The Checkershadow Illusion

Every term when I’m preparing my 101 notes on illusion, I’m amazed by just how good the checkershadow illusion produced by Edward Adelson is. I use this as a way to get the students to feel the force of Descartes’ worries about the reliability of sense perception. Here is the illusion.

The point, as many of you will know, is that A and B are the same shade on the screen. Seeing this is, to say the least, non-trivial. I’ve made a small powerpoint demonstration of it, which I’ll be using in class.

The reason for making this presentation was that I wasn’t convinced by Adelson’s own demonstration. Here is the picture he uses to show that A and B are the same shade.

To me, A and B still look different. (I’d be interested in knowing whether other people agree.) So in my powerpoint, I’ve slowly covered up everything except A and B to make the point more vivid.

In my presentation the space between A and B is covered up slowly, and I think the phenomenology of this process is quite interesting. When I watch the last space between A and B get covered up, it doesn’t look like A gets lighter, or B gets darker, but it does look like they are getting more similar in shade. It is really quite mysterious, and I really can’t put into words the feeling it induces.

It might be interesting to change around which parts get covered up in which order to see what is necessary for A and B to appear to be the same. Anyone who wants to do so should feel free to modify my slides and distribute them. (Note that the original pictures are not copyrighted, and indeed Professor Adelson has gone out of his way to make the pictures easy to distribute.)

UPDATE: As Michael Smith pointed out to me, someone who was really doubtful about the claim that A and B are the same shade could simply copy the graphic above onto their own computer and then copy and paste out the squares to see. (I was enough of a sceptic that I once did this.) This works, indeed here is Michael’s version of what you end up with.

But I do like having a dynamic visual demonstration as well, particularly for 101 lectures!

25 Replies to “The Checkershadow Illusion”

  1. I agree — A does look a little darker than B in the second picture. (Though I’d seen it before, and hadn’t noticed it; but I think I had that thought just before reading the text below the picture.)

    In your slide show (great show!), B did start to look darker to me when the third element got blued out.

  2. I just don’t believe it! A and B don’t look the same to me in Adelson’s demonstration – and in your powerpoint it looks to me like B gets darker. So much so that I’ve decided to trust my experiences and reject all the evidence I have to the contrary. Testimony is weak anyway.

    Berkeleyan idealism beckons …

  3. Brian,

    I like your PowerPoint presentation very much, particularly because of the phenomenological questions it raises, but I’m not sure that it’s more effective than Adelson’s demonstration in revealing the illusion. The reason for this is that it can seem to someone (such as Ross, above) that one of the squares might actually be getting darker. On the other hand, I agree that a single look at Adelson’s demonstration isn’t very impressive, since the vertical bars just look graduated in shade. However, if you use your hands and a thumb to cover up the checkerboard outside of the vertical bars and between squares A and B, then I think that you get a very convincing demonstration of the identity of their shades.

    As for the phenomenological issue raised by your demonstration, consider Bill Brewer’s description of his response to a similar transformation of the Müller-Lyer illusion:

    “[S]uppose that you are faced with the Müller-Lyer diagram. Gradually the hashes at the ends of each of the two main lines shrink in size, until eventually they vanish. If you are like me, then you do not have a sequence of experiences representing the two main lines as gradually changing in length — one growing and/or the other shrinking — until they coincide…. Instead, you gradually come to realize that any previous inclination to take them to be unequal in length was mistaken, as the power of the hashes to mislead in this way diminishes. You are evidently presented in experienced throughout with the very same pair of lines, equally extended in space as they actually are, whose unchanging identity in length becomes gradually more apparent to you, as their similarities with an alternative configuration of unequal lines at different distances become less salient, as any suggestion of depth given by the hashes disappears.” (“Perception and Content,” EJP 14:2, 2006, pp. 170-1.)

    The parallel response to your demonstration would not be to see the shades of A and B becoming more similar (as you claim to), rather gradually to see that A and B are (and were all along) of the same shade. I, for one, am not sure how to describe my experience in this case (and I haven’t tried the corresponding transformation of the Müller-Lyer). I almost want to say that it’s indeterminate whether it seems to me that A and B are becoming more similar in shade or whether it seems to me that their identity in shade is gradually being revealed. And this, I suppose, is why I’m not convinced that your demonstration is superior to Adelson’s.

