by John Updike
Since z = 2.5 constitutes a plane, then by setting z equal to the transformed coördinates of the model carbon molecule atoms Dale creates a series of more complex intersections, an array of traces on the gray screen that shifts as the angle of the Tree is shifted and the viewport and its scale are modified. He watches the screen intently, waiting for some pattern—a snowflake, a face—to emerge. The black dots dart and swarm from one edge of the screen to the other like midges above a summer pond, but Dale fails to see any message, any indicative configuration, in their staccato sway.
His idea (as I, on the other side of the sciences/humanities divide, intuit it) has the simplicity of desperation: given that the three-dimensional primitives accumulated in this computer memory sufficiently represent the array of created things, by crashing them together—using one set of phantom polyhedra to clip another with its defined edge-planes—he is giving God the opportunity to insert His version of the shape, the talisman, beneath all forms. Mathematically, since all these polyhedra and fractal patterns (as in the Tree) are stored as strings of binary numbers, a certain limit will be approached in the churning that constitutes, for God, an opportunity to declare Himself, even more clearly than He has declared Himself in the preposterous odds of Creation, the miraculous aptness of the physical constants, the impossibilities of evolution, and the consciousness that flits above the circuitry of our neurons. The Devil’s advocate within Dale, the intellectual conscience, might argue that God’s opportunity already lay, sufficiently abundant, in the colossal vocabulary of form and information that stretches from here to the quasars, and that even upon our cosmically negligible planet exists as a virtual infinity of declared, achieved entities. If God, that is, did not speak clearly in the rain and the grass, or through Behemoth and Leviathan, why would a computer’s plenitude of logic gates give Him voice? Because, Dale might answer, on the computer screen numbers become points and vectors of light and are available to our apprehension with the purity of syllogisms. Vector lines are potentially the bright bones of what is, as Wittgenstein put it, the case. Really, Dale’s reasoning boils down to no more or less than prayer, a way of making himself vulnerable to visions: Byzantine saints and Plains Indians sought the same end with sleeplessness, flagellation, and hooks beneath the skin. In his nocturnal project there is something of self-mortification, an ordeal in which the computer is made to share.
The display file library contains pre-generated images of airplanes and cubes, duodecahedra and starfish, three-dimensional letters used in animated television-station logos and even a small animatable man, with stovepipe legs and B-spline–form shoulders and a face composed of over a hundred tiny tinted planes and bicubic patches attached to difference equations whose variables can be manipulated to produce expressions of joy or anger, grief or concentration, and to shape the mouth, cheek muscles, and eyes in ways appropriate for pronouncing syllables of speech; the effect, when rounded by Giroud shading and illumined from a single point by the same algorithms that remove hidden surfaces, is eerily real, though the man moves relative to the way we do as mercury moves relative to water—in quicker jerks, and with a more pronounced tension when static. As midnight tiptoes past, Dale crashes these volumes together, calling up for display now the points and planes of intersection and now, subtracting volume from volume and sweeping the remainder in an arc along a cubic curve, producing marvellous moldings such as would decorate a mansion in Pandemonium or a picnic pergola on Mars’s far side. Having switched into the double-buffered color raster now, he was calling upon the host computer—housed on the floor below, where a fan cooled its brow—to load the data bus with prodigious amounts of visual information, twenty-four bits per pixel, 1024 × 1024 pixels on the screen, each refreshed every thirtieth of a second. In crackling lurid color the strange forms rotate, rotate in silent spasms that hint of the storms of computation behind each hesitant visual tug. Discontented even with the stripy and dimension-aping marvels conjured up, Dale taps into the mechanism additional strictures and permutations. Commands in a rigid little language (setq … defun … map-car … eq … prog) cause electricity docilely to run through the circuits, the flipflops, the adders and half-adders, the endless infallible transistor gates, each a mere twenty microns in dimension, less than the finest hair on Esther’s breast.
