Wednesday, February 06, 2008

Does the Sun Look One Foot Wide?

Aristotle says that the sun looks one foot wide (De Anima 428b, On Dreams 458b). Writers in later antiquity repeat this claim without challenging it (e.g. Cleomedes II.1), though they are troubled to explain how it can look one foot wide given how far away it must be -- hundreds of meters at least! Their assumption seems to be that there is some illusion or trick of optics at work.

Does the sun look one foot wide?

Do stars look tiny? Do people look no bigger than ants when you stare down at them from twenty stories up?

People say these sorts of things, but how literally should we take them? Maybe the people below look normal-sized, but only very far away -- far away enough that there's something unusual about how they look that tempts us to say they look tiny, though really that's not quite the right way to describe how they look.

Or consider skyscrapers in the distance: Do they look small, or do they look huge? I find myself doubtful of both those ways of putting it. Alva Noe might say they look huge in looking small (but not tiny?) given how far away they look. But I'm not sure I understand that. One problem: Don't they look small because they look like they're less far away than they actually are? (In which case, they don't look so far away at all and consequently they don't look huge in virtue of looking very far away.)

If we say simply that the skyscrapers look like large things far away, then I wonder two things: (a.) Why are we tempted to say they look small? (This temptation manifests itself cross-culturally, e.g., in the ancient Chinese philosopher Xunzi); and (b.) What do we do about outright illusions?

Look at Poggendorff's illusion:

You know the line is straight, but it still looks crooked. Right? Likewise, could it be that although I know the skyscrapers are large they still look small? Surely it's too purist to say things never look other than how you know them to be.

There are outright illusions with distance -- things looking smaller, in an illusory way, than they actually are. (This is part of why we often badly misjudge the speed of large, far away things.) Such illusions should have a different effect on the visual experience of size than does the non-illusory visual experience of "smallness" with great distance, if the advocate of the view that skyscrapers look like large things far away is right. But I'm I can't seem to find in myself the required difference in visual experience.

Should I then simply get on board with saying that distant objects look small? Among other things, I worry that the geometry of that view will lead us ultimately to say that things far away look simply flat (or concave) -- with the unpleasant consequence that a far-away road receding to the horizon looks like it goes straight up. That couldn't be right, could it?

(And don't get me started on painters.)


Anonymous said...

I think the "smallness" in some cases is how much something takes up of your visual field. A single star takes up a very small part of my visual field when I look up in the sky. So I say it looks tiny.

Also stars look to me like points of light, they have no other features. And I think of a point as being a very small thing, only the smallest things in everyday life are so small I can't distinguish any features about them except that they exist or maybe their color.

I don't know about skyscrapers because I've never lived or worked above the 5th floor.

The Uncredible Hallq said...

I tend to think that *unusually distant* things look small. When I encounter an object at a distance I'm used to seeing it, it seems the right size, but when I have a perspective I get only rarely (say, an airplane) things look small. I've heard that people from jungle tribes not used to open spaces will see anything at any significant difference as small.

As for the moon, I don't pay much attention to its size, except when I have a reference point that's usually absent. When I hold up a finger to it, it looks small. When I see it against the horizon, it looks big.

Anonymous said...

This is something of a non sequitur: I think that "People look like ants" (uttered from the top of the Eiffel tower, for example) is not really a remark about size. From up there, you can see so many of them all at once but can make out no details of their activity. The meaning of their movements is lost. So they look like ants not just in the sense of subtending a small visible angle, but more importantly in the sense of being an insignificant horde.

Saying the the sun is an inch wide seems less natural to me, because it is not evocative in the same way.

Anonymous said...

Hey Eric, very interesting post,

I also think that there is something related to the 'unusual distance' there.

Here is a speculation...

Maybe it could be related with our ability for recognition? I mean, we see a thing from front from 1 meter, and than we can recognize it from 2 meters, and maybe somewhat rotated, etc... We wouldn't be much of a functional "recognizers" if we only recognize the things in the exact same circumstances in which we saw it before.

But, probably this works just in some limits, and maybe this is where the problem lies. When we look from the 20 stories high building the first time, this 'automatic recognition' doesn't work. Maybe the conceptualization 'repairs' the recognition after some time, or we just ignore those 'glitches' of the recognition not being able to do relations on such distances.

