Monthly Archives: December 2015

2015 in review

The stats helper monkeys prepared a 2015 annual report for this blog.

Here’s an excerpt:

A San Francisco cable car holds 60 people. This blog was viewed about 730 times in 2015. If it were a cable car, it would take about 12 trips to carry that many people.

Click here to see the complete report.


The Truth Of Bishop Berkeley (Part 1) — With Green Bungee Cords Again

In a previous post on Bishop Berkeley’s claim that depth cannot be seen, The Truth Of Bishop Berkeley (Part 0), I argued that this claim does follow from Berkeley’s theory of Ideas, at least as I construed that theory in that post.  Here, I want to argue for something like Berkeley’s claim without appealing to any version of his problematic theory of Ideas.  The motivation for doing so is to capture within a Merleau-Pontyian framework what I think is the germ of truth in Berkeley’s claims regarding depth.  This germ is the claim that, at least in the case of the planes seen or imaginatively pictured end-wise to one’s gaze, there is no straightforward (so to speak) visual presentation of depth.

There is, however, a projection of depth that forms the visual field itself.  I will be much occupied with this projection in future posts.

In the process of uncovering the germ of truth in Berkeley’s claims regarding the invisibility of depth, I hope to deal a serious blow to Berkeley’s Theory of Ideas, and advance one step (my first step) in my project, my essay, my attempt to see whether one can transform George Berkeley, bit by bit, into Maurice Merleau-Ponty.

Let me advance the following thought experiment.  The aim of this experiment is to show that as an edge (for the sake of simplicity, let’s say it is the left edge) of an initially wholly-frontal plane moves away from you in depth, you see less and less of any given section of that plane, and, of course, of the plane as a whole.  That is to say, less and less of these get presented visually to you.  Starting from the initial situation in which you see all of the plane and each of its sections, you end up seeing none of these.  At first these get visually presented to you in their entirety; then nothing of them gets presented to you visually.

The Thought Experiment:  Suppose that an extremely, extremely, thin square of gold leaf foil is stretched out in front of you, parallel to your face and to the front of your body.  The thickness of this foil is 0.134 microns, or about 500 gold atoms.  Thinner than the wavelength of light, this is too thin to see.  So were the foil to be turned edge-wise to your eye, it would surely disappear.  Nothing of it would be presented to you visually.

With the mind’s eye, you divide the foil square into four equal sections from the top.  A darker rectangle runs down from, say, in the third section from the right and taking up about a quarter of that section.  (Don’t ask me how this section would be made darker.  This is a thought experiment; you can do what  you like with the gold leaf as long as what you do does not violate physical law too blatantly.  So just do it!  Make the section darker than the rest of the foil square.)

Now suppose that the foil square is steadily turning in such a way that its left edge is moving away from you.  At some point, the darker rectangle will, after first turning into a blur, eventually disappear.  For at some point you are seeing so little of the darker rectangle that your visual system can no longer obtain a clear view of it…and eventually cannot get any view of it at all.

To step out of the thought-experiment for the nonce and into a real experiment, you can try the following.  (Of course, I am sure the claims I made above are not controversial…still…it is always good to cover one’s bases as completely as they can.)  Take a bungee cord, like the polyester-green one shown below.  Taking a gel pen or some other suitable instrument, mark a line segment on it.  At first holding the cord parallel to the front of your body, steadily move the left edge away from you.  You will observe the dark line segment becoming, first, a blur, then disappearing altogether.



Back to the thought experiment.  The fact that you eventually saw so little of the darker section of the foil that it became a blur — and then saw nothing of it — strongly suggests that, as the foil was turning away from you, you were steadily seeing less and less of darker section.

Perceptual Constancy As A Fly In The Ointment (If I May Compare My Claims To Something Creamy and Oily, Such As An Ointment):   However, the phenomenon of perceptual constancy in general, and shape constancy in particular, prevents me from making this claim with absolute confidence.  For if this claim were true, the darker section would be steadily becoming thinner and thinner in the shape it looks to have.  But I have encountered theorists (I am looking at you, professor Suzanne Cunningham) who will deny this because they are prone to making extreme claims about shape constancy.  These theorists will deny that the darker rectangle is looking steadily thinner and thinner, just as they will deny that the two edges of U.S. 285, that absolutely straight road in New Mexico that goes on for mile after mile after mile after mile…these theorists will deny that the two edges of this road look to you to be converging at the horizon even while driving in the scene in New Mexico.  In the photograph, they will say, yes, the two edges converge.  When we project onto a 2-dimensional surface the very 3-dimensional Highway U.S. 285, then we get lines that actually converge.  But in the actual scene itself, one does not see (according to these theorists) lines that converge at the horizon.  Perceptual constancy ensures that we just see two lines in parallel:




So it is claimed.

