Some Notes on Reversible Perspective: Part I, Sensation as Sign

© Peter Macapia 1995

marcel duchamp, handdrawn stereopticon slide

This essay is about the history of an epistemological problem. The history begins with the identification and analysis of an optical illusion called reversible perspective, in particular the one known as the Necker cube. I trace how a debate forms around this illusion, how it functions to explain theories of spatial perception and the meaning of sensations, how it is used to map sensation as a linguistic-like object, how that mapping becomes problematic, and how it turns the notion of epistemic privacy inside out. Although I refer primarily to the work of David Brewster, Charles Wheatstone, Hermann von Helmholtz, and the philosopher Ludwig Wittgenstein in this narrow history, it is neither their advances, nor their relations, nor even the object of the illusion itself that interests me, but rather the history of a certain kind of failure -- the inability to explain how sensations mean, how perception works. Wittgenstein's presence in this essay serves to multiply that problem in several directions, one of which will be the relationship between perception and language in the work of Marcel Duchamp.

This essay has three parts. The part that I present here will draw on the work of Brewster, Wheatstone, and Helmholtz. The second part, to be published in the next issue, will focus on the work of Helmholtz and Wittgenstein. In the third part I will discuss the relation between vision and language in the work of Marcel Duchamp.

One could say that for nineteenth century physiology the Necker cube, along with other examples of reversible perspective and other kinds of optical illusions, was the flickering site of a paradox, the explanation of which demanded a series of methodological contortions. For two related reasons: one, in order not to give up the autonomous essence of perceptual experience, [1] -- the great discovery and foundation of nineteenth century physiological optics --, optical illusion, as an instance of the abnormal, had to be accounted for as a condition of the normal; two, analysis and explanation had to shift in order to make the first possible. The first twist: as part of a claim to establish precisely what constituted normal perception, psychological explanation was sought where physics and physiology failed to explain how illusions were precisely immanent to normal perception. Or rather, for that special occasion, a psychological supplement had been invented. For it never bridged the physiological facts of visual perception to the assumption that perceptual experience is uniquely subjective, except (and here a second twist) through the philosophical claim that such a bridge can be shown, but not said; that one could feel it, but not explain it.

Analysis of optical illusions: analysis of the meaning of sensation. The two went hand in hand in nineteenth and early twentieth century physiology and psychology. They were used to explain each other, and their explanations vacillated in response to the question 'What kind of thing is a sensation, what ontology does it have?' Analogies are possible: It is like this, and like that: it is like a piece of raw data, and it is like a linguistic item. What Wittgenstein brought to this problem was far from a theory of perception. Rather was it a more focused way of eliciting questions about experience, in particular its linguistic limits.

     The Necker Cube 

The epistemological transformation in the first decades of the nineteenth century marked a shift in the meaning of perception -- the scientific mapping of stimulation, the identification of perception as a product of the body's physiological structure, the location of knowledge within the subject's nervous tissue. It also meant a new conception of the world as something opaque to experience, or rather of the body as opaque to the transparency of the world. One could no longer interpret reality, defined as the external world in Renaissance and Enlightenment epistemologies, as something perceived outside oneself, as detachable from one's flesh. Light and color were now effects of the nervous system rather than ontologically independent causes of vision. Here I refer the reader to Jonathan Crary's discussion of perceptual autonomy in the nineteenth century physiological optics.

This perceptual autonomy found its formal origin in Goethe's transformation of the paradigm of experience and knowledge: the transformation from the camera obscura as an epistemic model of objectivity to one of subjectivity; from the model of a transcendental ego passively reviewing, on an adjacent wall, the images entering through the aperture, to a model of subjective vision, for which the aperture now functions by burning an impression on the retinae, and from which the subject was unable to sever themselves whether they closed their eyes or shut up the aperture and closed out the external world. [2]

Following Crary we may illustrate this transformation by comparing Descartes and Goethe. Descartes: "Suppose a chamber is all shut up apart from a single hole, and a glass lens is placed in front of this hole with a white sheet stretched a certain distance behind it so that the light coming from objects outside form images on the sheet . . . the room represent the eye." [3]

Goethe: "Let a room be as dark as possible; let there be a circular opening in the window-shutter about three inches in diameter. . . the sun being suffered to shine through this on a white surface, let the spectator from some little distance fix his eyes on the bright circle thus admitted. The hole being closed, let him look towards the darkest art of the room; a circular image will now be seen to float before him." [4]

