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.