My semi-technical introduction to computer graphics will, however, provide only a half-answer, one that, in particular, cannot address the necessary comparison between paintings and computer images or between subtractive and additive color mixing. Simplified accordingly, a computer image is a two-dimensional additive mixture of three base colors shown in the frame, or parergon, of the monitor hous ing. Sometimes the computer image as such is less apparent, as in the graphic interface of the newfangled operating systems, sometimes rather more, as in ‘‘images’* in the literal sense of the word. At any rate, the generation of 2000 likely subscribes to the fallacy—backed by billions of dollars—that computers and com puter graphics are one and the same. Only aging hackers harbor the trace of a mem ory that it wasn’t always so. There was a time whon the computer screen’s display consisted of white dots on an amber or green background, as if to remind us that the techno-historical roots of computers lie not in television, but in radar, a medium of war. Radar screens, though, must be able to address the dots, which represent attacking enemy planes, in all dimensions and to shoot them down with the click of a mouse.
The computer image derives precisely this addressability from early-warning systems, even if it has replaced the polar coordinates of the radar screen with Cartesian coordi nates. In contrast to the semi-analog medium of television, not only the horizontal lines but also the vertical columns are resolved into basic units. The mass of these so-called “pixels” forms a two-dimensional matrix that assigns each individual point of the image a certain mixture of the three base colors: red, green, and blue. The discrete, or digital, nature of both the geometric coordinates and their chromatic values makes possible the magical artifice that separates computer graphics from film and tele vision. Now. for the first time in the history of optical media, it is possible to address a single pixel in the 849th row and 720th column directly without having to run through everything before and after it. The computer image is thus prone to falsification to a degree that already gives television producers and ethics watch dogs the shivers: indoed. it is forgery incarnate. It deceives the eye, which is meant to be unable to differentiate between individual pixels, with the illusion or image of an imago, while in truth the mass of pixels, because of its thorough address ability. proves to be structured more like a text composod entirely of individual letters.
For this reason—and for this reason only—it is no problem for a computer monitor to switch between text and graphics modes. The twofold digitality of coor- dinates and color value, however, creates certain problem areas, of which at least throe should be mentioned. First, tho three color canons of traditional television or computer monitors are simply not sufficient for producing all physically possiblo colors. Rather, experi ments (which the industry seems to have considered too costly) have shown that it would require nine color canons to even begin to approach the visible spectrum.1 As it stands, the so-called “RGB cube.” the three-dimensional matrix of discrete values of red, green, and blue, is a typical digital compromise between engineers and management experts. Second, discreto matrices—the two-dimensional matrix of geometric coordinates no less than the throo-dimonsional matrix of color values—pose tho fundamental problem of sampling rate. Neither nature, so far as wo believe we understand it.
II.
The optical media, having changed Western culture—not coincidentally—simul taneously with Gutenberg’s printing press, always approached optics as optics. From the camera obscura to the television camera, all these media have simply taken the ancient law of reflection and tho modern law of refraction and poured them into hardware. Reflection and linear perspective, refraction and aerial per spective are the two mechanisms that have indoctrinated the Western mode of perception, all counterattacks of modern art notwithstanding. What once could be accomplished in the visual arts only manually, or. in the case of Vermeer and his camera obscura,* only semi-automatically, has now been taken over by fully auto matic technical media. One fine day. Henry Fox Ihlbot set aside his camera clara, to which his imperfect drawing hand had lent its quite imperfect support, and adopted a photography that he celebrated as the pencil of nature itself. One day. less fine. E. T. A. Hoffmann’s Nathanael shoved aside his lover Clara, hold a per spective glass or telescope to his eye. and jumped to his certain death. Computer graphics ure to these optical media what the optical media are to the eye. Just as the camera lens, literally as hardware, simulates the eye. which is lit erally wetware. so does software, as computer graphics, simulate hardware. The optica] laws of reflection and refraction remain in effect for output devices such as monitors or LCD screens, but the program whose data directs these devices trans poses such optical laws as it obeys into algebraically pure logic. These laws are generally, it should be noted from the outset, by no means all the optical laws valid for fields of vision and surfaces, shadows and effects of light; what is played out are these selected laws themselves and not, as in the optical media, just the effects they produce. It’s no wonder, then, that art historian Michael Baxandall can go so far as to suggest that computor graphics provide the logical spaco of which any given perspective painting forms a moro or less rich subset.
