Zero - Charles Seife [39]
—BLAISE PASCAL, PENSÉES
Pascal was a mathematician as well as a scientist. In science Pascal investigated the vacuum—the nature of the void. In mathematics Pascal helped invent a whole new branch of the field: probability theory. When Pascal combined probability theory with zero and with infinity, he found God.
Probability theory was invented to help rich aristocrats win more money with their gambling. Pascal’s theory was extremely successful, but his mathematical career was not to last. On November 23, 1654, Pascal had an intense spiritual experience. Perhaps it was the old Jansenist antiscience creed that was building up in him, but for whatever the reason, Pascal’s newfound devotion led him to abandon mathematics and science altogether. (He made an exception for a brief time four years later, when he was unable to sleep owing to illness. He started doing mathematics and the pain eased. Pascal believed that this was a sign that God was not displeased with his studies.) He became a theologian—but he could not escape his profane past. Even when it came to arguing about God’s existence, he kept coming back to those crass gambling Frenchmen. Pascal argued that it was best to believe in God, because it was a good bet. Literally.
Just as he analyzed the value—or expectation—of a gamble, Pascal analyzed the value of accepting Christ as savior. Thanks to the mathematics of zero and infinity, Pascal concluded that one should assume that God exists.
Before considering the wager itself, it is easy to analyze a slightly different game. Imagine that there are two envelopes, marked A and B. Before you are shown the envelopes, a flip of the coin determined which envelope has money in it. If the coin toss was a heads, A has a brand-new $100 bill inside. If the coin came up tails, B has the money—but this time, it’s $1,000,000. Which envelope should you choose?
B, obviously! Its value is much greater. It is not difficult to show this using a tool from probability theory called an expectation, which is a measure of how much we expect each envelope to be worth.
Envelope A might or might not have a $100 bill in it; it has some value, because it might have money in it, but it isn’t worth as much as $100, because you’re not absolutely sure that it contains anything. In fact a mathematician would add up all of the possible contents of envelope A and then multiply by the probability of each outcome:
The mathematician would conclude that the expected value of the envelope is $50. At the same time, the expected value of envelope B is:
So the expected value of B is $500,000—10,000 times as much as the expected value of envelope A. Clearly, if you are offered a choice between the two envelopes, the smart thing to do is to choose B.
Pascal’s wager is exactly like this game, except that it uses a different set of envelopes: Christian and atheist. (Actually, Pascal only analyzed the Christian case, but the atheist case is the logical extension.) For the sake of argument, imagine for the moment that there’s a 50-50 chance that God exists. (Pascal assumed that it would be the Christian God, of course.) Now, choosing the Christian envelope is equivalent to choosing to be a devout Christian. If you happen to choose this path, there are two possibilities. If you are a faithful Christian and there is no God, you just fade into nothingness when you die. But if there is a God, you go to heaven and live for eternity in bliss: infinity. So the expected value of being a Christian is:
After all, half of infinity is still infinity. Thus, the value of being a Christian is infinite. Now what happens if you are an atheist? If you are correct—there is no God—you gain nothing from being right. After all, if there is no God, there is no heaven. But if you are wrong and there is a God, you go to hell for an eternity: negative infinity. So the expected value of being an atheist is:
Negative infinity. The value is as bad as you can possibly get. The wise person would clearly choose Christianity