  4. Oops: I cut and pasted my previous comment from Wordpad and forgot to change the u-umlaut to ‘ue’. Hence the ‘ü’ in ‘Müller-Lyer’, which should read: ‘Mueller-Lyer’.

  5. That’s odd, the vertical bars don’t look at all graduated in shade to me. They just look darker than B. At least they look darker than the centre of B; there isn’t a particularly clear border between them.

    (Somewhat embarrassing confession – I hadn’t realised the point of the bars was that they are the same colour as A and B. I thought the point was to remove the contrast effects, which they don’t do. So I hadn’t checked what the bars look like in comparison to B, which is another pretty interesting effect.)

  6. In “Mind and World” (172), John McDowell writes:

    “In the presence of the original sample, a subject who has the concept of a shade is enabled to classify items as possessing the relevant shade, or not, by direct introspection for colour match. We can retain, for a while at least, a capacity to classify items as possessing the relevant shade or not, in a way that corresponds with the verdicts we would have given on the strength of direct introspection for colour match, even after the original sample is no longer in view.”

  7. This is just great. In a recent talk, my cognitive psychologist colleague Emre Ozgen has shown so many of these things that one really gets scared. Human, all too human!

  8. Here’s something I thought of after reading Ross’s comment, though I wouldn’t want to say it was what Ross had in mind. There is a case to be made that A and B are different shades in the original picture. The case that they are not seems to suppose that shade is not background dependent, or at any rate not background dependent enough that the differences in background to A and B matter to shade.

    Is that obviously right? After all, some other colour properties seem background dependent (I think being brown is an example, though I don’t have Hardin’s “Color for Philosophers” with me, which would have the relevant details.) In favour of thinking shade is background dependent in this case is the strong evidence of our eyes that A and B are different shades in the initial picture. And against… at least some of our unreflective attitudes that moving them around in the way that Michael or Brian or others do doesn’t change their shades suggest that it doesn’t matter, as does our willingness to believe we are faced with an illusion, though of course those unexamined assumptions could be the error.

    So Ross, don’t panic – you can keep the testimony of your eyes in this case without going Berkeleyan! You just need to abandon the principle about shade not depending on background.

    Everyone else: why should we stick with the claim that A and B are the same shade, and reject the thought that they are different because of background dependence? (I’m inclined to reject that background dependence claim too, but I’m not yet sure if that’s supported by the best reasons.)

  9. I don’t have time right now to give full consideration to the point that Daniel raises, but here’s what occurs to me. There is no question that we regularly take ourselves to be able to compare and to individuate shades independently of background, so any argument for background-dependence is going to bear the burden of proof. And there’s going to have to be more to such an argument than appeal to the so-called “testimony of the senses” in surprising cases. Here’s why (modifying a passage from p. 29 of Sense and Sensibilia):

    “What is wrong, what is even faintly surprising, in the idea of something having a particular shade but looking to have a different shade sometimes? Does anyone suppose that if something has a particular shade, then it jolly well has to look thus shaded at all times and in all circumstances? Obviously no one seriously supposes this.”

    So then I think the reason we should stick with the claim that A and B are the same shade is that there’s nothing surprising about the fact that the same shade should look different under different circumstances, even if there is something very surprising about this particular circumstance.

  10. Daniel, there might be a problem of definition. How do you define the background shade so as to define the backgrounded shade in terms of it? Shade, you might want to say, is a reciprocal relation. But in that case, it is the product of reciprocation. What are the things that reciprocate? “The shades of a and b depend on each other.” How is that not viciously circular?

  11. I have thoughts that are similar to Daniel\‘s (and I think that the issue of background, or perhaps context, dependence is crucial), but I think I would put things in an importantly different way.

    First, why call this, or the other pictures to which Brian links, illusions? This implies that they cause you to have a mistaken view of what is really the case. But why make that metaphysical assumption? Why assume that in one context the squares show what they really are, while in another context they are deceptive? Neither Adelson\‘s gray bars nor Brian\‘s progressive blocking out of the picture moves A and B from a state of being context bound to a state of being context independent. They both just change the context. Why find one of those contexts ontologically primary?

