We've all experienced a highly improbable event in our lives. Probably many, in fact. Some of us more than others, some more seemingly improbable than others. There is such a thing as the Law of Large Numbers that explains these coincidences and "miracles".
The Law of Large Numbers simply stated (sans math): with a large enough sample many odd coincidences are likely to happen.
Coincidence: an occasion when two or more similar things happen at the same time, especially in a way that is unlikely and surprising.
Miracle: an unusual and mysterious event that is thought to have been caused by a god, or any very surprising and unexpected event.
On a side note, I was disappointed with Dictionary.com's listing on these words so I thought I'd go to the Cambridge Dictionary. The definition above is from the Dictionary of British English. Out of curiosity, I looked up the word miracle in the Cambridge Dictionary of American English:
Miracle: an unusual and mysterious event that is thought to have been caused by God, or any surprising and unexpected event.
A very subtle but telling difference! I think I'll be using the British version from now on.
Anyway, I digress, again! I like how the definition of miracle is either caused by god, or (moving the goalposts) unexpected. Those are two very different kinds of events. One is something supernatural, manipulated by god's hand. The other is something merely surprising. And yet the definition combines them, basically rendering it rather meaningless.
So let's get to the numbers that Michael Shermer shared in his article. He says:
I cannot always explain ... specific incidents, but a principle of probability called the Law of Large Numbers shows that an event with a low probability of occurrence in a small number of trials has a high probability of occurrence in a large number of trials. Events with million-to-one odds happen 295 times a day in America.
Shermer quotes CERN physicist Georges Charpak and University of Nice physicist Henri Broch from their book, Debunked!: ESP, Telekinesis, and Other Pseudoscience:
In the case of death premonitions, suppose that you know of 10 people a year who die and that you think about each of those people once a year. One year contains 105,120 five-minute intervals during which you might think about each of the 10 people, a probability of one out of 10,512 — certainly an improbable event. Yet there are 295 million Americans. Assume, for the sake of our calculation, that they think like you. That makes 1/10,512 × 295,000,000 = 28,063 people a year, or 77 people a day for whom this improbable premonition becomes probable. With the well-known cognitive phenomenon of confirmation bias firmly in force (where we notice the hits and ignore the misses in support of our favorite beliefs), if just a couple of these people recount their miraculous tales in a public forum (next on Oprah!), the paranormal seems vindicated. In fact, they are merely demonstrating the laws of probability writ large.
So, for example if 23 random people are asked their birthdays, there is a 50% chance that at least 2 of them celebrate the same birthday. It may seem like an amazing coincidence, but it's not amazing at all.
Then Michael Shermer refers to a review of the above book by another physicist, Freeman Dyson. He talks about Littlewood's Law of Miracles:
“In the course of any normal person’s life, miracles happen at a rate of roughly one per month.” Dyson explains that “during the time that we are awake and actively engaged in living our lives, roughly for eight hours each day, we see and hear things happening at a rate of about one per second. So the total number of events that happen to us is about thirty thousand per day, or about a million per month. With few exceptions, these events are not miracles because they are insignificant. The chance of a miracle is about one per million events. Therefore we should expect about one miracle to happen, on the average, every month.”
So a miracle is basically a one in a million event, according to Littlewood who was a University of Cambridge mathematician. And we all have about a million little events in our lives every month. So we all get a miracle a month, or thereabouts (actually 35 days). See how cool math is? Of course, a miracle a month is rather commonplace, isn't it?
Then, when observing and reporting events, there is the ever present loom of confirmation bias and anecdotal evidence, which is not very reliable, if at all.
One thing I've never understood is when people see Jesus or Mary in bird poop or a pizza pan or a stump. (Basic everyday pareidolia, of course). Nothing special happens except that they recognize a face in a random pattern. But before you know it a shrine is constructed and people are kissing the bird poop and praying at the stump. Not being religious, I find this completely silly, but they are True Believers. Does the miracle follow the sighting? I never hear about anyone claiming a bonifide miracle from one of these sightings. (Then again, no true miracle has ever been verified, not scientifically). And Mary needs a better agent if she's reduced to showing up in bird poop, but that's just my humble opinion.