Something similar might be the case for the moon and the star, just with the difference that our perception really can't handle such sizes and distances, so we can't relate it to the concept of 3d ball (at least not intuitively in the perception), so we relate it to a smaller flat 2-d disc and dots (I guess without any real sense for the size or the distance)

Probably that's why those objects would be closest to some idea of veil of perception / visual field.

BTW, I agree with your argument against saying 'looking huge in looking small'. It doesn't seem as a right thing to say.

Anonymous said...

I think it's important to distinguish looking up at something far away and looking down or along the horizon. At some distance our stereoscopic sense fails us -- the difference in angle between the direction our eyes are facing becomes too small for our brain to register. When we are looking at things on the ground, our brain still compares with other objects, or with our own knowledge. We compare skyscrapers to other nearby buildings, or to trees. We know how big people are. Etc. We have none of this information when gauging how big the sun is.

Also don't overlook the most overlooked register of distance: so-called "atmospheric perspective". We gauge size much more easily when the air isn't clear.

Because of all of this, I think that the better test for our inability to gauge size is looking at very large planes fly overhead. I used to work near a military base, and I was constantly under the impression that the planes were flying *very close* overhead, when in fact they were just very very large planes.

Without really looking into it, I would assume that our brain places everything past the limit of stereopsis _at_ that distance. Unfortunately, I couldn't find that limit with a little bit of googling. I would think that someone who had formed no opinion about the size of the sun would reasonably accept any size larger than insinuated by that limit of stereopsis... but that seems a lot bigger than a few feet, to me.

Hey, and don't be too hard on painters. For every painting with bad perspective, there's a bad early scientist or philosopher. Everybody was proven wrong when the camera started churning out a new kind of proof.

arnold Trehub said...

The brain's mechanism for conserving size constancy makes the perceived size of a distant object relatively larger than its retinal size. This is why we can recognize a particular object at a distance of 100 feet even though it was initially viewed and learned at a distance of 10 feet. So a distant sky scraper can look huge because of our size-constancy machinery, and at the same time it can look tiny compared to the size of a nearby tree. The neuronal mechanisms responsible for all this stuff also explain the moon illusion (See Trehub, A. *The Cognitive Brain*, pp. 242-247).

Eric Schwitzgebel said...

Thanks for all the interesting comments, folks!

I like the idea, Hallq and Tanasije, that part of the phenomenon has to do with the contrast between how something looks from the "usual distance" and how it looks from unusually far away; and maybe also what happens when our usual ways of recognizing the sizes of things break down.

I don't know, Ian, about the idea that everything beyond the limit of stereopsis is visual experienced as being at that limit. Stereopsis tends to be confounded with other depth cues in real life (you mention atmospheric cues), but it's hard to believe that effective true stereopsis extends beyond a kilometer or so. H.H. Price (whom I mentioned a few posts ago) seems to think that that about that distance everything looks flat, but few others seem willing to go along with that. (I might also mention that it's not failure to appreciate the laws of perspective that worries me about painters, but the overplaying of those laws -- and the same goes for comparisons of visual experience to film media.)

Kenf & P.D.: That seems right -- but is the experience of "tiny" the same as the experience of "it takes up a small part of my visual field"? I guess that's the question!

Arnold: Yep! But what is the experience of size constancy? Are you with Noe on this one, saying that it looks small and it looks large (maybe the latter in virtue of the former)?

arnold Trehub said...

Eric: The *experience* of size constancy is the experience that an object in view has not changed its real size (e.g., a huge sky scraper) despite the fact that it looks tiny because it is far away (and projects a much smaller image on our retinas than it would if we were closer to it). Innate brain machinery compensates for the variation in the projected retinal size of an object as our viewing distance changes. If this didn't happen, we would have a terrible problem in learning to categorize and name things in the visual world.

Eric Schwitzgebel said...

Thanks, Arnold, for clarifying that aspect of your view! But surely also the size of the buildings manifests itself phenomenologically differently when the buildings are seen from far away than when they are seen from close up? Your visual experience in the two cases is not exactly the same. So how do you characterize *this* difference in experience? That seems to me the real challenge!

