Coincidences and miracles

Do unlikely synchronicities "mean anything?"

My wife and I recently took a long road trip, and to pass the time she’d downloaded a variety of podcasts and audiobooks to listen to. We started with an old favorite, Radiolab, a long-running podcast whose eclectic offerings suit my rather all-over-the-place interests perfectly.

The episode we began with is called “The Bad Show,” and is about the spectrum of bad behavior from the banal to the truly evil. It explored why people do bad things—and more specifically, the strange mixture of good and evil we humans so often are. One of the individuals used as an example was the curious figure of Fritz Haber, a German chemist whose most striking accomplishment was the invention in the first part of the twentieth century of the Haber process, a chemical synthesis pathway that turns atmospheric nitrogen into ammonia. It’s the first step in the production of chemical fertilizers, and because of this he is widely credited with saving the burgeoning world population from starvation.

But.

One gets the feeling that Haber didn’t do it out of any warm feelings toward his fellow humans. He comes across as icy and perhaps amoral—that he’d created his invention more to prove that it could be done than because of the good it would do. I’d learned about the Haber process in my college chemistry class, but I didn’t know the rest of the story—that Haber also figured out a way to weaponize chlorine gas, and his deployment of that process to the front lines during World War I earned him the moniker of “the father of chemical warfare.” He also developed an insecticide called Zyklon A—a variant of which, Zyklon B, was the main poison used in the gas chambers during the Holocaust.

Chilling stuff.

Anyhow, this seemed like grim listening, so after few minutes of this we opted to switch to something a little more upbeat. One of the audiobooks Carol had downloaded was a science fiction/fantasy story called The Harbingers, about people who suddenly find out they can do magic, so we started chapter one. And about ten minutes in, the main character—an anthropology professor who is in consultation with a lawyer over an as-yet undisclosed crime—is strongly objecting to the lawyer’s contention that no one in academia has ever done real good for the world as a whole. The anthropologist gets angry, and brings up an example…

…Fritz Haber.

And there it was, the entire story again, not a half-hour after we heard about it on Radiolab. Haber’s saving the world from starvation, with the lawyer’s rebuttal going into the atrocities Haber was directly responsible for during World War I and afterward.

I got a sudden sense of surreality, and looked over at Carol, who seemed equally perplexed. I said, “Did we just experience a glitch in the Matrix?”

[Image licensed under the Creative Commons Karry manessa, Coincidence with Smile, CC BY-SA 4.0]

Coincidences can be bizarre and startling, especially ones like this one—where we heard twice in a half-hour’s time about a story neither of us had ever heard before. And some people think they Mean Something—in the cosmic sense, not just that “weird things happen sometimes.” Author Sharon Hewitt Rawlette certainly thinks so, and goes into great detail about it her recent book, The Source and Significance of Coincidences:

For me, a coincidence is something that is not blatantly supernatural. It could be just chance. But there’s part of you that says, “This seems more meaningful than that.” And maybe just seems a little too improbable to be explained as chance. It seems too meaningful to you, personally, given where you are in your life. It’s something that makes you wonder, “Is there something more?”

So strange coincidences, according to Rawlette, are significant. If you buy her argument, our running into Haber twice meant something. But if so... then what? How do you tell the difference between some random repetition, and something more meaningful?

Rawlette tells us what her criteria are:

I don’t think there’s a really cut and dry answer. There are a variety of factors that I look at in my own life when I’m trying to figure out whether something is just a coincidence or something more. One of those is how improbable it really is... But I also think an important element is how you feel about it. What is your intuition telling you? How strongly do you feel about it? And is it telling you something that really seems to help you emotionally? Spiritually? Is it providing you with guidance?

Here, we’re moving onto some seriously shaky ground.

First of all, there’s improbability. How do you judge that? I’d say that the probability of hearing about a particular German chemist on two unrelated podcasts is pretty damn low, but that’s just a hand-waving “seems that way to me” assessment. Amongst the difficulties is that humans are kind of terrible at statistical reckoning. For example, let’s say you throw two fair coins twenty times each. With the first coin, you get twenty heads in a row. With the second coin, you get the following:

HTTHHHTHTHTTHHHTHTTH

Which one of those two occurrences is likelier?

It turns out that they have exactly the same probability: (1/2)^20. A very, very small number. The reason most people pick the second as likelier is that it looks random, and comes close to the 50/50 distribution of heads and tails that we all learned was what came out of random coin-flips back in the seventh grade. The first, on the other hand, looks like a pattern, and it seems weird and improbable.

The second problem with peculiar coincidences is that we’re only assessing their probability after the fact. Like with the coin-flip example, it’s only after it happens that we say, “…wait, what?” I’ll agree with Rawlette’s approach insofar as to say that in the first case (twenty heads in a row), I’d want to keep flipping the coin to find out what would come up next, and if I keep getting heads, to see if I could figure out what was going on. The second, corresponding much more to what I expected, wouldn’t impel me to investigate further.

But the fact remains that as bizarre as it sounds, if you throw a (fair) coin a huge number of times—say, a trillion times—the chance of there being twenty heads in a row somewhere in the array of throws is nearly 100%. (Any statisticians in the studio audience could calculate for us what the actual probability is; suffice it to say it’s pretty good.)

