It's impressive, the wizardry we place in the hands of the 3-D graphics programmer. He is barely out of college -- or perhaps not even that -- and we entrust to him a mechanism for turning the world inside out. And the mechanism itself is pure simplicity: a 4x4 mathematical matrix. Armed with this little matrix, he can take any scene, real or imagined, apply a coordinate system to it, and then recompose the scene point by point until we see it from an entirely different perspective. That is, he can project the scene any way he wishes -- which includes projecting it realistically onto a two-dimensional surface. Moreover, he can do all this with absolute fidelity to the original.
Well, almost. Absolute fidelity, it turns out, is as challenging a standard to meet in this context as it is in some others. To see just how challenging, we need to look back toward the age of faith, to when the projective laws -- usually called the laws of linear perspective -- were just being discovered.
Brunelleschi's cunning extended even further, however, for instead of painting a sky in the upper part of the work, he put burnished silver there. Now, with the aid of the mirror, the astonished viewer saw wind-blown clouds drifting across the top of the painting. Here, in this calculated confusion of real world and artifice, the technological quest for virtual reality was launched.
So, too, was the controversy. The new, perspectival art struck viewers with the force of a powerful and deceitful illusion, as had even Giotto's earlier, purely empirical experimentations with perspective. "There is nothing," Boccaccio said, "which Giotto could not have portrayed in such a manner as to deceive the sense of sight." Much later the Dutch artist Samuel van Hoogstraeten, acknowledging that his task was to "fool the sense of sight," went on to urge that the painter must thoroughly understand "the means by which the eyes are deceived."
This is not so easy -- as those who try to represent three-dimensional reality on the surface of goggles know all too well. How can a painting -- a flat, two-dimensional surface -- appear to be what it is not? How can it look like a three-dimensional scene? In what sense does the flat work of art incorporate the laws of full-bodied reality -- and in what sense does it fall short of that reality?
Of course, the world had not yet really disappeared for Brunelleschi and his contemporaries. But in discovering the practical rules of strict, geometric perspective, he performed a momentous act of abstraction that hastened the world upon its vanishing course. Where we might have expected him to see the Baptistery, what actually captured his attention was a "visual pyramid": the collection of straight lines raying from all the building's surfaces to his own single, fixed eye. Each of those lines mapped a point of the Baptistery to a point on the "picture plane" -- the artist's canvas. By mapping a few definitive points in this fashion, Brunelleschi could easily fill in the rest of the picture in near-perfect perspective.
In technical terms, the perspectival rendering of a scene is a projection of the scene from an eyepoint, as sectioned by the plane of the canvas. You can obtain the same effect by tracing the scene on a window while keeping one eye closed and the other eye absolutely stationery. Or else by using a camera.
And so the artist learned, with simple tools and an increasingly practiced eye -- to perform the same magic our programmer now summons with her 4x4 matrix. While the methods differ -- the artist no doubt possessing a fuller and more concrete sense for what he is actually doing, if only because of his necessarily "primitive" methods -- the underlying mathematical conceptions remain the same. To arrive at these conceptions was one of the remarkable accomplishments of the Renaissance.
During the medieval era there had been no coordinated sense of mathematical space: an "all-pervasive and uniform space as we now conceive it was then unimaginable." /1/ What did exist was more like an inner space -- a space of meaning, a space of concretely felt interrelationships by which the individual was bound to the cosmos, nourished and sustained. It was a sense for these inner patterns -- not the mathematical distribution of objects within an abstract, containerlike space -- that (so oddly for us) gave organization and coherence to a medieval painting. Space did not present itself independently of things; it was more like the qualitatively varying presence of things, and derived its local "shape" from them. But in the art of linear perspective,
Space is created first, and then the solid objects of the pictured world are arranged within it in accordance with the rules which it dictates. Space now contains the objects by which formerly it was created .... The result is an approximation to an infinite, mathematically homogeneous space. /2/
"Space now contains the objects by which formerly it was created." This is an art historian speaking, and he is referring to changes in the techniques of the painter. But the question remains: were these changes forced upon the artist by a truer knowledge of the world, or were they imposed upon the world by the artist? Was the new art of perspective objectively valid, or did it merely become a habit of our subjectivity?
In other words, if God hadn't wanted us to represent the world in perspective, He wouldn't have created it that way.