Tho complete virtualization of optics has its condition of possibility in the com plete addressability of all pixels. The three-dimensional matrix of a perspectival space made into discrete elements can be converted to a two-dimensional matrix of discrete rows and columns unambiguously but not bijectively. Every olemcnt posi tioned in front or behind, right or loft, above or below is accorded a matching virtual point, the two-dimensional representation of which is what appears at any given time. Only the brute fact of available RAM space limits the richness and resolution detail of such worlds, and only the unavoidable, if unilateral, choice of the optic mode to govern such worlds limits their aesthetics. In the following I would like to try to present the two most important of those optional optic modes, raytracing and radiosity. That being said, it is important to emphasize from the outset what a revolution it is, compared to analog optical media, that computer graphics make optic modes optional at all. To be sure, photography and film allowed for a choice between wide-angle or telephoto lenses and a wide selection of color filters. But since photography’s hardware simply did what it had to do under tho given physical conditions, there was never any quostion of what the optimal algorithm for images might be. Conversely, computer graphics, because it is software, consists of algorithms and only of algorithms. The optimal algorithm for automatic image synthesis can be determined just as easily as non-algorithmic image synthesis. It would merely have to calculate all optical, i.e. electromagnetic, equivalencies that quantum elec trodynamics recognizes for measurable spaces, for virtual spaces as well; or, to put it more simply, it would have to convert Richard Feynman’s threo-volume Lectures on Physics into software. Then a cat’s fur, because it creates anisotropic surfaces, would shimmer like cat’s fur; then streaks in a wine glass, because they change their refraction index at each point, would turn the lights and things behind them into complete color spectra.
Theoretically, nothing stands in tho way of such miracles. Universal discrete machines, which is to say. computers, can do anything so long as it is programma ble. But it is not just in Rilke’s Malte Laurids Brigge but also in quantum electro dynamics that “realities are slow and indescribably detailed.’’7 The perfect optics could be programmed just barely within a finite time, but, because of infinite mon itor waiting times, would have to put off rendering the porfect imago. Computer graphics are differentiated from the cheap real -time effects of the visual entertain ment media by a capacity to waste time that would rival that of good old painters if its usors woro just more patient. It is only in the name of impatience that all existing computer graphics are based on idealizations—a term that functions here, unlike in philosophy, as a pejorative. A first fundamental idealization consists of treating bodies as surfaces. In con trast to computer medicine, which out of necessity must render these bodies as three-dimensional, computer graphics automatically reduces tho dimensions of its input to the two dimensions of its output. That would exclude not just transparent or partly transparent things like the above-mentioned streaks in a wine glass. It is also more than apparent that things like cat fur or lambs-wool clouds (at least since Benoit Mandelbrot) have neither two nor three whole-numhered dimensions, but rather a so-called Hausdorff dimension of 2.37.
Not coincidentally, computer generated films like Jurassic Park do not even attempt to compete with the fur coats in Hans Holbein’s The Ambassadors, they content themselves with armored and thus optically unadorned dinosaurs. Even with the perfection of the fundamental reduction of bodies to surfaces, of Hausdorff dimensions to pictorial material, computer graphics will still ultimately need to face tho question of what virtual mechanism shall be used to represent which surfaces. Two algorithms present themselves as options, but these practically contradict each other and. consequently, govern mutually exclusive aesthetics. Realistic computer graphics, i.e. those that, unlike mere wireframe models, are supposed to be able to compete with the traditional arts, are either raytracing or radiosity—but not both at the same time.
