the perspective of the scene? Answer: the smaller one, nearly unbelievable.

Comments

The “moon illusion” consists of two phenomena: (1) the moon appears larger than it actually is, and (2) this enlargement is much stronger on the horizon than at the zenith. Generally, any celestial object near the horizon looks larger than if the same object is high on the sky. But it really is an “illusion”: stellar objects do not change their size with their elevation in the sky. You can test this easily yourself: With an outstretched arm, 2/3 of the pinky cover the moon, irrespectively of its elevation. Actually, there is a tiny wee effect near the horizon: The moon is vertically shrunk a wee little bit because the light rays pass through denser atmosphere near the horizon.

The painting

The moon in the painting is of “aesthetically correct” size. By placing the mouse over the picture (or tapping it) the actual size is seen (picture from Rock 1984, based on the painting by Honoré Daumier »O Lune! … Inspire-moi ce soir quelque petite pensée…« 1844).

[The painting reminds me of Spitzweg’s “Der arme Poet” (1839). With “Poète dans la mansarde (1842)” and “Locataires et Proprietaires: Brigand de proprietaire (1847)”, Daumier repeatedly took up this topic.]

Aristotle and the moon illusion

In many sources Aristotle is credited as the first to describe the moon illusion. However, he did not mention the moon when he wrote (be prepared, I find his logic difficult to follow). Aristotle (Meteorology, Book III, section 4) wrote:

Sight is reflected from all smooth surfaces, such as are air and water among others. Air must be condensed if it is to act as a mirror, though it often gives a reflection even uncondensed when the sight is weak. Such was the case of a man whose sight was faint and indistinct. He always saw an image in front of him and facing him as he walked. This was because his sight was reflected back to him. Its morbid condition made it so weak and delicate that the air close by acted as a mirror, just as distant and condensed air normally does, and his sight could not push it back. So promontories in the sea ‘loom’ when there is a south-east wind, and everything seems bigger, and in a mist, too, things seem bigger: so, too, the sun and the stars seem bigger when rising and setting than on the meridian.

The case of “a man… morbid condition” would now be recognized as a heautoscopy (Brugger et al. 2006), thus a psychological, not a physical phenomenon. That “stars seem bigger” is a surprising statement, since generally they are point sources. Still, the sun (which you should not gaze at w/o protection!) subtends the same angle as the moon, so we may as well accept Aristotle as the first descriptor of the moon illusion. Aristotle attributed the illusion to atmospheric conditions; he was no experimenter.

Explanation

Most plausible to me is the size constancy hypothesis. Von Helmholtz (1911) ascribes this to Ptolemy, some hundred years after Aristoteles. For our visual system to arrive at the size of a visual object, it has to multiply the size on the retina (e.g. 10,000 ganglion cells wide) with the perceived (assumed) distance. In case of the moon, the retinal size is always the same, but what about the perceived distance (the reality, ≈300,000 km, is not accessible and beyond comprehension anyway)? I would here like to introduce the concept of a “default distance”. When nothing is known about the distance (e.g. in the desert, gazing at a moon at zenith), but a distance multiplicand is needed (see above), a default is assumed by our perceptual system. I suggest this default is an “accessible” distance (e.g. by walking), so a kilometer or so (likely with marked interindividual differences); this results in a perceived moon size. When context indicates that the moon is farther away than “default”, the muliplicand is larger, and thus the moon appears larger. “Context” could be, for instance, provided by mountains at the horizon (→farther away than default), or terrain in general. Mistiness of the air lets the moon appear more distant due to aerial perspective (Aristotle’s “atmospheric conditions”). So: the moon illusion occurs whenever the perceived distance is larger than the individual default distance. The “flattened vault of the sky” is the same phenomenon.

Amazingly, when you bend over and look through your legs, the moon illusion is greatly diminished (Coren 1992, Higashiyama & Adachi 2006)! This underscores the influence of context on size constancy.

If you see photos of a huge moon with comments like “the blood moon is particularly large tonight”, they were taken with a telelens (long-focus): That changes the relative size of near and far objects and in the image the moon really is enlarged. This has nothing to do with the moon illusion.

Sources