by Jim Holt
The restaurant itself had a curiously 1950s feel to it, with older waiters in black tie, like extras in a Marx Brothers movie, and lots of crystal and brocade everywhere. Across the room, a local torch singer in sequins, accompanied by a pianist, belted out “At the Copa.”
As I listened to my distinguished interlocutor above the music—“They need p and q, these boys, they need p and q!” he exclaimed, alluding to a pair of premises I had lost track of—a sort of metaphysical tristesse came over me. Earlier, on the road, I had had a near encounter with le néant. Now here I was in a provincial restaurant that, to a New Yorker like myself, seemed a vestige of a departed past, the snows of yesteryear. It was as if the Copa had never left Pittsburgh. In this eerily unreal setting, I could almost feel the Spontaneity of Nothingness. Okay, it was a mood, not a philosophical argument. But it filled me with the conviction that Grünbaum’s ontological certitude—watertight, bulletproof, sunk-hinge, angle-iron, and steel-faced though it was—could not be the last word. The mystery of existence was still out there.
I was driven back to my hotel without incident. Slightly addled by the quantities of champagne and wine I had consumed, I lay down and drifted off to sleep without turning down the bedspread. The next thing I knew, the dawn light was filtering through the curtains and the phone was ringing. It was the Great Rejectionist.
“Did you sleep well?” he buoyantly asked.
5
FINITE OR INFINITE?
Compared to the eternal cosmos envisaged by the ancients, our own universe is something of a Johnny-come-lately. It seems to have been around a mere 14 billion years or so. And its future may well be bounded too. According to current cosmological scenarios, it is destined either to disappear abruptly in a Big Crunch some eons down the road, or to fade gradually into a dark and chill nothingness.
The temporal finitude of our universe—here today (but not yesterday), gone tomorrow—makes its existence seem all the more insecure and contingent. And mysterious. A world with solid ontological foundations, it seems, just wouldn’t behave like this. It would exist eternally and imperishably. Such a world, unlike the finite Big Bang universe, would have an aura of self-sufficiency. It might even harbor the cause of its own being.
But what if our own world, contrary to current cosmological thinking, did turn out to be eternal? Would the mystery of its existence then become less acute? Or would the sense of mystery vanish entirely?
THE TEMPORAL NATURE of the world has long been a hotly contested issue in Western thought. Aristotle held the cosmos to be eternal, with no beginning or end in time. Islamic thinkers disagreed. The great philosopher and Sufi mystic al-Ghazālī, for instance, argued that the very idea of an infinite past was absurd. In the thirteenth century, the Catholic Church declared it to be an article of faith that the world had a beginning in time—although Saint Thomas Aquinas, showing some loyalty to the Aristotelian tradition, insisted that this could never be proved philosophically. Immanuel Kant argued that a beginning-less world led to paradox: how, he asked, could the present day ever have arrived if an infinite number of days had to pass first? Wittgenstein, too, felt there was something odd about the idea of an infinite past. Suppose, he said, you were to come across a man reciting to himself, “. . . 9 . . . 5 . . . 1 . . . 4 . . . 1 . . . 3 . . . finished!” Finished what? you ask him. “Oh,” he says with relief, “I’ve been reciting all the digits of π backward from eternity, and I finally got to the end.”
But is there anything truly paradoxical about an infinite past? Some thinkers object to the notion because it entails that an infinite series of tasks might have been completed before the present moment—which, they say, is impossible. But completing an infinite series of tasks is not impossible if you have an infinite amount of time in which to perform them all. In fact, it is mathematically possible to complete an infinite series of tasks in a finite amount of time, provided you perform them more and more quickly. Suppose you can accomplish the first task in an hour; then the second task takes you a half hour; the third takes you a quarter of an hour; the fourth takes you an eighth of an hour; and so on. At that rate, you will have finished the infinite series of tasks in a total of just two hours. In fact, every time you walk across a room you accomplish such a miracle—since, as the ancient philosopher Zeno of Elea observed, the distance you cover can be divided into an infinite number of tinier and tinier intervals.
