Bizarre Illusions

Why are people amazed when you say, "Tiles A and B are actually the same color -- check for yourself!" but they roll their eyes heir eyes when you say, "There are no squares in this image -- check for yourself!"?

It's about expectations. People expect to be able to take (physical) objects that appear to be different colors, examine them under a variety of contexts, and always perceive them as different. People incorrectly extrapolate that expectation to images, and thus find the fact that removing the context reveals these images to be the same colorRGB surprising. They also expect to be presented with representations, so pointing out the fact that they're looking at a representation seems silly to them.

Of course, it probably wouldn't do much to help me understand why they can count random smears on a canvas as "art"...

By way of reversing the ADBOC concept, I disagree denotationally but confirm your connotation. As you explain in the cousin several times removed post, many kinds of art are bullshit. Cultural preferences that would not be particularly likely to be rediscovered if all trace was removed. This differs from other forms of art which are more specifically directed at aesthetic preferences intrinsic to humans.

Of course, immersing yourself in a culture and experiencing the flow of status first hand is the perhaps the best way to get an intuitive anthropological understanding. I found, for example, that having done a research degree in a subfield of AI helps me understand how peer affiliation by persisting with researching silly ideas can be counted as 'science'.

http://lesswrong.com/lw/1om/bizarre_illusions/1iub

That last line is coming from a decidedly unrational state of mind!

I was never able to do it with this one before, either. What I'm doing now is concentrating hard on the two tiles of interest, until the rest of the picture fades into the background. The two tiles then seem to be floating on a separate top layer, and appear to be the same shade.

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!)

Your understanding of the word 'colour' does not match what properties of the world your brain is trying to identify and categorize when it interprets 'colour'. The interesting constant property of objects in the world that makes 'colour' useful to your visual system for purposes of object identification and categorization is really the surface properties that interact with incident lighting. Your brain attempts to ignore effects due to lighting variation and assign a 'colour' label to objects that is more or less an invariant property of the surface under a variety of different lighting conditions. This is in general not a solvable problem since the same incident photons can be produced by a number of different lighting and material combinations. Optical illusions like this merely reveal the heuristics your visual system uses to identify the relevant constant aspects of the scene and ignore the irrelevant lighting variation. They generally work quite well.

As others have pointed out, the difficulty here is more in the semantics of "color" than in the optics.

As a simplification, we can consider the projected color.P of a tile to be a product of its surface properties (color.S) and the intensity of the incident light. The illusion straightforwardly contrives one of these terms - the light intensity - so that the color.P of tile A equals the color.P of tile B. But the brain, interpreting the image as a 3D scene with light and shadow, reports the color.S-es of the tiles, which are different under that very reasonable and useful interpretation.

I'm sorry if this is a big distraction from the point of your post. I'm still interested in the point, so perhaps you can find another way of getting it across.

In the spirit of not disputing definitons, may I suggest: A and B are the same colorRGB, but, interpreting the image as a picture (as the eye does), not the same colorALBEDO.

Edit: Correction - "as the visual system does".

They are the same screen-color, but different inferred-colors.

Your comment and this comment were adjacent in my message folder which I found amusing.

Thomblake wrote:

Caring about what's right might be as arbitrary (in some objective sense) as caring about what's prime, but we do actually happen to care about what's right.

It's funny how we do care.

Hmm... I agree this is compelling. However, since I'm resistant to updating my world view about 1-the-discriminated-prime-number, I'll continue to proffer counter-arguments:

• the Fundamental Theorem of Arithmetic is pretty important, but may still not be the "essence" of what prime is

• the FTA itself requires the "except 1" clause: "all natural numbers can be uniquely factored into primes except 1" -- which would make someone thing 1 ought to be prime

• the FTA already assumes 'modulo permutations', we could easily throw in 'modulo 1'

• Wikipedia -- the first and last authority on such things -- carefully writes in an entire sentence unto itself, "The number 1 is by definition not a prime number," suggesting just how arbitrary this is. (My own emphasis added.)

The best argument I came up with for not including 1 as prime, because I tend to worry about how things are constructed, was with the seive of Eratosthenes.

The seive of Eratosthenes says that you can find the primes by starting with all the natural numbers > 1; let 2 be the first prime number, and then begin eliminating all multiples of 2 and the multiples of subsequent primes as you find them. If you included '1' in the first step, then you would eliminate all the numbers in the first step.

A factor of a number M is a number that evenly divides M with no remainder. Zero has infinitely many factors, definitely not prime.

...regarding -1, I can't think of anything relevant that I know about the relationship between negative numbers and prime numbers.

Later edit: Then I completely changed my mind... and decided 0 and -1 should be prime relative to how I would define it's essence. I note that you intuited what I really meant by prime better than I did!

I'm just not seeing what obvious reality it highlights, so either I'm particularly dense or it's not in fact obvious.

So, rephrasing: what reality is being highlighted by the "illusion" ?

Your prime number analogy suggests that it's in fact the "both colors are the same" assertion which is an illusion. The perceptual reality is that the pixels in these areas are discriminated as different colors. The illusion consists of looking at pixel with identical RGB values and thinking "Oh, these have the same position in colorspace, I expect my brain to perceive them as identical."

The reality suggested by the "illusion" is that this expectation doesn't hold in general, it's a stupid model. A smarter model would take more things into account before it predicted what our brain will perceive as identical colors.

But this is very much non-obvious...

I think what you're trying to say is that the phenomenon becomes highly expected, not aberrant with respect to your world model.

Somewhat related: I think we do have a 3D map of the environment even for things that we aren't looking at at the moment. For example I feel as if I had a device in my brain that keeps track of which people are in which parts of the house right now (or where some emotionally-loaded objects are). I don't have to exert conscious effort specifically for this.

Another thing: it's interesting to think about why we can see dots and lines and shapes at all. By this I mean, why do these low-level things reach our conscious awareness? You aren't consciously aware of your blood sugar level or hormone levels. You do feel a sort of aggregated well-being feeling consciously but the details don't reach the conscious level. It's a strange and bizarre thing to think about what vision could be like if our consciousness didn't have access to dots and shapes and colors style low-level image data and we only "felt" the gist of it, for example by only feeling our current 3D model in some way. (It could be similar to blindsight.)

One answer could be that our vision is so complicated that the unconscious parts just can't cope with it fully, they can't analyze it sufficiently, and conscious processes (evolutionarily recent brain parts) need access to the basic "pixel-data" like things as well.

But again, maybe when we intentionally try to look at specific dots (as if looking at pixels, interpreting the visual field as a screen), we maybe aren't really looking at the low-level input but rather a reconstruction. Maybe we are seeing lines, corners and other geometric primitives laid on top of one another, like an SVG image, not like a BMP image. Maybe we don't really have conscious access to the low-level visual signals, we just have access to a reconstruction.

I don't think neuroscience has found out these things already, but it should be possible to read off of connections of brain areas.

I'm not sure if the eye-brain interaction is the relevant part. Even if you change "eyes" to "the visual system", the point of "these are of a different color is the very thing your visual system is trying to tell you" remains true.

"my optic system"? "my visual system"?