The images on the slightly outcurved screen aggregate and extend; he rotates them, in obedience to a persistent panicky sensation that something lies behind the generated garish objects, some spider or coin hiding in the illusionistic space where even shadows and reflections can be conjured with the right commands. The computations cannot swing the altered viewpoint into place fast enough, and Dale seeks to trick his unseen opponent by calling for a tilted mirror to be placed behind the occulting images—a relatively simple procedure in computer graphics wherein, each pixel being considered as a tiny peephole, the line of sight passing through all non-occulted x and y values is specified bounce at a certain value of z (a sliding value, since the mirror is tilted). This bounce command, attached to a specific angle of “reflection” (12° in this case), collects from the graphics memory store, pixel by pixel, the information defining the back surface of the occulting object, converted at the average rate of 160 nanoseconds per pixel. The back side looks much like the front; Dale still cannot find that lost gold coin, that spider spinning its web, that hostile secret the computer is harboring.
The merged images, as the heaped-on transformations dispassionately work upon them, look increasingly like skeins of glutinous polychrome yarn. They look organic, as if a certain process of magnification and refinement is bringing up into view a core fibrosity in things. There is, Dale supposes, on the analogy of the real world, a crystalline level beneath these fibers; but the powers of computer graphics, unlike those of the electron microscope, are not yet powerful enough to reach it. Dale reasons, however, that the computer world, being man-made, will hold its analogous deep structure at a coarser level than the world God has knitted out of quarks. He has devised a composer program that applies torque to his chaotic accumulations, squeezes them as a giant machine might press layers of shale for a drop, a glistening drop, of underlying principle. This drop will show itself, he believes, as an oil leak fans outward from a leaking engine, spreading its peacock sheen between the rusted and sodden accumulations of debris. This statistical iridescence is what he is looking for, an aligning like that of the rods within the ancient trilobite eye. From time to time he stops to take a readout of the equations being visually expressed or to make a hard-copy design on the laser printer. He has been running these experiments and accumulating this ingenious chaotic evidence for some weeks now, all through Lent. But tonight he feels a climax approaching, a crisis and an atonement, atonement in its root sense of at one; after some hours he feels his fingers on the keys tingling as if electricity were flowing into him: his nerves and the majestical electronic architecture of the CPU and its memory are kludged together.
At some point in the evening he must have eaten his unappetizing pastrami sandwich, for the crumpled and grease-spotted bag lies on the terminal table, next to the drained milk carton and gray control mouse. At some point he must have arisen and gone to the bathroom down the hall past the vending machines and on his way back spoken to Ike Spiegel, for he finds in his head dirty traces of his doing this, leftover punch lines of jokes. “Two: one to call the electrician and one to mix the martinis.” “Nu, don’t vorry, I like sitting here in the dark.” “So boys will talk to them.” Spiegel laughed. The hairy spaces of skin between his shirt buttons framed by double elliptic arcs jiggled. Even sitting down, Ike had a stand-up comedian’s rapid mirthless patter. Take it or leave it, here comes another. The lead-up to the third punch line comes back to Dale. “Why do girls have vaginas?” Like a punched button, he laughed; but it seemed less a joke than a mere sad truth.
His fingers flicker with their rat-scrabble on the feather-light plastic keyboard, crashing together yet two more agglomerations of verti
ces and parametric cubic curves. Out of the instant ionic shuffle a face seems to stare, a mournful face. A ghost of a face, a matter of milliseconds. How little, after all, it takes to make a face. A few dots on a piece of white paper will cause an infant to smile and reach out in recognition. Amy Eubank’s studies show that we can distinguish a friend from a stranger at seven hundred yards.
The face is gone. A screenful of gluey polychrome yarn has replaced the image that had seemed to stare out, its eyes deep sockets of undying, grieving life. Dale tries to think how to re-execute the computation—polygons clipped by polygons—but his mind is so blank that the first half of another of Spiegel’s jokes comes into it: How many WASPs does it take to change a light bulb? He asks the machine for a dump, and across the cubicle the printer chews away with its frantic pointed teeth. In his agitation Dale lifts up from the sticky warm swivel chair and goes down the hall for a Diet Coke. The machine grinds loose the desired red-on-white cylinder from within its guts and after a second’s tumble slaps it into the waiting trough. Then, as if taking thought, it with an offhand clatter spills back his two quarters and dime. Some wise guy has rigged it to refund. These clumsy machines are constantly being outsmarted by the smart alecks on the floor. And how many Jewish mothers? Maybe you had to be Jewish to understand that joke.
