I much appreciate the care and courtesy with which Mr. Norman Turner has dissected and criticized my views on perspective as I expressed them in a number of my writings. I readily concede many of the points he makes, but I am all the more puzzled by his failure even to mention the purpose of perspectival construction that secured its worldwide success and which, for want of a better word, must still be called the achievement of “illusion”. I have long been convinced by J. J. Gibson that our experience of the visual world as we move around our environment differs radically from what he calls the snapshot vision of conventional representation and so I also accept Mr. Turner’s subtle analysis of our experience on measuring the projected size of a distant tree against the upright pencil. But I am sorry he ignored the result of such measurement when it is placed on the canvas in its appropriate setting: the small patch will then be seen again as a distant tree and will do so even more convincingly if we look at the canvas with one eye through a viewing tube. It was this experience that prompted me to formulate the paradox that the world never looks like a picture but a picture can be made to look like the world. But even if Mr. Turner were outraged by this defiance of logic one is bound to ask if has never seen an illusionistic stage set, has never looked up at a Baroque ceiling painting or looked into the peepbox displayed in the National Gallery in London? I admit that these effects do not disprove the existence of those inevitable geometrical problems arising from the projection of a 3-D array on a flat painted surface, but I believe that our failure to be disturbed by these flaws must be due to what Michael Kubovy in his excellent book, The Psychology of Perspective and Renaissance Art (Cambridge University Press, 1986), has described as “the robustness of perspective.”

            I believe there is a suggestive analogy here between this “tolerance” of our perceptual system and the slight deviation from strictly mathematical harmony that is called temperament in music and is defined in The Oxford English Dictionary as “the adjustment of the intervals of the scale . . . so as to adapt them to purposes of practical harmony: consisting in slight variations of the pitch of the notes from true or “just” intonation, in order to make them available in different keys.” The power of this slight fudge was of course triumphantly demonstrated in Bach’s “48” and has enabled his successors to delight our ears with ever more daring modulations.

            I believe the same to be true of the slight fudges sometimes demanded of the painter in eliminating lateral distortions. We can all thrill to Raphael’s “School of Athens” without regretting that he painted the globe as a sphere and not like an egg.[1]


E. H. Gombrich




            In “Some Questions About E. H. Gombrich on Perspective,”[2] the essay to which Sir Ernst responded, I said defenders of what I call the literalist approach to perspective commit a "fallacy of misplaced concreteness." I meant by this that when Sir Ernst attributes to our experience of real things the characteristics of linear perspective, as he persistently does in his several writings on the subject, despite a number of disclaimers such as the above acknowledgement of J. J. Gibson, he conflates an intellectual achievement and things in the actual world as they offer themselves to us unadorned by such ideas. The fallacy “consists in neglecting the degree of abstraction involved when an actual entity is considered merely so far as it exemplifies certain categories of thought."[3]  We might in a comparable though not identical vein attribute to a thing the traits evoked for it by a verbal metaphor, though very likely we would not. We would understand that in a verbal metaphor dissimilar objects are melded in a fictional image to transformative effect. We would not confuse components of the figure of speech with that which subsists in the real world prior to such symbolic interdictions. Saying, for example, that an oak spreads its sheltering arms, we would not suppose the tree has human arms in fact. We should similarly note that when a perspective image is abstracted from the oak, as in a photograph, projective geometry and the tree are melded in a fictional image to transformative effect. We should avoid uncritically thinking that the perspective image equals our unmediated visual contact with the actual tree.