If you are inclined toward this conviction, then you may be surprised to hear the question put by psychologist R. L. Gregory:
It is an extraordinary fact that simple geometric perspective took so long to develop -- far longer than fire or the wheel -- and yet in a sense it has always been present for the seeing. But is perspective present in nature? Is perspective a discovery, or an invention of the Renaissance artists? /3/
Gregory is here alluding to a twentieth-century scholarly squall that the respected German art historian, Erwin Panofsky, kicked up in 1925 with the publication of his Perspective as Symbolic Form. Panofsky, whose essay was both brief and difficult, argued that the conventions of linear perspective were cultural symbols, not absolute truths. They are "comprehensible only for a quite specific, indeed specifically modern, sense of space, or if you will, sense of the world." /4/ However obscure Panofsky's actual thesis may have been, its time was at hand, and many others echoed his theme. For example, Sir Herbert Read:
We do not always realize that the theory of perspective developed in the fifteenth century is a scientific convention; it is merely one way of describing space and has no absolute validity. /5/
The inevitable "common-sense" backlash was equally vigorous. Physiologist M. H. Pirenne, responding to Panofsky, declared flatly that "`the strange fascination which perspective had for the Renaissance mind' was the fascination of truth." /6/
The dispute continues into our own day, and has tended not so much toward resolution as toward exhaustion among the manifold, tortured byways of argument -- from the physiology and psychology of sense perception to the subtleties of epistemological theory. It seems characteristic of the past few centuries that the question "what belongs to the mind and what belongs to the world?" leads us in so many different arenas to the same brick wall -- or mental block.
Yes, let's face these facts. But no facts can stand alone. We must establish at least a minimal context. For a start, here are three things to think about:
Jan Deregowski speculates that those who have difficulty interpreting perspectival drawings are unable to "integrate the pictorial elements. They see individual symbols and cues but are incapable of linking all the elements into a consolidated whole." /7/ This is a particularly striking thought, for we are accustomed to thinking of perspective as having introduced a coherent, universal, pictorial space in which objects can for the first time find their "proper" places relative to each other. Shouldn't this make it easier for the unacculturated observer? Apparently not.
Before the operations, he was undaunted by traffic. He would cross alone, holding his arm or his stick stubbornly before him, when the traffic would subside as the waters before Christ. But after the operation, it took two of us on either side to force him across a road: he was terrified as never before in his life. /8/
S. B. -- as in many such cases -- became rather depressed, and tended to withdraw from his previous, highly active life. (While blind, he had even ridden a bicycle, with the help of a friend.) "Some of the cases revert very soon to living without light, making no attempt to see. S. B. would often not trouble to turn on the light in the evening, but would sit in darkness." Having first given up living, S. B. died three years later.
Samuel Edgerton voices a perplexity shared by others:
How curious that an understanding of the mathematics of human pictorial representation occurred so late -- and so locally -- in history .... Today we are the tired children of [the] discovery; the magic of perspective illusion is gone, and the "innate" geometry in our eyes and in our paintings is taken for granted. Linear perspective has been part and parcel of psyche and civilization for too many centuries, which is perhaps far less astonishing than the fact that it eluded men of all civilizations for a thousand years prior to the [fifteenth century]. /9/
But the muddying of our context grows even worse when we turn to the actual use of perspective in art.
To represent something in geometric perspective is to project it from a single, fixed eyepoint. If you wish to view "correctly" a drawing created in this way, you must close one eye and position yourself (with respect to the drawing) exactly where the original eyepoint was; otherwise, your perspective as viewer defeats the perspective "hardwired" into the drawing. With paintings such as Da Vinci's The Last Supper -- extending the length of one wall of a monastery's refectory -- the perspective had to be "fudged" in order to keep the image from looking quite false to the monks seated far away from the painter's viewing point.
More importantly, we do not normally see with just one eye. Open a second eye and some of the depth effect of the painting is lost. That is, with binocular vision we perceive depth quite effectively, so that we immediately recognize the "real painting" for what it is -- a flat surface with blobs of paint smeared across it. We defeat the artist's "deceptive" intentions.
But this is not all. In the sense that really counts, perspective gives us mathematically incorrect results. Have you ever noticed how paltry those mountains seem in the photographs you bring home from vacation? You're not just imagining things. The mountains are seen relatively larger in reality than they are in the photograph, despite the fact that the photograph yields an image in "perfect" perspective. Through an effect known as size constancy scaling, we pick up on various cues about the distance of an object, and then compensate for great distance by seeing the object larger than geometry and optics would seem to allow.
You can test this by holding one upraised hand at arm's length in front of you, with the other at half that distance and not visually overlapping the first. If you look alternately at your two hands, you are unlikely to see the nearer hand as double the size of the further one, but only a little larger -- despite the fact that the retinal image of the one is twice as large as the other. Is your brain playing a nasty trick upon your eyes? Before you answer yes too quickly, ask yourself: which estimate of your hand sizes is closer to the truth of the hands themselves?
