“You may believe that spiritual experiences are just illusions,” said the Priest, “but I know what I have felt and experienced. And I could never deny it.”

“This isn’t about your ability to deny your feelings and experiences,” I explained. “The question is: do your feelings and experiences constitute good evidence? And the answer is, no, they do not. They don’t always mean what we think they mean, and we can be fooled.”

“Okay,” said the Priest, “in all fairness, I can see how some of my spiritual experiences might have been coincidence. But there’s no way I could dismiss all of them as pure coincidence.”

I’ve heard a few people say this. What they’re saying is that they’ve had experiences where something happened that seemed a) spiritually appropriate in some way, and b) too unlikely to have happened by pure chance.

But notice the assumption: that we can guess the likelihood of an event, and tell when an event is less likely to happen than random chance.

The truth, however, is just the opposite: People are rotten at guessing probabilities, especially when the probabilities are very small. It doesn’t come naturally to us.

Here’s a test you may have heard before. Which is more likely: getting killed by a shark, or getting killed by falling airplane parts?

It’s airplane parts, by thirty to one. We overestimate the risk of shark attack because we have all heard examples of shark attack. This is a cognitive quirk called the availability heuristic; events seem more likely if we can easily recall examples of them. An interesting demo here.

Another one: you’re more likely to die by a meteor impact than by lightning.

Probability of death

Asteroid/comet impact 1 in 20,000
Flood 1 in 30,000
Hit by lightning 1 in 10,000,000

I must confess, that meteor stat surprised me. Here’s the explanation:

What is the approximate probability of a given person being killed by a meteorite?
1 in 20,000. If this statistic sounds incredibly high given that you’ve probably never heard of anyone who was killed by a meteorite, it’s because the data is skewed. Every so often an impact large enough to wipe out just about all life on Earth occurs, and in between times, pretty much no one is killed by a meteorite. So while you have a 1 in 20,000 chance of being killed in this manner, the statistic is not much different for the entire population of Earth combined. If an asteroid large enough to kill people hits, it will probably kill a lot more than a few; but there’s a 19,999 in 20,000 chance that it won’t happen in your lifetime. Hence the statistic. If I had asked what the probability was of any given person being individually STRUCK by a meteorite, the answer would be astronomically higher.

We can use statistics to calculate the probability of events that have happened. And in fact, in natural language processing we calculate the probability of unseen events using a range of techniques under the heading of smoothing. But this doesn’t come naturally to our reptile brains.

The fact that lotteries exist shows that people are awful at probability guessing. Religious belief is often sustained by erroneous guesses about the likelihood of events.

Note: I am aware that my sources are a bit contradictory on the relative probability of lightning vs. tornado. Different estimates are probably due to different assumptions.