            That said, Sir Ernst was justified in holding my feet to the fire on the question of illusion. Only it seems to me that what’s going on such situations is much more interesting than outright deception. When with one eye I look at an anamorphosis from the provided peephole, peer into a peepbox, or look into an Ames room, I relinquish binocularity and movement. Bodily and mentally, I’m thrust into my optical array, consistent with linear perspective. I occupy the optical projection much as an actor occupies his role. Just as an actor becomes Lear or Othello even as he remains himself, so do I, peering into a perspective contrivance, lend myself to perspective phenomena even as I remain apart. My attention has been directed to the factor of my visual capacity I usually transcend, the bare optical display, and I’m taken by it, visually swept away. I encompass something I routinely know nothing of -- the geometry of light passing into my eyes. That which is initially fundamental to my vision, though greatly exceeded by the entirety of my vision, becomes the stripped-down whole of my visual occupation. It’s a remarkable instance of what Michael Polanyi called "indwelling."[4] The result is what defenders of literalism are pleased to call "illusion," and it is certainly enchanting. Yet this enchantment is of a curiously complex sort, compared to routine visual experience.

            The National Gallery's A Peepshow with View of the Interior of a Dutch House, by Samuel van Hoogstraten, mentioned by Sir Ernst, is a case in point. It's true of this box with a house interior painted on its inner surfaces that the dog and chair partly on the "wall" and partly on the "floor" stand as continuous wholes when viewed through the provided peepholes, but also true that I’m well aware of the transaction as it occurs. There is dissonance, by no means unpleasant, between the perspective conjuring and my ready understanding that the painted interior and its accoutrements are a creation. I enter into the spirit of this creation even as I stand with feet planted on the floor of the National Gallery; and I feel both the visual constraint and the floor. This double awareness saturates my awareness; it is the double awareness of the actor playing his role or of my witnessing his performance as seen through a proscenium, in thrall to the play while marginally cognizant of my seat, the theatre, the audience all around, with whom I share a communal experience. If van Hoogstraten's contraption reduces vision to it's optical component, so that I’m led to see in terms of the purely geometric display, as described by perspective logic, neither do I believe for an instant that I’m looking at unmanipulated reality. The word "illusion" seems at least in this instance to require scrupulous qualification.

            Which is not to say there are no parallels between Sir Ernst's view of perspective and my own. Agreeing that perspective pictures are mimetic, though wanting to carefully distinguish what mimesis consists of, I proceed on a different line of reasoning to a different conclusion. To me the point of what Michael Kubovy calls "the robustness of perspective" is merely (or remarkably, if you like) that the construct actively fosters an appearance, doing so by a uniquely mathematical, proto-scientific means that is extraordinarily compelling, and that no doubt accounts for its “worldwide success.” Yet the legibility of perspective pictures from any and all viewing positions has more to do with the legibility of pictures of any and all sorts than with perspective pictures, per-se. We are strongly disposed to read virtual space into marks on a surface, regardless of the sort of picture we are looking at, and from where. What sets perspective pictures apart is their optical connection, but only their optical connection. As with all pictures, the position we read them from, if the reader will forgive me, is neither here nor there. Though we cannot see the optical array falling through our lenses and onto our retinas, though our visual abilities are not bound by what the bare optical array provides (for then we would be confined to an eternal present), no kind of picture other than a perspective picture evokes the geometry of optics within our looking at pictures or things. This unique circumstance makes it all too easy to mistake perspective images for the revealed truth of how we see, rather than likenesses pertinent to physical facts, yet likenesses created in our minds. The concrete results of perspective, i. e., perspective contraptions, diagrams and pictures, would little pertain to appearances did they not first pertain to human discovery.

            Thus to Sir Ernst's comment, "the world never looks like a picture but a picture can be made to look like the world," I’m obliged to say this is paradoxical only under the above-named fallacy of misplaced concreteness. If the phenomenal world and pictures of it are not conflated, the relation between them is neither constant nor paradoxical. The world doesn't look like a picture and a picture doesn't look like the world, except that sometimes the world does look like a picture, when a picture looks like the world. It is a question of semantic relationships between concepts, actual entities and appearances that we freely and creatively bring into play. Though Sir Ernst was rightly chary of saying in so many words that perspective pictures are experientially “real,” his reasoning kept taking him to the edge of this very conclusion; and it is within this context that he finds his paradox.

