Posts Tagged ‘Illusions’

I spoke at TED in NYC in December of 2012 on my grand unified theory of illusions. For more information, see my earlier book, The Vision Revolution. (For those with a strong stomach, see this journal article.)


Mark Changizi is Director of Human Cognition at 2AI, a managing director of O2Amp, and the author of HARNESSED: How Language and Music Mimicked Nature and Transformed Ape to Man and THE VISION REVOLUTION. He is finishing up his new book, HUMAN 3.0, a novel about our human future, and working on his next non-fiction book, FORCE OF EMOTION.

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You’ve heard that space is curved – that’s gravity. You’ve also been told that you cannot really understand curved space. Sure, you can come to know curvy mathematics by studying general relativity or differential geometry, but you cannot grasp curved space in your bones…for the obvious reason that, in our everyday human-level world, space is flat, and so we have a brain for thinking flat.

Or, at least, that’s what they say.

But there is at least one variety of curvy mathematics that your brain comprehends so completely that you don’t even know you know it. It concerns your visual field, and your innate understanding of the directions from you to all the objects in your environment.

In thinking about your visual field, it is best to imagine a sphere around your head, recording the directions to all objects in one’s environment. Call it the “projection sphere,” since it records in which directions objects project light toward us.

So, if you are standing in front of a row of six vertical poles, then they will project onto your sphere as shown below. In this figure, one imagines that you, the observer, are at the center of the sphere, looking in the direction of the cross.

Consider now the way these poles project…

First, notice that each pole appears straight in your visual field. They are not straight in the figure above, but remember that the observer in the figure is at the center of the sphere looking out. Each pole is straight on this projection sphere — and thus in your visual field — because each is what is called a “great circle,” extending in this case from the bottom to the top of the sphere like lines of longitude.

Second, observe that the poles are parallel to one another at the equator.

Yet, despite being straight lines that are parallel to one another, they intersect! Namely, the lines intersect at the top and bottom of the sphere.

Can this really be?

It can really be, and it is possible because of the non-Euclidean nature of the geometry of the visual field.   The geometry that is appropriate for the visual field is the surface of a projection sphere, and the surface of a sphere is not flat / Euclidean, but, well, spherical.

There are three main kinds of geometry for space: elliptical (including spherical), Euclidean (or flat), and hyperbolic.  How does one tell them apart? One way is to simply measure the sum of the angles in a square drawn in that space.

In Euclidean geometry, the sum of the angles in a square is 360 degrees. But for elliptical geometry the sum adds up to more than 360 degrees. In hyperbolic geometries, on the other hand, the sum comes to less than 360 degrees.  Back to the visual field, then, let’s “draw” a square on it and sum up its angles.

The figure above shows a square in your visual field. Why does it count as a square? Because (i) it has four sides, (ii) each side is a straight line (being part of a great circle), (iii) the lines are the same length, and (iv) the four angles are the same.

Although it is a square, notice that each of its angles is larger than 90 degrees, and thus the square has a sum of angles greater than 360 degrees.  The visual field is therefore elliptical, and spherical in particular.

One does not need to examine figures like those above to grasp this. If you are inside a rectangular room at this moment, look up at the ceiling. The ceiling projects toward you as a four-sided figure. Namely, you perceive its four edges to project as straight lines. Now, ask yourself what each of its projected angles is. Each of its angles projects toward you at greater than 90 degrees (a corner would only project as exactly 90 degrees if you stood directly under it).

Thus, you are perceiving a figure with four straight sides, and where the sum of the angles is greater than 360 degrees.

Your visual field conforms to an elliptical geometry!

(The perception I am referring to is your perception of the projection, not your perception of the objective properties. That is, you will also perceive the ceiling to objectively, or distally, be a rectangle, each angle having 90 degrees. Your perception of the objective properties of the ceiling is Euclidean.)

It is often said that non-Euclidean geometry, the kind needed to understand general relativity, is beyond our everyday experience, since we think of the world in a Euclidean manner. While we may think in a Euclidean manner for our perception of the objective lines and angles, our perception of projective properties — i.e., the directions from us to the world around us — is manifestly non-Euclidean, namely spherical.

We do have tremendous experience with non-Euclidean geometry, it is just that we have not consciously noticed it. But once one consciously notices it, it is possible to pay more attention to it, and one then sees examples of non-Euclidean geometry at every glance.


This piece was adapted from my book, The Brain from 25000 Feet (Kluwer), and first appeared so adapted at Sept 30, 2010, in Science 2.0.


Mark Changizi is Director of Human Cognition at 2AI, and the author of The Vision Revolution (Benbella Books) and the upcoming book Harnessed: How Language and Music Mimicked Nature and Transformed Ape to Man (Benbella Books).

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In the world of Harry Potter the one thing you don’t want to be is a “muggle”. Muggles are the regular folk lacking magical powers, and discrimination and prejudice against them is rampant. Muggles are not merely unable to attend Hogwarts School of Witchcraft and Wizardry, but are kept ignorant of the school’s very existence. In fact, muggles are kept in the dark about the entire cryptic world of magic altogether. The sorcerers struggle for the heart and soul of humankind’s freedom as the muggle folk blindly graze. Muggles are mutton.