It did not take long for the artists of the Renaissance to begin realizing the limitations of linear perspective. Michelangelo scorned Duerer's geometric methods, and claimed reliance upon the "compasses in the eye." Eventually, art as illusion -- which is to say, art as the imitation of something else -- passed into triteness. The camera made it too easy. The artist began inquiring more deeply into the underlying laws of seeing, of light, and of form. Art moved -- or wanted to move -- closer to the seminal chaos within which the world itself first takes on form.
If we equate "seeing in perspective" with certain abstract, mathematical characteristics of the perceived world, then surely the human race has always seen in perspective, even if it was only during the Renaissance that we first noticed perspective and discovered how to represent it properly. The abstractions have always been there for the abstracting, whether or not people were capable of performing the act of abstraction. Light rays have always traveled in straight lines.
But, then, it is rather strange to argue that our ancestors saw what they were incapable of noticing. What the mathematician abstracts from our seeing is not the seeing itself. The puzzlement of non- Westernized people when looking at perspectival drawings; the struggles of those who receive sight tardily; and the sober lessons drawn by Western artists after their initial excitement with perspective -- all declare that seeing involves much more than geometry and optics. Or, at least, it did before our own day. For it's true -- and a matter of frightening import -- that our own seeing has become increasingly abstract -- which is why some who would instruct us in art urge us to "draw on the right side of the brain." /11/ It's also true that our habit of abstraction is born of an extreme subject-object polarization; only a detached subject looking at an object from a considerable subjective distance can analyze that object and abstract from it a set of mathematical properties.
I asked above: did the new art of perspective possess objective validity, or did it merely become a habit of our subjectivity? What we need to understand is that the very possibility of asking such questions first arose in the Renaissance. For it was then that Western man first began to experience the world as an abstract, mathematical "container" full of objects wholly separate from himself, and to experience himself as an isolated, subjective interior gazing out through the window of his eyes upon a separate world.
Virtual reality may assist us. Suppose you are wearing a headset with all the related paraphernalia and are exploring a virtual world. Is that world subjective or objective? Neither answer quite suffices by itself. Subjective, you say? Yes, by all means. Its forms, "spoken" in a programming language, are now sustained by your own participation. Whatever you may think about a tree falling in the woods where no one hears it, there's a strong case to be made that the room you're exploring is not really there except insofar as your eyes and other senses are helping to create it.
Objective, you say? Yes -- that, too. Even if for now this is the weaker side of the dual truth, there is undeniably an objective component here. You cannot redesign the room according to your fancy. It has an objective or given character, sustained intersubjectively among those who may inhabit it. If you move a book from the chair to the table, that is where another occupant of the room will find it. There is, moreover, objectivity in the entire representational apparatus, just as there is in a two-dimensional painting.
Now imagine that you and others are in the same virtual room. Assume further that the software affords the group of you some means for collectively reconceiving the room -- not by moving things around, but rather by recreating it, so to speak, from the "inside," at the level of the software. What is now subjective and what is objective? If the collective subjectivity determines the objective forms, and if the objective forms in turn determine what each individual experiences subjectively -- well, it becomes risky to classify things too rigidly as subjective or objective.
What I am suggesting, then -- and for the moment I will leave it a bald suggestion -- is this: quite apart from the "reality status" of our virtual room, the description just given roughly captures the way we are situated in the real world. If, as so many seem to think, virtual reality points toward a new paradigm, it is a paradigm having less to do with new, high-tech experiences than with our participation in the world -- a participation ancient and powerful in its origins (if all but vanished from modern experience) and echoed only faintly in the modern technologies. I will return to this shortly.
Bringing all this to bear on the issue of perspective, we can say neither that perspective is objectively inherent in the world, where it could only be discovered, nor that it was a mere convention waiting to be invented. Rather, our Renaissance predecessors saw a different world than the ancients saw, and at the same time the world was becoming different because of the way they saw it. Their world, like ours, was virtuality continually on the way toward reality.
The debate over perspective -- was it discovered out there or invented in here -- became possible only with the radicalization of this polarity. It is resolvable only when we recognize the mutual interpenetration that unites the apparent opposites: there is something of the subject in the most adamantine object, and an objective, world-sustaining presence in the sheerest subject. Cut off the smallest piece of one end of the magnet, and you will find that it still possess both a south pole and a north pole. It is as impossible to conceive a pure subject or pure object as it is to conceive a pure north or south pole. But it is quite possible to lose sight of their mutual participation. Such is our plight today as in our radical subjectivity we imagine ourselves to confront a radical objectivity.