The latter became the essence of physiological optics: the study of perception for which no immediate external referent exists; the study of the after-image, of real and apparent movement, and optical illusions in general. But also a study of the meaning of sensation. For a crisis in meaning and representation faced the Romantic celebrations of this perceptual autonomy, to the effect that, Surely, visual perception must be more than the quantifiability of sensation, something more than an abstract relation between stimulus and excitation? To understand the body as the productive location of experience meant that one might perceive sensation where there is no stimulation; that no external signifying structure existed as such (as we shall see, this was one of Helmholtz's most adamant claims). In what follows I trace a number of attempts to account for that meaning.

In 1826, Sir David Brewster published his latest research in the Edinburgh Journal of Science on a long familiar, yet scientifically unexplored subject, the conversion of relief; an optical illusion now generally called reversible perspective that involved a change in the three-dimensional appearance of an object. [5] In a letter to Brewster, the Swiss crystallographer L. A. Necker wrote of the same phenomenon which he discovered while examining crystals under a microscope, the reversing figure of certain geometrical shapes (which he exemplified in the form of a cube now known as the Necker cube), "a sudden and involuntary change in the apparent position of a crystal or solid represented in an engraved figure." [6]

The importance Necker attributed to his observations, however, was not so much the illusion itself as the sensation which accompanied it: At the time the change took place a particular sensation was felt in the eye -- evidence, he suggested, that what produced the experience was an optical and not merely (as had first been thought) a mental operation which was performed. But he neither described the particular sensation nor explained how it escaped him earlier when he had mistaken it for a mental operation. This may be owing to Brewster's influence, for prior to publishing the letter, Necker had personally discussed his observations with Brewster, who then suggested that Necker write him a letter providing a more detailed account. As it turned out, the "more detailed account" conformed perfectly to Brewster's recently formulated law of distinct vision. Necker mentions this law at the end of his letter: "...after a more attentive analysis of the fact, it occurred to me, that [the illusion] was owing to an involuntary change in the adjustment of the eye for obtaining distinct vision..." By "law of distinct vision" Brewster had meant that a certain portion of the retina's center receives impressions more distinctly than others. When passing over a particular detail in the visual field, that portion of the retina brings the detail into distinct and clear vision. This operation, we should note, is sensual, and involves the sensation of a physical/physiological fact.

During the 1820s Sir Charles Wheatstone had been studying spatial perception and binocular vision, using axonometric geometric forms similar to Necker's cube, for research on a his theory of binocular vision. In "Contributions to the physiology of vision" he dismissed Necker's account of the phenomenon of reversal, which, it seemed, sparked the debates with Brewster over the nature of sensation and spatial perception that continued for two decades. Before I elaborate what is at stake in those debates I should first make it clear exactly what Brewster's conceptions of sensation involved and how he linked it to the larger problem of spatial perception.

The eye for Brewster is an organ that perceives space directly, not as a matter of estimating distance, but rather through registering the differences between objects perceived in their actual locations. Formulated in terms of his law of visible direction, this means that the eye sees objects in their actual spatial locations. He cited this law in a debate with J. le R. D'Alembert over the extent of optical distortion, arguing that since the refractions of the crystalline lens were so minute, a line perpendicular to the point of impression on the retina ". . .does not deviate from the line of real visible direction more than half a degree, a quantity too small to interfere with the purposes of vision." [7] The apparent position of an object coincides with its real position in space: the line of visible direction would coincide with the line of real direction, and also with the incident and intromitted ray. In short, this posits that the eye sees objects where they exist in actual, not just visual space.

Brewster then goes on to specify the role of sensation in this perception. He rejected D'Alembert's theory that stars appear closer than they actually are, and claimed that the eye ... does not see distances directly: the mind only estimates them, and, according to its means of judging, forms a right or a wrong opinion. This is a consequence of the fact that we see a star at the very place where it is, and whether we consider it nearer or more remote than it is, whether we think that it touches our eye, or exists at the remotest verge of space, the position of the optical axis of each eye remains as before, and our vision of the star is not affected by the truth or falsehood of our judgment. [8] Vision, in other words, is purely a matter of sensation.

