Why we shouldn’t be so in awe of coincidences
There is an old meme that lists a seemingly eerie number of coincidences between the lives and deaths of Abraham Lincoln and John F Kennedy. On the surface of it, it seems a dazzling series of spooky coincidences, but as you work your way through them one by one fact-checking, you realise that some of them are plain not true, others are entirely superficial (the number of letters in a name), and others really aren’t that big a coincidence because there aren’t that many options (for example, both men had to die on one day of the week, so the fact that they were both shot on a Friday shouldn’t really be that surprising). Nonetheless, it’s easy to be blown away by the sheer weight of coincidences when written down on a page.
I was reminded of this when I attended Robert Matthews’ talk at New Scientist Live, in which he reminded his audience that not only do long-shot coincidences happen, they aren’t as unlikely as they would first appear.
Matthews began by taking a novella titled Futility, published back in 1898, which documents the sinking of the world’s largest ship on its maiden voyage from England to New York. The ship in the book – Titan – was called “unsinkable” and yet was eventually sunk when it hit an iceberg.
Fourteen years later, a real-life “unsinkable ship” – the Titanic – sunk in near-identical circumstances. The number of similarities between the fictional and real ship seem simply uncanny: they had the same number of propellers; they were described as roughly the same length (800ft vs 882ft); and they were even struck by the iceberg on the same side of the ship.
“We see glimmerings here of how we can be fooled by coincidence,” explained Matthews, pointing out that one by one, the coincidences aren’t really all that. If you’re making a book about the biggest ship ever made, for example, you have to ground it in reality, so is it really so surprising they ended up at a similar length to what was built 14 years later?
Likewise, a big ship needs a big name, which limits the similes further. “SS Midget isn’t going to cut it really, is it?” asks Matthews. A lexicon of hundreds of thousands of words shrinks to single figures when only suitable terms are considered, so it’s hardly surprising the vessels shared similar-sounding names. And as for the iceberg? “Even at the time back in the 1890s, there was concern about the threat of icebergs. So clearly, given that jellyfish aren’t going to sink a boat like that, we’re running out of alternative fates for the ship.”Likewise, coincidences do happen, especially when you view them in context. Take former England cricket captain Nasser Hussain’s 14-long run of losing coin-tosses. As Matthews points out, he’d been in 45 test matches alone, not to mention all the club cricket he’d been in, and all the other cricket played around the world. Coincidences do happen from time to time, and because they’re exceptional we tend to take notice.
“We tend to think of randomness as nice, smooth and even in the long run, and as soon as we see clusters of events we think ‘woah, there’s something weird going on here,’” explains Matthews. “But random phenomena are very capable of generating amazingly long streaks – as lots of people have discovered on roulette tables in Las Vegas.”
“Next time you’re watching a football match, bet a friend that any two of the players on the pitch will have a birthday within a day of each other”
Speaking of gambling, there is a way you can turn humanity’s tendency to be dazzled by statistics to your advantages – not at the bookies, Matthews is keen to add (“good luck with that”), but against friends. It plays off a phenomenon known as the birthday problem. Next time you’re watching a football match, bet a friend that any two of the players on the pitch will have a birthday within a day of each other.
It sounds like a ridiculous long shot, but the odds are actually far more stacked in your favour than our brains are trained to notice, at around 89% – far better odds than you’d get betting on the winner of the match. “There are lots of opportunities to bring about that coincidence,” explains Matthews. “We’re giving it loads of chances to appear.”
To demonstrate it, Matthews used the recent Manchester United vs Manchester City and Rangers vs Celtic matches. In each of those, he found two winning combinations in each. Pitting all four teams against each other with the same line-ups in an imaginary league, he demonstrated at least one match in every single head to head – and four of those on exactly the same day. “If you’re rugby fans, definitely go for it – because the probabilities there are off the scales!” A nice way to get your ticket cost back if you find someone who will fall for it.
In fact, when it comes to probability in general, Matthews thinks it’s a good idea to “follow the money”. Remember the Bermuda Triangle superstition of the 1970s and 80s? As he points out, that area is actually around 1,000,000 square kilometres of sea and airspace, giving plenty of scope for unusual things to occur. “Ask an insurer – they’re not interested in superstition, they’re just interested in the facts. And when Lloyd’s of London looked at this, they left the premiums just the same.”
New Scientist Live runs for the next four days at the ExCeL Centre in London. Tickets are available here.