The point of this rather extreme denialism is to block one argument for the sense datum theory.  (The edges of the physical road do not actually converge; nonetheless, lines are converging; a fortiori there are things that are converging; and these must be something mental, i.e., sense data.)  I do not want to dismiss this hard-line take on shape constancy outright, since I think that, in fact, there is a certain amount of truth to it, and I will be discussing shape constancy in particular and perceptual constancy in general in a later post.

Nonetheless, I will point out now that at some point you no longer see enough of the darker rectangle to see it in a non-blurry fashion, and very soon thereafter, as the foil square turns away from you, you see nothing of the darker rectangle at all.  Were the extreme version of perceptual constancy mentioned above correct, this change from clear and distinct to blurry then invisible would have to be sudden and abrupt, something that strikes me as highly implausible.  Nonetheless, gradual or sudden, the change does occur at some point.

Then, when the foil square is completely edge-wise to your eye, you no longer see it at all.  It has disappeared.  There is no longer a visual presentation to you of the square of extremely, extremely thin gold foil.

As long as the foil was at a sufficient slant to you, there was a visual presentation of it in depth.  There was a visual presentation of depth at a slant.  But when the slant became too extreme, that visual presentation became a mere blur; and when the foil came to be completely edgewise to your eye, that visual presentation to you ceased to exist altogether.

A plane can be seen in depth only when it exists in depth at a slant.  By ‘plane’ I mean a physical surface whose thickness is too small to count and therefore can be abstracted away.  There is no visual presentation of such a plane in depth when that plane is situated completely edgewise to the eye.  If there is a steady diminishment in how much of the plane gets presented to you visually as it turns away from you in depth, as I think there is, then we can say that the more the plane is situated in depth relative to you, the less visible it is.  (Again, fuller argument to come later.)  The more depth, the less visibility (i.e., less gets presented to you visually).  When the plane is completely frontal to you, 100% of it gets presented (subject, of course, to the limitations of your visual system).  When the plane is completely in depth relative to you, 0% of it gets presented to you visually.

When the plane is situated at varying degrees of slant relative to you, then, to corresponding degrees less of the plane gets presented to you visually.  Or so I claim.  We will see whether, in the end, I can get away with this claim.

With these arguments/claims in mind, let’s modify the second paragraph of Berkeley’s A NEW THEORY OF VISION to make him say something like:

II.  It ought to be agreed by all, that Distance [of an object in depth], of it self and immediately, cannot be seen except when this is Distance at a slant.  For Distance being a Plane sufficiently thin as not to have a visible edge, it becomes invisible once it is directed end-wise to the Eye.


I think something like this was the content of the Aha Erlebnis I experienced some decades ago when I encountered Berkeley’s NEW THEORY OF VISION in that cottony-red book in my parents’ library.

So far I have been discussing just visual presentation, which will always include at least an element of receptivity/passivity.  The square of gold foil causally impinges on your physical body, and without this impingement you would not be enjoying/suffering the concrete visual presentation of the foil.  When the foil is situated at a slant to you, you have an experience of depth that includes this passive component.

But the experience of depth also includes an active element, which I would like to briefly discuss now.  This active element is projection.  One can imaginatively project the depth of the plane.  You can, for example, — or at least I can — visually imagine a point that is situated about half-way across the foil that exists edgewise to the eye.  In doing so, you posit, that is to say, place the point at that location.  (Interesting word, that is, ‘place’ — suggestive of a kinaesthetic action.)  The point can be pictured as a spot, say,  with some color (white, black, wine red, sea-glass green, burnt sienna, and so on) with just barely enough size to be visualized.  Or perhaps there need not be any visual image at all.  I might imaginatively feel, probe with the imagination’s finger, so to speak, the distance to what I think is the half-way point of the foil square, with the attendant sense that here is a point that could become large enough to be visualized, a potentially ‘visible’ point.  In other words, there is an easy translation from imagined feeling to imagined seeing.

I will be having much more to say about this imaginative projection in future posts.  In particular, I will be asserting that this imaginative projection is based on a more fundamental motor intentionality ala Merleau-Ponty.

The blur:  I noted above that, in the case of the bungee cord, one will eventually see a blur instead of the mark made by the gel pen, and, in the case of the foil square, a blur instead of the darker rectangular section.  This fact already creates trouble for Berkeley’s concept of a Minimum Visibile, and it becomes completely devastating to that notion when one brings into the picture empirical work attempting to define a threshold at which one becomes aware of a sensation.  And if the concept of a Minimum Visibile goes, then Berkeley’s whole notion of purely mental items called ‘Ideas’ that form the building blocks of our perception goes as well.

