Why do I keep thinking A and B are different colors?
Meanwhile I am thinking 'Wow! My brain can automatically reconstruct a 3D image from limited 2D input and even compensate for shadows and lighting. That is orders of magnitude more complex than the reverse, generating such images from a model such as those we add 3D cards to computers for'.
I don't particularly consider this an 'illusion', especially when it is not simultaneously acknowledged that it is an 'illusion' that A and B are squares on a 3D 'square X a bit' thing that also has a cylinder on top of it.
Wow, good point! I never thought about it like that. It raises the question: Why are people amazed when you say, "Tiles A and B are actually the same color -- check for yourself!" but they roll their eyes when you say, "There are no squares in this image -- check for yourself!"? In both cases, you can respond with, "Well, yeah -- if you don't interpret it like the scene it's trying to represent!"
I'm not a very good artist, so learning about how to create these illusions sounds like a good reason to take an art class, and help me appreciate what artists are doing. (Why didn't the first major breakthrough in cognitive science come from painters and sketchers?)
Of course, it probably wouldn't do much to help me understand why they can count random smears on a canvas as "art"...
I would much prefer to drink something that actually tastes good. If I want to further enhance this with a group of friends, great. But stop telling me beer tastes good. Keeping up with habits you've developed in pleasant situations is what "tastes" good. The psychoactive effects of a socially-acceptable product "taste" good. Beer, however, does not taste good.
It looks to me like you're trying to curry the 2-place predicate "tastes good to X" into a 1-place predicate "tastes good", without really specifying the X that you're supplying as an argument. Surely X isn't "everyone". And it can't just be "many/most people", since you've attached other conditions (like "psychoactive taste changes don't count").
In my experience, most things taste different the second or third time around. The stomach and intestines are connected to the nervous system, ya know - you get direct neural feedback on the things you put in your body. If that feedback is negative, you might find that substance A isn't quite so tasty the second time around. Does any modification of a taste count as a "refinement" in your eyes, rather ...
I am being stupid when my eye looks at this illusion and I interpret the data in such a way to determine distinct colors.
Not at all. In the context of the scene that this picture represents, A and B are absolutely different shades. On the contrary, I think your perceptual system would be poor indeed if it did not reconstruct context, and under-interpreted the picture as a meaningless 2D array of pixels.
(BTW, as with the necker cube, I find that I can consciously exert to experience the interpretation that I choose, without too much difficulty.)
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...
I identified a useful and cogent point in your post and it was this: Whenever you receive data from any source (your brain, your eyes, a drug study, Less Wrong) you've got to be aware of how that data has already been packaged. Taking the data at face value -- for example imagining your brain is actually making a claim about the RGB values of the pixels -- can lead to problems, misconceptions, mistakes.
Your eye didn't evolve to report trivia like, "These two colors are actually the same." Your eye is reporting the most useful information - from which direction the light is coming, the shaded region under it, and the fact that the floor is tiled.
Which is more amazing - this picture, or a picture that somehow tricked the average person into noticing two colors were the same, but didn't notice the picture also had floor tiling, light directionality, and shading? I'd say this picture is pretty tame in comparison to the picture that could do that.
I am being stupid when my eye looks at this illusion and I interpret the data in such a way to determine distinct colors.
Tell that to your ancestors who escaped from the saber-tooth cat hiding in the shadows at dusk.
A side note: The only reason that prime numbers are defined in such a way as to exclude 1 and negative numbers is because mathematicians found this way of defining them a bit more useful than the alternative possibilities. Mathematicians generally desire for important theorems to be stated in a manner that is as simple as possible, and the theorems about primes are generally simpler if we exclude 1. There is a more detailed analysis of this question here:
if you use a poor definition such as, "Prime is a number that is only divisible by itself and 1."
I have a fondness for this particular definition, and like to think of 1 as a "very special" prime number. To the extent that I usually give a little speech whenever an opportunity arises that (ahem) the only reason I know of that '1' is excluded from the primes (more often than not) is because almost every theorem about prime numbers would have to be modified with an "except 1" clause. But a natural definition (anything along ...
I'd have to pretty strongly disagree. To me, the "essence" of primes is that you can factor any number into primes in a unique way. That's the most natural definition. They're the multiplicative building blocks of the natural numbers; everything can be reduced to them. If 1 were prime, you could no longer factor uniquely.
I think you're really failing to grasp the content of the unique factorization theorem here. Firstly we don't think about factored numbers as products of primes up to permutation, we think of them as products of distinct prime powers (up to permutation, I suppose - but it's probably better here to just take a commutative viewpoint and not regard "up to permutation" as worth specifying). But more importantly, you need to take a multiary view of multiplication here, not a binary one. 1 is the empty product, so in particular, it is the product of no primes, or the product of each prime to the 0th power. That is its unique prime factorization. To take 1 as a prime would be like having bases for vector spaces include 0. Almost exactly like it - if we take the Z-module of positive rationals under multiplication, the set of primes forms a free basis; 1 is the zero element.
Uh? What do you mean by "obvious" in that last sentence?
(Post otherwise interesting, and I for one like them short.)
There's a rather awesome colour constancy optical illusion in this American Scientist article - click on the enlarge image link on the rubik's cube image. I've mirrored the image here in case the link goes dead. The blue tiles in the left image are the same shade of grey in RGB terms as the yellow tiles in the right image. H/T to this article.
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.