The Science Of Illusions In Four Easy Steps
By Mark Changizi | December 24th 2009 12:00 AM | 7 comments | Print | E-mail | Track Comments

Mark Changizi is Director of Human Cognition at 2AI, and the author of The Vision Revolution (Benbella 2009) and Harnessed: How...

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Many illusions are like spherically curved space. Below on the left (fig. 1 ) is a geometrical illusion, and on the right is a ball with some great arcs drawn on it.

Notice the similarities: the distortions in the illusion are qualitatively similar to the non-Euclidean nature of the contours on the ball.

Why? Is there something in perception that’s like curved space?

figure 1

The set of directions from you to things in the world is a curved space. When you are far from horizontal and vertical lines in the world, as shown on the top left (fig. 2), the lines project toward you fairly straight in your visual field; the ball on the top right shows how the lines project toward you. (Imagine you’re standing at the center of the ball, and moving in the direction of the cross, the imaginary ball moving along with you everywhere you go.)

When you get closer, as shown on the bottom left (fig 2), the lines project toward you with much more of a spherically curved-space quality, as the ball on the bottom right shows. E.g., the separation between the vertical lines at the center are greater than at high or low elevations.  This shows that your visual field is inherently a spherically curved space. And the curviness of the visual field is more apparent when objects get nearer (and thus fill more of the visual field sphere). Why, then, do we experience the illusion in Figure 1?

figure 2

Converging lines look like optic streaks from forward movement. The photograph on the left (fig. 3) was taken in a car moving forward, and ends up with optic streaks with a vanishing point indicating the car’s heading. The middle figure illustrates the streaks as contours, and the right figure is an exaggeration of the streaks.

Our eye fixations in real life are a bit like snapshots of a camera, and when your eye is presented with these stimuli, it thinks you are actually moving toward the vanishing point of the converging lines. Recall that the illusion in Figure 1 had converging lines like this, leading one to wonder whether the illusion (the perceptual distortions of the horizontal and vertical lines) is due to the visual system mistakenly believing that you are moving forward.

figure 3

Perceiving the present requires anticipating the next moment, and explains the illusion. Your brain would like to take the light that hits your eye and instantaneously create a perception. But it takes around a tenth of a second to create a perception, and by then a forward-moving observer has moved forward a little bit (as shown on the left), and the geometrical layout in one’s visual field has consequently changed (as shown in the middle).

Because of this eye-to-perception delay, you have evolved to build a perceptual guess of what will happen in the next moment, so that by the time that perception of the near-future is elicited, the future has arisen, and you thereby get a truthful perception of the present. When presented with a grid as shown in the upper right (fig. 4) but with converging lines overlaid as on the bottom right, your brain guesses it is moving toward the center, and so in the next moment the geometries of the grid will change to greater “display” their spherical curviness.

Your brain creates a perception of the geometries as they will distort in the next moment, and thus the illusion looks like the spherical space geometry in the middle bottom. It is an illusion here because you are not actually moving forward. In real life, though, you would typically encounter radial lines like that when you are moving forward, and the “illusion” would lead to correct perception.

figure 4

A dallop of non-Euclidean geometry, visual ecology, and future-seeing…and wallah, you have an explanation for the illusions.

A very interesting read. I have always enjoyed illusions, especially creating them. Here's a classic illusion of which I have created my own representation.

Mark -- Thanks for an interesting discussion of illusions. I wonder if you would comment on another illusion that incorporates actual, rather than perceived motion. I first noticed this as a teenager while walking on a large water pipe that crossed a wooded gulley. (Teenagers do this sort of thing.) When I reached the other side and looked up, a pipe-sized section of the forest seemed to be moving upward in my visual field! It seemed as though my brain accommodated the actual motion of the pipe while I was walking over the gulley, producing an illusion that slowed down its motion so that I could better keep my balance. In later years I noticed the same effect if I stared at a rotating disk for 30 seconds or so, then looked up at the wall. A disk-sized section of the wall seemed to be rotating in the opposite direction for a few seconds. This illusion was probably discovered and named years ago, but I wonder if you have anything to say about its neurobiology.

Tiff -- Here is my take on one of your points:

You wrote: “Our visual system is built off the RAM structure of our brain's design for smell, smell came first then other senses layered on top of it.”

Smell, defined as the sensing of volatile or soluble substances in the environment, certainly came first in the course of biological evolution, but at the level of the bacterial response called chemotaxis. When multicellular organisms with nervous systems appeared during the Cambrian radiation half a billion years ago, the ability to sense light also developed in the form of compound eyes: trilobites could “see”. Then 300 million years ago the first vertebrates appeared as fishes, with a nervous system that included a primitive brain and spinal cord. Their sensory nervous system could respond to smell, vision and tactile response to vibrations we would call sound. Then fast forward to the first mammals, small rodent-like animals that co-existed with the ruling dinosaurs. They probably did make a nocturnal living, as you suggested, by catching insects. But at this point the first mammals could respond to a full range of sensory inputs, basically what we have inherited 100 million years later.

Hi Dave,

Yeah, that's the motion aftereffect, indeed.  Akin to all kinds of adaptation to stimuli, so that we're optimally sensitive to modulations around baseline.  Any particular question?  And thanks for the response to Tiff!

-Mark
This is really interesting. Optical illusions have a very unique effect on the brain.

Mark

I couldn't help but think of this article today when I nearly tripped while walking through an airport.  The problem was that I stepped on one of those "moving walkways", except that it wasn't moving.  As a result, my brain tried to compensate for the normal case of when it is moving and I stumbled.  What's so disturbing about that event, is that even when you know that the walkway isn't moving, you still respond as if it were (conditioning, I guess).
Gerhard: for an added bonus score, stare down at the end of a moving walkway whilst remaining stationary yourself, for about one minute.  Now stand erect, tilt your head backwards, stare at the ceiling and take one pace forward. :)

Mark:  it seems that the motion illusion is also a time illusion - as has been remarked before, the 'now' we experience is a delayed signal from the past.  From your article, I would assume that the mental 'now' is at every moment a synthesis between what was expected, what happened and what is freshly expected.  Accordingly, my experience of 'now' must be a fiction, a blend of memory of what was and inspired guesswork about what is to come.  This, if true, would be yet another counterintuitive finding of science: memory is more accurate than current experience!
Patrick,

Let me wait and see how our health reform bill ends up before I take your advice.  Don't need to create any new "pre-existing" conditions. :)