Category theory doesn't take 10 years to explain. You should be able to explain to a willing, intelligent friend in two full days, and get them to a point where they see the beauty.
I've done similar things, like explaining the elegant beauty of aircraft component structural analysis -- got a decent appreciation across in 10 minutes. ("You know how a chain is as strong as its weakest link? A component is as strong as its weakest failure mode...")
The point is, you can explain it. That's a lot more than you can do for (much of) art, it seems.
The point is, you can explain it. That's a lot more than you can do for (much of) art, it seems.
Art can be explained. There just aren't that many people capable of explaining it; explaining things is a difficult skill.
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.