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.)
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.
If you go to an Art or Design school. Seeing and producing illusions like this is one of the assignments that they usually will give you in a 2D design class.
As it has been described above, if you can concentrate (if school, we learn how to look at them by squinting as we would when discerning simple shape or color—or, if you have ever learned how to look at one of those weird 3D images made out of what looks to be paint splatter) on the two squares, then you will be able to see that they are indeed the same shade (not color, color is used to describe something else)
Ah, that worked for me. For people wondering how to do the technique to see “Magic Eye ” images, you focus your eyes so that the image doubles and and overlaps the image. That causes a stereoscopic illusion when done on any things that overlap. You could practice it here. Focus your eyes so that the the first abc overlaps the second abc—now you have three abc’s in your vision, the 1st and 3rd abc are being seen out of one eye and the abc in the middle appears to be almost 3d.
a...b...c......................a...b...c
In this case, I could see that A and B are the same color by tilting my head and then focusing so I saw a double image of A overlapping B.
Exactly… We spent a total of 6 weeks in Art School design class learning how to do this specific trick with a variety of images. From color, to line length (you know those “which line is longer” tricks that make you think one line is longer when they are usually the same length), to line thickness, to shading and tinting aliasing.
We spent those weeks consuming a lot of aspirin and Tylenol.
We were taught that if you put your nose right in the center of the image, and then let your focus go, and pull back from the image, that at a certain distance from the image (as your focus is still at ∞) various structures of the image will begin to resolve. So contrasts, similarities, and shades will all resolve at different focal lengths from the image.
It was rare that any one person would be able to pick up immediately upon all the effects perceptible in an image. I was able to pick up on certain shades of the color green that are used in contrast to red, but it took me a long time to get the shading of black-white (as in this optical illusion—and it is but one of many).
When we were tested on this, we would not be told what was similar, or where optical tricks were used, and we would have to pick them out of an image (and this was long before the internet, so we couldn’t just go online to do a search for optical illusions to find images to study that had their illusions spelled out for us). So, it is a skill that can be learned. For me, eventually I had to learn how to focus upon each square with a different eye, while squinting, and letting the focus go back and forth between my right and left eye. eventually, I get the images resolved as a single shade as I go back and forth between my eyes.
(A) Cover up areas of the image to see what causes what to change color in your perception. Slowly reveal the full image again and sometimes A and B look alike
(B) Let your focus drift until the lines of the image get fuzzy. Look at the two squares without actually looking at them. I find that the colors look alike here. If I “snap” focus back they still look alike but nothing is fuzzy anymore.
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.
When we covered this phenomenon in my psychology degree it was referred to as colour constancy. I now work as a 3D graphics programmer and so know a lot about the physics of light transport. The illusion does not surprise me any more, in fact it seems a little surprising that I ever could have thought that the RGB colour value of an onscreen pixel was directly related to the property of objects in the real world that we call ‘colour’.
Well said (including your later comment about color constancy). Along the same lines, this is why cameras often show objects in shadows as blacked out—because that’s the actual image it’s getting, and the image your own retinas get! It’s just that your brain has cleverly subtracted out the impact of the shadow before presenting it to you, so you can still see significant contrast and colors in the shadowed objects.
Along the same lines, this is why cameras often show objects in shadows as blacked out—because that’s the actual image it’s getting, and the image your own retinas get! It’s just that your brain has cleverly subtracted out the impact of the shadow before presenting it to you
That doesn’t explain why faithful reproductions of images with shadows don’t prompt the same reinterpretation by your brain.
Blacked out shadows are generally an indication of a failure to generate a ‘faithful’ reproduction due to dynamic range limitations of the camera and/or display medium. There is a fair amount of research into how to work around these limitations through tone mapping. High Dynamic Range cameras and displays are also an area of active research. There’s not really anything to explain here beyond the fact that we currently lack the capture or display capability to faithfully reproduce such scenes.
Sure it does—Faithful reproductions give the shadowed portion the appropriate colors for matching how your brain would perceive a real-life shadowed portion of a scene.
