Cover Image: October 2008 Scientific American Magazine See Inside

A Perspective on 3-D Illusions

Paint and architectural illusions provide clues to how your brain reconstructs 3-D images














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Another spectacular trompe l’oeil illusion is at the Palazzo Spada, a palace in Rome that we visited last summer (c). Francesco Borromini created the illusion of a gallery 37 meters long in the courtyard with a life-size sculpture in daylight at the end of the archway. The gallery is actually only eight meters long, and the sculpture is just 60 centimeters tall. Even today artist Julian Beever creates perspective illusions in his sidewalk art.

A Matter of Perspective
The Leaning Tower of Pisa is not famous for its painted trickery, but it offers another architectural example that elucidates the brain’s processing. In the Leaning Tower Illusion, discovered by Frederick Kingdom, Ali Yoonessi and Elena Gheorghiu of McGill University, two identical side-by-side images of the same tilted and receding object appear to be leaning at two different angles (d).

The Leaning Tower Illusion—which won first prize in the Neural Correlate Society’s Best Visual Illusion of the Year Contest in 2007— ­reveals the way in which the visual system uses perspective to help reconstruct 3-D objects. We say “reconstruct” because the visual system has no direct access to 3-D information about the world. Our perception of depth results from neural calculations based on several rules. Such rules include perspective (parallel lines appear to converge in the distance), stereopsis (our left and right eyes receive horizontally displaced images of the same object, resulting in the perception of depth), occlusion (objects near us occlude objects farther away), shading, chiaroscuro (the contrast of an object as a function of the position of the light source) and sfumato (the feeling of depth created by the interplay of in- and out-of-focus elements in an image as well as from the level of transparency of the atmosphere itself). The Leaning Tower Illusion shows that the brain also uses the convergence angle of two reclining objects as they recede into the distance to calculate the relative angle between them.

The illusion does not occur when we view two leaning Japanese manga girls (e), even though the two cartoon images are tilted. The reason is that the cartoon girls do not appear to recede in depth, so our brain does not expect that they would converge into the distance. This phenomenon demonstrates that the brain applies its depth perception tool kit only in specific situations.

3-D from 2-D
Just as the painter creates the illusion of depth on a flat canvas, our brain creates the illusion of depth based on information arriving from our essentially 2-D retinas. Visual illusions show us that color, brightness and shape are not absolute terms but are subjective, relative experiences actively created by complicated brain circuits. This is true not only of visual experiences but of any sensation. Whether we experience the feeling of “redness,” the appearance of “squareness,” or emotions such as love and hate, these are the results of the electrical activity of neurons in our brain.

In the movie The Matrix, Morpheus asks Neo: “What is real? How do you define real? If you’re talking about what you can feel, what you can smell, what you can taste and see, then real is simply electrical signals interpreted by your brain.” What the movie doesn’t tell us is that even when Neo awakens from the fake world of the “Matrix” into the “real world,” his brain will continue to construct his subjective experience, as all of our brains do, and this experience may or may not match reality. So in a way, we all live in the illusory “matrix” created by our brain. Years before The Matrix, neurologist and Nobel laureate Sir John Eccles wrote: “I want you to realize that there exists no color in the natural world, and no sound—nothing of this kind; no textures, no patterns, no beauty, no scent.”


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  1. 1. quantumcipher 01:52 AM 10/16/08

    This article was particularly interesting, informative, but ultimately pessimistic. Although our perceptions of the world around us reside solely of our neurons, you have to remember that your perceptions and subsequent microcosm of thought is not where that world ends nor begins. Life, and the world around us, is more than just an illusion created by our neurons, and we should take time to appreciate the beauty & complexity of this "illusion" we see around us.

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  2. 2. sentience_iza_virtue 12:56 PM 10/16/08

    Based on the title, I expected a more detailed explanation of the inner workings of optic/neural interactions. Maybe the title should have been - "A history of 3-D illusionists"? The slide show was fascinating, but would have been more illuminating had they added secondary gif animations, moving a single line from one to the other to convince the skeptical. (I did it myself just to prove to my brain they were!)
    I also expected the talented sidewalk painter to get more than a one line credit - "Even today artist Julian Beever creates perspective illusions in his sidewalk art." Surely not the way to inspire readers to check out his work, which is pretty awesome. No honorable mention of bodypainting illusions, either, though some are not just sexy but creatively deceptive to the mind's eye.
    Final rant- the layout of SciAm articles is not user-friendly. IMHO, there was no good reason to strew this over 3 pages.

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  3. 3. rosabrand 09:56 PM 10/16/08

    Its bad enough that this nonsense is being inculcated in academia philosophy classrooms. Its an entirely different thing to suggest that reality is a figment of our imagination. Just try telling a starving child that his/her hunger is a figment of his/her imagination or a cancer patient that their condition is simply chemical in the brain not anything concrete as reality. Both the philosophical and scientific implications of his thesis are more devastating than any abuses people could suffer, because it suggests that not only should we accept on scientific grounds that nothing is real but that we couldnt possibly perceive anything real if it hit us in the face. A person is then left to whim or the loudest voice that forces an agenda. Sorry, Mr. Macknik and Ms. Martinez-Conde, you can fool all of us with this rhetoric. Try some sciences that actually help mankind, not blind and deafen him to the truth.

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  4. 4. WarDog927 in reply to rosabrand 02:02 PM 10/17/08

    to rosabrand. i think you read into it too much. lol.

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  5. 5. ralphskinner@hotmail.com 03:59 PM 10/19/08

    hunger and pain are subjective reality, they are real to the person experiencing them.
    That is different from oblective reality, or how our brains interpret outside reality

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  6. 6. fostvedt 06:02 AM 6/7/10

    It's just as provoking as always to read about how the "real world" is somehow disconnected from the experience of the human mind. They both exist in context of one another and are intricately bound together. I pose that you could might as well say that the "real world" is an illusion conjured up by an experiential founding as well as you could pose the statements made by this article. I think the way the terms 'illusion' and 'real' are used in sciences of the mind in general undermines this philosophical possibility. Besides, people feel a little miserable about being some caleidoscopic error factory floating around in the nowhere ever disconnected from what is 'real'.

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