So Kant and al-Ghazālī were wrong. There is nothing absurd about an infinite past. It is conceptually possible for there to have been an infinite succession of sunrises before the one this morning—provided there was an infinite span of time in which they could have occurred.
Scientific thinkers, by and large, have not shared such philosophical qualms about eternity. Neither Galileo nor Newton nor Einstein had any problem conceiving of a universe that was infinite in time. Indeed, Einstein added to his field equations a fudge factor—the infamous “cosmological constant”—to ensure that they would yield a universe that was static and eternal.
But astronomical observations soon revealed that, contrary to Einstein’s intuition, the universe was not static. It was expanding, as if from an initial explosion. Even in the face of this evidence, some cosmologists still clung to the hope that the universe might be eternal. In the late 1940s, Thomas Gold, Hermann Bondi, and Fred Hoyle proposed a theoretical model called the “Steady-State Universe,” which managed to be both expanding and eternal. (Gold and Bondi claimed that they came up with the idea after seeing the horror film Dead of Night, the dream-infused plot of which loops around on itself endlessly.) In their model, the empty space left behind by the ever-retreating galaxies is continuously filled by new particles of matter, which pop into existence spontaneously thanks to a “creation field.” Thus despite the expansion, a constant density of matter is maintained. Even though it is constantly expanding, the Steady-State Universe always looks the same. It has no beginning and no end.
Another cosmological model of eternity is the “Oscillating Universe,” which was first proposed in the 1920s by the Russian mathematician Alexander Friedmann. According to this model, our universe—the one that originated some 14 billion years ago with the Big Bang—emerged from the collapse of an earlier universe. And, like that earlier universe, ours too will eventually stop expanding and collapse back on itself. But when it does, the result will not be an all-annihilating Big Crunch. Instead, a new universe will rebound out of the fiery implosion, in what might be called the Big Bounce. And so on and so on, ad infinitum. In this model, time becomes an endless cycle of destruction and rebirth, rather like the dance of the god Shiva in Hindu cosmology.
Both the Steady-State Universe and the Oscillating Universe make the problem of cosmic origination go away. If the universe is infinitely old—if it has always been around, in other words—there is no “creation event” to be explained. Unfortunately for lovers of eternity, the Steady-State model is no longer taken seriously by cosmologists. It was done in by the detection, in 1965, of the background radiation left over from the Big Bang, which furnished decisive evidence that our universe had a fiery beginning after all. The Oscillating model has fared better, but it is plagued by theoretical gaps. So far, no one has been able to explain exactly what sort of unknown repulsive force could overcome the attractive pull of gravity at the last moment of collapse and cause the universe to “bounce” rather than “crunch.”
So at the moment, anyway, the odds seem to favor a finite past for our universe. But what if our universe is not all there is? What if it is a part of some greater ensemble?
One of the great lessons of the history of science is that reality always turns out to be more encompassing than anyone imagined. At the beginning of the twentieth century, our universe was thought to consist of just the Milky Way galaxy, sitting all by itself in an infinite space. Since then, we have learned that the Milky Way is merely one of a hundred billion or so similar galaxies. And that’s just the observable universe. The current theory that
best explains the Big Bang is called the “new inflationary cosmology.” As it happens, this theory predicts that universe-engendering explosions like the Big Bang should be a fairly routine occurrence. (As one friend of mine observed, it would be very odd if the Big Bang came with a label that said, “THIS MECHANISM OPERATED ONLY ONCE.”)
In the inflationary scenario, our universe—the one that suddenly popped into existence some 14 billion years ago—bubbled out of the spacetime of a preexisting universe. Instead of being all of physical reality, it’s just an infinitesimal part of an ever-reproducing “multiverse.” Although each of the bubble universes within this multiverse had a definite beginning in time, the entire self-replicating ensemble may be infinitely old. The eternity that seemed lost with the discovery of the Big Bang is thus regained.
