Do Chinese Philosophers Think Tilted Coins Look Elliptical?

by Eric Schwitzgebel (guest blogger)

[Cross posted at The Splintered Mind]

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.)

11 replies on “Do Chinese Philosophers Think Tilted Coins Look Elliptical?”

  1. Eric,

    The Mozi has some discussion of optics, but I’ll have to track it down–or someone who already as read that section should pipe in. I’m just remembering that Joseph Needham discusses it in Volume IV(?) of Science and Civilisation [sic.]. I think there’s also some version of that discussion in Chinese Science (Needham, Nakayama, and Sivin), which is a volume that one can actually find in most libraries.

  2. Hi Eric,

    Early Chinese epistemology doesn’t really focus on the question of how things appear, probably because the major theoretical concern is with the ability to discriminate things properly, not with accurate representation of reality. The appearance/reality distinction plays little or no role. Perceptual discrimination is not seen as based on subjective appearances, representations, or experiences.

    I have a paper in progress on related issues posted here. You might find it helpful (sorry for the self-promotion, everyone). I also recommend having a look at Jane Geaney’s book On the Epistemology of the Senses in Early Chinese Thought.

    The point of the mirror metaphor in Xunzi, I think, is not that (for instance) appearances before the mind can or should accurately represent how things are. It is that if the mind is as empty and still as a mirror, the agent’s responses to things will be appropriate and reliable. The agent will be able to discriminate shi-fei 是非 properly because her heart (mind) is upright and unbiased. The Zhuangzi passage I think makes a similar point: an empty mirror-mind produces appropriate responses to things.

    So those passages may not really be relevant to your question.

    The Xunzi passage you mention is indeed a key passage to study in drawing contrasts with how appearance is handled in other traditions. Another important bit of text is the beginning of the paragraph you cite, which mentions examples such as mistakenly taking a tree to be a person while walking in the dark or taking a “mo mo” sound to be “xiong xiong” when covering your ears. Another passage that comes to mind is Mohist Canons B10, which identifies four common sources of epistemic error. The first is accidental circumstances, as when a heavy fog causes someone to mistakenly take a person to be an ox.

    Notice that these examples don’t frame the issue as one of how things appear, but of how circumstances can lead us to “take” (yi wei 以為) a familiar thing to be something else. Strictly speaking, no concept of appearance, looking, or seeming is involved.

    My rough translation of the Xunzi passage you quote is:

    “So from a mountain top looking at oxen, [they are] like sheep, but someone seeking sheep doesn’t go down to lead them away. It’s that the distance obscures their largeness. . . .”

    Notice that there is no explicit claim about appearance (the text does not say oxen “look like” sheep). The claim is that from a distance, oxen are similar to sheep with respect to size, because the distance obscures the difference between them.

    My interpretation of the underlying theory is that, measured by the size scale we apply from nearby, oxen and sheep are obviously dissimilar in size. But by the scale we apply from a distance, the difference between them is much less significant, so they count as “similar.” However, Xunzi’s point is that anyone exercising normal cognitive competence knows that you should discriminate animals’ size from up close, not far away. So although they really are similar from a distance, that similarity is irrelevant.

    To return to the point of your original inquiry, if we could ask him, would Xunzi (or whoever wrote that part of Book 21) say that oxen “look small” from a distance? This is a tricky question, since he doesn’t consider the issue in those terms. I’m not sure how to answer. My suggestion is that he’d say No. I think he’d say that from a distance, oxen may be indistinguishable from smaller animals. But that doesn’t mean they “look small,” since part of understanding how to discriminate “small” animals from “large” ones is understanding that you do so from nearby. In our terms, a competent user of the concept small would not apply it to distant animals viewed from a mountaintop.

  3. Eric,

    Only after posting the above did it occur to me that the tree/chopsticks example is more relevant to your question than the oxen/sheep one. I should have focused on that instead. (Silly me.) Moreover, I think that one may indeed concern projective distortion.