The Financial Philosopher said...


Great post! I started a comment then decided to create an entire post out of it!

I drew an analogy to the detrimental behavior of investors to perceive risk as too low when "real risk" is actually quite large.

Here's the link if you want to read it:

Thanks for provoking thought, as always...

Anonymous said...


You say to Arnold, 'But surely also the size of the buildings manifests itself phenomenologically differently when the buildings are seen from far away than when they are seen from close up?'

But can't we simply say that it is not the size that manifests itself phenomenologically differently but the distance. I mean, as I approach some person, I don't really experience the person getting bigger, but getting closer. (Although in some cases where because of the initial distance like in case of the moon one might not to be able to judge the size, so with getting closer to actually have better 'feel' of the size, so in those cases one might probably speak that the thing is 'growing' phenomenologically.)

arnold Trehub said...

Eric: This is a good example of why we need to take account of the detailed structure and dynamics of the brain mechanisms that constitute the biophysical stuff of our phenomenal experience. Our immediate phenomenal experience of a building seen far away (looks small) is certainly different from our phenomenal experience of the same building seen up close (looks big). But, at the same time, we do not have the phenomenal experience of the building itself having changed size. How can this possibly happen? In The Cognitive Brain (1991) I describe in detail the minimal neuronal mechanisms and systems that can explain what puzzles you.

Briefly, the difference between the phenomenal experience of a building seen far away and the building seen up close is reflected directly in the relative neuronal size of the representation of the building within the brain’s retinoid structure under the two different viewing conditions. At the same time, the neuronal representation of the building’s unchanging intrinsic size is given by the retinoid’s size constancy mechanism under the two conditions. In my theoretical model of the cognitive brain, our phenomenal experience is constituted by neuronal activity within the retinoid system, which gives us a transparent representation of the world from a privileged egocentric perspective. For a more extensive account, see Trehub (2007). Space, self, and the theater of consciousness, Consciousness and Cognition.

Eric Schwitzgebel said...

Cool post, Financial -- Thanks!

Yes, Tanasije, it seems plausible to say that the buildings look closer as I approach them. That's not, I take it, inconsistent with saying that the phenomenological manifestation of their size is somehow changing to (which is expressly not to say that their apparent size is changing!). Size maybe isn't the most obvious case of this. Consider shape as an analogy: The obliquely viewed coin and the rectilinearly viewed coin both look circular, but that circular shape manifests itself phenomenologically to me differently in the two cases (such that in one case I'm tempted, I think erroneously, to say it "looks elliptical"). Would you grant that? And if so, would you grant the parallel for size?

Eric Schwitzgebel said...

Well, Arnold, I'll have to chase down your article. It sounds interesting!

I'm inclined to think there should be some back-and-forth between behavioral psychology, neuroscience, and introspection in figuring out what our stream of conscious experience really is. I'm not a fan of leaping quickly to neuronal models; but I also don't think we should ignore them. I apologize for not knowing more about yours!

Anonymous said...

Hey Eric, I'm afraid I actually won't grant that. I will grant that given certain conditions we might mistake an obliquely viewed circular coin for an perpendicularly seen ellipse, or the other way around, we might mistake an ellipse for an obliquely view circular coin (e.g. on a nicely painted picture). But I don't think that any of those has any primacy over the other. I don't think that 'ellipse seen perpendicularly' is phenomenologically somehow more basic than 'circular coin seen obliquely'. Why should it be? (Except if we imagine some two-dimensional veil of perception view related with the phenomenological experience) If we remove the idea of some 'standard' direction of view, simply the form/direction of view becomes a pair about which we need to talk as gestalt in the experience.

So, to return to the issue of size, can we talk about phenomenal experience of size without there being distance? How do we talk about phenomenal experience of size, without seeing the object of that size from some distance? There can't be any variable 'size' which can change independently in the phenomenal experience. Because there is no 'standard' distance to which those would be related. So to say, we can speak only about size/distance pair in the phenomenal experience (except we assume veil of perception, which is on some certain distance, but I know you wouldn't want to go there).

Eric Schwitzgebel said...

