Called "Littlewood's Law of Miracles," after British mathematician John Edensor Littlewood, the man who first codified it in this way, it goes something like this:
- Let's say that a "miracle" is defined as something that has a likelihood of occurring of one in a million.
- We are awake, aware, and engaged on the average about eight hours a day.
- An event of some kind occurs about once a second. During the eight hours we are awake, aware, and engaged, this works out to 28,800 events per day, or just shy of a million events in an average month. (864,000, to be precise.)
- The likelihood of observing a one-in-a-million event in a given month is therefore 1-(999,999/1,000,000)1,000,000 , or about 0.63. In other words, we have better than 50/50 odds of observing a miracle next month!
So, like the Hallmark cards say, Miracles Do Happen. In fact, they're pretty much unavoidable.
Peter Paul Rubens, The Miracle of St. Ignatius (1617) [Image is in the Public Domain]
You hear this sort of thing all the time, though, don't you? A quick perusal of sites like Miracle Stories will give you dozens of examples of people who survived automobile accidents without a scratch, made recoveries from life-threatening conditions, were just "in the right place at the right time," and so on. And it's natural to sit up and take notice when these things happen; this is a built-in perceptual error called dart-thrower's bias. This fallacy is named after a thought experiment of being in a pub while there's a darts game going on across the room, and simply asking the question: when do you notice the game? When there's a bullseye, of course. The rest is just background noise. And when you think about it, it's very reasonable that we have this bias. After all, what has the greater evolutionary cost -- noticing the outliers when they're irrelevant, or not noticing the outliers when they are relevant? It's relatively obvious that if the unusual occurrence is a rustle in the grass, it's far better to pay attention to it when it's the wind than not to pay attention to it when it's a lion.
And of course, on the Miracle Stories webpage, no mention is made of all of the thousands of people who didn't seem to merit a miracle, and who died in the car crash, didn't recover from the illness, or were in the wrong place at the wrong time. That sort of thing just forms the unfortunate and tragic background noise to our existence -- and it is inevitable that it doesn't register with us in the same way.
So, we should expect miracles, and we are hardwired to pay more attention to them than we do to the 999,999 other run-of-the-mill occurrences that happen in a month. How do we escape from this perceptual error, then?
Well, the simple answer is that in some senses, we can't. It's understandable to be surprised by an anomalous event or an unusual pattern. (Think, for example, how astonished you'd be if you flipped a coin and got ten heads in a row. You'd probably think, "Wow, what's the likelihood?" -- but any other pattern of heads and tails, say, H-T-T-H-H-H-T-H-T-T -- has exactly the same probability of occurring. It's just that the first looks like a meaningful pattern, and the second one doesn't.) The solution, of course, is the same as the solution for just about everything; don't turn off your brain. It's okay to think, at first, "That was absolutely amazing! How can that be?", as long as afterwards we think, "Well, there are thousands of events going on around me right now that are of equally low probability, so honestly, it's not so weird after all."
All of this, by the way, is not meant to diminish your wonder at the complexity of the universe, just to direct that wonder at the right thing. The universe is beautiful, mysterious, and awe-inspiring. It is also, fortunately, understandable when viewed through the lens of science. And I think that's pretty cool -- even if no miracles occur today.
In 1983, a horrific pair of murders of fifteen-year-old girls shook the quiet countryside of Leicestershire, England. Police investigations came up empty-handed, and in the interim, people who lived in the area were in fear that there was a psychopath in their midst.
A young geneticist from the University of Leicestershire, Alec Jeffreys, stepped up with what he said could catch the murderer -- a new (at the time) technique called DNA fingerprinting. He was able to extract a clear DNA signature from the bodies of the victims, but without a match -- without any one else's DNA to compare it to -- there was no way to use it to catch the criminal.
The way police and geneticists teamed up to catch an insane child killer is the subject of Joseph Wambaugh's book The Blooding. It is an Edgar Award nominee, and is impossible to put down. This case led to the now-commonplace use of DNA fingerprinting in forensics labs -- and its first application in a criminal trial makes for fascinating reading.
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