Hyperbolic Mary

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Originally uploaded by Pete Mandik.

Paul Churchland, in his recent “Chimerical Colors: Some Novel Predictions from Cognitive Neuroscience” (2005), describes very odd color experiences that are predicted by a neural model of chromatic information processing. In brief, the differential fatiguing and recovery of opponent processing cells gives rise to afterimages with subjective hues and saturations that would never be seen on the reflective surfaces of objects. Such “chimerical colors” include shades of yellow exactly as dark as pitch-black and “hyperbolic orange, an orange that is more ‘ostentatiously orange’ than any (non-self-luminous) orange you have ever seen, or ever will see, as the objective color of a physical object” (p. 328). Such odd experiences are predicted by the model that identifies color experiences with states of neural activation in a chromatic processing network. Of course, it’s always open to a dualist to make an ad hoc addition of such experiences to their theory, but no dualistic theory ever predicted them. Further, the sorts of considerations typically relied on to support dualism—appeals to intuitive plausibility and a priori possibility—would have, you’d expect, ruled them out.

Who would have, prior to familiarity with the neural theory, predicted experiences of a yellow as dark as black? One person who would not have thought there was such an experience as pitch-dark yellow is Ludwig Wittgenstein, who once asked “[W]hy is there no such thing as blackish yellow?” (1978, p. 106). I think it safe to say Wittgenstein would be surprised by Churchland’s chimerical colors. At least, I know I was, and I literally grew up reading Churchland. However, to be certain that we have an example of someone who is surprised—for I would like to conduct a thought experiment about them—let us consider someone, call him “Larry”, who has seen yellow and black and in general all the typical colors a normally sighted adult has seen. Suppose that Larry has never had a chimerically colored afterimage such as hyperbolic orange or pitch-dark yellow. Suppose further that Larry is aware of none of the neuroscience that predicts the existence of such experiences. Now, let us compare Larry to Hyperbolic Mary. Like Jackson’s Mary, Hyperbolic Mary knows all of the physical facts about how human color vision works, including the predictions of chimerically colored afterimages. Suppose also, that like Mary toward the end of Jackson’s story, Hyperbolic Mary has been let out of the black and white room and has seen tomatoes, lemons, grass, cloudless skies, and the like. In short, she has had the average run of basic color experiences. Let us stipulate that she has had all the types of color experiences that Larry has had. The crucial similarity between Mary and Larry is that not only have they seen all of the same colors, neither has had chimerically colored afterimages. Neither has experienced hyperbolic orange or pitch-dark yellow. The crucial difference between Larry and Hyperbolic Mary is that only Hyperbolic Mary is in possession of a theory that predicts the existence of hyperbolic orange and pitch-dark yellow. And here’s the crucial question:

Who will be more surprised upon experiencing chimerical colors for the first time, Larry or Hyperbolic Mary?

I think it’s obvious that Larry will be more surprised. I also think this has pretty significant implications for what we are to think the knowledge of what it is like consists in. One thing that knowing what it is like consists in is something that will determine whether one is surprised or not. Fans of Jackson’s Mary must grant this, for they are fond of explicating Jackson’s Mary’s ignorance of what it is like in terms of her alleged surprise at seeing red for the first time. Well, Hyperbolic Mary is less surprised than Larry on seeing chimerical colors for the first time. This shows that she must have more phenomenal knowledge—more knowledge of what it is like to have certain experiences—than did Larry. Mary was able to represent, in introspection, more properties of her experiences than Larry. And her introspective capacity was augmented by her neuroscientific concepts.

Churchland, P. (2005). “Chimerical Colors: Some Novel Predictions from Cognitive Neuroscience.” In: Brook, Andrew and Akins, Kathleen (eds.) Cognition and the Brain: The Philosophy and Neuroscience Movement. Cambridge: Cambridge University Press.

Wittgenstein, L. (1978). Some Remarks on color, ed. G.E.M. Anscombe, Oxford: Blackwell.

21 Responses to “Hyperbolic Mary”

  1. Tad says:

    Wow! Pete - thanks for an excellent post.