I agree with you, Tanasije, in what you say about the ellipse/circle case (as in fact I argue at length in a recent essay)! But all that is, I think, compatible with granting that there is a phenomenological difference in the look of that circular shape when viewed from one angle than when viewed from another. (Siewert argues for this nicely in his recent commentary on Noe, "Is the Appearance of Shape Protean?".)

In other words, the circular shape of the titled coin doesn't present itself to me exactly the same way in experience as the circular shape of the rectilinearly viewed coin.

I assume you still want to deny that. You'll say, perhaps, that there's no way the shape appears in experience in those instances, full stop. There's only the way the-shape-and-perspectival-angle-on-it appears, and of course there's a difference between the experience in those two cases since the perspective is different. (This would correspond to your comment about depth and size.)

Hm! I must admit I'm temporarily at a loss over how to choose between those competing views. I wonder if there might be a way to accommodate both of them as terminological variants of each other. Importantly, they both deny that the obliquely viewed coin looks elliptical.

And part of me still wants to say that the buildings in the distance look small. Is there no phenomenologically reality in that at all, despite its cross-cultural appeal...?

arnold Trehub said...

Eric, why can't we say that our phenomenal experience is just that the distant building *looks* small but *is* very big? Or that the tilted coin *looks* like an ellipse but *is* circular? The opposing phenomenal geometric representations naturally co-occur within the right kind of neuronal machinery in the cognitive brain.

You can get a good idea of how the compensatory activity of our size-constancy mechanism makes this happen by forming a retinal after-image of a small square and then fixating a large blank card that you can tilt. If you tilt the card away from you on a horizontal axis, the square after-image looks like a rectangle elongated on the vertical axis! If you tilt the card on a vertical axis, the square becomes a rectangle elongated on the horizontal axis! (See *The Cognitive Brain* pp. 92-93). These changes are predicted from the neuronal properties of the retinoid system and its size-constancy mechanism.

Anonymous said...

I don't see anything problematic with saying that buildings in the distance look small, even if one accepts that talking about phenomenological experience, size can't be fully separated from the distance.

It would mean that buildings in the distance look as small things near us look IF we succeed to abstract from their distance or somehow otherwise loose the sense of distance.

Eric Schwitzgebel said...

Funny, Arnold, I'm not getting the effect you say. I'll have to try it again later with a better square. As for simply granting that the buildings in the distance look small, maybe that's right -- yet I'm worried that it doesn't quite do complexity to our experience of their size; and as I mentioned in the post I'm worried about how the geometry of that will work out. Among other things, will it commit us to saying that roads in the distance look like they're going straight up? That seems weird.

Eric Schwitzgebel said...

I think I'm starting to see better where you're coming from, Tanasije. Do you think the parallel would be to say the coin "looks circular" to the extent we can abstract from angle of presentation (or something like that)?

Anonymous said...


I would say that the coin looks like an ellipse (in the case of an oblique viewing of the coin) to the extent that we abstract from the angle of viewing.

Let me quote from Kohler's Gestalt Psychology[p73] (after presenting a subject with two cardboard rectangles of different sizes, the smaller is closer to the observer, the bigger is further away):
It is quite true, the rectangle at the greater distance appears much larger than the nearer one. But this is precisely what the Introspectionist does not accept as a true statement about the sensory facts. [...] He will invite us to look through a hole in a screen which he holds before our eyes. The two rectangles now appear on homogeneous background, because the screen hides all other objects. Under those conditions the difference between the sizes of the rectangles will probably be somewhat reduced. [...] He may darken the room, and turn the light only for a fraction of a second. This serves to exclude the movement of the eyes and of the head. [...] [Given] practice I cannot here describe, and after some training, the rectangles may indeed assume the same size, even if the screen with its hole and any other devices are omitted.

So, I take it that this so called 'training' is abstraction training, which does what the devices were doing for the "untrained introspectionist". That is, with abstraction we forcefully remove one part of the information, and we end up with a situation where we (in lack of the aspect which we removed), can't say the distance of the objects. So, they might be close and small, or distant and big. But, again none of those two is more basic than the other. We might say that the distant rectangle seems small and close (as the other one), but we may as well say for the other one seems big and distant. There can be simply "seems small" or "seems big" without having on mind certain distance.