Third is that we run smack into a cognitive phenomenon called dart-thrower’s bias—our hard-wired tendency to notice what seem to us to be outliers. The name comes from a thought experiment. Imagine you’re at a bar chatting with some friends, and over on the other side is a group of strangers playing darts. When do you notice the darts game?

The answer, of course, is when one of the players does something unusual—scores a bullseye, or misses by a mile and skewers the bartender in the forehead or something. Otherwise, it just forms part of the background noise of the experience, and we ignore it completely. Likewise, we don’t pay any attention to all the times we listen to two different podcasts in a row and they’re about entirely different topics, because that experience is so damn common. The times the topic is identical stand out—and thus, we tend both to overcount such experiences, and weigh them more heavily in our attention and our memories.

It reminds me of the amusing statistics of “Littlewood’s Law of Miracles,” named after British mathematician John Edensor Littlewood, the man who first codified it. Littlewood’s Law 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 0.632. In other words, we have better than 50/50 odds of observing a miracle next month!

Of course, this is some fairly goofy math, and makes some silly assumptions (one discrete event every second, for example, seems like a lot). But Littlewood does make a wonderful point; given that we’re only defining post hoc the unlikeliness of an event that has already occurred, we can declare anything we want to be a miracle just based on how surprised we are that it happened. And, after all, if you want to throw statistics around, the likelihood of any event happening that has already happened is 100%.

So, like the Hallmark cards say, Miracles Do Happen. In fact, they’re pretty much unavoidable.

Rawlette, of course, would reject this argument out of hand. The problem is, she doesn’t seem to have any rigorous criteria for telling the difference between random coincidence, meaningful coincidence, and something that is a deliberately targeted “sign” or “message” directed at you personally, other than how you feel about it:

I think the most impactful coincidences in people’s lives tend to be most improbable. It’s very hard to explain them away. But, the counterpart to that is that those coincidences also seem to have a very strong emotional impact on us. They’re not only very improbable—very strange—but they carry a very strong emotional weight. And we can’t escape that they’re significant somehow, even if we’re not exactly sure what the message is. And, often, they do turn out to be life-changing.

So you are estimating how likely something is, assessing whether it was likely after the fact, deciding what the event’s significance is, and deciding what the message (if any) consisted of. It’s putting a lot of confidence in our own abilities to perceive and understand the world correctly, isn’t it? And if there’s one thing I’ve learned from years of teaching neuroscience, it’s that our sensory/perceptive and cognitive systems are (as astrophysicist Neil deGrasse Tyson put it) “poor data-taking devices... replete with ways of getting it wrong.” Hell, I don’t trust my own brain most of the time. It’s got a poor, highly-distractible attention span, an unreliable memory, and gets clogged up with emotions all too easily. It’s why I went into science; I learned really early that my personal interpretations of the world were all too often wrong, and I needed a more rigorous, reliable algorithm for determining what I believed to be true.

Now, I won’t say I’m never prone to giving emotional weight to events after the fact. As an example, I was quite close to my Aunt Pauline, my grandfather’s youngest sister (youngest of twelve children!). Pauline was a sweet person, childless and ten years a widow, when I was going to college at the University of Louisiana. Every once in a while—maybe every two or three months or so—I’d stop by her house on the way home from school. It wasn’t far out of the way, and she was always thrilled to see me, and would bring out really amazing coffee and a tray of cookies to share as we chatted. One day, it occurred to me that it’d been a while since I’d seen her. I don’t know why she came to my mind; nothing I can think of reminded me. I just suddenly thought, “I should stop by Aunt Pauline’s and see how she’s doing.”

So I did. She was cheerful as ever, and we had a lovely visit.

Two days later, she died of a heart attack at age 73.

I don’t think I’d be human if the thought “how strange I was impelled to visit her!” didn’t go through my mind. But even back then, when I was twenty years old and much more prone to believe in unscientific explanations for things, it didn’t quite sit right with me. I visited with Aunt Pauline regularly anyhow; it certainly wasn’t the first time I’d gotten in my car at the university and thought, “Hey, I should drop by.” I had lots of other older relatives who had died without my being at all inclined to visit immediately beforehand. The “this is weird” reaction I had was understandable enough, but that by itself didn’t mean there was anything supernatural going on.

I was really glad I’d gotten to see her, but I just didn’t—and don’t—think I was urged to visit her by God, the Holy Spirit, the collective unconscious, or whatnot. It was simply a fortuitous, but circumstantial, coincidence.

Anyhow, all this rambling is not meant to destroy your sense that the universe we live in is mysterious and beautiful. It is both, and much more. I am just exceedingly cautious about ascribing meaning to events without a hell of a lot more to go on than my faulty intuition. I’d much rather rely on the tried-and-true methods of science to determine what’s out there, which for me uncovers plenty enough stunningly bizarre stuff to occupy my mind indefinitely.

On the other hand, if today I flip on the radio and hear about Fritz Haber again, I’ll happily reconsider my stance—all arguments about the statistics of flipping twenty heads in a row notwithstanding.