    My only worry: I don’t think the dualist need deny that knowledge of neurophysiological facts can be used to expand knowledge of qualitative facts beyond some base with which you need to start. This example reminds me of Hume’s missing shade of blue. If you’ve experienced enough related qualia and add some assumptions you can imagine unexperienced qualia. Hyperbolic Mary has experienced a bunch of qualia related to chimerical colors, plus she has theoretical knowledge far more sophisticated than what Hume deploys to infer his missing shade of blue, and this is enough to infer chimerical color qualia. But this doesn’t show that you could infer it from theory alone, without some basic acquaintance w/ color qualia.

    So I guess the example spells trouble for anyone who thinks theoretical knowledge of neurophysiological facts places no constraints on what to expect of one’s qualia. But are dualists committed to this? All they claim is that some unspecified minimum of acquaintance w/ relevant qualia is necessary for qualitative knowledge of some domain, not that it’s sufficient for knowledge of the whole domain. This is kind of Hume’s point, I think: he acknowledges that there are some minor exceptions to the claim that no sensory simple can be known without first being experienced, but in general the claim is true. Not sure how the case of chimerical colors throws doubt on this. Can the experimental methodology be extended to suggest more radical revelations? Can knowledge of neurophysiology, for example, predict the nature of qualia radically unlike any we’ve experienced, acquired via, e.g., some special kind of training or perhaps neural rewiring? That would be a troubling result for the dualist.

    The chimerical color case is a much more devastating problem for the Wittgensteinian view, which I take to be related to the Dennettian view I’ve defended at times on this blog. If these chimerical colors never occur in real things, yet are as vivid and compelling as colors perceived in normal circumstances, then it seems that color qualia must be brain states.

    Very nice post.


  2. Pete Mandik says:

    Hi Tad,

    Thanks for your remarks.

    What I take the case of Hyperbolic Mary to help show is that the intuitions that drive the knowledge argument are pretty unreliable. Lots of people have the intuition that black and white Mary can predict (what it is like to see) novel shades of gray but no shades of red whatsoever. The point I’d like to make is that this is just people making stuff up. Introspection and intuition don’t give us any principled ways of drawing the line between cases like Mary’s red and Hume’s blue. If it did, why didn’t Wittgenstein or Larry predict chimerical colors?

    I think you ask some crucial questions. One of them is:

    Can knowledge of neurophysiology, for example, predict the nature of qualia radically unlike any we’ve experienced, acquired via, e.g., some special kind of training or perhaps neural rewiring?

    What I’d like to emphasize is that no one knows, via introspection and intuition, what counts as “radically unlike any we’ve experienced”.

  3. Brian says:

    One seemingly important disanalogy between b/w Mary and Hyperbolic Mary is that Hyperbolic Mary’s new color seems to find natural description in terms of her previously experienced quale (e.g. “blackish yellow”) whereas b/w Mary’s new color does not (e.g. it doesn’t seem plausible to give a description of what a red experience is like in terms of shades of gray). One might argue that Hyperbolic Mary has just predicted the existence of a kind of color quale that is a novel reorganization of already known experiential color “primitives” whereas b/w Mary is faced with the apparently more daunting challenge of imagining an entirely new color primitive altogether.

  4. Hey Pete,
    After you read the Churchland’s theoretical presentation of of chimerical colors, didn’t you actually check out the afterimage experiments by yourself? Weren’t you eager to check “what does those colors look like”?

  5. djc says:

    I’d say that materialism and dualism are completely on a par here. Both materialists and dualists can use the science to support psychophysical principles connecting neural activation patterns to conscious experiences. The difference is that for a materialist these principles will be identities but for a dualist these will be laws. But that difference doesn’t affect anything here. E.g. the principles will be no more “ad hoc” for the dualist than the materialist — in either case, they’ll be inferred from the empirical data. (It’s crazy to think that dualism somehow precludes attention to neuroscience in theory construction. Descartes didn’t make that mistake.) And whether the principles are identities or laws, it’s obvious that a Mary who knows these principles will be in a position to know more about phenomenology than a Mary who doesn’t know these principles, precisely because these principles are explicitly principles about phenomenology. Of course this takes us beyond the situation of a Mary who is given knowledge of neurophysiology alone.