BTW, on the next page, Kohler also points that to the phenomenon Arnold mentioned.
if an afterimage is projected on planes of different angles in relation to the eye, the image will seem to change its shape as we project it on one plane or another... Small world :)

Anonymous said...

Oops, made a mistake: "There CAN'T be simply "seems small" or "seems big" without having on mind certain distance."

Eric Schwitzgebel said...

Wow, interesting quote from Kohler! I'd guess that in the end he wouldn't endorse that sort of introspective abstraction (isn't that supposed to be the lesson of Gestalt psychology?), but I'll have to go track it down!

I do wonder whether this "abstraction" really gets at something that is there to be discovered prior to the training. For example, why a flat ellipse rather than a concave ellipsoid? The latter makes more geometric sense, since projection onto a flat plane creates serious problems for size and shape constancy of objects off the central line of sight. (If size is supposed to vary with visual *angle* subtended, the proper projection would be onto a sphere, not a plane, thus generating the concave ellipsoid.)

Anonymous said...

Let me just add this comment, so not to be misunderstood about what I mean by "abstraction".
I don't mean we have size+distance in the experience, so that by abstraction we remove the distance, and we are left with the size.

Instead what I meant is that in the experience we have 'size AT distance', and that by abstracting from the distance, we are left with 'size AT unknown distance' (so again, it isn't *just* size). As we don't know the real distance, but we can't even make sense of size at no distance, we are free to 'play' in our mind with the distance. Or, what we are left with is underdetermined, it can be big thing far from us, or small thing close to us.

So in the case with the two cardboard rectangles as in Kohler's example, when we abstract from their distance, and then *take them to be* on same distance, they will appear equal in size.

I don't know if Gestalt psychology might have problem with this kind of view. (I never read the book to its end :) )

arnold Trehub said...

Eric: You said "I do wonder whether this "abstraction" really gets at something that is there to be discovered prior to the training. For example, why a flat ellipse rather than a concave ellipsoid? The latter makes more geometric sense, since projection onto a flat plane creates serious problems for size and shape constancy of objects off the central line of sight. (If size is supposed to vary with visual *angle* subtended, the proper projection would be onto a sphere, not a plane, thus generating the concave ellipsoid.)".

This highlights the need to separate the optical projection transformations which hold *only* up to the retinal representation. Thereafter, all brain transformations are determined by neuronal mechanisms operating on *retinotopic* and *spatiotopic* excitation patterns rather than geometric patterns.

The biological transformations underlying our immediate experience of size and shape over different visual perspectives are automatic and do *not* depend on introspective abstraction.

Anonymous said...


You say that "thereafter, all brain transformations are determined by neuronal mechnanisms operating on *retinotopic* and *spatiotopic* excitation patterns."

May I ask (and I hope Eric won't mind)...
Are there researches of how those neuronal mechanisms behave in the case when there is not enough information coming from the senses to fully determine the size/distance (like in the deliberate setup in the experiment Kohler described)? (btw, the parallel with Necker's cube here comes to mind).
Also, related to my assuming that in trained introspectionists something similar happen, that is, that they can intentionally suppress the information, is there some research done in this direction (maybe possibly in relation to attention) ?

arnold Trehub said...

Tanasije and Eric:

You will not understand phenomenal experience unless you first take account of the crucial fact that we have no sensory transducers that can directly give our brain an internal representation of the coherent volumetric properties of 3D space. This means that that the brain must have an innate biological mechanism that provides a phenomenal representation of 3D space within which all phenomenal features are properly bound and registered. The *retinoid system* in my theory of the cognitive brain serves this function.

There is never enough information given by our senses to fully determine size-distance relationships. The operating characteristics of the 3D retinoid mechanisms have to complete the job in order to give us a useful phenomenal experience of the world from an egocentric perspective.

If you want to understand illusions like the Necker cube illusion, you have to understand the role of the heuristic self-locus (HSL) in my retinoid model (see *The Cognitive Brain*, Ch. 4 "Modeling the World, Locating the Self, and Selective Attention: The Retinoid System). Briefly, the HSL acts like an excitatory neuronal stylus as it moves through 3D retinoid space, inducing edges of neuronal discharge along the path it traces.