    Xunzi says that from the foot of a mountain looking up at trees on the mountainside, “trees of ten ren [80 ft.] are like chopsticks” 十仞之木若箸.

    The oxen/sheep example is potentially ambiguous as to whether the objects compared are distant oxen and distant sheep or distant oxen and nearby sheep. But the tree/chopsticks example is surely comparing distant trees with nearby chopsticks, since distant chopsticks would be too small to see.

    Although the text does not use the terminology of “looks” or “appears,” it is saying that, viewed from a distance, the height of tall trees is like that of short sticks. This is all you need to have an example of a remark about projective distortion, I think. It’s the only such remark in early Chinese texts that I know of, though. (Nor do I know of any comparisons between visual experience and painting.)

    My previous post was intended to help explain why we don’t find much discussion of perceptual distortion in early Chinese texts. Because of the theoretical orientation of pre-Qin epistemology, the question of how well visual experience reflects or represents reality isn’t a focus of attention. Instead, texts such as Xunzi Book 21 and Lushi Chunqiu 13.3 and 16.7 are interested mainly in how bias, prejudice, carelessness, interference with our normal functioning (such as from alcohol), or external conditions (such as distance) can affect how we discriminate things.

  4. Thanks for the tips, anodos and Manyul! Protagoras 356 I was aware of but not the Mohist discussion. (Are you thinking of Canons B10, which Chris mentions, or something else?) Chris: That is incredibly helpful. I’ll definitely look at your paper and Geaney’s book.

  5. Eric; actually, the Canons B16-23 are about optics more specifically. In the Needham, Nakayama, and Sivin volume I mentioned, Graham and Sivin have an article called “A systematic appropch to the Mohist optics” in which they provide detailed commentary on the Mohist discussions of shadow distortion, and image distortion in concave and convex mirrors. I would think that is pretty relevant to what you’re looking for. It is not about “perspective distortion” per se, but a very much related distortive effect that “tilt” and distance of light has on shadows. I don’t know enough about mirror optics, but the material in B21-23 on concave and convex mirrors seems to indicate at least technical interest in distortions of images. Does that engage questions about “perceptual” distortion? I don’t really know; the contrast is between the thing mirrored and the mirror image. Prima facie, that seems to engage questions about how things appear versus how they really are (pace Chris Fraser), but are they epistemological questions? What do you think?

    In any case you should read this Graham and Sivin piece; they also provide some reference to other possible optics-related passages in the Mohist Canons.

  6. For anyone interested, here’s the relevant text, courtesy the Wesleyan etext project (n+1 the numbering Graham and Sivin use), along with Graham and Sivin’s translation from the Needham, Nakayama, and Sivin volume:


    “A shadow does not shift. Explained by: remaking. Where the light reaches, the shadow disappears.”


    “Shadows are two. Explained by: redoubling. When two lights flank one light, whatever is illuminated by one light is in shadow.”


    “The turning over of the shadow is because the criss-cross has a point from which it is prolonged with the shadow. Explained by: ‘point.’ The light enters and shines [lit. ‘the light’s entry is a shining’] like the shooting of an arrow” (Sivin); or …The light’s entry into the curve is like the shooting of arrows. (Graham) The entry of that which comes from below is upward; the entry of that which comes from high up is downward. The legs cover the light which comes from below, and therefore form a shadow above. The head covers the light from above, and therefore forms a shadow below. This is because at a certain distance there is a point which coincides with the light. Therefore the revolution of the shadow is on the inside.”


    “The shadow cast in the direction of the sun. Explained by: reversion. When the sun’s light, reflected, illuminates a man, his shadow will be located between the man and the sun.”


    “The size of the shadow. Explained by: tilt and distance. When the post slants the shadow is shorter and bigger; when the post is upright the shadow is longer and smaller. If the flame is smaller than the post, the shadow is bigger than the post. It is not only because it is smaller, but also because of the distance.”


