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Should I have been worried? Is three plane crashes in eight days surprising enough that we should suspect flying is getting more dangerous? David Spiegelhalter, Winton Professor for the Public Understanding of Risk from Cambridge University, says not. Three plane crashes in eight days might seem highly unlikely, but statistical analysis shows that the chances of this happening at some point in any ten-year period is actually pretty high – around six in ten, more likely than not.
What does randomness look like, really?
The fact is, true randomness doesn’t look like what we think randomness looks like. Any truly random process will end up having clusters (see the linked article for a nice statistical explanation, if that’s your kind of thing). Just like stars randomly distributed across the night sky end up forming groups, if plane crashes occur randomly over ten years, sometimes two or three will end up falling close together. When Apple first released the iPod Shuffle, people complained that the “random shuffle” wasn’t random enough – they would sometimes hear the same song twice in a row. In fact, Apple’s mistake had been to make their shuffle function truly random – meaning it paid no attention to whether a song had been played recently or not, and so would sometimes play the same song twice. They later changed their “random shuffle” to be less random so that it would seem to users to be more random. Talk about crazy.
Why we’re bad at noticing randomness
All those worried Facebook statuses actually tell us more about human psychology than they do about the danger of flying. Why are we so bad at noticing true randomness? Why do we see patterns and clusters and assume something more suspicious must be going on? Part of the problem is that we seem to be wired to look for patterns in things even where they don’t exist. The human brain also seems to have a strong tendency to attribute agency to things – to assume that randomly occurring events must have been planned or caused by someone.
There’s a convincing evolutionary argument for how we developed this tendency. Suppose you lived thousands of years ago, and one day, you hear a rustling sound in the bushes nearby. Maybe it’s a predator; maybe it’s a gust of wind. If you run away screaming and it turns out it was a gust of wind – or worse still, one of your cave-mates playing a trick on you – you might feel a bit silly and suffer a few weeks of teasing. On the other hand, if you reason it’s probably fine and decide to hang around – doing whatever it was our ancestors did when hanging around in bushes – and it turns out you’re wrong, it’s a predator…Well, you might not be so lucky. I know who I’d rather be. And it’s pretty clear who is going to stick around long enough to pass on their mildly neurotic genes.
The other reason we fail to see randomness for what it is is that we focus on the clusters and ignore the much bigger picture in which they occur. If you throw a die five times, and get five sixes in a row, that’s pretty surprising. It’s a lot less surprising if you throw the die a thousand times and get five sixes in a row at some point. If your dating strategy is to pick a random person from the street and you find someone you’re perfectly matched to the first time, you’re a lot more justified in believing in fate than if it takes you several years of somewhat awkward encounters with strangers. Because we focus on the patterns – the string of sixes, that person we just met with whom we have so much in common – and not the wider picture – the astonishing number of dates we had to go on to meet him or her – we find the patterns more surprising than we should. I’m not saying the stars didn’t align to bring you together, just that probabilistically, you were going to meet someone you liked sooner or later.
It makes sense that humans might evolve a tendency to see clusters in randomness and dream up deep explanations for or causes of events that are actually entirely random. But while this tendency was clearly useful in a predator-heavy ancestral environment, it may be more costly in the present day. It certainly made me much more afraid of flying that day than I had reason to be.