Pascal’s Wager (A Different Calculus)

Blaise Pascal was a mathematician who is best known for making a special wager.

His famous wager was this: Pascal said that each of us bets with our lives whether an afterlife exists. Given the possibility that an afterlife does exist and, assuming an infinite gain or loss associated with belief or unbelief in said afterlife (as represented by an eternity in heaven or hell), any rational person should live as though an afterlife exists and seek to believe in God who will reward him or her with a pleasant afterlife (based, presumably, on a Judeo-Christian understanding of what permits entry into heaven and hell).

By the standards of its day, Pascal’s wager displayed an unconventional rationalism. Rather than assuming that the Catholic view of God and a moral life was the right way to live, Pascal considered the possibility that one could choose to live another, less moral life (from the Catholic perspective). Pascal thus assessed the wisdom of living in accordance with the Catholic faith against the risks of choosing a different path. And he concluded that the rational choice was to do what was necessary to give one’s self a chance at the Catholic version of the afterlife.

Today, we know a few things that Pascal did not. And so I’d like to make a few modifications to Pascal’s wager. In light of what we’ve learned over the past 350 years, we should reassess Pascal’s odds that the Judeo-Christian understanding of heaven and hell is correct. I won’t pretend to know the odds with any certainty, but I do think it’s worth expressing skepticism over how Pascal handicapped the odds. Based on his wager, Pascal assumes that the existence of a Catholic heaven and hell is as likely as not. Given the size of the universe, I think we should reconsider those odds. It’s doubtful that Pascal appreciated how small the earth is in proportion to the size of the universe. It’s estimated that there are about 200 billion galaxies with 1,000,000,000,000,000,000,000,000 planets. As such, any particular narrative-based explanation of heaven and hell from the creatures on any one planet, from a stochastic perspective, commands only an atom-compared-to-Mt. Everest’s chance of reflecting reality.

Let’s consider a thought experiment to explain what I mean here. Imagine if you were to discover a previously unknown-to-the-outside-world civilization in Papua New Guinea. After spending a few months with the tribe, you learn their language and many of the customs. The members of the tribe then share with you their version of a creation myth, an elaborate story about a great bird, the sun, and a prophet from a prior era. You enjoy the stories, but you don’t put much credence in the creation myth. After all, what are the odds that this remote tribe with little technology or connection to anything with the outside world has direct insight into the origins of the universe?

From an outsider’s view, it’s much less than an even-odds proposition. It’s doubtful that Pascal would have suggested that we bet our lives by living in accordance with the principles of this tribe’s religion.

There are, by a factor of billions of billions, more planets than there are tribes of people on this planet. Now, imagine an alien race from one of those planets observing our civilization from another galaxy. They would probably consider the stories of Jesus and Mohamed in much the same way that we view the tribe’s stories about the great bird, the sun, and the prophet. What are the odds that this remote tribe on this small and distant planet has direct insight into the origins of the universe? Of course, we don’t know if there alien races on other planets. If there is no intelligent life on other planets, Christianity would be the most popular religion in the universe. Maybe that means that Christianity’s vision of an afterlife is more probable than the tribe’s in Papua New Guinea. But popularity seems a strange measure by which to judge the merits of a religion. Pascal’s wager wasn’t based on Christianity’s popularity, it was based on his belief that it was the divine truth of God. And if we take Christianity’s popularity as a religion as a reflection of divine providence, then we should reflect on what that might mean down the road. Demographers estimate that there will be more Muslims than Christians by the end of the century. If that happens, does that mean that Christianity is less likely to be the ultimate truth?

Ultimately, Pascal’s wager is just a bet on the home team. He’s like any other homer who goes to Vegas to bet on his guys to win the World Series. Pascal’s wager isn’t about a rational calculation of the odds. Rather, it’s a bet that his experience, his biases, and his culture’s stories reflect reality.

None of this is to say that Pascal was wrong. Sometimes you win when you bet on the home team. If you believe that you’re the center of the universe, then your explanations of the universe may carry some weight. Maybe your home team does perform better when you wear your lucky jersey and you sit on your favorite chair. But if you recognize that you’re probably not the center of the universe, the calculus changes. With that, the odds of our own ancient stories explaining the origins universe become vanishingly small.