## Thursday, January 17, 2013 ... /////

### Growing Moon near the horizon and binocular vision

When you see the Moon near the horizon, it appears larger than when the Moon floats somewhere in the middle of the sky.

If you haven't joined the club of witnesses of this optical illusion, you're a rare exception and you're invited to try to explain the illusion as seen by the humans whose vision is not as objective as yours. ;-)

Needless to say, the actual angular size of the Moon – and the size of the spot on your retina – is the same regardless of our satellite's distance from the horizon (although both fluctuate roughly by 10% due to the eccentricity of the Moon's orbit). The usual explanation is that the optical illusion is a variation of the Ebbinghaus illusion.

The Ebbinghaus illusion is what makes you think that the left orange is smaller than the right orange on the picture below:

Do you agree? Remarkably enough, their sizes are equal (check it by a piece of paper!). The left orange looks smaller because you are automatically comparing it with the surrounding large blue disks so the left orange is smaller relatively to objects around it which is why the brain misinterprets this comparison as the Moon's being smaller in the absolute sense. The opposite comment applies to the right orange – among dwarfs, almost everyone is a giant.

The Physics arXiv Blog discusses a paper by Antonides and Kubota that disagrees with this explanation. Instead, it proposes a similar interpretative explanation that depends on our having two eyes – and probably the stereoscopic vision.

They say that the explanation at the beginning of this article is unlikely to work because the reported effect is usually too large (while it's relatively smaller in the case of the Ebbinghaus picture above). Moreover, the effect disappears on the photographs, they emphasize.

Let me tell you something. I don't believe that stereoscopic vision is in any way necessary for the optical illusion of a "large Moon near the horizon". Clearly, no one can stereoscopically distinguish the distance 380,000 kilometers from infinity. Even the distance 5 kilometers on a typical horizon is indistinguishable from infinity. Both eyes are looking in directions that are totally indistinguishable from two parallel directions in practice. The brain may be "thinking" about the distances it would calculate from the binocular vision but all the actual results for the Moon's distance (and the distant houses' distance) are infinity regardless of Moon's size – which means that the binocular vision plays at most a trivial role.

An explanation I offer to you doesn't depend on binocular vision but it differs from the Ebbinghaus illusion, too. But I don't claim I am the first one who formulated it. It's likely that I have heard it somewhere in the very form mentioned below.

What we actually mean when we say that the Moon looks larger is that the brain determines that the "absolute size of the Moon" – and not the angular size – is larger when the Moon is near the horizon. Now, you may protest that the absolute radius of the Moon is always 1737.5 kilometers, regardless of its orientation relatively to the Earth and your town.

That's fine but our eyes and brains are clearly incapable of estimating that the absolute radius is this number. You may quantitatively calculate (and the eyes and brains may subconsciously estimate) the absolute radius as the angular radius multiplied by the Moon's absolute distance from the Earth. However, the latter just looks infinite!

I think that our brains never think of the distances as being infinite. In fact, they don't even think about the unimaginably long distances such as 380,000 km. Instead, they try to imagine that the distance of the Moon from the Earth is the minimum possible distance that doesn't contradict any observations that the eyes and brains are "forced to see".

When the Moon is in the middle of the sky, above your head, there is nothing to compare the Moon with so your brain instinctively thinks that the Moon is rather close, perhaps 1 kilometer (which already looks like infinity, whether or not you use stereoscopic vision, focusing of your lenses, or any other method). So your brain estimates that the Moon's radius is about 4 meters (you don't say it loudly but your brain thinks that it's a 4-meter white ball flying above the fields, doesn't it?). Note that 4 meters is smaller than the right answer 1,700 kilometers by the same factor by which the actual distance 380,000 km was reduced to 1 km.

However, when you see the Moon next to buildings that are 5 kilometers from you, the brain decides that the Moon can't possibly be closer than the buildings (especially if the Moon is partly behind them), so you subconsciously "expand your idea about the size of the Universe" and decide that the Moon is a ball of radius at least 20 meters (at the distance of 5 kilometers or so from you). A 40-meter ball looks larger than an 8-meter ball and that could explain the effect.

This explanation predicts that the perceived size of the Moon should depend on the absolute distance of the "objects at the horizon" from you, i.e. on the apparent distance to the horizon. Yes, I am also afraid that this prediction will fail but I still have the courage to offer this possibly wrong explanation. ;-)

Would you say that my explanation is inequivalent to the Ebbinghaus one?

#### snail feedback (18) :

I agree with your explanation but would the apogee and perigee (50345 kilometers difference) make a difference too ?

Dear Shannon, do you really agree?

