You Can't Always Believe What You See With INQ's Ambiguous Illusion Kit


Inq’s Ambiguous Illusion kit is treasure trove of transmogrification, full of shapes that don’t behave as they should. Rotate the arrow around, and it always points in the same direction! A square, a pentagon, and a hexagon somehow appear to be complete circles when viewed from behind, but when seen from directly above, the shapes look like strange hybrids of both forms. WHAT’S GOING ON?

The pieces in your kit are some of the most unusual individual shapes ever devised: they exhibit what their creator calls “anomalous mirror symmetry” and are examples of anamorphosis, the process of making something that appears one way when viewed from a specific perspective, but may not appear at all when viewed from any other one. You can see this in two ways with your kit: you can place the objects in front of the included mirror and view the objects from both sides, or put them on the included base and simply rotate them around.

These shapes were created by Kokichi Sugihara, a professor of engineering at Meiji University in Tokyo. Sugihara first came across these types of objects when he created a fascinating computer program with an unusual function: when you gave it a 2-dimensional drawing, it would come up with a list of 3-dimensional objects that could create that drawing when projected onto a flat plane (think of it like taking a shadow and backwards computing all the things that could have cast that shadow). Sugihara became interested in what would happen if he fed it “impossible objects” – the same sorts of M.C. Escher-like designs that Jake covered in an incredible Vsauce3 video. On a randomly related note, Sugihara is also known as a showman: when he first unveiled his mind-bending shapes, he appeared onstage dressed up as an old prospector, including a helmet and pickaxe.

But back to your illusion kit–what’s happening here? It’s a fantastic display of the distinction between vision and perception (or specifically, visual sensation and perception). Sensation is the raw visual data sent to your brain; perception is how the brain interprets that information. Basically what happens is that it uses an algorithm, a series of shortcuts to help process all that data. To some degree, this is a reflection of the law of parsimony, often referred to as Ockham’s razor: the brain can’t really afford the time or resources to fully consider all the bizarre possibilities for what it sees, so it goes with the choice that makes the fewest assumptions. In this case, which is more likely, that a brilliant mathematician would try and fool the brain with a series of strange angles and shadings on a weirdly shaped object, or that you’re just looking at an arrow?  

So what perceptual tricks are we dealing with here? Sugihara himself thinks the most relevant is that the brain likes to perceive right angles, whether they really exist or not.  If there are a set of three lines in different directions, it’s primed to see them as angles, with edges that converge. You’re also being tricked because of the slopes on these shapes, which create shadows and even small areas of occlusion, or the blocking of visual data. When that happens, there is a perceptual trick called “visual completion” where our brain fills in the gaps; we see partially hidden surfaces as complete. And visual simplicity theory suggests that we have a strong tendency to see the simplest or most complete shape possible.

In the case of the arrow, for example, when you look at it from the top down, you can see that the real object is a symmetrical shape; but when you view it from the side, the undulating surfaces throw the brain into a bit of a tizzy trying to sort out what you’re looking at; it settles on the most familiar object that makes sense, in this case an arrow. Our experiments show the objects in your kit are best viewed from an angle between 40° and 80°.

Sugihara considers these ambiguous objects to exhibit an entire new type of symmetry, one you can now enjoy in your own home.  If you’d like to see his original paper announcing the creation of these shapes, it gives more insight into the detailed geometry of the forms. And if you’d like to check out another of Sugihara’s amazing discoveries, look at his topology-disturbing objects, a series of shapes that have radically different shapes–even different numbers of openings–when viewed from different sides.

And remember: you can’t always believe what you see.

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