The fact that 86 percent of Americans believe in God is well known. Less well known is that, according to a 2001 Gallup poll, 46 percent of Americans with postgraduate degrees think the Bible “answers all or most of the basic questions of life.” It’s a startling figure if you’ve attended graduate school in the last quarter century — for nowhere is belief in divine inspiration, or in divinity itself, more often pooh-poohed than in masters and doctoral classrooms. This, despite the fact that the smartest people in history have believed in a Higher Power. Socrates. Plato. Aristotle. Augustine. Maimonides. Aquinas. Da Vinci. Copernicus. Newton. Jefferson. Einstein. What unites them is not faith in the Judeo-Christian God, or even in a personal god, but rather in a divine presence whose existence somehow sustains the natural world.

Float the idea that God sustains the world in a graduate-school seminar, however, and it’ll likely be met with rolling eyes . . . or else, more politely, with a Joseph Campbell-style rationalization, a kind of anthropological group hug that translates: Naturally, the idea that God sustains creation is true and wonderful insofar as all myths are true and wonderful. But what if you argued that God’s sustaining of the world was literally true? In that case, you’d get roughly the same reaction as someone who insisted that Santa Claus really was making his lists and checking them twice.

So here’s a thought experiment: Suppose I toss a coin in the air. The odds are exactly equal it will land heads or tails. Suppose, then, it lands heads. If I toss the coin again, do the odds change? No, the fact that the coin landed heads the first toss has no effect on the second — the name given the superstition that the first toss affects the second is “The Monte Carlo Fallacy.” Even in the unlikely event that the coin turned up heads twelve times in a row, on the thirteenth toss the odds would still be exactly equal. I can never, in short, predict the very next toss based on what’s happened before. Paradoxically, however, if I toss the coin a million times, I know the outcome will be half heads and half tails. Though individual tosses are unpredictable, and though no previous toss affects a subsequent toss, the result of many tosses is certain in advance; it’s so certain, indeed, that if the result didn’t turn out equal, I’d know the coin had been tampered with.

Question: How does predictability emerge from unpredictability? How is it possible that no single coin toss affects another, yet the cumulative weight of many tosses somehow binds together independent outcomes?

The agnostic reply is that it’s the law of averages. Yet that only begs the question, only assigns the phenomenon a name. The deeper issue is why the law of averages works. What unseen will shepherds the coin through the indifference of individual tosses, never letting it stray too far from the necessity of its fate? The necessity holds, moreover, whether one coin is tossed a million times, or a million coins are tossed simultaneously; the result will be half heads and half tails.

Likewise, on a subatomic level, quantum physics instructs us that we cannot predict the behavior of individual electrons, but the concerted behavior of billions of them is certain. Indeed, the very fabric of the universe depends on the seemingly inexplicable working out of such probabilities.

It was just such an insight, long before quantum theory, that led Aquinas to argue that God’s creation of the world shouldn’t be understood as a one-time event — what we’d now call the Big Bang — but as an ongoing creation that underwrites the world as it is. It’s God’s ongoing creation, in effect, that ensures probabilities become actualities over the long haul. The English theologian Richard Hooker called God’s sustaining principle “the law of nature” and asked, rhetorically, “See we not . . . that obedience of creatures unto the law of nature is the stay of the whole world?”

But of course we’re less concerned, and rightly so, with the behavior of tossed coins or subatomic particles than with human behavior. So much fashionable agnosticism notes the beastly ways people act towards one another and asks if it’s possible, or even worthwhile, to believe in a God who allows terrible events to occur. The traditional response to such objections has been that God gave people free wills — and that freedom entails the possibility of bad outcomes. But if that’s the case, if people are really free, is God really in control?

The British physicist-theologian John Polkinghorne has recently suggested a way to understand this paradox — how God might have made people free yet still held absolute sway over his creation.

Polkinghorne likens the fate of individual lives to the behavior subatomic particles — or, for that matter, to coin tosses. What happens to one person is inherently unpredictable. But what happens in the aggregate is absolutely determined. That is, you and I are free to create our own fates. But the course of history, the outcomes of multitudes of fates, is subject to God’s guiding hand. In this view, good triumphs over evil in the long run for the same reason that order emerges from the seeming chaos of electrons or that coin tosses eventually come out even. All are manifestations of God’s ongoing creation of the world.

We can also reconcile the paradox if man really have no free will.

But most would recoil at this idea, for it immediately destroys all concepts and consequences of accountability, and raises the spectre of chaos and anarchy and lawlessness.

There is however another possible position, namely that of restricted free will: you can freely will but only over a restricted set of actions or options, and for which you can be held accountable, and for which the conseqences are attributable to your will in some direct but limited way.

Using a mathematical analogy, if free will is a function F, then man is restricted to only a certain domain, say the close interval [0,1] and not from minus infinity to plus infinity. Further the function F may have a restricted mapping, let say it is F’, perhaps it cannot exceed a certain upper value, for example.

Now then you may ask what is the meaning of all these?

Well maybe it is to educated us as to what free will really is, ironic as it may be. It is like a child or a student in school, where toys or laboratory problems are used to teach before he gets out into the real world.