Umm, that’s not what I meant by “faithful reproductions”, and I have a hard time understanding how you could have misunderstood me. Say you took a photograph using the exact visual input over some 70 square degrees of your visual field, and then compared the photograph to that same view, trying to control for all the relevant variables*. You seem to be saying that the photograph would show the shadows as darker, but I don’t see how that’s possible. I am familiar with the phenomenon, but I’m not sure where I go wrong in my thought experiment.
* photo correctly lit, held so that it subtends 70 square degrees of your visual field, with your head in the same place as the camera was, etc.
I thought you meant “faithful” in the sense of “seeing this is like seeing the real thing”, not “seeing this is learning what your retinas actually get”. If you show a photograph that shows exactly what hit the film (no filters or processing), then dark portions stay dark.
When you see the scene in real life, you subtract off the average coloring that can be deceiving. When you see the photo, you see it as a photo, and you use your current real-life-background and lighting to determine the average color of your visual field. The darkness on the photo deviates significantly from this, while it does not so deviate when you’re immersed in the actual scene, and have enough information about the shadow for your brain to subtract off the excessive blackness.
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.
As others have pointed out, the difficulty here is more in the semantics of “color” than in the optics.
Yeah. I missed the semantic shift. All it took was someone pointing out that there were two uses of Color drifting around and almost all the comments snapped back into making sense.
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.
The point is that an illusion generally gives off a sense of bizarreness because we are expecting X but the illusion gives us Y. In the case of the color example, I once expected boxes A and B to appear to be the same color (perceived) if and only if they were the same color (RGB). The illusion shows this is not the case. Being curious, I sought to understand the underlying principles behind why we perceive two different colors. Once this is understood, the illusion should no longer seem bizarre but a trivial example of the underlying principles.
In trying to find where I went wrong with the post, I come up with this:
“Color” is an extremely ambiguous term. I should have seen this one coming.
I think some people thought I was trying to give an explanation of the illusion in the post. I was not.
I think some people thought I was saying that the visual system itself was stupid or broken and we needed to “fix” our brain to adjust for its shortcomings. I was not. I was trying to say that our feeling of “bizarre” was stupid because we are expecting something different from our visual system than what the visual system provides.
I deliberately wrote this post more aggressively and concisely than I generally write. Perhaps this degraded its clarity even further.
I am half tempted to take this post down, rewrite it, and put it back up, but I don’t know how much that would help.
Well, don’t do anything that takes down the comment section. Many of the comments are insightful and, um, say things that should have been in your original post.
Demystifying optical illusions, and visual cognition in general, is a very good exercise in rationalist reduction.
Okay. Do you think it would be valuable to just edit the post in place?
As best as I can tell, these are the trouble paragraphs:
Today I looked at the above illusion and thought, “Why do I keep thinking A and B are different colors? Obviously, that is not what my visual system is trying to tell me.” I am being stupid when my eye looks at this illusion and I interpret the data in such a way to determine distinct colors. That information is not being transmitted and received. If it were, the illusion wouldn’t be an 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 system is reporting True 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. Once I have found 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 should highlight an obvious reality.
Is this better?:
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 I look at this illusion and 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 it were, the illusion wouldn’t be an 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 system is reporting True 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, the visual system is distinguishing between [what term goes here?], not individual RGB style colors. Now that I have right answer, this optical illusion should become as uninteresting as questioning whether 1 is prime. It stops being weird, bizarre, and incredible. It merely highlights an obvious reality.
It seems to me that you are still using the word colour in a way that suggests you haven’t really grasped the insight that makes this illusion seem not-bizarre. That insight is fundamentally that the statement “this ball is blue” is not equivalent to the statement “a digital photo of a scene containing this ball would have pixel values of 0, 0, 255 at pixel locations where light from the ball reached the sensor”. It is a much more complex (and more useful) statement than that. The bad assumption is that ‘colour’ when used to refer to a property of objects in the world determined through visual perception has any simple relationship with RGB values recorded by a digital camera. You still seem to be talking as if RGB values are somehow ‘true’ colours.
