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A Scientist's Notebook
by Gregory Benford

Pascal's Terror

The silence of those infinite spaces terrifies me.
-- Blaise Pascal, 1623-1662

With this memorable sentence, a thoughtful, religious Frenchman saw that the problem of infinity unlocked by modern science was basic. It remains so today.

Most awful of the perspectives opening to the seventeenth century mind was the stillness of the yawning heavens, their moral blankness. There was no music of the spheres.

Blaise Pascal was a Catholic who confronted his own doubts by thinking in terms of the shadow modern science cast over the ebbing theological intellectual landscape of his era. He saw science as a new door to knowledge, one that had to be reconciled with the ancient path of religion.

To Pascal, a man in love with the absolute--whether in his deft calculus of probabilities or in his acute theology--that refusal of the universe to tip its hand, to lend purpose to human action, was terrifying. Though Aristotle had said, "either an outright denial or an outright acknowledgment of the being of the infinite leads to many impossibilities," the ancient world had not earnestly grappled with the implications.

Not that the modern view is comforting, of course. Consider that as you walk along, your step taking you forward maybe a meter, the Earth's spin carries you a thousand times farther to the east. The Earth's slow circle about its sun bears you westward even more: 60 kilometers.

But the sun is no fixed point, either. It wanders among the nearby stars, who are in a similar random rush, so while you make one step your local Sun Express takes you thirty kilometers off toward the star Vega. The sun's grave gyre about the hub of our galaxy is faster, so the pinwheel swirl of the spiral brings you another five hundred kilometers along a course that will not repeat for 250 million years.

And even our beloved Milky Way is not a reliable, fixed mass. It carries you along another thousand miles or so, as it arcs around its nearby galaxies, and with respect to even more distant but powerful masses. All is ferment. Perhaps, thinking of it makes getting around harder. Or maybe it seems easier, when you consider how much is being done for you, without your ever knowing.

And all this transpires in utter quiet.

Pascal had to struggle with a genuinely infinite real universe, and not merely the mathematical infinities of Greek mathematics. Worse, he had to confront an infinite, silent Creation, one he believed was made by a God who later sent delegates and texts to help us.

*     *     *

The two aspects of Pascal's terror are somewhat separable. I'll discuss immensity first, and silence next month.

Astronomy had thrown open the vast window available through the telescope, and it could not be shut again. Distances beyond human ken seemed to rob our lives of purpose. On so vast a stage, who could plausibly believe that we stood at stage center?

This fear is very old. Rudy Rucker describes it and much else in his enjoyable Infinity and the Mind, the standard work for non- mathematicians on the many species of infinity. As he notes, the Greek word for infinity is apeiron, meaning unbounded, but also undefined, indefinite. This links immensity with chaos in Greek thinking. The word applies to crumpled newspaper, crooked lines, the arbitrarily complex. Aristotle felt that " . . . being infinite is a privation, not a perfection and the absence of a limit."

Reflect that the Odyssey follows a man who moves back and forth between civilized places and the rim of the unknown, confronting monsters and strange places, then returning. Odysseus proves his abilities by controlling his emotions (and employing a linguistic trick to elude the Cyclops, plainly a civilized art). One can read this founding document of western civilization as a science fictional voyage of discovery, both of lands and of the nature of a truly civilized personality. But nowhere does he venture into chaos, not even when he visits Hell. There is always a system, an orderly universe.

One wonders what the prospect of the night sky meant to any Greeks who guessed its true size. Or those who entertained the notion that it might go on forever.

The problem hasn't gone away. Infinity of scale still inspires fear and awe, and futility.

John Updike keeps wrestling with it, particularly in his overtly theological novels such as A Month of Sundays. His Roger's Version is expressly about the argument from design, which Hume supposedly disposed of long ago but which keeps cropping up in such newfangled guises as the astrophysicists' Anthropic Principle. (This hotly debated thesis holds that we can "predict" many of the properties of the universe because if matters were different, we---and other intelligent life---wouldn't exist.)

Among mainstream writers, Saul Bellow keeps nibbling at the vacancy of "realistic" life (and literature) beside the universe's yawning gulf. Less intellectual authors ruminate less acutely. Norman Mailer tried to punch it in the jaw, but seldom makes contact unless he slides into fantasy, as in his Ancient Evenings.

Some have noticed that you can go the other way, approaching the infinite through the infinitesimal. William Blake's world in a grain of sand reverberates through the miniature worlds of Jorge Luis Borges, often with an air of seeking to purge immensity by retreating into the labyrinthian minute. His most anxious works, though, prefer the denumerably infinite--- that is, the prospect of counting forever, meeting infinity by exhaustion. His garden of forking paths reduces the infinities of time to an enclosed area, framing the paradox. His library of Babel opens endlessly and meaninglessly, since it contains all truths and all lies, with no way to tell the difference.

Some of these literary methods of grappling with infinity seem to come from a kind of cultural agoraphobia. In a way this is easy to understand.

Consider the Hilbert Hotel, named for the German mathematician David Hilbert. A customer comes, only to find that, though the hotel is infinitely large, it is filled. So he proposes that the room clerk simply move the person in room 1 to 2, and the occupant of 2 to 3, and so on. Presto!---a new room is available. The point is that common sense is useless here. One plus one equals two, but one plus infinity always equals infinity.

The nineteenth century discoveries in the mathematics of infinity have led to a cool knowledge of analytical properties, but no deeper gut feeling. Physicists subtract away infinities in their calculations, arranging cancellations so that the masses of observed particles come out right---but they don't fathom what's going on any more than Pascal did. (For more on this, consult William Proudstone's engrossing Labyrinths of Reason.)