The relation between sensation and spatial perception became even more complicated when Brewster defended his theory of the monocular conditions of spatial perception against Wheatstone's theory of binocular vision. The law of visible direction supported the law of distinct vision. And what made their correlation possible is the fact that we have a center of visible direction, that we see with only one eye at a time. This is not possible for binocular vision, Brewster insisted, since such a center could not exist except where the optic axes of the two eyes converge upon the same point in space, i.e., at great distances -- in which case it would not matter whether there were two or two hundred eyes. But what really must be grasped here is that the law of distinct vision is a function of monocular vision and spatial perception.

What makes the perception of a three-dimensional pyramid possible is the fact that only a small part of retina's center receives clear impressions of those areas to which it is aimed. The minute differences between focused and unfocused areas on the retinal picture enables one to distinguish three-dimensional objects from two-dimensional representations. [9] The epistemological consequences are clear: what an observer sees is really there at the point where he sees it and ontologically independent. Sensations have nothing to do with signs or mental representations. The law of distinct vision makes it clear that the mind directly responds to the eyes' actions as though of the same surface; that the eye is able to sense differences, to adjust itself; that the eye knows, in a sense, what it is looking for.

When the eye adjusts itself to distinct vision of its apex, all the more distant parts are seen indistinctly, but the eye quickly surveys the whole, adjusting itself to distinct vision of its base and of its edges, and by these successive efforts, at one time contracting the pupil and the eyebrows to see the near parts, and expanding them to see the more remote ones, it obtains a knowledge of the relative distance of its different parts. The vision of the pyramid thus obtained is nearly perfect. [10]

And so it is really the eye itself which does the knowing. Indeed, the eye immediately recognizes the contents of its perception, knows how to read 'pyramid.'

Brewster modified his theory of monocular vision over time. He granted a few concessions to Wheatstone's theories. But he adhered to two fundamental points, which are essential to grasp in order to understand just what was at stake in his theory of sensation. 1) the eye never fails to recognize what it sees, with the exception that under special external circumstances misrecognition is possible, but only as a result of physiological causes. 2) the eye sees what is really there in the visual field. The example of three-dimensional pyramid was implicitly about what the eye saw, the thing that lay in front of it. So that, even when Brewster accepted certain aspects of Wheatstone's theory of binocular vision, and agreed that the convergence of two optical axes on an object produce a more correct judgment than with a single eye, he reiterated but they do not in the least degree improve our vision of the pyramid, which is independent of them. [11]

In other words, Brewster's was a theory of the identity, of the point to point correspondence between perception and its object: "for whether we look at the real solid itself, or its representation when constituted by its two dissimilar pictures, we see only individual points of the object single, but the eyes with the rapidity of light, run over all its parts, converging the optical axes upon each, and recognizing by this operation the third dimension in space which constitutes a solid figure." [12]

In sum, the eye is the seat of perception; "We know nothing more than that the mind, residing as it were, in every point on the retina, refers the impression made upon it at each point to a direction coinciding with the last portion of the ray which conveys the impression." [13] The monocular visual subject thus diminishes to a stable yet mobile point of consciousness, one that draws into itself the temporal lag brought about by the rapid scansion of that tiny retinal surface which scurries over and touches, as it were, the objects within its field of view, collecting them into the present. [14]

We can now see what Brewster resisted in Wheatstone's theory of binocular vision: a theory of the mediated nature of perception, the dissemination of optical information as signs throughout the body, the synthesis of those signs into the form of a perception, the recognition of an object, and ultimately the experience of three-dimensional space that did not distinguish between the veridical and the simulacral, between actual perception and its simulation in the stereoscope. What for Brewster had been a single point of consciousness that collapsed the spatio-temporal disjunctions between mind, retina, and object became literally split in Wheatstone's stereoscope. [15]

Yet it was in terms of the Necker cube that Wheatstone developed his theory of sensations as signs. As I pointed out earlier, the phenomena of the Necker cube was a major point of contention between Wheatstone and Brewster. When Brewster defended Necker's original thesis reversal, he stated that it was physiological, the effect of the "adjustment of the eye for obtaining distinct vision." [16]

For Wheatstone that "sensation" was nothing more than psychological. Based on experiments with geometrical solids from Euclid's 11th book of geometry and three-dimensional models, Wheatstone suggested that the effects of conversion were related to mental contemplation. By following the lines of the cube with an intention or "clear idea" to see it one way or another, the cube will appear to shift. The effect reversal was a matter of the will. [17]

