Thursday, December 11, 2008

Do Chinese Philosophers Think Tilted Coins Look Elliptical?

[Cross posted at Manyul Im's Chinese Philosophy Blog]

In my 2006 essay "Do Things Look Flat?", I examine some of the cultural history of the opinion that visual appearances involve what I call "projective distortions" -- the opinion, that is, that tilted coins look elliptical, rows of streetlights look like they shrink into the distance, etc. I conjecture that our inclination to say such things is due to overanalogizing visual experience to flat, projective media like paintings and photographs. In support of this conjecture, I contrast the contemporary and early modern periods (in the West) with ancient Greece and introspective psychology circa 1900. In the first two cultures, one finds both a tendency to compare visual experience to pictures and a tendency to describe visual experience as projectively distorted. In the latter two cultures, one finds little of either, despite plenty of talk about visual appearances in general.

I didn't do a systematic search of classical Chinese philosophy, which I love but which has less epistemology of perception, but I did find one relevant passage:
If you look down on a herd of cows from the top of a hill, they will look no bigger than sheep, and yet no one hoping to find sheep is likely to run down the hill after them. It is simply that the distance obscures their actual size. If you look up at a forest from the foot of a hill, the biggest trees appear no taller than chopsticks, and yet no one hoping to find chopsticks is likely to go picking among them. It is simply that the height obscures their actual dimensions (Xunzi ch. 21; Basic Writings, Watson trans., p. 134)
Though I can recall no ancient Chinese comparisons of visual experience and painting, both Xunzi and Zhuangzi compare the mind to a pan of water which can reflect things accurately or inaccurately, an analogy that seems related (Xunzi ibid. p. 131, ch. 25, Knoblock trans. 1999, p. 799; Zhuangzi, Watson trans., Complete Works, p. 97). In medieval China, which I know much less about, I noticed Wang Yangming saying such a comparison was commonplace (Instructions for Practical Living, Chan trans., p. 45).

So my question is, for those of you who know more Chinese philosophy than I, are there other passages I should be looking at -- either on perspectival shape or size distortion or on analogies for visual experience? I'm revising the essay for a book chapter and I'd like to expand my discussion to China if I can find enough material. Any help would be much appreciated!

(I also wouldn't mind more help on Greek passages, too, if anyone has the inclination. Some of the more obvious passages are Plato's discussion of painters in the Republic and Sophist, Aristotle's discussion of sensory experience as like impressions in wax, Sextus's lists of sensory distortions in experience and his discussions of wax impressions, Epicurus's discussions of the transmission of images, discussions of the sun as looking "one foot wide", and Euclid's and Ptolemy's optics.)


  1. Hi Eric,

    I agree with you that a tendency to overanalogize visual experience to flat media is responsible (or at least partially responsible) for a certain trend in post-Renaissance reflection on the way space is represented in visual perception. I think it’s important, however, to distinguish between the opinion that things in some sense “look flat” (so that, e.g., tilted coins look elliptical) and the opinion that things in some sense look smaller as their distance from us increases. It is, of course, very often the case that people analyze both apparent shape and apparent size talk in quasi-pictorial terms (the sense-datum theorists, Peacocke, Lycan, Noë). But I think that many people would readily acknowledge that there is a sense in which the cowboy on his horse appears to grow smaller while riding into the distance, while finding it hard to acknowledge -- or even understand the motivation for saying -- that the cowboy on his horse in some sense looks flat or 2-D.

    The reason, I would suggest, is that we do see an object’s angular size in addition to its constant, objective size. And, importantly, for present purposes, we can explain perceived angular size without any reference to a 2-D visual field or imaginary frontal plane. Perceived angular size is simply the difference in egocentric direction between two visible distal points (Joynson 1949, McCready 1985). The concept is nicely explained by McCready in the following passage:

    (quote) All modern researchers agree that we do not perceive or "sense" the retinal image (a proximal stimulus) or its properties, as such: Instead, perception is "distally focused." That is, we have (we create) visual images only of external objects and their properties. There certainly is no "sensation" which could be called the "perceived retinal image size", R' mm. One reason why some researchers did not use the concept of the perceived visual angle, V' deg is because they felt that to use V' deg was tantamount to accepting the ancient, obsolete idea that a person somehow "senses" the retinal image's size.