In our world we are all muggles, but at least we can be content knowing we’re not missing out on all the cool stuff.

…because in the real world there’s no magic.

Or is there?

There may not be “true” magic in our world, but we have illusions. Gobs of them. And who’s to say illusions are not magic? Perhaps in Harry Potter’s world the spells only seem like magic because the natural principles underlying them are not well understood. And maybe sorcerers like Harry Potter have an inborn knack for employing these natural principles.

Illusions, I submit, are examples of real world magic. And the purveyors of illusions – artists and cognitive scientists – are our world’s sorcerers.

But not all real-world sorcery is made alike. Just as the spells taught at Hogwarts vary in potency, the illusions of our world vary in potency.

The three tiers of magic. 

The three tiers of illusion potency.

And Chris Chabris and Dan Simons, the authors of the new book The Invisible Gorilla, are among the most powerful of the real-world sorcerers. Their book is an engaging romp through a variety of cognitive illusions, with the theme that our intuitions often fail us. The book is written so well it would make Gladwell envious (and maybe a wee bit angry), and yet we must remember that these are the scientists themselves discussing their own discoveries and experiments. They have somehow mastered both the science and its communication.But it’s their master sorcery I wish to focus on here. Their illusions are at the top tier of real-world magic.

To appreciate just how powerful is their sorcery, let’s start at the lowest level of real world sorcery, and build up to “the invisible gorilla.”

The first level of visual sorcery includes illusions such as the Ames Room, the rotating mask illusion, and the uphill marbles illusion. Such illusions are exciting, but they are conceptually simple parlor tricks. These entry-level visual illusions rely upon ambiguity, or the fact that the light coming toward the eye does not uniquely determine what the world is like out there. The strategy is to devise an unusual scene that happens to look like something more common, and then let the hilarity ensue. For the Ames Room the true scene is a radically geometrically distorted room that happens to look like a normal square room from the right viewpoint; and the hilarity ensues when people stand in the two corners, in which case one person appears to be a giant relative to the other. Other examples of this first level are illusions like the Necker cube, rabbit/duck, vase/face and old-hag/young-maiden, where the strategy is to devise an image that could equally be due to two different scenes.

Why are these ambiguity illusions mere muggle magic? For starters, it is entirely unmysterious why the illusions occur. Magic needs to be enigmatic! And there’s a deeper reason why these ambiguity illusions don’t count as high sorcery: in a sense they are not illusions at all. One’s brain elicits a perception of its best guess about what is out there given the light the eye received. It just happens that the light sent to the eye was rigged so that the best guess would fail.

The more potent tiers of magic are not of this “ambiguity” kind. In “real” illusions the brain creates a perception that is not even consistent with the light that was sent to the eye! That is, for the higher tiers of sorcery, of all the scenes that could potentially have sent that light to your eye, your brain guesses a scene not among those! Now that’s an illusion!

The second level of visual sorcery includes the geometrical ones like the Hering illusion, where the two vertical lines project nearly parallel to one another in your eye, but you perceive them as bowing away from one another at the center. That’s a perception that is not consistent with the stimulus, and that makes it a real illusion, and a real mystery. These stimuli have the power of making people perceive something that couldn’t possibly exist out there. In my research I have argued that illusions of this kind are explained by your brain attempting to anticipate what the scene will look like when the perception is finally constructed a tenth of a second later, in order to overcome neural delays. In short, I have argued that the brain has mechanisms for anticipating the near future so as to thereby perceive the present. Here’s a short, four-slide introduction to the idea.

And now we get to level-3 sorcery, the dark and gorilla-ey stuff. Whereas the level-2 illusions involve perceiving angles a few degrees off, level-3 illusions can be radically stronger. …like invisible gorillas. In the real stimulus, as everyone knows, Chabris and Simons have a movie of basketball players, and during the video a person dressed up as a gorilla walks in, bangs on her chest, and walks off. For observers asked to count the number of ball passes, about half fail to see the gorilla. Their visual system has “gorilla all over it,” but they don’t see it because they don’t attend to it.

Now that’s magic. And not only is the invisible-gorilla illusion a radically stronger illusion than level-2 illusions, but it is also as or more enigmatic: although it is somewhat plausible that a lack of attention will lead to missed stuff, why shouldn’t the brain have bottom-up mechanisms that shift attention to large dangerous beasts that approach you menacingly?!

The sorcery of Chabris and Simons is so potent one suspects they’ve been dabbling with the darker forces of he who shall not be named. It can make those of us involved with level-2 optical illusions cower with respect at these superior sorcerers. It certainly made a muggle out of me.


This originally appeared June 29, 2010, at Psychology Today.

Mark Changizi is Director of Human Cognition at 2AI, and the author of The Vision Revolution (Benbella Books, 2009) and the upcoming book Harnessed: How Language and Music Mimicked Nature and Transformed Ape to Man (Benbella Books, 2011).

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Why do we see illusions? I talk about it with Jorge Salazar at EarthSky. See the podcast, at about 4 minutes in.