  6. Paul Gowder says:

    Wait a second, though. I’m not sure that the fact that Hyperbolic Mary experiences less surprise suggests that she has to have some kind of knowledge. Consider the following. Pink Unicorn Mary is also just like Larry, except that she has been exposed to a theory about the existence of pink unicorns. Someone convincingly fakes a pink unicorn and parades it in front of Pink Unicorn Mary and Larry. Pink Unicorn Mary will be less surprised. Does it follow that Pink Unicorn Mary had some kind of additional knowledge? It can’t be knowledge about pink unicorns, obviously, because everything she was told about pink unicorns was false. But it also can’t be phenomenonal knowledge. Larry could be equally well able to imaginatively represent what a pink unicorn would look like if it existed, but he’d still be surprised if he saw one.

    So while it’s obvious that Hyperbolic Mary will be less surprised, it’s not obvious that her relative lack of surprise will come from any knowledge of what black-yellow would look like (incidentally, having read Churchland’s paper, do you have any knowledge about what black-yellow would look like?), rather than simply lack of surprise because she had access to a concept (in the Kantian sense) to which she could match her new phenomenal knowledge.

  7. Paul Gowder says:

    Further — It seems to me that knowledge of yellow-black without having seen yellow-black has gotta be the same kind of knowledge as knowledge of e (the mathematical constant, not the letter). I know what e is — I can read off a handful of digits, I know a few places where it shows up — but I don’t have phenomenal knowledge of it in any coherent sense. I don’t know what it might be like to “experience” e, I can’t know that. My knowledge about e is purely conceptual. Similarly, I’d suggest Hyperbolic Mary’s knowledge about yellow-black is purely conceptual. She knows something called “yellow-black” might exist, so she has the capacity, should she ever experience yellow-black, to plug it into her preexisting concept, but that hardly means she knows anything about what the experience of yellow-black might actually be like.

    I really want to repeat the parenthetical question I posted in the last comment, only out of the parenthesis. There’s three knowledge states at play in your mind, over time.

    State 1: Never having heard of the notion of yellow-black. No phenomenal knowledge of it.

    State 2: Having heard of the notion of yellow-black, but only in the negative: you read (I surmise) Wittgenstein before reading Churchland. Did this negative description confer phenomenal knowledge on you somehow? For example, when reading the passage in question, did you manage to think something yellow-black up and visualize it in your brain? Did you have any first-person sensations about what this thing, this yellow-blackness, might be like, even in the face of Wittgenstein’s claim that no such thing could exist?

    State 3: Having now read Churchland, did this — the reading of the claim that yellow-black DOES exist, without any kind of a description of yellow-black (I assume) beyond that bare characterization that’s not meaningfully different from Wittgenstein’s — do you now have some kind of image of what yellow-black might be like? Do you have any representation of what it might be like to experience yellow-black?

    There’s more. On your — lets call it the surprise theory of phenomenal knowledge — on your surprise theory of phenomenal knowledge, you’re committed to a difference between state 2 and state 3. Because if you saw yellow-black in state 2, you’d be just as surprised (right?) as if you saw it in state 1.

    But if you’re committed to a difference between state 2 and state 3, is that sustainable? After all, the only difference between state 2 and state 3 was the content of the claim. “X does not exist” became “X does exist.” No additional information is transmitted in the second of those two statements about what it might be like for X, except that what it might be like includes the property of existence. So I don’t think the difference between state 2 and state 3 could fly.

  8. flic says:

    Lots of times schizophrenics won’t name color (with the exception of the colors black, white and sometimes red) directly in their linguistic descriptions, but they will describe the color in the most private of ways, without actually naming the color. Imagine that!