Wheatstone first linked the phenomenon of reversal to the notion that sensations were signs in his account of memory in "Contributions to the Physiology of Vision-Part the First." "If we look with one eye at a solid geometrical figure," we will find that one of two possible figures will present itself, either the one to be intended or the converse. But it is the figure encountered most frequently in previous experience that more readily presents itself to the mind. Should the figure be unfamiliar to the observer, it will shift more easily. [18]

This observation suggested that sensations are somehow stored in memory and compared with present sense experience. This account of memory and sensation as sign, which he deduced from the study of reversible perspective, aided his theory of binocular vision and spatial perception, where he addressed the notion of sensation as sign more explicitly. The essential difference between the appearance of an object seen with two eyes and the same object seen with only one eye was that the former provides the most vivid belief of the solidity of an object of three-dimensions. [19]

And yet, he asked, how is it that people with the use of only one eye still form correct notions of solid objects and avoided mistaking their impressions for pictures? He responded that "although the simultaneous vision of two dissimilar pictures suggests the relief in the most vivid manner, yet there are other signs which suggest the same ideas to the mind, which, though more ambiguous than the former, become less liable to lead the judgment astray in proportion to the extent of our previous experience." [20]

The mind not only collects but also compares data; the mind associates with the idea of a solid object every different projection of it which experience has hitherto afforded. At great distance, those with only one eye have the same visual experience as those with two eyes. "A person deprived of the sight of one eye sees therefore all external objects, near and remote, as a person with both eyes sees remote objects only, but that vivid effect arising from the binocular vision of near objects is not perceived by the former; to supply this deficiency he has recourse unconsciously to other means of acquiring more accurate information." [21]

Sensations as signs supply present experience through unconscious association and produce ideas. [22] In his opening description of binocular parallax, he writes about the interchangeability between these signs, as pictures, and one's visual impression of the world. In terms of distant views, there is no difference between the appearance of an actual scene and one that is depicted,
hence pictorial representations of distant objects, when those circumstances which would prevent or disturb the illusion are carefully excluded, may be rendered such perfect resemblances of the objects they are intended to represent as to be mistaken for them; the Diorama is an instance of this. [23] The diorama does not work for objects close up. The stereoscope, however, does.

It being thus established that the mind perceives an object of three dimensions by means of the two dissimilar pictures projected by it on the two retinae, the following question occurs: What would be the visual effect of simultaneously presenting to each eye, instead of the object itself, its projection on a plane surface as it appears to the eye? [24]
The answer, of course, would be that visual effect is exactly the same in both cases.

The theory of identity between object and perception, so rigorously advanced by Brewster, is completely shattered in Wheatstone's analysis of the functioning of the binocular vision.
Let me push this difference a bit further to underline what exactly it says about their positions on subjectivity. To take up once again the issue of reversible perspective, Wheatstone had maintained that the phenomenon of reversal was the result of a mental activity. According to Brewster it was completely physiological. I earlier used Brewster's description of the Necker cube to make the point that the illusion is owing to the structure of the eye. Here I would like to use another optical illusion of reversal that will clarify Brewster's suggestion that the illusion is not immanent to subjectivity or consciousness as such. Evidence for the physiological source of illusion, according to Brewster, could be found in an experiment where the relief of a figure seen on the surface of a coin, whose source of light is consistent, will reverse when observed through an inverting lense.

The proof which the eye thus receives of the seal being raised overcomes the evidence of its being hollow, derived from our actual knowledge and from the sense of touch. In this experiment the deception takes place in our knowing the real direction of the light which falls on the seal; for if the place of the window, with respect to the seal, had been inverted as well as the seal itself, the illusion could not have taken place. [25]

The explanation suggests that the eye actually sees correctly but that its information is inaccurate. This is a subtle but important point. The visual subject is a stable entity. The origin of the illusion is external to the subject.

But according to Wheatstone, the phenomenon described by Brewster doesn't require an inverting lense: it can take place under even illumination and without a lense. If we suppose a cameo and an intaglio of the same object, he writes, the elevations of the one corresponding exactly to the depressions of the other, it is easy to show that the projection of either on the retina is sensibly the same. [26] In other words, physiologically, the cameo and the intaglio are the same. The illusion is immanent to subjectivity, and based on a misreading of cues, oriented not by an innate disposition but rather by former experience, something internal rather than external to the subject. What one sees is information in the sensible form of signs. With two eyes, Wheatstone suggests, more information is acquired, the means of judgment heightened, and the illusion less likely occur.

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