The bad assumption is that ‘colour’ when used to refer to a property of objects in the world determined through visual perception has any simple relationship with RGB values recorded by a digital camera.
I think the key for me in understanding this type of illusion (and the general phenomenon of colour constancy) was to realize that ‘colour’ in common usage (“this ball is blue”) is perceived as a property of objects and we infer it indirectly based on light that reaches our retinas. That light also has a ‘colour’ (subtly different meaning) but it is not something we perceive directly because it is not very useful in itself.
This makes perfect sense when you think about it from an evolutionary perspective—we evolved to recognize invariant properties of objects in the world (possibly fruit in trees for primates) under widely varying lighting conditions. Directly perceiving the ‘colour’ (RGB) of light would not tell us anything very useful about invariant object properties. There is enough overlap between the two meanings of colour for them to be easily confused however and that is really the root of this particular illusion.
In computer graphics we commonly use the term ‘material’ to describe the set of properties of a surface that govern how it responds to incident light. This encompasses properties beyond simple colour (“shiny blue ball”, “matte blue ball”, “metallic blue ball”). I don’t know if that usage is well understood outside of the computer graphics field however.
I completely agree with you. At this point, I am just trying to clean up the article to help clarify the answer behind the illusion. Does the phrase, “I should stop thinking that the visual system is reporting RGB style colors” mesh okay? That is the only location of RGB as of this edit.
Thanks. Do you have any other suggestions that may help clarify the article? Your explanations have been very helpful. Learning the terms was apparently something I never bothered to do. Oops. :P
I think the key for me in understanding this type of illusion (and the general phenomenon of colour constancy) was to realize that ‘colour’ in common usage (“this ball is blue”) is perceived as a property of objects and we infer it indirectly based on light that reaches our retinas.
This happened sometime this morning. The more I read here, the more I understand it in the sense that I know the name of the relevant field, a whole bunch of new terms, and more details about how we perceive colors. It gets less and less bizarre as the day goes, which is always fun. :)
It sounds like you’re trying to come up with a sentence or two that captures all of the insight on color that the commenters have given. While I’m a big fan of summarizing, and a big critic of those who can’t, I don’t think you can get it to work here. Instead of your final bolded change (the others are good), just point to or quote a few good comments that show what the visual system is doing, and how the optical illusions trick it.
In this case, the visual system is not trying to distinguish between individual RGB style colors (more details in the comments).
EDIT: I updated it with something similar. Hopefully it was an improvement. :) Thanks again for your help (which isn’t to say that I wouldn’t mind more help...)
I am half tempted to take this post down, rewrite it, and put it back up, but I don’t know how much that would help.
Taking this and SilasBarta’s thoughts together: can you apply this same meta-principle to something substantially different in a new post, written with a recognition of these confusions? That post could cite this post with a “Followup to:” line, and elaborate on your discovery in some way.
I would be disinclined to that course, but hard-pressed to justify it more effectively than by my idiosyncratic generalization of one of a number of principles I have heard—I quote from the post:
Don’t try to rewrite history. Look, we make mistakes. We all do. Sometimes we post an essay and we get stuff wrong in it. Sometimes that stuff makes the whole essay wrong. Sometimes, we put up an essay innocently and it turns into a firestorm of controversy we never meant. Sometimes, we find ourselves in a crucible on all sides.
The temptation is to go back. Revise. Reword what we said. Take the essay down entirely.
It is never a good idea. Ever.
I don’t think you have anything to be ashamed of in this post. It’s not deep, it’s not extraordinary in its conclusions, but it is correct and brief. The complaints seem to me best addressed by elaboration and discussion—things which require far more than a brief edit placed at the end of the post.
As SilasBarta mentioned, there’s a lot of commentary on this post that is worth preserving, and should be preserved with the original post. It would be unfair to the commenters to render their comments incomprehensible—even briefly—by distortion of that to which they responded.