  9. Pete Mandik says:


    Brian: One thing I’d like to raise doubts about is whether our intuitions about and introspections of our color qualia reliably tell us about which are primitive and which are not. How does one know that black and white Mary can’t figure to what it is like to see red? Are our intuitions reliable enough to tell us whether, say, blue and yellow Mary could figure out red or whether purple and orange Mary could figure out green? The pitch-dark yellow case is supposed to raise doubts about all such intuitions about what can and cannot be combined wrt color qualia. Intuitively, no color can be as dark as the darkest black without thereby being black. Further, this is intuitive for “dark” hues such as blue and purple as well as for “bright” hues like yellow. Larry would find pitch-dark yellow utterly unintuitive. And he’d be wrong about whether there could be such a thing. Why think, then, that people’s intuitions are right about what Jackson’s Mary can figure out?

    Tanasije: I did try the procedures. I wasn’t terribly surprised when I did. I figure that’s because I read the article first.

    Dave: The physicalist theory predicts that such-and-such neural activity gives you pitch-dark yellow qualia instead of pitch-dark dancing qualia or no qualia at all. I don’t see that dualism provides any basis for favoring the one prediction over the other.

    Paul: You are right that the mere presence of surprise doesn’t indicate knowledge. It only indicates prior belief. However, if we are talking about something already agreed to be a fact, and we note that Mr. X is less surprised by that fact than Mr. Y, we have good reason to attribute more knowledge to Mr. X. Or, at least, good reason to attribute a true belief concerning that fact that Mr. X but not Y had. In the case of Hyperbolic Mary, the fact in question is the fact of what it is like to experience pitch-dark yellow afterimages. Suppose that Larry figures it isn’t like anything at all, since he figures that such a thing is impossible. Suppose that he figures you may as well ask him what it is like to look at four sided triangles. Hyperbolic Mary, on the other hand, predicts that what it is like is like seeing something that is exactly as dark as the darkest black but nonetheless is yellow. Suppose further that she is right. If you don’t feel like supposing this, read Churchland’s paper, follow the procedures, and try it for yourself. What does all of this show? It shows that given some body of phenomenal knowledge that Hyperbolic Mary and Larry have in common, plus some physical knowledge that Larry doesn’t have, Hyperbolic Mary was able to gain some additional phenomenal knowledge prior to having actually experienced pitch-dark yellow. Her lack of surprise when she finally experiences pitch-dark yellow confirms that her prior belief of what it would be like was correct. Ditto for my lack of surprise.

  10. Eric Thomson says:

    I don’t experience the novel colors (e.g., yellow darker than black). Does anyone here really experience these incredible new colors?

  11. djc says:

    Pete: Physicalism alone doesn’t make any prediction about qualia here. A specific physicalist theory, identifying qualia with certain activation patterns, makes such a prediction. Likewise dualism alone doesn’t make any prediction, but a specific dualist theory, with laws relating qualia to certain activation patterns, makes such a prediction. And insofar as the physicalist uses empirical evidence to support this particular physicalist theory, the dualist can use the same empirical evidence to support the corresponding dualist theory. So again, physicalism and dualism are on a par.

  12. Pete Mandik says:

    I agree that this is about specific physicalist and dualist theories and not physicalism and dualism in general. But here’s where a worry about ad hoc additions arises. The prediction in question was made by a specific physicalist theory. No dualist theory I’m aware of made the prediction. I’m assuming that questions of ad hoc additions have more to do with who actually got there first, not who could have.

  13. Pete,
    I agree that Larry will be more surprised by the experience than Hyp.Mary, and that in some case we can consider Mary having knowledge that Larry doesn’t have. I will analyze those situations later, first let me say how I look at the Churchland’s “discovery”…
    Churchland put forward a hypothesis (a theory), which resulted also in prediction (as a good scientific theory) that in such and such situations there will be experiences of chimerical colors.
    The prediction itself has its confirmation in the direct phenomenal experience. But then if the confirmation of the theory is required for becoming some kind of knowledge, this means that we can’t have knowledge without having phenomenal experience of that kind.

    So, let’s return to Hyp.Mary, and ask what makes her knowledge to be knowledge?