Of course that apogee and perigee makes a difference as well - that was what I mentioned under the word "eccentricity of the Moon's orbit". ;-)

For understanding optical illusions you
should realize that they are playing tricks with your brain, doing
something it usually does. Have a meeting with a friend in your room
and ask him or her to walk to the door. In that case on your retina
in a two-dimensional array his image will shrink rapidly into a
becomes a ridiculous dwarf each time he walks away. A marvellous
thing happens: it makes from the dwarf someone as big as the person
who just stood in front of you. Of course, the moon is not a friend
walking away but your brain interprets it as an unknown object at a
certain distance. The larger the estimated distance, the more it has
to be undwarfed in order to get the real image (according to your
brain). On your retina the moon at the horizon is as large as the
moon above you. Consequently, your brain interprets the moon above
you as something closer by than at the horizon. The sky is like a
ceiling and the moon like a lamp above your head which you can
almost touch (don't equate your rational knowledge with the knowledge
of your visual system). The horizon is much farther away. You know
that from experience, whether or not you see buildings. Therefore,
your brain makes the moon bigger in the same way as it does with your
dwarf friend. Test the explanation by letting people make distance
judgements. By the way Lumo, a somewhat related subject is a thing of
four billion light years across at a distance of nine billion light
years. It seems that the Cosmological Principle is in trouble. I'm

What about the sun? I've never noticed that the sun looks bigger at sunset, though that might be because I seldom stare at the sun except at sunset.

I didn't read the fresh paper, but when I was intrigued by the Moon Illusion some 10 years ago, I read a few. One explanation did involve binocular vision. It was mostly related to the confusing signals that the eyes produce when they are moving trying to attain focus on the Moon (and on the foreground objects). For me personally, closing one eye never destroyed the illusion. Other explanations, that I find more plausible, are related to the imagined shape and size of the Sky Dome to which the Moon is glued, and to the perception of the closer foreground objects in the dark as being at the horizon, or vice versa.
When I learned that there are so many ways my eyes can deceive me, I found it much easier to accept the explanation that the Moon is just a light show. After all, no one has ever been there, right? ;)

"Sky Dome" is the winner. The earth is flat as a tabletop and the sun, moon and stars travel along the hemispherical firmament overhead.

I have never been to the "southern hemisphere". Marsupials are a myth. There is no "Australia".

Your explantation I heard a long time ago as the Ponzo illusion ( http://en.wikipedia.org/wiki/Ponzo_illusion). I haven't read the paper yet, I will this weekend, but I really don't see how binocular vision could lead to such an effect (just like you said).

it is the same. huge at sunset, small in the sky .http://curious.astro.cornell.edu/question.php?number=230

I though the Moon's eccentricity was playing the bigger role in the visual effect...

Dear Shannon, these are two completely different and independent effects so the word "the" in "the visual effect" is deeply confusing.

1. The perigee/apogee distance difference is *really* changing the angular size of the Moon by 10-15 percent while the near-horizon "enhancement" is just an optical illusion.

2. The near-horizon enhancement is said to increase the perceived size of the Moon by up to 100% while the perigee/apogee difference only makes 10-15%. So the former is stronger, not the latter.

3. The Moon is near the horizon (or at the zenith) independently of whether it is near the perigee or apogee.

Thanks Lubos. It's very annoying to realise how much our brain is playing tricks on us. I hate it.

The moon is always 2/3 of a thumb nail at arms length for me. Oddly enough, this does not destroy the illusion.

How do you explain that the Ebbinghaus illusion goes away when you close one of your eyes? You don't need to use a ruler.

Sorry, it doesn't go away for me. If I look at the picture with one eye only, I still see one orange much larger than the other. If you see something else, it must be your personal idiosyncrasy I just can't explain! ;-)

So it's nothing do with the cheese then?

Some years ago I thought of a way to prove that the moon on the
horizon was not magnified. One doesn't need to go outside to do
this.

Recall that the moon still appears round and not oval when
appearing big on the horizon. This means that any magnification
would need to be present on the horizontal axis. The moon
exhibits about a half a degree of angle to us. Imagine a circular
constellation that has 720 stars spaced half a degree apart.
Imagine its plane bisects our earth. Now with the constellation
above us, we should be able to see 360 stars spaced half a degree
apart. Imagine now that the earth rotates 90 degrees so that the
constellation circumnavigates our horizon with its 720 stars. If
there was magnification on the horizontal axis, the total angular
distance of the circle of stars would need to be more than 720 x
0.5 degrees, which is more than 360 degrees. But that is impossible!

Given that a powerful enough telescope can see stars in every
portion of the sky, it would be possible to define such a
constellation in reality.