And, if I may be frank, if the idea which inspired this post is interesting, it is probably capable of generalization. The idea of my own which I promoted to a post I did so because I saw that it was applicable beyond the scope of its origination, and in a manner which was natural, elegant, and interesting. It proved of interest to a number of people here, despite its unabashedly algebraic treatment. If you can find a profitable extension of your concept, it will be likely to be worth reporting in a followup post (and if you are concerned about the appropriateness of it, I—as one remaining upvoter of the OP—will have sent my email to you in a PM, and be willing to comment on any draft you wish to send).
If you cannot find a profitable extension of your concept, it is probably not worth the time to revise. Consider your post dubiously successful (it is still in positive territory, is it not?) and leave it be.
I don’t think you have anything to be ashamed of in this post. It’s not deep, it’s not extraordinary in its conclusions, but it is correct and brief. The complaints seem to me best addressed by elaboration and discussion—things which require far more than a brief edit placed at the end of the post.
It’s not so much that I am ashamed; I am just frustrated. The behavior of this post caught me completely off-guard. It was upvoted to +5 within a few hours and people started asking questions. After my responses, the post dropped to +1. The karma itself doesn’t mean much to me, but the feedback here was evidence of something greater than a non-interesting or incorrect post.
People were willing to talk about it, so I stuck it out for as much feedback as I could. The investment was completely worth it. I got several comments worth of extremely valuable insights to my writing style and how to better post here at LessWrong.
I think the post itself failed, but the whole experience has been a net gain.
As SilasBarta mentioned, there’s a lot of commentary on this post that is worth preserving, and should be preserved with the original post. It would be unfair to the commenters to render their comments incomprehensible—even briefly—by distortion of that to which they responded.
I agree. My intent in the revisions has been to keep people from being distracted by my quirks and leading them into a wonderful discussion in the comments. This particular illusion has a lot more history behind it than I originally thought; I learned a lot.
And, if I may be frank, if the idea which inspired this post is interesting, it is probably capable of generalization. The idea of my own which I promoted to a post I did so because I saw that it was applicable beyond the scope of its origination, and in a manner which was natural, elegant, and interesting. It proved of interest to a number of people here, despite its unabashedly algebraic treatment. If you can find a profitable extension of your concept, it will be likely to be worth reporting in a followup post (and if you are concerned about the appropriateness of it, I—as one remaining upvoter of the OP—will have sent my email to you in a PM, and be willing to comment on any draft you wish to send).
Thank you very much. I have to sit on the events of today and ponder if there is a next step to take. If a followup is coming I will certainly take you up on your offer.
An addendum—as far as my recollection of the original goes, your edits appear reasonable, although I would not have risked them on my own post. I congratulate you on a successful revision, but my offer stands.
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.
This is perhaps beating a dead horse, but “albedo” is supposed to be a ratio between reflected and incident lights, and I would bet that the albedo of these two patches of screen is also identical, just as their RGB values are identical.
Not in the actual 3D scene that your brain interprets the picture to be of, only in the context of a 2D printout of the image (albedo is not really a relevant property for emissive display devices like LCDs or CRTs).
When I said “interpreting the image as a picture”, I meant, “interpreting the image as a picture of a checkerboard with a cylinder casting a shadow on it”—the albedos in question are of the squares A and B on the depicted board.
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.)
Hmm. I can with the necker cube, but not at all with this one.
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.
That worked! Cool!
If you go to an Art or Design school. Seeing and producing illusions like this is one of the assignments that they usually will give you in a 2D design class.
As it has been described above, if you can concentrate (if school, we learn how to look at them by squinting as we would when discerning simple shape or color—or, if you have ever learned how to look at one of those weird 3D images made out of what looks to be paint splatter) on the two squares, then you will be able to see that they are indeed the same shade (not color, color is used to describe something else)
Ah, that worked for me. For people wondering how to do the technique to see “Magic Eye ” images, you focus your eyes so that the image doubles and and overlaps the image. That causes a stereoscopic illusion when done on any things that overlap. You could practice it here. Focus your eyes so that the the first abc overlaps the second abc—now you have three abc’s in your vision, the 1st and 3rd abc are being seen out of one eye and the abc in the middle appears to be almost 3d.
a...b...c......................a...b...c
In this case, I could see that A and B are the same color by tilting my head and then focusing so I saw a double image of A overlapping B.