All this is ground Owen Barfield has worked over throughout the greater part of this century. A philologist, Barfield employs semantics to explore the changing balance between subject and object throughout human history. What he says about the medieval era is particularly germane to our inquiry. For example, regarding nonperspectival art:
Before the scientific revolution the world was more like a garment men wore about them than a stage on which they moved. In such a world the convention of perspective was unnecessary. To such a world other conventions of visual reproduction, such as the nimbus and the halo, were as appropriate as to ours they are not. It was as if the observers were themselves in the picture. /12/
Or, again, Barfield refers to the Middle Ages as a time when the individual "was rather less like an island, rather more like an embryo, than we are." An embryo, too, recalls the notion of polarity, or interpenetration of opposites. It exists by virtue of the mother, and the mother bears it as an expression of her own nature.
How do we escape our cultural conditioning and understand what could be meant by wearing the world as a garment, or experiencing it as an embryo? Perhaps, in some ways, it will be easier for us once we have spent some time in a virtual reality booth! But we also have what may be a more promising option: we can attempt to get "inside" the consciousness of earlier cultures. No one assists us more vividly in this task than Barfield, who is worth quoting at some length as he asks us to imagine what it was like to stand in the world as a citizen of the medieval era:
If it is daytime, we see the air filled with light proceeding from a living sun, rather as our own flesh is filled with blood proceeding from a living heart. If it is night-time, we do not merely see a plain, homogeneous vault pricked with separate points of light, but a regional, qualitative sky, from which first of all the different sections of the great zodiacal belt, and secondly the planets and the moon (each of which is embedded in its own revolving crystal sphere) are raying down their complex influences upon the earth, its metals, its plants, its animals and its men and women, including ourselves .... Our own health and temperament are joined by invisible threads to these heavenly bodies we are looking at.... We turn our eyes on the sea -- and at once we are aware that we are looking at one of the four elements, of which all things on earth are composed, including our own bodies. We take it for granted that these elements have invisible constituents, for, as to that part of them which is incorporated in our own bodies, we experience them inwardly as the "four humors" which go to make up our temperament. (Today we still catch the lingering echo of this participation, when Shakespeare makes Mark Antony say of Brutus:... The elements... A stone falls to the ground -- we see it seeking the center of the earth, moved by something much more like desire than what we today call gravity.... /13/
So mixed in him, that Nature might stand up
And say to all the world, This was a man.)
Now, perhaps, we can catch our first true glimpse of the Renaissance achievement. For us to enter into the medieval experience of the world would be rather like stepping from the audience into a play: as participants sucked into the story -- trapped inside our relationships to everything and everyone around us -- we could no longer detach ourselves and view the events from a distance. Conversely, what Brunelleschi and his contemporaries had to achieve was to shed those innumerable threads that bound them to their environment, and that made them both participants in the world and prisoners of it; they had to step out of the story. The world they observed was now in some sense flatter -- like a picture or movie -- and they could even watch their own characters in a kind of distant, objective fashion -- the way, in our modern subjectivity, we are inclined to observe ourselves at ever greater removes. (I have already noted that our penchant for the prefix meta- serves as one measure of this detachment.)
It may, incidentally, seem odd to speak of the new world of "in-depth" perspective as flatter than what went before, but it is necessary. As Barfield remarks, the perspectival rendering of a photograph couldn't appear lifelike to us if the world had not become photolike. That is, we are accustomed to having stepped out of the picture, and now all it requires is a certain abstract, mathematical depth to make an image look "solid." Such is the only kind of depth our surroundings still retain for us once we have been ejected from their story. But it is an extraordinarily flat sort of depth compared to the thickly textured matrix of meaning that results from being in the story.
Technological instruments like the telescope and the microscope, the telephone and the television, the automobile and the airplane, are not merely or even primarily instruments which bridge distance. Rather, they are instruments called into being by the distance we have created, by the distance we have put between ourselves and the world. /14/
This is no less true of more modern, computerized communication devices. The compulsive efforts to "overcome the barriers between people," the verbal torrents now flooding online channels, and the reconceptualization of these torrents as information streams look very much like symptoms of the rapidly increasing distance between us. Having been ejected from the world's story, we find ourselves now ejected even from one another's stories. Our lives no longer interpenetrate; words pass between us like inert objects -- like spacecraft hurled through space to the moon and back. So we throw more and more words across our new, ever more remote communication channels, hoping we might finally connect.
But the distance between us cannot be bridged in this way. Like the telescope, our instruments of communication only increase the distance. Our real need is to rediscover what it means to participate in each other's lives and worlds. This requires attention to precisely those potentialities of human exchange our efficient technology is teaching us to ignore.
