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June 28, 2008

Who you gonna believe? Me, or your lying eyes?


What if I told you the two tabletops above have identical shapes and sizes?

You'd say no way.

That's precisely what I said.

From Gerd Gigerenzer's fascinating book, "Reckoning With Risk: Learning To Live With Uncertainty": "Roger Shepard's 1990 'Turning the Tables' (top), a depth illusion..., illustrates how our perceptual system constructs a single, certain impression from uncertain cues. You probably see the table on the left as having a more elongated shape than the one on the right. The two surfaces, however, have exactly the same shape and area, which you can verify by tracing the outlines on a piece of paper. I once showed this illustration in a presentation during which I hoped to make an audience of physicians question their sense of certainty ('Often wrong but never in doubt'). One physician simply did not believe that the areas were the same shape. I asked him how much he wanted to bet, and he offered me $250. By the end of my talk, he had disappeared."

"What is going on in our minds? Unconsciously, the human perceptual system constructs representations of three-dimensional objects from incomplete information, in this case from a two-dimensional drawing. Consider the longer sides of each of the two tables. Their projections on the retina have the same length. But the perspective cues in the drawings indicate that the longer side of the left-hand table extends into depth, whereas that of the right-hand table does not (and vice versa for their shorter sides). Our perceptual systems assume that a line of a given length on the retina that extends into depth is actually longer than one that does not and corrects for that. This correction makes the left-hand table surface appear longer and narrower."

"Note that the perceptual system does not fall prey to illusory certainty — our conscious experience does. The perceptual system analyzes incomplete and ambiguous information and 'sells' its best guess to conscious experience as a definite product. Inferences about depth, orientation, and length are provided automatically by underlying neural machinery, which means that any understanding we gain about the nature of the illusion is virtually powerless to overcome the illusion itself. Look again at the two tables; they will still appear to be different shapes. Even if one understands what is happening, the unconscious continues to deliver the same perception to the conscious mind. The great nineteenth-century scientist Hermann von Helmholtz coined the term 'unconscious inference' to refer to the inferential nature of perception. The illusion of certainty is already manifest in our most elementary perceptual experiences of size and shape."

As has been remarked in the past, "If you can't tell a difference then there is no difference."



your avatar's on the line....

June 28, 2008 at 02:01 PM | Permalink


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Hey! How come when I turn my laptop sideways, the right-hand table still looks wider and shorter and the left-hand table still looks longer and thinner? Is it because of the legs (thus, the context of objects and how my mind expects tables to look)?

Posted by: | Nov 25, 2008 12:55:18 AM

Measurements taken directly from my flat screen monitor by digital caliper:

Table on left.

Long sides 67.5 & 68.1 mm
Short sides: 26.5 & 29.1 mm

Table on right.

Long sides 62.3 & 64.8 mm
Short sides 30.3 & 30.7 mm

I will concede that identical shapes can look vastly different in different perspectives, however (at least on my monitor, and perhaps this is the problem?) this picture is not an accurate example of that illusion.

Posted by: Tim | Jun 29, 2008 6:42:00 AM

That is amazing. I thought when lookin at this -"what's this Joe guy been smokin?" You still don't get it unless you measure. Hey let's go find the guy that stiffed you on the $250.

Posted by: wistrade | Jun 28, 2008 3:55:32 PM

Identical? Not quite.

I grabbed the larger version of the image, fired up good old photoshop, and rotated the "wide" version to match the "long" version, then layered them.

Here's the result: http://www.openthefuture.com/images/notquite.png

They're definitely close, close enough that your larger point remains true. But they're definitely not identical, and one could argue that the seemingly slight differences are still enough to trick the eye.

Interesting post, as usual.

-Jamais Cascio

Posted by: Jamais Cascio | Jun 28, 2008 3:26:31 PM

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