Here's how it works:
Draw a Necker cube. Fixate the lower left junction of lines (call this A). Follow the oblique line to its terminal junction (call this B). If your HSL moves from near to far going from A to B in 3d retinoid space, the cubic plane attached to B will be experienced as the back surface and the plane attached to A will be perceived as the front. If your HSL moves from far to near going from A to B, then the plane attached to A will be the back surface and the plane attached to B will be the front. Neuronal fatigue will naturally account for unpredictable flips in the phenomenal orientation of the cube.

Excursions of the heuristic self-locus also explain
how 2D perspective works to give us an experience of 3D depth. Recent fMRI experiments have given us empirical findings on spatiotopic transformations that are predicted by the retinoid model.

Eric Schwitzgebel said...

Arnold, I'm sorry I don't know your model well enough to comment on it firsthand, yet!

Of course there must be some structures in the brain that can somehow generate a three-dimensional representation (or a set of three dimensional representations, possibly conflicting) of the world. But it does not follow that our phenomenology cleanly accords with any particular stage in that process. I worry that you're assuming that it does. (Of course, you may have an argument that it does, that I haven't read!)

MT said...

Speech is rife with ambiguities, which we resolve routinely and with high accuracy from context, and what you're talking about seems about par for the course. There's a seeming narcissism about these statements that's bugged me in the past--in that the speaker is insinuating universality or absoluteness of his or her subjective experience; but since the experience typically is common human psychophysics in circumstances familiar and recognizable to the listener, I think it's licensed or reasonable. Aristotle's foot isn't recognizable to me, but he was speaking a couple thousand years ago. I recognize what people mean nowadays in talking about distant objects, such as the moon, in units of "the width of your thumb" (outstretched)...a handy concept taught both in art and astronomy. Aristotle's remark makes me think the ancients slept outdoors with feet facing eastward and the sun rising between them. Or vice versa with the moon, which is "the same size," if you know what I mean.

arnold Trehub said...

Eric: You wrote "Of course there must be some structures in the brain that can somehow generate a three-dimensional representation (or a set of three dimensional representations, possibly conflicting) of the world. But it does not follow that our phenomenology cleanly accords with any particular stage in that process. I worry that you're assuming that it does."

If our phenomenology doesn't accord with any particular stage in the neuronal processes of the brain, then with what does our phenomenology accord?

I have presented arguments in support of my theoretical claim in other contexts. Here is a summary:

I have proposed what I take to be a law of conscious content which asserts that for any experience, thought, question, or solution, there is a corresponding analog in the biophysical state of the brain. As a corollary to this principle, I have argued that conventional attempts to understand consciousness by simply searching for the neural correlates of consciousness (NCC) in theoretical and empirical investigations are too weak to ground a good understanding of conscious content. Instead, I have proposed that we go beyond NCC and explore brain events that have at least some similarity to our phenomenal experiences, namely, neuronal analogs of conscious content (NAC). In support of this approach, I have presented a theoretical model that goes beyond addressing the sheer correlation between mental states and neuronal events in the brain. It explains how neuronal analogs of phenomenal experience (NAC) can be generated, and it details how other essential human cognitive tasks can be accomplished by the particular structure and dynamics of putative neuronal mechanisms and systems in the brain.

A large body of experimental findings, clinical findings, and phenomenal reports can be explained within a coherent framework by the neuronal structure and dynamics of this theoretical model. In addition, the model accurately predicts many classical illusions and perceptual anomalies. So I believe that the neuronal mechanisms and systems that I have proposed provide a true explanation for many important aspects of human cognition and phenomenal experience. But I can't prove it. Of course, competing theories about the brain, cognition, and consciousness can't be proved either.

Providing the evidence is the best we can do.

Eric Schwitzgebel said...

That's certainly ambitious! My own general inclination is to be suspicious of clean models; but I'll have to check the details of your published work on this to form a more informed opinion about your specific arguments!

Eric Schwitzgebel said...

Interesting thought, MT -- a "foot" meaning literally the same visual arc as what can be covered by your foot at foot's length, rather than an objective unit of measure.

My sense from some of the later discussion is that they conceived it more in terms of objective size, but it's worth re-examining with your suggestion in mind!