    “If one stands upright looking down at the mirror the shadow turns over, and the more there is of it the less there seems to be. Explained by: reduced area. In a plane mirror the shadow is reduced. The appearance, shading, distance, and inclination differ from those of [the object in] the light. When mirror and shadow are aligned, [object and shadow] approach and withdraw together. When they are not aligned, [object and shadow] turn toward or away from each other. The ch’ou of the man looking at himself are mirrored in the mirror without exception. The ch’ou of the shadow are numberless but must go beyond the mirror plane; they are therefore [squeezed into] the same places. Since this is so of all the parts of his body, it mirrors their portions.”


    中之內。 鑒者近中則所鑒大,景亦大。遠中則所鑒小,景亦小,而必正。起於中緣正而長其直也。
    中之外。 鑒者近中則所鑒大,景亦大。遠中則所鑒小,景亦小,而必易。合於而長其直也。
    “When the mirror is concave the shadow is at one time smaller and inverted, at another time larger and upright. Explained by: outside or inside the center. Inside the center: If the man looking at himself is near the center, everything mirrored is larger and the shadow correspondingly larger. If he is far from the center everything mirrored is smaller and the shadow correspondingly smaller. But it is sure to be upright. This is because [the light] opens out from the center, skirts the upright object and prolongs its straight course. Outside the center: If the man looking at himself is near the center, everything mirrored is larger and the shadow correspondingly larger. If he is far from the center everything mirrored is smaller and the shadow correspondingly smaller. But it is sure to be inverted. This is because [the light] converges at the center… and prolongs its straight course.”



    “When the mirror is convex, the shadow is at once time smaller and at another time larger, but it is sure to be upright. Explained by: …. If the man looking at himself is near, everything mirrored is larger and the shadow correspondingly large. If he is far, everything mirrored is smaller and the shadow correspondingly small. But it is sure to be upright. The shadow goes beyond the plane and therefore recedes at the edges.”

  7. Thanks for those passages, Manyul. What do you think about the character being translated as “shadow”? In the first few fragments, it seems clearly to be shadow in the contemporary sense but I wonder in the later fragments whether it means something closer to “image” — or do you think the topic is really the inversion and such of shadows per se when reflected in concave mirrors? I see that Mathews also lists “image” and “reflection” as translations.

    Mao (“appearance” in this translation) is also an interesting character in this context, especially in light of Chris’s views.

  8. Eric and others,

    I’ve filled in Graham and Sivin’s translations of two “explanations” (B19 and B22 above–B18 and B21 in Graham and Sivin); in my haste the other day, I left off substantial bits of them.

    Ying 景 should probably be read as “shadow,” not “image,” even in the mirror passages. The Mohist interest in the mirror passages seems actually to be about shadows that appear within the mirror. For example, in B23 (“Wesleyan” numbering), “鑒者近中則所鑒大,景亦大” reads coherently as making a point about shadows in the mirror: “…everything mirrored is larger (所鑒大) and the shadow correspondingly larger (景亦大),” and so forth for similar lines.

    Something interesting: Graham and Sivin offer a second translation of the “ch’ou” bit of B22, suggesting an emendation of chou 臭 to ze 澤, “lustrous” (pp.131-2):

    “‘Everything lustrous in the man looking at himself is mirrored in the mirror without exception. The lustrous features of the shadow are numberless, but must go beyond the mirror plane; they are therefore (squeezed into) the same places. Since this is so of all members of the body, it mirrors their portions.’ …. [For] the Mohist the reflected features of the face are additional to the ying, which even in the mirror is still the shadow, the outline of the image.”

    I wish Graham were around to explain this to us; maybe Sivin, or someone who understands this at least better than I do, could. I’m sure there’s some simple explanation about polished metal mirrors that I’m missing.

    Yes, Eric, mao 貌 is interesting, though it could be more specific in range than “appearance” here–maybe, “feature” (of the face?).

  9. Mao 貌 is sometimes the surface features of something, as contrasted with xing shape 形. But sometimes it just seems to be, roughly, “characteristics” or “features.”

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