A couple of Chronicles ago I mentioned Blaise Pascal’s idea of the “two infinities,” a conception that can be said to inaugurate the era of modernity. For despite the limited nature of microscopes and telescopes in the 17th century, Pascal intuited that now that we had become able to see microbes on the one hand and Jupiter’s moons on the other, there would be ultimately no limit in either direction. This simple intuition has held up surprisingly well, to the extent that recent discoveries seem increasingly to suggest that physicists looking for a definitive “theory of everything” are barking up the wrong tree.
Pascal was a serious Christian, a Jansenist, who made use of his investigations into the science of probability to redefine religious faith in a way that strikes me as equally unshakeable: Since the validation of this faith would provide benefits incommensurable with those of the everyday world, we should be willing to bet on God’s benevolent existence even were there only an infinitesimal chance that the bet would be successful.
Perhaps an easier way to envisage this wager would make use of the “St. Petersburg Paradox,” where one flips a coin until tails turns up and receives 2 to the power of the number of consecutive heads. It is easy to see that the “expectation” of this action is infinite: ½ the time one gets $1, ¼ the time, $4, 1/8 the time, $8… thus $1 + 1 + 1… ad infinitum. But we all know that the gambler cannot afford to pay the infinite expectation for one or any number of chances. What this “expectation” really means is that if you keep playing the game long enough, no matter what fixed payment you give each time, the payoff will eventually come out in your favor—the catch being that the number of games you’ll need before you come out ahead also approaches infinity.
On this analogy, our bet on God is the equivalent of the coin never turning up tails: although its chances of happening are infinitesimal, the payoff is infinite.
In any case, we must remember that Pascal was both a brilliant mathematician and a sincere believer, and that he saw this kind of reasoning as demonstrating less the “truth” of his belief in God than the advantage to the gambler of making the bet, which he therefore considered a way of demonstrating to the religious skeptic, given the infinite difference between death and eternal life, the necessity of making it.
I think that in our age, when so many of us are at best agnostic, Pascal’s logic offers the closest we can come to a “demonstration” of the validity of religious belief—which, translated into strictly anthropological terms, can simply be understood as betting that, in terms of the human species to which we belong, “life is worthwhile.”
And put in these terms, the necessity of making a deliberate act of affirming such belief becomes unnecessary. Whether we do so or not, the idea that a benevolent God protects the human race from destruction and chaos has only one real argument in its favor—the fact of our survival itself.
After all, “something”—call it Providence—has kept our species alive through the generations, and the mechanism through which this force is actuated, whether through a conscious divine will analogous to our own, or by a set of conditions determined by chance, is unknown to us. And to assume that humanity will continue to endure does not imply that we should sit back and do nothing, but that we should continue making our usual efforts at more than mere survival, and keep hoping that they will succeed—and this is true regardless of the nature of the reassurance we receive from the external conditions of our existence.
Pascal’s point is valid whether we “believe” in anything at all beyond the worldly realities we have experienced and the deductions we have been able to draw from them. What I must insist on is that 400 years ago, when science had just begun to suspect the “two infinities” of possible experience—a phenomenon that can be imagined along other dimensions than space and time that we may eventually learn of—the situation of faith was already fully defined. Pascal’s reasoning is independent of how many dimensions of ignorance we suffer from. His point is simply that we cannot know for certain what the future has in store for humanity, but we can only bet on the chance that in place of some indifferent Fate, there is a benevolent force—even if a purely statistical one—that will keep humanity going—or failing that, a universe that will continue to generate self-conscious, creative beings like ourselves.
For at the very least, the reason we are here at all is that, given enough billions of years, the Darwinian survival of the fittest forms of matter/energy evolved from even the most undifferentiated original state will produce beings as complex as ourselves. And given trillions and quadrillions of years, who can imagine what marvels might arise?