The face, he seems to remember, had long hair but no beard; the traditional iconography is evidently wrong. Men of the Middle East that you see on television giving interviews all seem to have three-day accumulations of bristle. How do they manage that, every day? Like putting the lawnmower on a higher setting.
The long cream-colored hall with its pinned-up Snoopys and baby pictures is silent. In Dale’s skull echoes the sound, perhaps a half-hour old, of Spiegel packing up and leaving. The linguistic analyst stamped flat a beer can on the floor beside the trash receptacle and shouted good night. Dale has this entire brightly lit sector of the Cube’s seventh floor to himself and, back in his cubicle, falls to his knees between the swivel chair and the display terminal. He prays for an illumination that will relieve him of this tension, this guilt, the tension and guilt of being a thinking animal. There is a swimming reddish void behind his eyelids; the void vaguely pulses and has some structure, a microscopic grain with a rapid downward movement, like rain on a sheet of glass. He leans his brow against the slightly outcurved screen; it is cooler than he, yet slightly warm. Radiation. Give himself cancer of the brain. He backs his head away and stiffly stands, resolving to keep at it for another hour or so. He feels on the edge of a breakthrough. Yet he postpones sitting at the terminal.
He goes to the window. The city as seen from the window is settling slowly, like the ashes of a still-glowing fire. In the post-midnight sky a wide-awake moon, five-eighths full, glides amid flakes of cirro-cumulus, a broadening scattering, a lake of luminous wavelets. Seven stories below, the little trapezoidal park, with its bronze statuette of Lady Lovelace, shows a softening of the trees, their twigs no longer, as in winter, merely linear, but now blurred, thickened by buds, tip droplets aching to unfold into leaves and get the photosynthetic cycle rolling again. Dale’s eyes sting; his body, too long bent into the sedentary position, longs to stretch out, to lay its length on a bed, beside Esther, her green eyes thirsty for his slime, her slender questing trembling hands. They have had, like many of the classic lovers, no decent bed, ever—a dirty mattress in an attic, a narrow student’s pallet beneath a plastic cross.
He returns to the terminal and tries again to find that trace, that divine hint. He takes the numerical printout of the crank-up that produced the ghost of the face and has the computer count the 2s and 4s for random recurrence; indeed, he does find a small statistical edge over the strict .200 that probability would indicate for two digits—.208673, the .0086+, even if consistently generated, not quite enough to base a theology on. More promising, however, is the deviation from the .01 that should represent the statistical incidence of the configuration 24 in integer pairs from 00 to 99. Instead of .0100, the computations showed an incidence of .013824, an almost inexplicable nearly four in one thousand more than chance alone would have generated, and it ends with a 24! The same statistical tests, run off on non-biological primitives—tables, chairs, airplane wings, polyhedra, Koch curves, old fractals used for texturing—yield frequencies within .001 of the predictable random norm, which indicates to Dale virtually beyond doubt that his statistical dusting of the biologically derived models had revealed, if not one of God’s fingerprints, a whorl or two. There is something there.
But beyond all this numerical quibbling Dale still hopes—he is greedy, spiritually greedy; he is climbing his Tower of Babel—for a graphic confrontation, a face whose gaze could be frozen and printed. Refreshed by yet another Coke with its increments of caffeine and carbohydrate, he tries to retrace the steps that gave him his haunting glimpse; he tries to ascend, gate by gate, through the immense binary maze that the mere touch of a button can reshuffle and double. He alters angles, he zooms, he changes parameters. He loses track of time. The small morning hours are much like one another. Vague sounds from elsewhere in the building—elevator doors opening and closing, cables singing in the black shaft, surges of humming on the floor below—indicate the presence either of other night workers or else of automated workings, of timers and thermostats inflexibly sending their signals. It has grown colder, outside and within. The coldness that, beginning in his fingertips and on the backs of hands, has travelled up through his wrists and forearms toward the cage of his chest he takes for Heavenly inspiration; in the microscopic maze where a single fleck of fallen dust would block a passage like a boulder and the finest hair come crashing down like a cathedral beam, he is drawing closer to the dragon, to the fire-breathing secret. As a child he would feel thus timorous descending to the cellar, where his father, in that Akron house with thin walls, had set up the Christmas train, and whose obedient switchings and reversings proved to the boy a fascination and a mystery, as if a kind of corpse lay down here waiting to be activated, a spindly metal body with a narrow, heavy, alive head, the locomotive. The locomotive had a glowing single eye and, when touched to the tracks, its wheels would angrily spin. Working alone, conquering his awe and feeling of trespass, Dale became more adept at the mysteries of the Lionel than his father, and began to buy new equipment—more track, a more versatile transformer—out of his allowance. He was on his way.
