The Psychology of Coincidence

One old urban myth tells a story about a man running to work who had forgotten his tie. His wife found the tie where he left it at home and quickly tried to ring him on his work phone in order to tell him to come back and get it if he wanted it.

As she called though, she miss-typed the number and instead called a nearby payphone. As it just so happened however, the payphone she called was actually the payphone just outside his office. Out of curiosity, the tie-less man answered the phone on his way past and lo and behold: he got the message.

Coincidences like this can often leave us wondering if there aren’t greater forces at play. Or at least they make great stories for us to tell down the pub. In fact, there is nothing special about even the most unlikely of coincidences and all they really do is to shine a light on our psychology and the susceptibility of the human brain to be fooled.

Here we will look at why coincidences are in fact not all that strange and at why our brains are still amazed by them nevertheless…

Patterns and Coincidences

Firstly, it is useful to consider that the human brain is designed in order to identify patterns. This is something that we do particularly well, because it has great survival value. Noticing patterns allows us to predict what is about to happen, which in turn allows us to avoid danger and catch prey.

Thus we are constantly looking for patterns and connections and that in turn means that we will sometimes see them where they don’t exist. For instance, if we notice rocks in the formation of a face on the surface of Mars, we will see this as a pattern even though it’s just a collection of rocks (and it doesn’t help that the human brain is also designed to look for human faces).

In fact, we are so prone to seeing connections where they don’t exist, that there’s even a term for it: ‘apophenia’.

One of the most amusing examples of apophenia in action, was when Apple received complaints that the shuffle feature on their iPods wasn’t really ‘random’. Users complained because they kept hearing the same song repeated in a sequence – which of course is random. Apple actually had to redesign their shuffle feature with an algorithm in order to make it feel more random, while in actuality it was no longer random at all…

Unseen Connections

But we’re also not perfect at doing this and thus we don’t always consider all of the elements at play. For instance, the above story is a lot less amazing when you consider the fact that phone numbers in the same areas are more similar. This then means that it’s very easy to accidentally call the number of a payphone right near the building that you were actually trying to call.

It’s still relatively unlikely that he would be walking past at that exact moment, but it’s actually a lot less unlikely. The other day I caught myself singing the theme tune of an old TV show that hadn’t aired for years, only to later notice and advert for it on the side of a bus. That might seem like a coincidence, until you consider the possibility that I might have noticed the advert earlier that day but just have failed to consciously register it.

Sometimes we see connections where there are none and falsely attribute something to coincidence. Other times we don’t see the connections and the same thing happens.

The Law of ‘Near Enough’

Have you ever heard that playing The Wizard of Oz and Pink Floyd’s Dark Side of the Moon at the exact same time results in a perfectly synched experience? That almost seems to line up perfectly so that the audio exactly matches the film?

This is a result of what we call the ‘law of near enough’. While they might sync ‘pretty well’, the two do not really sync ‘perfectly’ by any means. Nevertheless, the human brain so enjoys coincidences and patterns that we are happy to accept that this is an almost ‘magical’ coincidence because it’s ‘close enough’.

This is partly why predictions of the future by people such as Nostradamus seem so accurate. These predictions are famously vague and obtuse and as such they can fit ‘near enough’ in describing a vast range of events that have really transpired.

Cognitive Biases

Sometimes our brain thinks something is a coincidence simply because of a bias in our thinking. Our brains are wired in a certain way that sometimes makes them easy to fool. These ‘flaws’ in our logic are called ‘cognitive biases’ and they can often be responsible for our perception of coincidences. Here are some examples:

Gambler’s Fallacy

Gambler’s fallacy is the reason that we expect to throw a heads after we’ve thrown a tails ten times in a row. We expect this to be the case because it’s so unlikely to throw heads 11 times in a row. But what we’re forgetting is that physics isn’t taking those previous throws into account and thus we are actually just as likely to throw heads as we are tails – it’s always fifty, fifty.

Imagine if you used a computer to generate random numbers and those numbers were the Fibonacci sequence. You’d probably be somewhat amazed, but bear in mind that the likelihood of that happening is exactly the same as the likelihood of any other random sequence of numbers occurring. Just because we have assigned significance to that particular sequence, doesn’t mean that it’s any less likely to occur.

Confirmation/Selection Bias

When I was younger I became determined that I was able to make lampposts turn off when I walked underneath them. The reason? Five times in the past, I had walked underneath a lamppost, only for it to magically turn off just as I passed underneath it. I looked online and found there were actually communities of people who all believed they had this power.

But my more rational friend told me to make certain by waiting by the lamppost after I walked past. It turned out the lamppost was just faulty and was flickering – as is common for lampposts. Thus there was a good chance it would turn off as I walked underneath it.

More damning was the fact that the hundreds of thousands of other lampposts I walked under didn’t turn off. But because of something called ‘confirmation bias’, I only took notice of the times that it did turn off. In confirmation bias or ‘selection bias’ we take notice of things that support our hypothesis because they are note-worthy and memorable and we ignore all the evidence contrary to the hypothesis.

Another example is the Great Pyramid in Giza. Did you know that the latitude of the pyramid is the exact same number as the speed of light? The speed of light is 299792458 m/s while the latitude of the pyramid is 29.9792458 degrees North.

But this is less amazing when you consider that the pyramid is quite large and that actually that number is picking a very precise point on the pyramid – only the first four digits are the same by pure chance. Furthermore, there are countless other numbers in science and countless other historical buildings. If these two didn’t line up, then another two likely would. That’s confirmation bias at its best!

The Law of Truly Large Numbers

The above is also an example of the ‘law of truly large numbers’. When you have huge numbers involved, it becomes far more likely that there will be some noteworthy relationships and occurrences. We mentioned earlier how it was perfectly possible for the Fibonacci sequence to appear at random. Taking this further, the likelihood of that sequence occurring at random would increase more and more the more numbers you looked at. You might be surprised if it occurred the first time you generated some random numbers, but if you generated billions of random numbers, then you should be considerably less surprised. Thus it should follow that it wouldn’t be a ‘coincidence’ if someone happened to have a phone number was a ‘noteworthy number’. Especially when you consider the aforementioned fact that there are billions of noteworthy numbers.

In fact, you could consider that there are billions of things happening on the planet all the time to billions of people. So in fact coincidences aren’t strange at all, it would be much stranger if coincidences never happened.

And yet our brain still loves them because that’s the way our psychology works. Which is kind of great when you think about it: we’re hardwired to see magic in the mundane.

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