Exactly… We spent a total of 6 weeks in Art School design class learning how to do this specific trick with a variety of images. From color, to line length (you know those “which line is longer” tricks that make you think one line is longer when they are usually the same length), to line thickness, to shading and tinting aliasing.
We spent those weeks consuming a lot of aspirin and Tylenol.
Interesting, when I try this technique the shades seem even more distinct.
It takes some practice.
We were taught that if you put your nose right in the center of the image, and then let your focus go, and pull back from the image, that at a certain distance from the image (as your focus is still at ∞) various structures of the image will begin to resolve. So contrasts, similarities, and shades will all resolve at different focal lengths from the image.
It was rare that any one person would be able to pick up immediately upon all the effects perceptible in an image. I was able to pick up on certain shades of the color green that are used in contrast to red, but it took me a long time to get the shading of black-white (as in this optical illusion—and it is but one of many).
When we were tested on this, we would not be told what was similar, or where optical tricks were used, and we would have to pick them out of an image (and this was long before the internet, so we couldn’t just go online to do a search for optical illusions to find images to study that had their illusions spelled out for us). So, it is a skill that can be learned. For me, eventually I had to learn how to focus upon each square with a different eye, while squinting, and letting the focus go back and forth between my right and left eye. eventually, I get the images resolved as a single shade as I go back and forth between my eyes.
I found two ways to do it myself:
(A) Cover up areas of the image to see what causes what to change color in your perception. Slowly reveal the full image again and sometimes A and B look alike
(B) Let your focus drift until the lines of the image get fuzzy. Look at the two squares without actually looking at them. I find that the colors look alike here. If I “snap” focus back they still look alike but nothing is fuzzy anymore.
B works better.
The point of the illusion is that they seem different in context. Ignoring context to make them appear similar isn’t a proper resolution.
I don’t understand this. Are you saying that A and B are not the same color?
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.
When we covered this phenomenon in my psychology degree it was referred to as colour constancy. I now work as a 3D graphics programmer and so know a lot about the physics of light transport. The illusion does not surprise me any more, in fact it seems a little surprising that I ever could have thought that the RGB colour value of an onscreen pixel was directly related to the property of objects in the real world that we call ‘colour’.
Well said (including your later comment about color constancy). Along the same lines, this is why cameras often show objects in shadows as blacked out—because that’s the actual image it’s getting, and the image your own retinas get! It’s just that your brain has cleverly subtracted out the impact of the shadow before presenting it to you, so you can still see significant contrast and colors in the shadowed objects.
That doesn’t explain why faithful reproductions of images with shadows don’t prompt the same reinterpretation by your brain.
Blacked out shadows are generally an indication of a failure to generate a ‘faithful’ reproduction due to dynamic range limitations of the camera and/or display medium. There is a fair amount of research into how to work around these limitations through tone mapping. High Dynamic Range cameras and displays are also an area of active research. There’s not really anything to explain here beyond the fact that we currently lack the capture or display capability to faithfully reproduce such scenes.
Sure it does—Faithful reproductions give the shadowed portion the appropriate colors for matching how your brain would perceive a real-life shadowed portion of a scene.
Umm, that’s not what I meant by “faithful reproductions”, and I have a hard time understanding how you could have misunderstood me. Say you took a photograph using the exact visual input over some 70 square degrees of your visual field, and then compared the photograph to that same view, trying to control for all the relevant variables*. You seem to be saying that the photograph would show the shadows as darker, but I don’t see how that’s possible. I am familiar with the phenomenon, but I’m not sure where I go wrong in my thought experiment.
* photo correctly lit, held so that it subtends 70 square degrees of your visual field, with your head in the same place as the camera was, etc.
I thought you meant “faithful” in the sense of “seeing this is like seeing the real thing”, not “seeing this is learning what your retinas actually get”. If you show a photograph that shows exactly what hit the film (no filters or processing), then dark portions stay dark.
