## Saturday, May 26, 2007

### The Map: Probability and Miracles

Suppose we consider an event that is extremely unlikely. Resurrection is a good one. About 10 billion people have lived, and none have been resurrected. That means we can put the odds of being resurrected at about 1 in 10 billion.

Then someone claims that a prophet was resurrected, and that this resurrection is so improbable that it must be a case of divine intervention that validates the divine nature of the prophet.

However, the probability that someone makes up such a story in any 100 year period is close to 100% (because every century has its own bizarre fictions). Let's say that a story is so peculiar that we think the story unusual. Let's say that the story is so bizarre that we think it a one in a million shot.

Well, we will find that there's a 1 in a million chance that the miracle is made up, and a one in 10 billion chance that the story is true. That makes for a factor of 10,000 against the miracle.

If we are rational, we have to conclude that the miracle did not occur. It might have occurred, but the odds are so small that it's not worth our consideration.

In general, we conclude that any deity who tries to communicate with us using such one-time miracles is hoping we'll be irrational.

Objections

The objection to this claim is that, since Jesus is the son of God, resurrection is not improbable for him.

This is a ridiculously circular argument. Let's go back to step one:
someone claims that a prophet was resurrected, and that this resurrection is so improbable that it must be a case of divine intervention that validates the divine nature of the prophet.
It is because Jesus was resurrected that Christians believe Jesus is the son of God. The so established divine status of Jesus cannot then be the reason why we think he was resurrected in the first place.

Another objection is that my argument rules out resurrection as a divine intervention ever being persuasive. However, this objection goes nowhere as long as the deity keeps on doing the resurrections under laboratory conditions. Yes, I have difficulty believing that illusionist David Copperfield actually made the Statue of Liberty disappear. It's too improbable a miracle. And yet with enough evidence, the statistical weights can be moved, and I can be convinced that Copperfield has the powers he pretends to have. The same goes for God.

Finally, they point out that my argument doesn't disprove the Resurrection with certainty. True, but there are lots of things that are 10,000 to 1 against that we don't believe in. So why believe in the Resurrection?

Stumbling Blocks

Authority, perhaps? The Bayesian argument for the Resurrection was recently described (wrongly) by William Lane Craig, a highly respected figure in Christian circles. I don't think Christians want to call him on this atrocious attempt at statistical argumentation.

Nevin ":-)" said...

Let me state this argument another way:

Suppose we consider an event that is extremely unlikely. Winning the 55 ball Powerball is a good one. We can put the odds of winning the big jackpot at about 1 in 147 billion (an order of magnitude less likely than being resurrected).

If we are rational, we have to conclude that winning the Powerball did not occur. It might have occurred, but the odds are so small that it's not worth our consideration.

Of course, that isn't a rational argument at all, since the Powerball is won on a fairly regular basis. It would be irrational of me to believe that I am going to win it, but it is very rational of me to believe that it will be won by somebody.

Doctor Logic said...

Hi Nevin,

The odds you're quoting are off. It's one in 146million, not billion. Someone in the U.S. wins from time to time because there are, on average, 146 million plays for each winner.

We can also imagine how we would discover the odds if the Powerball mechanism was unknown. Imagine that the Powerball machine is a black box that either spits out a winner's ticket number or it doesn't. In that case, you could compute that the Powerball odds were about 1 in 146 million based on empirical data.

Now, let's imagine another scenario. Suppose that we had been playing black-box Powerball for thousands of years, and no one had ever one, despite billions of plays. Further suppose that someone claimed that, 2000 years ago, an Iron Age guy won, but lost his ticket before he could cash it in. Do we believe the claim? What if the claim is fairly commonplace, and all of the recent claims that were resolved turned out to be lies or delusions? I think it would be irrational to conclude that the story of the Iron Age lottery winner was true.