Mark Changizi is Professor of Human Cognition at 2AI, and the author of The Vision Revolution (Benbella Books) and the upcoming book Harnessed: How Language and Music Mimicked Nature and Transformed Ape to Man (Benbella Books).

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Ian Woolf of Diffusion Radio just reviewed The Vision Revolution, and you can hear the podcast here (15 minutes in).


Mark Changizi is a professor of cognitive science at Rensselaer Polytechnic Institute, and the author of The Vision Revolution (Benbella Books).

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David DiSalvo is a science writer for places like Scientific American, with his own Brainspin column at the True/Slant Network, and another column he calls Neuronarrative.

He recently interviewed me about my book, The Vision Revolution

Neuronarrative interview with me


Mark Changizi is a professor of cognitive science at Rensselaer Polytechnic Institute, and the author of The Vision Revolution (Benbella Books).

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It’s nearing the end of American football season, with the Super Bowl fast approaching. These games involve displays of tremendous strength, agility and heart. What you may not have known is that some of the most talented players out on the field are doing it all with their eyes closed.   Literally.    The American football player Larry Fitzgerald of the Arizona Cardinals made news last year when photographers captured him catching the ball with his eyes closed. He apparently does this all the time. And it is not just Fitzgerald who does this: after just five minutes searching online I found evidence that acclaimed college wide receiver Austin Pettis of Boise State, this year’s Fiesta Bowl Champion’s, closes his eyes when catching, as seen in the photo here.

Austin Pettis Boise State
How can these athletes be the best in the world, and yet close their eyes at what would appear to be the most important moment? It is less surprising than it first seems.

Our brains are slow: it takes about a tenth of a second between the time that light lands on your eye to the time that the resultant perception occurs. That is a long time. A receiver running at 10 meters per second (or about 20 mph) moves one meter in a tenth of a second. If the receiver’s brain were to take the information at the eye and turn it directly into a perception of what the world was like, then by the time the perception occurs a tenth of a second later, that perception would be tenth-of-a-second-old news.

The receiver would be perceiving the world as it was a tenth of a second before. And because he may move a meter in that amount of time, anything that he perceives to be within one meter of passing him will have already passed him – or collided into him – by the time he perceives it. The ball may be moving faster still, maybe 30 meters per second (about 70 mph) or more, in which case it can move 3 meters in a tenth of a second.

Seeing the world a tenth of a second late is a big deal. That’s why our brains evolved strategies for overcoming this delay. Rather than attempting to build a perception of what the world was like when light hit the eye, the brain tries to figure out what the world will probably look like a tenth of a second after that time, and build a perception of that. By the time that perception (of the guessed-near-future) is generated in the brain, it is a perception of the present, because the near-future has then arrived. A lot of evidence exists suggesting that our brains have such “perceiving-the-present” mechanisms. And I have argued in my research that a great many of the famous illusions are due to these mechanisms – the brain anticipates a certain kind of dynamic change that never ends up happening (because it is just a drawing in a book, say), so one gets a misperception.

Back to catching with your eyes closed. Consider now that the perception you have at time t is actually a construction of your brain: the brain constructs that perception on the basis of evidence the eye got a tenth of a second earlier. So, to accurately perceive the world at time t, one need not actually have any light coming into the eye at time t. …so long as one had light coming in a tenth of a second earlier. Perhaps Pettis can get away with his eyes closed at the catch because his brain has already rendered the appropriate perception by that time.

Of course, when his eyes are closed at time t (the time of the catch), it means he won’t have a perception of the world a tenth of a second after the catch; but by then he’s being tackled and would only see stars anyway.

Mark Changizi is a professor of cognitive science at Rensselaer Polytechnic Institute, and the author of The Vision Revolution (Benbella Books).

This first appeared on February 1, 2010, as a feature at ScientificBlogging.com.

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Click on each slide to see it in higher resolution.

Mark Changizi is a professor of cognitive science at Rensselaer Polytechnic Institute, and the author of The Vision Revolution (Benbella Books).

For more information about my theory, see LiveScience, New York Times, BoingBoing, SciAm. The best introduction is chapter 3 of The Vision Revolution. And the journal article is here.

This first appeared on December 24, 2009, as a feature at ScientificBlogging.com.

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Today I was on LateNightLive (of ABC Radio National) with host Phillip Adam.  In addition to divulging my enjoyment at running over pigeons, I got a chance to talk about sex, blood, the blind, writing, rabbit-heads and other topics from The Vision Revolution.

Late Night Live

Late Night Live

Check out the segment here. (Download the mp3.)

Mark Changizi is a professor of cognitive science at Rensselaer Polytechnic Institute, and the author of The Vision Revolution (Benbella Books).

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I was on the Lionel Show / Air America this morning, which was a blast!  Got to talk about my recent book, and about evolution, autistic savants, intelligent design, color, forward-facing eyes, illusions, and more. I really must get off the elliptical machine next time I do a radio show. Here’s the segment with me (or mp3 on your computer).

Mark Changizi is a professor of cognitive science at Rensselaer Polytechnic Institute, and the author of The Vision Revolution (Benbella Books).

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