    However, in terms of the present theory, V' deg does not concern a linear size value in meters, it concerns, instead, one's perception of directions. For instance, many theorists, notably Helmholtz (1962/1910) and Hering (1942/1879) have argued, convincingly, that the visual direction of a viewed point (its subjective egocentric direction) is determined by a combination of factors, with its final value due to a process that necessarily combines the position of the point's image on the retina with information about the position of the eye with respect to the head (and body). And, the final perceived direction, d, for an object predicts the direction the eye should turn to in order to focus directly upon it: Also, d predicts the direction the head or body should be aimed in order to let the person examine the object more closely or to reach toward it.

    For two points which have different egocentric directions, the person obviously is seeing the difference between those visual directions, and the magnitude by which they differ correlates primarily with the distance, R mm, between the points' retinal images. (unquote)

    Notably, although, as McCready suggests, perceived angular size, “correlates primarily” with retinal angle, an object’s perceived angular size is nonetheless modulated by its perceived distance in depth. This has been well known at least since Thouless, but Scott Murray and co-authors recently found that by using perspectival depth cues it is possible to modulate the magnitude of the cortical representation of angular size in V1 while holding retinal size constant (Nat. Neuroscience 9 (2006), 429-434). This means that the representation of angular size in V1 is not straightforwardly retinotopic and is not determined solely be feedforward connections. It also makes trouble for Rock’s view that there is a “proximal mode” of experience.

    The main point, however, is that angular sizes are relational, but objective spatial magnitudes that are readily perceivably by naïve subjects, i.e., subjects who are not in the grip of a philosophical theory or pre-philosophical tendency to analogize visual experience to flat media. In fact, there would be something wrong with our visual system if it did not accurately represent the changes in egocentric directions that correspond to larger and smaller angular sizes. The same can’t be said for the 2-D perspectival shapes of 3-D objects.

    All this is just a long way of saying that I am not sure that the passage from Xunzi you provide really is relevant – no more say than the fact that many children when looking down from the window of a tall building will say that the people on the ground look like ants. The angular sizes we see are the angular sizes of 3-D objects, not their 2-D projections on the retina or frontal plane.

    Also, it is true that one often encounters the metaphor of the mind as pan of water/mirror in which the perceptible world is reflected. The metaphor is pretty much ubiquitous. But, as a vision scientist friend pointed out in correspondence a while back, “When an object is visible in a mirror, the optical location of its reflection (known as the virtual image) is not on the surface of the mirror itself but some distance behind the mirror. When viewed directly, an object’s rim is generically a true 3D space curve. This is also true of the reflection of the object: the rim of the reflection is also a 3D space curve, not a 2D projection onto the plane of the mirror. Optically there is no difference between a mirror and a window.”

    So saying that perceiving things is in some sense like seeing them in a pan of water or seeing them in a mirror doesn’t by itself have the same implications as saying that perceiving things is in some sense like seeing them as depicted in a painting or drawing or photograph.

    The fact that the latter metaphor/simile is so much rarer, I think, provides support for “flat media” theory that you (as well as people like Gibson, Gombrich, and A.D. Smith) espouse.

    I hope these comments are useful.

    -Robert Briscoe

  2. Eric,

    Xunzi’s description, which I find quite apt, does not necessarily depend on his being Chinese. There is a similar description in a contemporary perception textbook (Palmer, 1999, Vision Science, Cambridge, MIT). After discussing the notion of size constancy, the fact that we generally perceive object sizes as constant although their retinal projections change with their distance from the observer, Palmer (p. 317) writes that ‘size constancy can break down quite dramatically in some circumstances. The most familiar examples occur in observing people, cars and houses at large distances, such as from the top of a tall building or from a low-flying airplane. If size constancy were perfect, everything would appear to be normal in size – ideally just as big as if you were standing next to them. But they don’t. Indeed they don’t even appear slightly smaller … Rather, they appear much smaller, like tiny toy versions of themselves.’

    Such effects are not hard to explain if one assumes, as many have done since Alhazen and Descartes, that size perception involves taking distance into account. In the situations described by Xunzi and Palmer (and, I think, Helmholtz as well, but I can’t find the reference), cues to distance may be impoverished and distances may be judged as smaller, in which case the retinal projections would correspond to objects with smaller physical sizes. I am not saying that such an explanation is necessarily correct, but rather that it fits within an established view of functioning of size perception.

    Dejan Todorovic

  3. Eric,

    I"m sorry that I have not read your article, but on the Greek side of course is the famed/mythical contest between Zeuxis and Parrhasius reported by Pliny the Elder, which implicitly makes use of the analogy.

    Also, I'm sure that you are thinking along with Panofsky's study Perspective as Symbolic Form...I only mention it in case you are not.

