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Probability Theory and the End of the Age

July 8, 2009

I read a book about zero while I was in Reno. (When my wife asked me what it was about, for once I could justify telling her, “oh, nothing”!) I don’t have much of a math brain, but Charles Seife’s book Zero: The Biography of a Dangerous Idea was absolutely captivating. This post isn’t so much about the book as a whole, but about one idea in it that got me thinking about the end of the age.

Chapter 4 introduces us to “the theology of zero.” Here we meet mathematician-turned-theologian Blaise Pascal. Before he encountered God on November 23, 1654, Pascal had invented a whole new brach of mathematics: probability theory. (Now those of you who have suffered through a statistics class know who to thank!) After his conversion, he took these tools, originally designed to help French aristocrats win more with their gambling, and used them to argue for the wisdom of believing in God.

Here was the gist of his argument, what came to be known as Pascal’s Wager. Imagine you are presented with two envelopes. The one marked “A” might have $100 in it, the one marked “B” might contain $1,000,000. A coin toss before you see them will determine which envelope has money in it. Which envelope should you choose?  Even people who haven’t studied probability theory would most likely answer “B”! Here is how those who have would explain why that is a good idea: each envelope has a value, but since we aren’t sure it will contain any money that value isn’t the full $100 or $1,000,000, but rather the sum of all possible contents. So envelope “A” has a 50% chance (heads) of being empty ($0) and a 50% chance (tails) of having $100. The mathematical equation (called an expectation) to determine the expected value of envelope “A” would look like this:

1/2 x $0 = $0

1/2 x $100 =$50

So 0 + 50 = $50. This is the expected value of envelope A.

The value of envelope B would be: 1/2 x $0 = $0

1/2 x $1,000,000 = $500,000

And $0 + $500,000 = $500,000. So clearly the smart choice is envelope B, with an expected value some 10,000 times greater than the expected value of envelope A!

When Pascal turned this formula from gambling to theology, he reasoned like this: Imagine that there is a 50/50 chance that God exists. So our two envelopes here are not “a” and “b” but “Atheist” and “Christian.” If you chose the Christian envelope, there are two possibilities. Either you are right and enjoy eternal life when you die, or you are wrong and fade to nothingness. So the expected value of being a Christian is:

1/2 chance of fading into nothing…1/2 x 0 = 0

1/2 chance of enjoying eternal life…1/2 x infinity = infinity

The expected value of this decision is infinite because half of infinity is still infinity! Thus the value of being a Christian is infinite! Now, what happens if you chose the atheist envelope? If you are correct and there is no God, you gain nothing from being right. Since there is no God and therefore no heaven or hell, you just fade away when you die. On the other hand, if you are wrong and there is a God, your choice will condemn you to endure eternal hell – negative infinity! So the expected value of being an atheist is:

1/2 chance of fading into nothing…1/2 x 0 = 0

1/2 chance of going to hell…1/2 x negative infinity = negative infinity. Negative infinity! The value of this choice is as bad as you can possibly get. The wise person, argued Pascal, would clearly chose Christianity over atheism. The wisdom of this choice is only reinforced as you realize that the value of this equation does not rest on the assumption that there is a 50/50 chance of their being a God. The odds can be 1/1000 or 1/10,000 or 1/1,000,000 or one in a gazillion. Because we are dealing with infinity, which by definition means you can take away as much as you want and its value remains unchanged, the infinite value (positive or negative) never changes. Unless you are prepared to argue (which even most avowed atheists are not) that there is a 0% chance that there is a God, it will always prove infinitely wiser to believe that there is, than that there isn’t.

Oddly enough, this post isn’t about evangelism, it is about the end of the age. My question as I was reading this chapter was if it could prove helpful to recruit Pascal’s Wager to answer some of the longstanding eschatological disputes within the church. We argue, among other things, about the reality or timing of the “final generation”, about the reality or nature of the millennium and about the reality or timing of the rapture. Of course, we should turn to Scripture rather than mathematics to answer these questions, but when we do we find each position well fortified with “proof” texts and well stocked with “problem” texts to unleash at the advancing hordes. Has Pascal’s probability theory pointed a way around the current stalemate – where everyone agrees the issues being considered carry massive implications, and everyone admits there is at least a slight a chance their conclusions are wrong?

Since this post is already too long, let’s test the benefit of this approach by applying it briefly to one aspect of the rapture question. To remind ourselves: if the pre-trib camp is right, the church is taken before things on earth get really bad; if the mid-tribbers are right, the church endures the first 3.5 years but gets to avoid the really bad final half of the 7 years, which the post-tribbers believe the church will endure both as objects of satan’s rage and participants with God in the release of His judgments and in-gathering of His harvest.

Thinking along the lines of Pascal’s Wager, it seems to me that a pre-tribber risks significantly more than a post-tribber if you imagine that both are wrong; since they would then have to navigate enduring a tribulation that they were not prepared for (mentally, spiritually, emotionally, physically) and avoiding a tribulation they were prepared for, respectively. I’m not sure what mathematical value you would assign to each possibility to churn out an equation, but the logic seems compelling to me. I suppose to complete the wager you would have to analyze not only what both sides risk in being wrong, but what they could possibly gain by being right. For example, how would you compute and compare advancing His Kingdom and sharing in His sufferings on the earth at the close of this present age (the post-tribber) over against getting to heaven and receiving the fullness of your inheritance some 7 years earlier (the pre-tribber)?!

The weakness of this whole approach is that it could turn our Bible reading and Bible obeying into a pragmatic, “logical” affair. This would be to miss the point that (1) in Scripture we have to do, not with a series of data points but with a Person; and (2) there will be plenty of times we are called to obey commands that don’t make any “sense” if you graph them on a cost-benefit analysis. But because there are so many good, Bible-loving people lined up on both sides of these end-times issues, and  because very few would be so presumptuous to say they have it 100% right, it might not hurt to think through these questions from this angle – what you gain from being right vs. what you lose by being wrong.

Let me know – do you find any wisdom in this wager?


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  1. tvd permalink

    I like this approach; as far as you stated we can take it. I have always look at it through the eyes of the Boys Scouts, “Be Prepared”. The Christian, I think, has nothing to lose by preparing their life for enduring the Tribulation. Learning how to love Christ in the midst of suffering, casting off idols, worshiping the only True King, etc. That sounds to me like the “normal” Christian life we are asked to live out in the New Testament.

  2. ashleyrobi permalink

    We as humans will tend towards believing what makes us feel safe and comfortable. However, our belief in something is not what makes it real or not real. Excellent point you make in this entry. I think this reasoning may be very helpful in conversations in the future. 🙂

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