            In respect to the business of "measuring the projected size of a distant tree against the upright pencil," for instance, it is relevant to admit I’m a painter. I paint landscapes from direct observation. All I do is measure. My involvement with the type of situation at issue is therefore not only one of theoretical speculation but of active, frequent engagement. Sir Ernst's account of measuring a tree and placing that interval on the canvas is at odds with what I have learned and am certain of. Leaving aside that the real tree isn’t observed as a single item seen in isolation, but rather as the sum of its leaves, branches and bark seen with neighboring trees across an intervening field; leaving aside that I direct my attention to the tree within an experiential manifold continually replenished with fresh observations because it transpires across time; leaving aside that my work treats the tree as separate from but also continuous with the painting as a whole; and that in my painting it is constituted not of one measurement but of several or many, all of which interact, as a sub-set, with each other and with the picture’s total set of measurements, I will accept for the sake of argument Sir Ernst's sparse account, and say simply this: Between an actual tree, its apparent size and the dimensions I attribute to it in my painting there is a fluid relationship having to do not with the optical array intromitted through my lenses, not with a literal matching of images to actual entities, but with processes of symbol-formation taking place in my mind and dwelling in my sight. My visual experience is not defined by the physical facts of optics, and the painted tree does not recreate my experience of the real one, as if, in looking at it, I re-lived my dynamic visual contacts with its actual parent. To the contrary, the painted tree lays down its own set of circumstances and conditions, its own network of correspondences, with internal coherence and closure, that point to the real tree, while arousing qualities of experience appropriate more to utterance than to my brute contacts with the world.

            As for Sir Ernst’s argument by analogy to Bach, as I wrote in “Some Questions” when it comes to literalism a miss is as good as a mile. Perspective either conforms, categorically, to visual experience, or it does not. To admit “slight deviation” is to effectively abandon literalist doctrine entirely. But if this admission cuts the foundation from under literalism it is also moot, for the scale Bach used in The Well-Tempered Clavier does not have as its object a discovered truth of our sensory interactions with the real world. Its object is like that of the painter who minutely adjusts his colors so they are more harmonious, more coherent in transition from one to another, more resolutely constructing a whole, hence more tellingly articulated and pleasing to the eye. Bach’s tempered scale is of the physics of sound, just as the painter's color adjustments are of the physics of light, but both are concerned with expression instead of physical reality. Criteria are those of cunningly wrought form, aural or visual, rather than of scientific law. Which also explains why we can thrill to the School of Athens without in the least concerning ourselves with Raphael painting circles instead of ellipses. There was no question in Raphael’s mind, I strongly suspect, of “fudging” an objective truth. It was not part of his program, in making this picture, to either convey or thwart the proto-science of geometric projection; we do not register, in looking at the spheres, a difference between what is before us and a "true" mathematical projection that is absent; and to our aesthetic faculties—to the waking within us of awe and delight by virtue of the picture's rhythmic grandeur—the issue is in any event irrelevant.

            No semantic construct seems to stand between us and our visual perceptions, which are strikingly immediate. We simply see what we see: “there it is,” we tacitly say. Vision, in short, is revelatory. And here is the root cause of the fallacy at issue, for we are ill prepared to take notice of and analyze constructs that bear on, and alter, immediate appearances. Add to this that vision initially depends on optics; that linear perspective gives a partial account of the optical array; that we can easily learn to see a correspondence between the optical array, real things and pictures of them; that in controlled circumstances such as provided by peepshows we occupy the geometry of optics and thereby experience "illusion;" and it is not difficult to understand why confusion came about in the first place and persists to this very day.





[1]. E. H. Gombrich, "Additional Thoughts on Perspective," Journal of Aesthetics and Art Criticism, Vol. 51, no. 1, winter, 1993, p. 69.


[2]. “Some Questions About E. H. Gombrich on Perspective,” Journal of Aesthetics and Art Criticism, vol. 50, no. 2, Spring, 1992.


[3]. See Alfred North Whitehead, Process and Reality, corrected edition (The Free Press/Macmillan, 1979), pp. 7-8.                                                                                         See note


[4]. See Michael Polanyi and Harry Prosch, Meaning (University of Chicago Press, 1975), chapter two.