  4. Wow, thanks for the incredibly helpful feedback, Robert, Dejan, and Kvond!

    Robert: Yes, I am growing more inclined to pull apart size distortion and shape distortion phenomenologically. I agree that we can see something like the angular size of a thing. Of course, it's worth noting that it's a step from noting that the angular size of an object is decreasing to saying that the object "looks smaller". I don't think the second follows straightaway, and perhaps not at all -- except in cases of illusion or misperception (which I'll mention in my reply to Dejan).

    I also agree with you about the actual optics of mirrors, but what matters for the impact of the metaphor on folk ways of thinking about visual experience is not the actual optics but the folk conception, and I'm inclined to think that the folk conception is as of a flat image on the mirror's surface, no?

  5. Dejan: Palmer is a wonderful contemporary source. In replying to your comment, I think it's important to distinguish carefully between things "looking smaller" due to illusion or misperception and things "looking smaller" due to ordinary veridical differences in perspective. If distance cues are impoverished, things might look smaller because we misperceive them (though intellectually we may not be taken in), but that gives no support to the view that veridical differences in perspective (such as differences in angular size, which Robert stresses in his comment) give rise to differences in apparent size. Unfortunately, few discussions of the impression we have that things in the distance look smaller clarify whether one or both of these sources of phenomenal distortion are at issue!

    Kvond: I really appreciate the references. I blush to confess that Panofsky was not on my mind when I wrote the essay, though his discussion of the conventionality of linear perspective is clearly relevant. (The Pliny seems to me not quite as relevant, since the issues is perspective, not illusion.)

  6. Hi Eric,

    I agree that it’s sometimes a step from noting that the angular size of an object is decreasing to saying that the object "looks smaller". It depends on what is intended by “looks smaller.” If all we intend is that less of the visual field is taken up by the object, then I don’t think that there’s a step (since we're just rephrasing the statement that its angular size is decreasing). I take it that when a child says that the people down below look like ants, she is operating with some implicit notion of size in the visual field. (There’s also a breakdown in size constancy to take into account here, but I don’t think that the child is really confused about how big the people down below are. At least I wasn’t when I’d say this sort of thing as a child.) Part of the problem is that we don’t have a separate expression for angular size, so we use the same expressions we use in order to talk about objective size. McCready has done a great job of spelling out the confusions caused by the failure to distinguish between angular size (distally conceived) and objective size in perceptual psychology.

    I’m not sure what to say about the folk conception of mirror reflections. (Is there a folk conception?) Reflections in mirrors don’t look to me like flat images on the mirror's surface. They rather seem to have depth. (Compare Aesop’s fable about the dog and his reflection.) Old Chinese mirrors were made of bronze, I believe, however, and I’ve never seen a reflection in a bronze mirror.

    Is the point of the comparison of the mind to a pan of water (Xunzi and Zhuangzi) a perceptual point, i.e., a point about what we see, or a more broadly epistemic point, i.e., a point about the need for accurate discernment of reality? It strikes me that many Western philosophers have used the mirror metaphor to make the latter point, e.g., St. Augustine and St. Bonaventure.


  7. Eric: "(The Pliny seems to me not quite as relevant, since the issues is perspective, not illusion.)"

    Kvond: I can certainly accept your minimization of this, but to let you know my thought process...I was responding to your primary thought that there has been a overanalogizing of vision to a plane surface. If there is anything which contributed to this, it would be the productions of painted illusions on plane surfaces, the way that distortions have to be painted in order to induce realisms. These distortions involve of course the symbolic form of Perspective the Panofsky argues for, but also I imagine in the Pliny example, where a flat surface painting can act as an exact replica of our visual impression. It seems reasonable to suspect that if flat surfaces can reproduce "reality" exactly, vision itself is much more easily analogized to flat surfaces, hence a rise of the perspectivist tradition with the capacity to paint illusionarily.

    Well, that is how my thought process went. All the same, I can certainly understand if you do not see the connection as relevant.

  8. Robert: Yes, if "looks smaller" is just a rough way of saying something like "occupies less of the visual field" then I agree there is no leap, or only a tiny leap. What about the child looking down from the skyscraper and saying the people look like ants? One possibility is that it's a report about the size of the visual field; another possibility is that it's a report about a certain sort of illusion due to the visual system's misperception of depth cues. Or maybe it's somehow both of these. They seem hard to disentangle! Or maybe it's still a third thing -- a sense of "smallness" that is neither illusory nor merely a report of visual angle subtended...?

    I appreciate and accept your reflections (no pun intended) about mirrors and water; I have no particular commitment on those issues.

  9. kvond: Ah, I see better now where you were coming from! Thanks.