The Probability of a Miracle

Golfers probably heard this story months ago. But I’m not a golfer, so I heard about it only a couple of nights ago on the local news. It seems that three friends were out playing golf together and scored back-to-back-to back holes-in-one on the same hole. Someone calculated the odds against this happening to be 27 trillion to one. Of course, a lot of people didn’t believe them, so they paid $4,000 out of their own pockets to undergo polygraph testing that proved that they weren’t lying about their claim.

What do I think about this? First of all, I think that if their claim is true, it’s one of the most amazing things I’ve ever heard. In fact, it’s so darn amazing that it strikes me as virtually impossible. I’m more inclined to believe that the polygraph results were false for some reason or other than I am to believe that three men went to a golf hole and scored consecutive holes-in-one.

What could have been wrong with the polygraph result? The person administering the test may have been bribed to report that the claim was not a lie. Or he (or she) may have been incompetent. Or the machine may have been malfunctioning. Or the men may have found a way to defeat the machine. Or they may have all have succumbed to the delusion that they shot consecutive holes-in-one when they really didn’t. In this case, they wouldn’t be lying in the sense of deliberately telling a falsehood as truth, and the machine would not detect them to be lying even though they weren’t telling the truth.

None of these possibilities seem very probable, and some seem more improbable than others. But none seem remotely as improbable to me as what these men claim that they did on that golf course.

But this raises an interesting issue for me. Just how do mathematicians go about estimating the probabilities of events such as these, and how accurate are these estimates? I guess it’s relatively easy to estimate the probability of a fair coin flipped in a fair way coming up heads on the next flip, but what about estimating the probability of a particular raindrop falling on the precise spot that it does, or of long-lost Uncle Elmer calling at a particular date and time, or of the universe as we know it existing, or of three men hitting back-to-back-to-back holes in one on the same hole?

Speaking of probability estimates, I’ve been watching a new series on CBS called Numb3rs. It’s about a mathematics prodigy and professor who helps his FBI agent brother solve and prevent crimes by using complex mathematical analyses and probability predictions. It strikes me as mostly nonsense, but intriguing nonsense that performs the valuable service of making math and intellect appealing to people, especially young people who have subsisted for far too long on an entertainment junk diet of mindless sitcoms, “reality” shows, and gun-blasting action programs. I can’t help but think that more than a few young men and women will be inspired by Numb3rs to go into math and science, and that this is surely a good thing.