With an eternal world—whether of the inflationary variety or some other—there is no inexplicable “creation moment.” There is no role for a “first cause.” There are no arbitrary “initial conditions.” An eternal world thus seems to satisfy the Principle of Sufficient Reason. The way it is at any moment can be explained by the way it was the previous moment. Indeed, its existence at any moment can be explained by its existence the previous moment. Should that be enough to dispel any lingering sense of mystery?
Many have thought so—prominently among them, David Hume. In Hume’s Dialogues Concerning Natural Religion, the character Cleanthes, who comes closest to being the author’s mouthpiece, gives two arguments that an eternal world requires no explanation for its existence. “How,” he asks, “can anything that exists from eternity have a cause, since that relation implies a priority in time and a beginning of existence?” It is assumed here that an explanation must invoke a cause, and that a cause must come before its effect. But nothing could precede a world with an infinite past, so such a world could have no prior cause and hence no possible explanation for its existence.
There are two problems with this first argument. To begin with, nothing in the concept of causation says that a cause must always precede in time its effect. Think of a locomotive pulling a caboose: the motion of the former causes the motion of the latter, yet the two are concurrent in time. Moreover, not all explanations must invoke causes. Think, for example, of the explanation for a rule in baseball or a move in chess.
Hume’s second argument is a better one. Suppose (he has his spokesman Cleanthes say) we think of the history of the world as a series of events. If the world is eternal, this series is an infinite one, with no first or last member. Now, each event in the series can be causally explained by the event that precedes it. Since there is no event that lacks an explanation, everything seems to be explained. “Where then is the difficulty?” Cleanthes asks. He is unimpressed by the obvious rejoinder: that even if each event in the series is causally explained in terms of an earlier event, the series as a whole remains unexplained. For the series as a whole, he insists, is not something over and above the events of which it is composed. “I answer that the uniting of these parts into a whole, like the uniting of several distinct countries into one kingdom, or several distinct members into one body, is performed merely by an arbitrary act of the mind, and has no influence on the nature of things,” Cleanthes says. Once all the parts are explained, he submits, it’s unreasonable to demand a further explanation of the whole.
Seen in this light, an eternal world looks like the cause of itself, since everything within it is caused by something else within it. Hence it requires no external cause for its existence. It is causa sui—an attribute usually reserved for God.
But there’s still something missing here. This infinite world is like a railroad train with an infinite number of carriages, each pulling the one behind it—and no locomotive. It can also be likened to a vertical chain with an infinite number of links. Each of these links holds up the link below it. But what holds up the chain as a whole?
Imagine yet another sort of series that has no beginning and no end, this one consisting of an infinite succession of copies of some book—say, the Bhagavad Gita. Suppose that each book in the series is faithfully copied by a scribe, letter for letter, from the preceding book in the series. Now, for each given copy of the Bhagavad Gita, the text is fully explained by the text of the preceding copy, from which it had been transcribed. But why should the whole series of books, extending back infinitely far in time, be copies of the Bhagavad Gita? Why not copies of some other book—Don Quixote, say, or Paradise Lost? Why, for that matter, should there be any books at all?
The preceding thought experiment, essentially due to Leibniz, is somewhat fanciful. But it can be sharpened up and made more scientific. Suppose you want to explain why the universe is the way it is at a given moment in its history. If the universe is eternal, you can always find earlier states in its history that are causally related to the state you’re trying to explain. But knowledge of those earlier states is not enough. You must also know the laws that govern how one state of the universe evolves into another.
To be more precise, consider the total mass-energy of the universe as it is today. Call this mass-energy M. Why does M happen to have the value it does? To answer that question, you might point out that total mass-energy of the universe yesterday was also M. But that is not by itself an explanation of its value today. You also need to appeal to a law—in this case the law of mass-energy conservation. The total mass-energy of the universe today is M because (1) the total mass-energy of the universe yesterday was M and (2) mass-energy is neither created nor destroyed. Now your explanation is complete.
