Illusions are cool. They make me think something is happening when it isn't. When offered the classic illusion pictured to the right, I wonder at the color of A and B. How weird, bizarre, and incredible.
Today I looked at the above illusion and thought, "Why do I keep thinking A and B are different colors? Obviously, something is wrong with how I am thinking about colors." I am being stupid when my I look at this illusion and I interpret the data in such a way to determine distinct colors. My expectations of reality and the information being transmitted and received are not lining up. If they were, the illusion wouldn't be an illusion.
The number 2 is prime; the number 6 is not. What about the number 1? Prime is defined as a natural number with exactly two divisors. 1 is an illusionary prime if you use a poor definition such as, "Prime is a number that is only divisible by itself and 1." Building on these bad assumptions could result in all sorts of weird results much like dividing by 0 can make it look like 2 = 1. What a tricky illusion!
An optical illusion is only bizarre if you are making a bad assumption about how your visual system is supposed to be working. It is a flaw in the Map, not the Territory. I should stop thinking that the visual system is reporting RGB style colors. It isn't. And, now that I know this, I am suddenly curious about what it is reporting. I have dropped a bad belief and am looking for a replacement. In this case, my visual system is distinguishing between something else entirely. Now that I have the right answer, this optical illusion should become as uninteresting as questioning whether 1 is prime. It should stop being weird, bizarre, and incredible. It merely highlights an obvious reality.
Addendum: This post was edited to fix a few problems and errors. If you are at all interested in more details behind the illusion presented here, there are a handful of excellent comments below.
AndyWood gave a good explanation, but let me elaborate. If you saw the scene depicted, but in real life -- rather than on a flat paper or 2D screen -- you would be correct to infer that the actual, invariant colors of the tiles are different. But, since they are just pixels on paper or a screen, their invariant colors are the same, and yet your eyes tell you otherwise.
So are the eyes "wrong" in any serious sense? Well, let me put it this way: do you want
a) a visual system that gives the right interpretation of scenes that you are actually going to encounter often, but is tripped up by carefully designed optical illusions?
or do you want:
b) a visual system that gives the right interpretation for carefully designed optical illusions, but fails to catch many attributes of common scenes?
(Yes, there is a tradeoff. Your visual system encounters an "inverse optics" problem: given the retina images, what is the scene you're looking at made of? This is ill-posed: many scenes can generate the same retinal images. E.g. a given square could be far away and big, or close and small. To constrain the solution set, you need assumptions, and any set of assumptions will get some scenes wrong.)
Yes, you are wrong to think that the tiles have different colors. You are not wrong to prefer a visual system that gets most scenes right at the cost of getting a few scenes (like this one) wrong.
(Incidentally, I really like this optical illusion, and have it by my desk at work. What's so great about it is that once you see it, you can actually strip away everything that you think is causing the illusion, and yet they still look different!)