It’s Not a Trick, It’s an Illusion

I’ve stumbled on the Best Illusion of the Year Contest a few times, but this is the first year I’ve thought about the illusions mathematically.

Dave Richeson wrote two posts about this illusion by Kokichi Sugihara, one of the top illusions from this year. In it, (topological) cylinders appear to have either square or circular cross-sections depending on what angle you view them from. He used Geogebra to show how to derive a curve that has the requisite properties and made a template so you can put your own deceptive cylinder together.

Naturally, Richeson’s posts led me down an illusive, illusory, illustrative, or perhaps just illusional, rabbit-hole. The illusions on the contest website highlight various perceptual habits most people’s brains share—our preference for right angles, the way we infer motion from changes in light, and the importance of context in identifying shade—but not so many of them have obvious mathematical connections. Then I got to a color illusion that really grabbed me.

In June, Vi Hart, mathemusician and virtual reality researcher, posted a long, interesting rabbit-hole of a post about color perception on the eleVR blog. It starts with that late-night dorm room question “is my red your red?” and considers how our color perception might influenced or be influenced by virtual reality. What color effects will we be able to learn about and play with as VR gets better and more widespread?

The mathematics of color is fascinating and perplexing to me. I was strongly indoctrinated into the red-blue-yellow primary paint color paradigm as a child, and it’s been hard to unlearn that enough to understand how we actually see color in light. Nick Higham, applied mathematician at the University of Manchester, has a post about mathematics and color that explains some of the nuances.

To me, the most astonishing thing about these illusions is that even when you know the mathematical and perceptual reasons you see what you do, you can’t help but see it. Right now I’m stuck on these drifting Gabors.