Perspective and the moon illusion

Judging distances

Not only how far away, but the way that you see it is very important.

with thanks to Henry Reed

One of the beauties of the night sky is the huge yellow moon skirting the horizon, so much bigger then the brighter moon we are used to seeing overhead, but the apparent size difference, noted and discussed from ancient times, is known to be illusory. This is easily demonstrated by comparing the size of the moon with the size of an index fingernail held at constant arm extension. Here the first surprise will be that in comparison to the nail, the moon is smaller than expected, typically from a third to a half of the nail’s width, it does not vary with the phase of the moon, the height in the sky and whether it is seen at day or night. So the common belief that the size phenomenon is due to atmospheric magnification can be ruled out. Then it can be argued that the moon is something special and the size effect is related to its emotional importance, but the weakness of this case is that the illusion is more pronounced, though less noticed, with the constellations; Orion and the winter triangle ( Sirius, Procyon and Betelgeuze ) being the best examples. They rise and set as great sprawls of stars, but overhead are far more compact, and this is strikingly noticeable at low latitudes. The sun also shows the effect, but for obvious reasons is not so widely observed. What the constellations emphasise is that the size illusion diminishes only gradually with elevation and is still quite noticeable at 20 degrees whilst the minimum size seems to be reached at about 60 degrees.

The conclusion that the illusion only applies to astronomical bodies that can be seen at any elevation is challenged by the phenomenon of holiday photographs.. What happened to those mountains? Why did they shrink?i

The second most favoured explanation for the illusion is the flattened sky effect. Most observers will agree that we perceive the sky not as a hemisphere, but as a flattened dish where the horizon appears to be further away than the zenith and the brain concludes that an object at the horizon must be bigger than one that produces the same size image when seen at the zenith and corrects the visual impression accordingly. This explanation has a good feel to it, but raises some interesting questions. For example; the moon is at the horizon; flanked by low hills and trees. A horseman gallops up and reins in in front of the yellow disc, or a bat flits past it. How are these objects perceived? The bat is a special case because it alone can fly past the moon when both are at high elevation, but, of course, we never know how far away it is. There are other objects that can be seen at all elevations and whose distance we can judge; these include the leaves of nearby trees and, more interestingly, the fingernail again, but this raises one of the great challenges of perception.

We live in a Cartesian world where the size of an object is not determined by its position or distance away and we have learned to absorb this into our body map, presumably created by the all-pervading muscle memory. We therefore know that our body parts do not (with some exceptions) change size with movement and so perceive them accordingly. However, to all intents and purposes, this Cartesian world is embedded in the visual world. Thanks to the amazing property of photons of totally ignoring each other, light is focusable to give realistic images of the whole universe, but necessarily obeying the inverse distance law. Things appear to be smaller when further away. There is a perceptual clash here, which must be resolved by compromise at the barrier of our personal space.

When we walk we see the body moving in a still world, but what the eye sees is quite different; the image of the world moves. If the brain’s contribution is weakened, as it may be by alcohol, then the real unreality of a still body in a moving world starts to encroach. Thus the brain is able to correct, seamlessly, the reality of the Cartesian world to the realities of the visual world.

A similar processing algorithm could also be applied to apparent size as a function of the angle of elevation of the line-of-sight. If this were to explain the moon illusion, it would also require that all objects were subject to a similar elevation-determined size illusion and this is of special interest because the main field of our visual activity is at low angle, arguably especially downwards. For example when standing close to another person the distance from the eye of their head is much less than that of their feet. An enormous correction is required to create the expected Cartesian reality.

The arguments now enter the world of subjectivity and may include the possibility that the details of the size illusion could be determined genetically or by developmental processes and differ between individuals, so that for some, or even many, the moon illusion might not exist .

The question, what size do things appear to have, now comes very close to home, but the answers remain elusive. Consideration of the human hand shows how difficult it is to discuss. From the furthest extension to the nearest point of distinct vision the distance of the hand from the eye and the linear size of its mage on the retina varies at least 10-fold, and the apparent area, in accord with the inverse square law, varies at least 100-fold. Because the brain ‘knows’ that there is no real size change, none of this is apparent. If asked the question, what size does the index fingernail appear to have at any distance from the eye, the first answer must be, it is always the same! That is the casual observing mode which serves our daily lives well, but if asked to make a more careful appraisal, it is hard to deny that there is a difference, but not on the theoretical scale outlined above, so, is there a default position that applies when we look beyond our personal space boundary and which, by extension, underlies the moon illusion?

The perceptual difference between the horizon and the zenith may be an entirely visual one, or it may be, in part due to our sensing of up and down from the gravitational field . Strangely enough, although gravitation acts vertically, the sense of vertically-up and vertically-down is nowhere near as strong as the sensing of the horizontal, which can be done in the dark and/or with the eyes closed. So although verticality is the primary datum, horizontality is dominant for our perception and if it does indeed influence size perception, then the relationship between the horizontal axis and the line-of-sight should be important.

The nature of the line-of-sight is easy to state but hard to define. It is indeed a paradigm for the expression hidden-in-plain-sight. Without it the visual experience would be very different, but its presence is never obtrusive. However, the moment cross-wires are mentioned, its nature is revealed. It is the line between a definite part of the fovea and the distant aiming point and its target is very small, certainly less than 1 minute of arc. It is a strong tie, perhaps the strongest tie, between the body map and the visual map.

The two models, the psychological model and the elevation model for the moon illusion can now be compared.

If the effect is purely psychological and comes from the fact that the moon is perceived as further away at the horizon than at the zenith. Does the horseman in front of the moon or the tree beside it escape the illusion, if so, how?

If size perception is controlled by a complex processing algorithm that uses as its guide the angle of elevation of the line of sight. The horseman, the tree and everything between the eye and the moon are subject to the same illusion and this mechanism has to be as robust as the analogous mechanism that creates the ‘moving eye in the stationary world illusion’.

     The psychological model, where the sky is perceived as a flattened bowl and astronomical objects as being on its surface does not provide a completely convincing explanation for the holiday snap disappointment effect and has no other implications for the distortion of perspective. However it is postulated that classical vanishing point perspective ( a true model of the visual world) is unsatisfactory, suggesting that modifying factors are at work.

    The elevation model, on the other hand, does have wide implications for perspective, especially concerning looking down. A larger part of our visual experience is arguably below the horizontal eye-line than above it, and the need to counteract fish-eye artefacts is acute. This leads to a prediction that the moon illusion would be even greater if the moon were to be seen below the horizon. It also focuses attention on the remarkable differences between looking down and looking up, as any hill walker or monument climber will understand.

By adding elements of the psychological model to the elevation model we can ask the question, what is our perception of below the horizon, the underworld and where in the imaginary map does the sun go when it drops over the edge? Regardless of the known reality of the spherical earth, the subjective feeling may tend to the cupcake model;

A smooth iced surface with a deep dark underneath

If this has any validity, it could colour the experience of looking down, which is, after all, one of the great sought-out experiences of our lives, perhaps known from childhood as the King-of-the Castle sensation, which could be explained if looking down magnifies apparent depth in way that looking up does not do to height.