Some authors seem to deny that infinity is interesting, since, finally, it is all the same. Yet this was disproved by Cantor in the nineteenth century, who showed that infinities can have different sizes. The set of irrational numbers, for example, is bigger than the set of whole numbers; they are called transfinite. This mingles with our knowledge that the universe may indeed be infinite.

Italo Calvino's science-fictional works, such as Cosmicomics, often reflect a way of joking away the immensities, a common response. In "The Denial of Death" Ernest Becker suggests that humans strike dramatic attitudes when they encounter reminders of "the suction of infinity."

Partly this fear lies in the incomprehensible nature of matters infinite, or as one schoolboy put it, "Infinity is where things happen that don't." Euclidean space lets straight lines meet at infinity, but nobody goes there, so it doesn't matter. Or does it?

People can care powerfully about infinity---vaguely, perhaps, but feelingly. Giordano Bruno, a sixteenth century cosmologist who announced the infinite plurality of worlds, died at the stake for his troubles. The universe we know today is about a hundred billion light years across, a distance which tumbles into the pit of meaninglessness number.

Science fiction should address this problem more clearly than conventional fiction, which often merely broods about it. In fact, many modern western texts evade the promise of the strangeness and immensity of, for example, other cultures (the infinity of human facets). The Jewel in the Crown, to pick a recent novel turned into upscale TV drama, promises to confront India in its richness, but ends up being about (surprise, surprise) the English class system. Sf may have inherited some of these reflexes.

After all, how otherwise to account for the pervasive use of faster-than-light travel? (Of course one can cite Artistotle's advice that dramas should use unity of time and place to heighten dramatic power. Nobody wants to hear about the whole voyage, and to the modern attention span, more than a few seconds spent getting to Alpha Centauri is far too much.) Going to the stars now routinely becomes very much like taking the stellar subway; you don't even get to look at the view. Collapsing the true scale of the universe this way robs it of significance and power. This is dealing with infinity by skipping over it, turning away.

Notice that swearing off the faster-then-light drug can have grand effects. Poul Anderson's Tau Zero takes a frail crew to speeds razor-close to light speed, employing the relativistic time stretching physics allows. Their payoff, as they lose all contact with humanity, is a vast view of the evolution of a (closed) universe as it swells, pauses, and then squeezes back down into an again-primordial fireball. Refusing to subvert the size of those vast spaces lifts the novel above the myriad dull quickie galactic empires.

The urge to diminish nature's scale runs deep. Two centuries after Pascal, another Frenchman sent an artillery shell to a fictional moon and began in earnest another subverting strategy: filling the infinities with people. Pascal thought of the heavens as forever serene and outside the human realm; Jules Verne made it a subway stop.

Of course, this savvy move made human adventure narratives possible, and all the attendant analogies with the West's frontiers. This persists; Robert Heinlein especially depicts the stars as frontier, raw and waiting to be tamed, rather than as a wilderness immense in mystery---the unknowable, the huge, the nonhuman.

To map is to claim. And once the galaxy was partitioned, weighed, its gravid pulses known, to some extent science itself had domesticated the infinite. The process proceeds eternally, as we now peer back at distant quasars, seeking to see the core fires of the first birthing galaxies. Very few sf narratives confront this grand scale---largely because it is fearsomely hard to populate it plausibly with people, but also, I suspect, because of that persistent terror.

Cosmological measurements of the mass density in the universe imply that the governing geometry of space-time is indeed open, which means the universe will continue to evolve to larger scales and flatter local space-time-- - forever. Unless there is about five times as much mass around than we can detect (which means it must be in the form of either dead black holes or energetic, super-light particles), our prospects are indeed infinite. Our latest measurements clearly predict a universe that accelerates its expansion, driven by some component we do not know---quintessence, some call it. The cosmos seems to rush forward to embrace its eventual infinity.

But at least the universe is filled with something. Emptiness itself signals infinity, too, because each seems the inverse of the other; divide one by infinity and you get zero.

Our defense against that is to either fill it (perhaps with ourselves) or wall it off. This has the quality of making a deal with infinity, allowing it limited expression. (Pascal himself had the impulse to bargain, even with God. His famous wager holds that skeptics might as well believe in God, since there is no loss if He doesn't exist after all.)

Another strategy for avoiding the implications of true infinities lies in the construction of great artifacts. Works bigger than men seem to imply in our deepest minds that we ourselves are more important than a glance would show.

I remember seeing my first skyscraper when I was ten (and thinking what an ugly word that was). My mother pointed to it outside the train station in Chicago and said, "Gosh, doesn't it make you feel insignificant?" I remember frowning up at the great stack of stone and thinking, "Why should it? We made it, not the other way around."

I suspect something like this animates Larry Niven's Ringworld, Asimov's Trantor, Bob Shaw's Orbitsville. The striking facet of the Ringworld is that it is indeed so vast that you cannot plausibly explore it in a human lifetime--but you can see it all in one glance, hanging in the sky.

This sense of locality promises closure, or at least a comfy relief from true immensity rather than embracing it. Such fictions capture the awe of infinity, but not its terror.

I find it intriguing that there is much modern horror fiction, but it is cozy, not confronting the terror of Pascal. After all, it cannot be personified, grappled, comprehended, even if before it we, for all our majesty, are as ants.

===THE END===


copyright © 2001 Abbenford Associates

Comments on this column welcome at gbenford@uci.edu, or Physics Dept., Univ. Calif., Irvine, CA 92717


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