    Thus, I think that Daniel\‘s error comes in saying that A and B are different shades in the original picture. Personally, I don\t see what is gained by saying that A or B are anything, when the italicized \“are\” indicates some kind or other of metaphysically deep reality. One could make the general point that Daniel is making about context dependence and dispense with, or at least bracket, such ontological issues in favor of phenomenological description…

  12. Jason, I’m not sure how your argument is meant t work. The position I’m interested in can, of course, allow that sometimes things of the same shade can look different, so all sides can agree that there’s nothing surprising about the fact that “the same shade should look different under different circumstances”. But A and B aren’t an entirely typical case of this – there is something especially surprising about A and B, which tends to prompt the judgement that they’re different shades, not just the sorts of judgements we make all the time that things are the same shade that look different because of lighting or whatever. I haven’t tried to spell out exactly what the difference is between A and B, on the one hand, and e.g. the cover of a book when some has direct light on it and some does not. But to the extent we’re inclined to believe they are different shades on the basis of looking, and this stays invariant under some of the usual tests for “different shade”, we’ve still got a case that we can see they are different shades, or at least we get good evidence from looking that they are.

    Chris, good question. I think there are two things to say – one is that interdefinition is not always vicious (compare e.g. Ramseyfying out belief and desire at the same time). The second is that a theory of colour needn’t specify the properties of the background relevant for shade in terms of shades – if they did it e.g. in terms of the triples of reflectance of the background, there wouldn’t be the risk of circularity. (Triples of R probably aren’t quite the thing – for a start some coloured things aren’t coloured because of reflectances, including the computer screens we’re seeing the illusion on – but lots of things other than shades would do here.)

    J.C., I’m not sure why you think I am saying that A and B are different shades, where that indicates “metaphysically deep reality”. Partly because I’m not sure what “metaphysically deep reality” is supposed to be in this context – if there’s real stuff that isn’t “metaphysically deep reality”, shades of colour might be among that stuff. One way the view I’m running up the flagpole is different from yours is that I don’t see what the problem is with saying that both contexts are correct – A and B are initially different shades, and when the background is changed they have the same shade. I agree the question of why we should call one rather than another an illusion can be raised while bracketing the question of which, if either, is “correct”, and that’s one of the points I’m interested in, but I’m interested in the further question as well.

  13. Daniel: Usually when we imagine defining something through Ramseyfication, we imagine that we can describe role realizers in a different vocabulary. That’s what you’re beginning to do when you introduce reflectances. If you were trying to preserve infallible shade-matching abilities I think you’d be bound to fail. In your response to Jason you make clear that’s not your objective. But then I wonder, what is the point?

    You don’t think we can tell how warm a thing is just by touching, do you? You know that how warm a thing feels depends on how cold your hands are. You might still think one can tell just by feel how intense the sensation of warmth is, but the sensation of warmth is clearly in you, not in the object touched. Why shouldn’t we take exactly the same attitude toward shade? We’re just extremely unreliable at judging shades. For the sake of argument I give you that we can tell whether two shade appearances are the same, but those appearances are in us, not in checkerboards or computer screens. (McDowell is wrong in the passage I quoted before because he means to be talking about properties of physical objects.)

    For purposes of demonstrating our unreliability in matching shades, some of the diagrams that Brian linked to at the Kitaoka site are better. The checkerboard case does not really show that we are no good at matching shades considered as persistent, lighting- and surround-independent features of surfaces. On the contrary, it shows we are very good at that. If we were really looking at a checkerboard then there really would be different pigments on square A and square B. This is a case of color constancy allowing us to detect a difference despite the fact that the two locations irradiate our retinas in the same way. We might do a lot better in recognizing rhombus A and rhombus B has having the same shade on the screen if we could prevent ourselves from “seeing” a checkerboard with cylinder on it casting a shadow.

  14. Daniel,

    I suppose that wasn’t much of an argument, more of a gesture in the direction of an argument. Here’s how that gesture might be filled out a bit more. (What follows echoes the point that Chris brings up in his last comment about warmth; but see the last two paragraphs below for divergences.)

