Coincidence and meaning
A friend and loyal reader of Skeptophilia sent me a link to an interview with author Sharon Hewitt Rawlette about her recent book, The Source and Significance of Coincidences, along with a note saying, "Would love to hear your thoughts about this."
I'm usually loath to give my opinion about a claim after reading a summary, book review, or interview without reading the book itself, but considering that I had issues with just about everything in the interview I can say with some confidence that it's unlikely the book would make me any less doubtful. Rawlette's idea is that coincidences -- at least some of them -- "mean something." Other than two events coinciding, which is the definition of coincidence. Here's how she defines it:
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?"
Coincidences can certainly be startling, I'll admit that. I was on my way to an appointment a while back and was listening to Sirius XM Radio's classical station "Symphony Hall," and one of my favorite pieces came on -- Beethoven's Moonlight Sonata. I was maybe two-thirds of the way through the first movement when I arrived, and I was short on time so regretfully had to turn the music off and get out of the car.
When I opened the door to the waiting room, there was music coming over the speakers. Beethoven's Moonlight Sonata -- at almost precisely the same spot where I'd turned off the radio.
Immediately, I wondered if they were also listening to Sirius XM, but they weren't. It was the usual selection of calming music you hear in doctors' offices everywhere. It really had been... "just a coincidence."
But did it mean anything? How would I know? And if it did mean something... what?
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 a random selection on a classical music station being the same as the selection playing in a doctor's office at the same time 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 coins twenty times each. With the first coin, you get twenty heads in a row. With the second coin, you get the following:
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 is that here -- as with Rawlette's coincidences -- we're only assessing their probability after the fact. In our coin flip patterns above, after they happen the probability that they happened is 100%. I'll agree with her insofar as to say that in the first case (twenty heads in a row), I'd want to keep flipping the coin to see 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 billion times -- the chance of their 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, of course, is that we run smack into our old friend dart-thrower's bias -- our hard-wired tendency to notice what seem to us to be outliers. We don't pay any attention to all the times we walk into the doctor's office (or anywhere else) and the music playing isn't what we were just listening to, because it's just so damn common. The times the music is the same stand out -- and thus, we tend both to overcount them and weigh them more heavily in our attention and our memories.
Rawlette also doesn't seem to have any sort of 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. 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 Neil deGrasse Tyson put it) "poor data-taking devices... full of ways of getting it wrong." 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.
I think one of the most important things, when you experience a coincidence, is to keep an open mind about where it’s coming from and what it might mean. Because it’s very easy to try to fit a coincidence into the way of thinking about the world that we already have—whatever our worldview is. And coincidences generally come into our lives to expand that worldview. They generally won’t fit neatly into the boxes that we have. We might try to shove them in there, so we can stop thinking about it and make them less mysterious, but they generally are going to make us question some things that we thought we knew about the world.What this puts me in mind of is the odd pastime of being a "Randonaut" -- using a random number generator to produce a set of geographical coordinates near you, going there, and looking for something strange -- about which I wrote a couple of years ago. People report finding all sorts of bizarre things, some of them quite disturbing, while doing this. I won't deny that it's kind of a fun concept, and no intrinsically weirder than my wife's near-obsession with geocaching, but it suffers from the same problems we considered earlier when you try to ascribe too much meaning to what you find. If you're told to go to a random location and look around until you find something odd, with no criteria and no limitations, you're putting an awful lot of confidence in your own definition of "odd." And, as I point out in the post, in my experience Weird Shit is Everywhere. Wherever you are, if you look hard enough, you can find something mysterious, something that seems like a coincidence or a message or (at least) a surprise, but all that means is you had no real restrictions on what you were looking for, and that the world is an interesting place.
- Assume that there are some numbers that are uninteresting.
- Let "x" be the first such number.
- Since being the first uninteresting number is itself interesting, this contradicts our initial assumption, and there are no uninteresting numbers.