If you ever have had the extent of your visual field tested, you will have faced the following conundrum:  you are supposed to say ‘now’ when, keeping your eyes focussed at the center of the tester’s screen, a dot appears at the periphery.  At first, you say ‘now’ when a blur appears in the periphery — it will never be a distinct point with clear boundaries after all.  But did you wait too long?  After all, if you are at all like me, you had the distinct feeling something was there a moment before you said ‘now’.  Doubtlessly if you attended more to what you see (an attention distinguishable of course from the act of focussing your eyes on the point), maybe you would have discerned the point visually rather than merely having the feeling it was there.  You say ‘now’ again.  But did you really see the point at that moment?  Maybe you jumped the gun a bit.  And if you got it right, maybe it was by chance.  So doubtlessly the mapping of points onto the screen that define the limits of your visual field will be a bit irregular.  To get a true picture of the extent of your visual field, perhaps those points need to be averaged out to form a smoother mapping of the boundary.

The psychologists Weintraub and Walker describe this conundrum very well:

When thresholds [such as how close a point has to be to the center of the tester’s screen before it appears to you] are measured, no discrete threshold appears.  There is always a range of stimulus values — from stimuli so weak that detection is no better than chance, through values detected with increasing probability, to values that are always detected.  A ‘threshold’ is an arbitrarily selected value of the stimulus, such as the intensity of stimulation that is detected exactly 50% of the time.  This arbitrary value for the threshold will differ from subject to subject.  It will differ with minor differences in the conditions under which the measurements are taken.  It will differ with even minor differences in the nature of the response that the subject is asked to make, and it will differ widely between two different responses such as ‘accurate verbal report’ and a ‘significant GSR’ [galvanic skin reflex].

Weintraub and Walker, quoted in M.C. Dillon, MERLEAU-PONTY’S ONTOLOGY  (Northwestern University Press, Evanston, IL), pp. 60-61. Dillon takes the quote from Weintraub and Walker, PERCEPTION, (Brooks/Cole Pub. Co., Belmont, CA, 1966), p. 77.


The gel-pen inked line on the bungee cord should never have become blurry in the first place, since as it became “thinner” it should have simply disappeared the moment its size became less than that of a Minimum Visibile.  A Minimum Visibile is a binary affair with sharp boundaries; it is either on or off, distinctly there or not.  For how could it constitute a unit composing perceptual wholes along with other Minimal Visibles?  If their boundaries were fuzzy, would two Minimum Visibiles gradually merge into one another rather than functioning as distinct units?  And even were one to allow the blur, it seems unlikely, based on what Weintraub and Walker describe, that there is a consistent size threshold past which we can no longer say ‘yes, this line is still visible.’

Clearly, then, there are no Berkeleyian (or Humean) Minimum Visibiles that can function as unitary bricks set together to build up the visual field.  How can one build a brick wall when no brick has a fixed, determinate boundary?  (Perhaps we could call these fuzzy-boundaried bricks, subject to mere probabilities, ‘Schrödinger’s bricks’.)  Add to this the fact that anything perceived is always a figure against a background (the background can be in front of and around the figure as well as behind it) and therefore always existing in relation to a context determining what it is, it becomes blindingly obvious that the Theory of Ideas (aka Theory of Sense Data) is dead, dead, dead.1  Certainly any attempt to resurrect that theory without coming to grips with the opening chapter of Merleau-Ponty’s PHENOMENOLOGY OF PERCEPTION is scandalously irresponsible.  (I am looking at you, professor Arnold Vandernat.)

Just as I am quite confident that Bigfoot aka Sasquatch does not exist, I am confident that there are no mental tokens called ‘Ideas’ or ‘Sense Data’.

To sum up:  In this post, I have perhaps succeeded in recapturing the content of the Aha Erlebnis I had when I first encountered Berkeley’s argument that depth is not visible.  In the process, using an experiment with a green bungee cord, I have put ‘paid’ to Berkeley’s notion of a Minimum Visibile in particular and to his Theory of Ideas in general.  (This is perhaps the ten-thousandth time this notion has been conclusively refuted.)

Nonetheless, in future posts I will be indulging a certain affectionate tolerance for this notion when discussing Berkeley’s claims that sight and touch are thoroughly entangled with one another, and that depth is constituted by the tactile/kinaesthetic sense.  For I think Berkeley comes very close to the truth in making these claims.









1 Lawrence Hass is very good at demonstrating this point. See his MERLEAU-PONTY’S PHILOSOPHY (Indiana University Press, Bloomington and Indianapolis, 2008), pp. 28-34.









Given that the today’s post deals so intensively with that Irish Bishop, George Berkeley, it is only fitting that today’s homage to Plato’s SYMPOSIUM should be a red-head.  Plato himself I suspect would have been more acquainted with red-headed Thracians than with red-headed Hibernians.



I am very much into red-heads at the moment.

There is too much beauty walking the earth for anyone to get anything done.



January 16, 2016:  Changed ‘perpendicular to’ to ‘end-wise’ in the first paragraph. Janu

January 17, 2016:  Made some other minor changes in an attempt to hide my scandalous lack of control over the subject matter….er, I mean, in order to streamline the argument a bit.