    We have a perfectly good method for testing the identity of shades: we hold samples up against each other under appropriate conditions. (And, as you admit, it is an unsurprising fact that the same shade can look different in different circumstances (as, say, determined by lighting). This is something that our judgments about shade almost always already take into account, just as our judgments about size are sensitive to size constancy.) So, here, first of all, is why we should call things like the checkershadow illusion illusions: they tend to mislead us into thinking that were we to cut out the relevant patches and hold them up next to each other, the shades would not match. We typically find it very hard to believe that they would; but they do. So, even if we define a property of objects — call it shayde — that is background-dependent and about which appearances are not misleading in the checkershadow case, there remains something about which appearances are misleading in the checkershadow case — namely, what will happen when we cut out the patches and hold them up against each other — that is, what will happen when we perform on those patches our standard test for identity of shades.

    Compare the case of the Mueller-Lyer. Here, two lines have a misleading appearance: they look to be of different lengths. The thing is, when we apply our standard test for identity of length (we break out the measuring stick), we find that the lines are identical in length. So, even if we define a property of objects — call it leyngth — that is background-dependent (or whatever) and about which appearances are not misleading in the Mueller-Lyer case, there remains something about which appearances are misleading in the Mueller-Lyer case — namely, what will happen when we break out the measuring stick and measure the lines — that is, what will happen when we perform on those lines our standard test for identity of length.

    So far then, I think we have no reason to think that shades (or lengths) are background dependent (or whatever), even if we do have good reason to think that the way a shade (or length) looks is thus dependent.

    This brings me to a point that Chris raises in his last comment. Chris, you say that “[shade] appearances are in us, not in checkerboards or computer screens.” But why should we say this? That the shade of A looks darker than the shade of B seems to be a very real property of the shade itself. (And we can account for this property by talking about how a shade’s surroundings can change the way it looks.) Moreover, how the shade looks is perhaps not a property of the checkerboard or the computer screen, but it certainly seems to be a property of the shade. And the shade is not “in the observer;” if anything, it’s “in” the checkerboard or the computer screen. So, at best, “how the shade looks” is a property of a property of the checkerboard or the computer screen.

    As for McDowell, I don’t see why he’s wrong: he just seems to be talking about shades as properties of objects, which seems just fine to me.

  15. I used this illusion in last year’s tutorials on Descartes. It’s great for provoking debate and shocking students out of their complacent belief in the trustworthiness of their senses. (Sadly I don’t have PowerPoint facilities in the room I teach in, your gradual covering works well to persuade they are the same.)

    I gave the students a printout along with the details of where it came from (Edward Adelson’s MIT site) and also the statement at the bottom that they are the same shade. Most were unconvinced that they were the same shade, after insisting they were I asked them to try to persuade themselves of this. The method of persuasion that they felt to be the most effective was folding the paper so the colours were side by side. This leads to some fruitful discussion about whether they were right to be more justified in their belief once they had done this what the implications are for sense acquired data. Much more evocative than imagining towers in the distance. I was hoping that someone would appeal to authority: it comes from an MIT website and so must be true, either no one thought of this or they don’t rate MIT faculty as a trustworthy.

  16. Jason:

    What I was calling “shade appearances” were sensations. I spoke of them as the visual correlates to sensations of warmth. So they are in us, not in the objects we perceive.

    A shade may appear a certain way to an observer, and a single shade may appear differently to an observer in different settings. In particular, a shade in one region may appear to me darker than a shade in a different region. I didn’t say that appearances in this sense were in us, but now that you bring them up, I want to say that it is also a little misleading to say without qualification that they are properties of the objects we perceive. Your’re right that they are, but only in the way that motherhood is a property; it is a property that a thing has only by virtue of standing in a relation to something else.

    I don’t understand why you are defending McDowell. Everything else you have been saying indicates a disagreement with McDowell. McDowell says we can reliably determine whether something is the same shade as a sample. (It’s important to him to say that as a way of answering the “grain” argument for nonconceptual content.) You quote Austin to the effect that we cannot, and you resist Daniel Nolan’s attempt to define shade in such a way as to maximize our ability to do that. So what do you agree with in McDowell?