    There are two situations I can imagine. One is that based on her knowledge of how brain works, she puts forward hypothesis of possible phenomenal experience (part of which would be chimerical colors). But lacking the ways to test her predictions, she can’t know that her theories are right, so as long they are mere theories about phenomenal experience, they can’t be considered knowledge about phenomenal experience (maybe you would disagree on this?).

    The other situation is where Hyp.Mary has contacted some people to test her hypothesis for her, and in this case it may become knowledge, but again, we have situation in which the change from mere theory to knowledge isn’t possible without somebody actually testing the hypothesis and having the experience of that particular kind.
    I would in this case say that Hyp.Mary has knowledge that Larry lacks, but Hyp.Mary doesn’t have to be scientist in order to have this kind of better knowledge that Larry. She might be an economist to which couple of friends reported having a chimerical colors experiences.

  14. Pete Mandik says:


    Would you say that, in general, there cannot be theoretical knowledge about future events? If so, that’s a pretty strong claim. If not, I don’t see why it should be true of phenomenal experience.

  15. Pete,

    I wouldn’t say that. It seems to me that as long as the theory should be some kind of knowledge, it would need to cover some relation between universals which would transcend the particularity in time, space; and in general particularity of things which appear in this or that situation, but which can be subsumed under universals in the theory.
    What I don’t see is how the step from mere hypothesis to some kind of knowledge about phenomenal experience can be made, without the predictions being confirmed by appeal to the phenomenal experience itself, which seems to me makes the knowledge about possibility of chimerical colors impossible without confirming that possibility in the phenomenal experience.

    Would you say that it was clear to Churchland that his theory is good, and maybe somehow a priori true,so much that he didn’t have to actually check the theory, that he actually knew that his predictions will be right? I can’t see how he could have known that his predictions would turn out to be good.

    On other side, take an example of Joey that has underwent the experience and “discovered” the colors by sheer chance. We have here a person that has knowledge that such things as “color which is both yellow and black” are possible, without actually having any theory of color vision.

    Admittedly, this is pretty confused comment, as I don’t go deep into the analysis of notions of knowledge, facts, etc.. Sorry about that, but just thought I might bring those issues for consideration.

  16. Pete Mandik says:


    Would you say that it was clear to Churchland that his theory is good, and maybe somehow a priori true,so much that he didn’t have to actually check the theory, that he actually knew that his predictions will be right? I can’t see how he could have known that his predictions would turn out to be good.

    Why wouldn’t it suffice that the theory so excellently accounted for non-chimerical qualia?

  17. Pete,

    Why wouldn’t it suffice that the theory so excellently accounted for non-chimerical qualia?

    I don’t know. I guess that connects to the problematical issue of what suffices for accepting of scientific theory.

    BTW, it doesn’t give account for gray bananas looking yellow.

  18. Alan Dix says:

    (sorry only just read this, I know a bit late)

    Interestingly, if Larry also knew all the theory of chimerical colours that Hyperbolic Mary knew, he would still be more surprised. Just becasue I’ve read your post doesn’t mean I wouldn’t be surprised to see pitch black yellow … and this surprise is precisely because of my prior experience of colour.

    So more knowledge/experience does not necessaruly mean less surprise and in this example Larry’s surprise is precisely an argument for the knowledge of experience being different from knowledge about exeprience.

    .. of course a really clever Hyperblic Mary could know she should be surprised .. is knowing you should be surprised the same as being surprised??

  19. Pete Mandik says:

    Hi Alan,

    I think you raise some pretty good points/questions. My response is pretty much my response to Paul here:


    There are lots of surprises and lots of ways of being surprised. What matters for the tale of Hyperbolic Mary and Larry is surprise over whether there is such a thing as visual experiences of pitch dark yellow. Larry incorrectly thinks that there is no such thing and even before having such an experience Hyperbolic Mary correctly believes that there is. Larry’s mistaken belief is grounded in what he thinks he has access to through introspection and intuition. Hyperbolic Mary’s correct belief is grounded in what she has access to through cognitive neuroscience.

  20. [...] See also my “Hyperbolic Mary“ [...]