There is in our use of communication technology something of the double-sided gesture referred to in the last chapter: we welcome a safe distance even as we hope to overcome it. Virtual reality is, of course, the perfection of this gesture. We speak of "immersive" virtual reality, but it is immersion in a "nothing" that is compounded of mathematical abstractions and cut off from Nature's lawfulness.
Our own hard-won separation, as Barfield points out, has proven a valuable gift -- one never to be discarded. But insofar as it has metamorphosed into an experience of ourselves as wholly and absolutely cut off from the world, it is a lie. Furthermore, it is an unnecessary lie, for it is possible to enjoy the antithesis of subjective "south pole" and objective "north pole" without proceeding to act as if the antithesis were a clean severance. That we do thus act and think cannot be doubted -- and we guard our habits with powerful taboos.
If you take this for an exaggeration, Barfield would have you contemplate some such proposition as this: if all life, all knowing and cognizing spirit, were removed from the universe, then nothing else -- no objects -- would be left either. No sun, moon, earth, or stars. Such a thought taken seriously is -- even for those who construct virtual realities -- forbidden by what our minds have become. And yet, as Barfield reminds us, it would have been just as impossible either to feel or think the proposition's denial during the medieval era. Can we claim to have escaped the parochial conventions of our own era without first understanding at least how the earlier experience was possible, and then how and why it evolved into our own experience?
Here is the danger of our fascination with virtual reality. Just consider one fact: the graphics programmer will almost certainly learn his entire trade without any professional exposure to art history and the issues I have been vaguely sketching. All this is unnecessary, irrelevant. His "art" has become pure technique, and the technique is everything. How far we are from the broad, humane ideals of an earlier age! Today, our innovations in the production of images seem controlled solely by the engineer's giddy fascination with technical feasibility. These innovations are immediately put to work by advertisers interested in their suasive powers and merchants interested in their entertaining powers.
So we accept the bombardment of our senses and our psyches by images -- printed, video, holographic, "virtually real" -- with little evident concern for our own creative effect upon the world when we participate in these ever more mechanical and mathematicized presentations of what once was sacred object and nourishing plenum of space. Like the Renaissance viewers at Brunelleschi's demonstration, we marvel at the new sensations we call "realistic" -- but we do not consider the changing standard of reality lying behind our exclamations.
If Brunelleschi's feat was both a discovery of what the world had already started to become and a harbinger of its future determination, so, too, we should look for a double significance in our current experimentation with virtual reality. It is not hard to find. Well before the advent of high-performance computing, we had already accepted the reduction of the world to virtual reality. For we have long "known" that the entire phenomenal display within which we live out our lives is merely a flickering, subjective drama, thrown up upon some unidentifiable (and philosophically illicit) screen in our brains. The "real" world of particles and fields has vanished into the physicist's equations and theoretical constructs, which are not all that distinguishable from the matrices and coordinates of the virtual reality programmer. Who does not accept that the painter's easel and canvas are illusions, manufactured of infinitesimal particles and immense tracts of empty space? So everything disappears into the momentary, subjective glittering of insubstantial surfaces, a wraithlike dance uncertainly mirrored in the ephemeral electronic pulsations of our brains. When the world had already become so virtual, could the technology of virtual reality have been far behind?
What is the status of virtual reality? And what of the real world? I suppose it is evident enough on the face of these terms that we're not asking two unrelated questions. But if it's a single question, the alternative responses are as divergent as they could be: will we continue one-sidedly upon the course first set by Brunelleschi, reducing the world ever more to an abstract virtuality, content to manipulate point-coordinates with our mathematical matrices? Or will we, from our new and individual vantage points, learn again to put on the real world as a garment -- now, however, not only being warmed by it, but also warming it from within through our own creative efforts?
1. Edgerton, 1975: 159.
2. White, 1972: 123-24.
3. Gregory, 1966: 164.
4. Panofsky, 1991: 34.
5. Cited in Gombrich, 1969: 247.
6. Pirenne, 1952.
7. Deregowski, 1974.
8. Gregory, 1966: 194-98. For a somewhat dated but valuable survey of the literature, see von Senden, 1960.
9. Edgerton, 1975: 4.
10. For a physicist's extended discussion of light in relation to the seeing subject, refer to Zajonc, 1993.
11. Edwards, 1979.
12. Barfield, 1965a: 94-95.
13. Barfield, 1965a: 76-77.
14. Romanyshyn, 1989: 73, 97. Romanyshyn's Technology As Symptom and Dream contains a superb treatment of perspective as an expression of man's changing relation to the world.
15. "Science and Quality," in Barfield, 1977b: 185.