  17. Of course, for the most part situations in real life that look like the depicted situation would be situations in which B has a lighter shade. (For its local brightness to be the same as that of A, even though only B is in the shade, it would have to be lighter.) So it’s precisely a mechanism designed to get things right in ordinary context that’s being exploited. That mechanism ensures that our senses are trustworthy— though fallible, as in a picture designed to suggest different strengths of illumination in the context, when the illumination is actually uniform.

    The point is that these aren’t properly used to cast doubt on the trustworthiness of our senses (cf. #15), unless trustworthiness requires infallibility.

  18. PS. This is why I think it does count as an illusion: it seems to us that there is unequal illumination, and as a result we make judgments about how the squares would look under equal illumination (viz. like A and an adjacent light square, or like B and an adjacent dark square), and we are wrong.

  19. Following up on David Manley’s suggestion: why not regard this as a case in which we simply perceive it, correctly, as a picture of a checkerboard where the squares in question have different shades? How would this be any more of an “illusion” than perceiving a Necker cube as protruding in some dimension and being unable to see it otherwise?

  20. Schwenkler: I think you would be right to say: we perceive it correctly as a picture according to which the squares in question have different shades. (In other words, the picture does represent such a situation.) But I also think we perceive it incorrectly as a picture IN which the squares have different shades. (That is, the picture uses different shades to represent that situation). We are wrong about the second thing, so in that respect we are deceived.

  21. David:

    That sounds reasonable to me. But the fact that we are subject to the second sort of illusion (or perhaps “deception” is better) just shows that we are bad at determining what pigments are used to compose pictures; I wonder if an experienced painter would be better at this than we “folk”. The primary point I was (or perhaps should have been) trying to make was that this illusion, powerful as it is, doesn’t show anything to be deeply wrong with our visual systems, and doesn’t give a very good motivation for skepticism (which was, I take it, the end to which Brian W. was using it). I.e., what our visual systems usually present to us when we look at pictures are the properties of the scenes therein represented, and they are (thankfully) very good at doing that. The task of “stepping back” from that basic perceptual stance and making “detached” judgments about pigments or paint chips is quite difficult, and the fact that we’re bad at it should probably seem unsurprising if we think about what vision is “for”.


  22. Chris,

    Regarding McDowell, you write: “McDowell says we can reliably determine whether something is the same shade as a sample. (It’s important to him to say that as a way of answering the “grain” argument for nonconceptual content.) You quote Austin to the effect that we cannot, and you resist Daniel Nolan’s attempt to define shade in such a way as to maximize our ability to do that. So what do you agree with in McDowell?”

    To begin with, I take it that the question is not one of reliability vs. unreliability. Neither Austin nor I would deny that we are generally reliable shade-classifiers. It’s just that sometimes we think we are when we aren’t. So if McDowell’s point is that we’re generally reliable, then there’s no disagreement.

    On the other hand, it seems to me that you’re suggesting McDowell is committed to something stronger than this, and that his position is not plausible, and, upon reflection, I think you’re right (if you’re suggesting this). It seems to me that McDowell is committed to denying that we can make mistakes in identifying shades. To allow for such fallibility, he would have to say that we may be wrong whether an experience represents a particular shade as it is. But just how the experience represents the shade is, on his view, presumably identical to the content of the demonstrative expression ‘that shade’, tokened in the presence of the relevant shade. (This is, as you note, necessary to meet the “fineness of grain” objection.) In this case, the experience necessarily represents the shade just as it is, and this seems unacceptable for the kinds of reasons that I offer in my previous comment (above). (For a nice discussion of this point in relation to illusion, see Brewer, “Perception and Content.”)

  23. Let me clarify my first point. It should have read:

    Neither Austin nor I would deny that we are generally reliable shade-classifiers. It’s just that sometimes we think we are reliable when we aren’t — e.g., when we’re looking at the checkershadow image. But this doesn’t undermine our supposed general reliability. (On the contrary, without general reliability, there’d be no checkershadow illusion.) So if McDowell’s point is that we’re generally reliable, then there’s no disagreement.

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