Increasingly often he encounters on the screen the protest Insufficient Free Memory or Are you sure? Beneath his commands the levels of operational hierarchy, language overlying language down to the elemental binary vocabulary, slide one within another like crystal spheres as the screen supplies Dale’s eyes with striped toroidal surfaces displaced in a jagged twinkling by others. He has loaded the simulator with a transformative function that subjects each successive crash to new parameters derived from the polynomials of the preceding phase: a kind of spiral that should tighten, he reasons, toward cosmic essence. Yet the displayed configurations do not simplify but, rather, fragment and complicate. They are blowing up.
The face again is what he hopes for, and yet dreads. Perhaps the coldness overwhelming his body is dread. Within these hollow small sliding hours his sensation enlarges that the presence cringing within the mazy electronic alleyways of the computer is inimical: It hates Dale’s seeking It, and will extract vengeance if he finds It. Suppose, in seeking God along these pathways, he takes a wrong turn and encounters a false god, one of the myriads who have tormented men, Moloch or Mithra or Siva or Osiris or transformed Lucifer or that Huitzilopochtli who demands and eats the living heart? Nevertheless, our young man presses again the keys that spell repeat, and the striped colors and cells of the screen shudder like grease-marbled water into which a pebble has been dropped. The new display resembles the one before, save that its patches are finer in scale and have been subjected to a torque that has generated whirlpools, concentric intensification of color layers that appear to tunnel downward like the fingers of a
rubber glove. With a slight squint and an adjustment (how? who is tapping that keyboard?) of the visual-interpretative cells within his brain, these same patterns appear to be cones rising toward him. In the crumpled strata between two of these cones, something anomalous seems embedded, in several colors. Dale zooms in, setting his viewpoint closer and enlarging the window. The anomaly, in shades of green intermixed with orange, appears to be illegibly foreshortened; he maps its image on a plane tilted first 85° on a vertical axis, and then a more cautious 72°, and thus arrives at an image he can read. It is a hand. A hand, patched of colors as if dabbled with glowing camouflage paint but its form emergent, even to palm creases: a hand relaxed on its back and its fingers curled together and not strictly distinguishable, but the knobbed form of the opposed thumb unmistakable. Its relaxation is curious. Is it relaxed because it has been slain, a hand nailed limp to the cross? Or is it more like the hand of the sleeping Samson, flung into the folds of Delilah’s lap while the enfeebling shears are plied? Is its limpness that of Adam before he was touched with life, or a limpness of exhaustion, of final despairing surrender? Dale inspects the image and can see no dark trace in the palm of a spike or stigma. The phantom configuration’s anatomy, fitted into the ambiguous three dimensions of the tortured, abstract pattern, appears complete to Dale; he believes that, with higher resolving power than the VAX 8600 can summon, knuckles and even fingernails and cuticles would emerge, just as the tendrilous graphics of a Mandelbrot set can be infinitely enhanced. Gazing at the hand transposes him to another plane and gives him peace: rapture passes through him as if its path had been cleared by the coldness he has been feeling for hours, his own selfish vitality ebbing from him as the night progressed. Frozen along his veins, scarcely daring breathe lest he jar loose a pivotal electron, he taps the commands to take a printout of the pattern. From the other side of the cubicle, near Amy Eubank’s lipstick-stained Styrofoam cups, that inhuman shrill chatter of the dot-matrix printer is launched. Imagine being consumed alive by such avid, implacable teeth! Dale is feeding God, that tender shadow on the underside of our minds, to those teeth.