Or is it? It appears that there are two ways in which the universe could have been radically different. It could have had a different total mass-energy throughout its history—say, M' instead of M. And it could have had a different law governing that mass-energy: a law that, for example, might have allowed the mass-energy to cycle back and forth over time between a pair of values, M and Mˇ. (To return to the Bhagavad Gita example for a moment, that would be as if the text kept getting translated back and forth from Sanskrit to English to Sanskrit to English and so on.) We still have no explanation of why there is this law and this precise value. Both appear to be contingent. Nor do we (yet) have an explanation of why there should be any mass-energy at all, let alone a law governing it. An eternal world can still be a mysterious world.
But we knew this intuitively already. Even if something is causa sui, its existence can still seem arbitrary. And an entity needn’t be eternal to be self-caused. It could also trace out a circular path in time, looping around on itself so that it has no beginning and no end. Something of the sort can be found in the 1980 movie Somewhere in Time. The main character (played by Christopher Reeve) is given a gold watch by an old woman. He then travels back in time and gives the watch to the same woman when she was in her youth—the very watch that she will, some decades later, give to him. How did this watch come into being? In its entire existence, which spans only a few decades, it never sees the inside of a watch factory. It exists even though it has no creator. It seems to be causa sui. (Some physicists call an entity with such a circular history a jinn, since, like Aladdin’s genie, it seems to be self-conjuring.) The existence of this gold watch is as inexplicable as the existence of the poem “Kubla Khan” would be if I had gone back in time to the autumn of 1797 and dictated it to a grateful Coleridge, who then published it so that two centuries later I could learn it by heart.
Could anything be more of an affront to the Principle of Sufficient Reason than a self-composing poem or a self-conjuring watch? Could anything be less self-explanatory than an Oscillating Universe, eternally bellowing in and out like some cosmic accordion, or an Inflationary Multiverse, endlessly frothing away like a just-uncorked bottle of Veuve Clicquot? Why such an absurdly busy cosmos? Why any cosmos at all, whether finite or infinite?
Why not nothing?
Interlude
Night Thoughts at the Café de Flore
“Et pour vous, monsieur? Du café? Une infusion?”
The waiter posed the question in a tone of weary impatience. It was, after all, nearly closing time at the Café de Flore, on a late-winter night in Paris. The evening had been a hefty one, and I felt I needed something more fortifying than the options proposed. My companion, an aging but handsome voluptuary named Jimmy Douglas, suggested, as an alternative, a strongly alcoholic herbal concoction I had never heard of. It would, he insisted, buck up my liver.
It certainly seemed to have worked for him. Despite a life of riotous excess and free indulgence of his voracious and irregular appetites, Jimmy had remained preternaturally youthful. Friends called him Dorian Gray. (It perhaps helped that, as an heir to the Quaker Oats fortune, he did not have to toil for a living.) In the 1950s, he was the paramour of Barbara “poor little rich girl” Hutton, taking up with her after her fifty-three-day marriage to the international playboy/diplomat/polo-star Porfirio Rubirosa (a tough act to follow). In the 1960s, Jimmy threw a joint party for the Beatles and the Rolling Stones in his grand apartment in the Faubourg Saint-Germain, which adjoined that of a former French prime minister. Now, decades later, he was regaling me with stories of Baron Gottfried von Cramm and Nancy Mitford and the Aga Khan, and urging me to decamp from New York to Paris, where, he claimed, the nightclubs were better and the bacterial flora kept one eternally young.
Sipping the bracingly pungent herbal stuff the waiter had brought me, I looked around the Flore. At that hour, the café was hardly the “fullness of being” described by Sartre. At a table in the back I spotted Karl Lagerfeld, with his characteristic ponytail, dark glasses, and high white collar, in hushed conversation with one of his muses, who was wearing what looked like black lipstick. Other than that, the place was pretty much empty: le Néant.