When you see the scene in real life, you subtract off the average coloring that can be deceiving. When you see the photo, you see it as a photo, and you use your current real-life-background and lighting to determine the average color of your visual field. The darkness on the photo deviates significantly from this, while it does not so deviate when you’re immersed in the actual scene, and have enough information about the shadow for your brain to subtract off the excessive blackness.
Been a long day, hope I’m making sense.
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.
Yeah. I missed the semantic shift. All it took was someone pointing out that there were two uses of Color drifting around and almost all the comments snapped back into making sense.
The point is that an illusion generally gives off a sense of bizarreness because we are expecting X but the illusion gives us Y. In the case of the color example, I once expected boxes A and B to appear to be the same color (perceived) if and only if they were the same color (RGB). The illusion shows this is not the case. Being curious, I sought to understand the underlying principles behind why we perceive two different colors. Once this is understood, the illusion should no longer seem bizarre but a trivial example of the underlying principles.
In trying to find where I went wrong with the post, I come up with this:
“Color” is an extremely ambiguous term. I should have seen this one coming.
I think some people thought I was trying to give an explanation of the illusion in the post. I was not.
I think some people thought I was saying that the visual system itself was stupid or broken and we needed to “fix” our brain to adjust for its shortcomings. I was not. I was trying to say that our feeling of “bizarre” was stupid because we are expecting something different from our visual system than what the visual system provides.
I deliberately wrote this post more aggressively and concisely than I generally write. Perhaps this degraded its clarity even further.
I am half tempted to take this post down, rewrite it, and put it back up, but I don’t know how much that would help.
Well, don’t do anything that takes down the comment section. Many of the comments are insightful and, um, say things that should have been in your original post.
Demystifying optical illusions, and visual cognition in general, is a very good exercise in rationalist reduction.
Okay. Do you think it would be valuable to just edit the post in place?
As best as I can tell, these are the trouble paragraphs:
Is this better?:
It seems to me that you are still using the word colour in a way that suggests you haven’t really grasped the insight that makes this illusion seem not-bizarre. That insight is fundamentally that the statement “this ball is blue” is not equivalent to the statement “a digital photo of a scene containing this ball would have pixel values of 0, 0, 255 at pixel locations where light from the ball reached the sensor”. It is a much more complex (and more useful) statement than that. The bad assumption is that ‘colour’ when used to refer to a property of objects in the world determined through visual perception has any simple relationship with RGB values recorded by a digital camera. You still seem to be talking as if RGB values are somehow ‘true’ colours.
Especially in the case of human tetrachromats.
I am trying to find a way to say what you said with one phrase or word. I feel like I am struggling to find a term.
I think the key for me in understanding this type of illusion (and the general phenomenon of colour constancy) was to realize that ‘colour’ in common usage (“this ball is blue”) is perceived as a property of objects and we infer it indirectly based on light that reaches our retinas. That light also has a ‘colour’ (subtly different meaning) but it is not something we perceive directly because it is not very useful in itself.
This makes perfect sense when you think about it from an evolutionary perspective—we evolved to recognize invariant properties of objects in the world (possibly fruit in trees for primates) under widely varying lighting conditions. Directly perceiving the ‘colour’ (RGB) of light would not tell us anything very useful about invariant object properties. There is enough overlap between the two meanings of colour for them to be easily confused however and that is really the root of this particular illusion.
In computer graphics we commonly use the term ‘material’ to describe the set of properties of a surface that govern how it responds to incident light. This encompasses properties beyond simple colour (“shiny blue ball”, “matte blue ball”, “metallic blue ball”). I don’t know if that usage is well understood outside of the computer graphics field however.
I completely agree with you. At this point, I am just trying to clean up the article to help clarify the answer behind the illusion. Does the phrase, “I should stop thinking that the visual system is reporting RGB style colors” mesh okay? That is the only location of RGB as of this edit.
Yes, I think ‘RGB colours’ is better than ‘True Colours’ in this context.
Thanks. Do you have any other suggestions that may help clarify the article? Your explanations have been very helpful. Learning the terms was apparently something I never bothered to do. Oops. :P
The article reads better now. So do you feel the bizarreness has disappeared now you understand the phenomenon better?
Yes. The key point that you mentioned here:
This happened sometime this morning. The more I read here, the more I understand it in the sense that I know the name of the relevant field, a whole bunch of new terms, and more details about how we perceive colors. It gets less and less bizarre as the day goes, which is always fun. :)
How is “Color gross of lighting conditions”?
It sounds like you’re trying to come up with a sentence or two that captures all of the insight on color that the commenters have given. While I’m a big fan of summarizing, and a big critic of those who can’t, I don’t think you can get it to work here. Instead of your final bolded change (the others are good), just point to or quote a few good comments that show what the visual system is doing, and how the optical illusions trick it.
How about:
EDIT: I updated it with something similar. Hopefully it was an improvement. :) Thanks again for your help (which isn’t to say that I wouldn’t mind more help...)
Taking this and SilasBarta’s thoughts together: can you apply this same meta-principle to something substantially different in a new post, written with a recognition of these confusions? That post could cite this post with a “Followup to:” line, and elaborate on your discovery in some way.
Would it be better to just replace the content of this post? I can archive the original in a comment here for future context.
I would be disinclined to that course, but hard-pressed to justify it more effectively than by my idiosyncratic generalization of one of a number of principles I have heard—I quote from the post:
I don’t think you have anything to be ashamed of in this post. It’s not deep, it’s not extraordinary in its conclusions, but it is correct and brief. The complaints seem to me best addressed by elaboration and discussion—things which require far more than a brief edit placed at the end of the post.
As SilasBarta mentioned, there’s a lot of commentary on this post that is worth preserving, and should be preserved with the original post. It would be unfair to the commenters to render their comments incomprehensible—even briefly—by distortion of that to which they responded.
And, if I may be frank, if the idea which inspired this post is interesting, it is probably capable of generalization. The idea of my own which I promoted to a post I did so because I saw that it was applicable beyond the scope of its origination, and in a manner which was natural, elegant, and interesting. It proved of interest to a number of people here, despite its unabashedly algebraic treatment. If you can find a profitable extension of your concept, it will be likely to be worth reporting in a followup post (and if you are concerned about the appropriateness of it, I—as one remaining upvoter of the OP—will have sent my email to you in a PM, and be willing to comment on any draft you wish to send).
If you cannot find a profitable extension of your concept, it is probably not worth the time to revise. Consider your post dubiously successful (it is still in positive territory, is it not?) and leave it be.
It’s not so much that I am ashamed; I am just frustrated. The behavior of this post caught me completely off-guard. It was upvoted to +5 within a few hours and people started asking questions. After my responses, the post dropped to +1. The karma itself doesn’t mean much to me, but the feedback here was evidence of something greater than a non-interesting or incorrect post.
People were willing to talk about it, so I stuck it out for as much feedback as I could. The investment was completely worth it. I got several comments worth of extremely valuable insights to my writing style and how to better post here at LessWrong.
I think the post itself failed, but the whole experience has been a net gain.
I agree. My intent in the revisions has been to keep people from being distracted by my quirks and leading them into a wonderful discussion in the comments. This particular illusion has a lot more history behind it than I originally thought; I learned a lot.
Thank you very much. I have to sit on the events of today and ponder if there is a next step to take. If a followup is coming I will certainly take you up on your offer.
An addendum—as far as my recollection of the original goes, your edits appear reasonable, although I would not have risked them on my own post. I congratulate you on a successful revision, but my offer stands.
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”.
This is perhaps beating a dead horse, but “albedo” is supposed to be a ratio between reflected and incident lights, and I would bet that the albedo of these two patches of screen is also identical, just as their RGB values are identical.
Not in the actual 3D scene that your brain interprets the picture to be of, only in the context of a 2D printout of the image (albedo is not really a relevant property for emissive display devices like LCDs or CRTs).
When I said “interpreting the image as a picture”, I meant, “interpreting the image as a picture of a checkerboard with a cylinder casting a shadow on it”—the albedos in question are of the squares A and B on the depicted board.
Ah, “inferred albedo”. In that case we agree.
Thank you.
They are the same screen-color, but different inferred-colors.