It All Adds Up

It all comes down to the numbers - at least it does according to Dr. Ric Crossman. You’d be amazed at what can be explained by fractions, decimals, percentages and statistics; let Dr. Ric guide you…

There is no creature or concept in this world or any other more evil than an octopus.

I am not even slightly kidding. Even seagulls are less villainous, and those beady-eyed sociopaths would happily shank you for half a soggy chip. They’d probably crash your funeral, too, so long as there was a buffet; squawking meanly as they viciously lunged at anyone who tried to reach for the salmon rolls.

Octopuses are much, much worse. Fiendishly clever, natural problem solvers, masters of disguise, able to do that Eugene Toombs squeezing thing (how fortunate for mankind the octopus has yet to develop a taste for human livers); they’re terrifying. If anything is going to rise up against mankind and claim the Earth, it won’t be the chimpanzees. It’ll be octopuses, marching implacably along our streets on two pairs of legs whilst firing their strange cephalopodic weapons with the other four.

In other words, I was quite scared enough of octopuses before the Germans discovered they were clairvoyant. With this latest revelation, I’m pretty sure our civilisation is doomed. Probably best to start crossing calamari off the menus now, before it’s too late. Yes, I know: calamari is technically squid. You think that distinction will save you? Plus, whilst we’re arguing about this, an octopus is stealing your car.

After all, that’s the kind of mean trick an octopus would pull. Note the cruelty in the subject Paul has chosen for his demonstration of psychic prowess: football. How like a malicious mollusc to simultaneously terrify and taunt us. I mean, what have we got that could possibly beat an octopus at football? Eight snakes? How would we train them to stay in formation?

Except... Maybe this isn’t quite as bad as it looks. I mean, seven consecutive predictions of what is essentially a binary variable – Germany wins or it doesn’t* – is a good track record, but it’s hardly staggering. If Paul’s unwitting human serfs had just tossed coins for each match rather than disturb their slumbering kraken, they would have had a 1 in 128 chance of doing just as well (in addition to saving the lives of fourteen perfectly good shellfish). Maybe Paul just got really lucky.

Whilst we’re on the subject, did he actually get as lucky as it appears? I’m no journalist, but I’d bet all the money in my pockets that “Octopus fails to predict match result” isn’t a headline anyone was itching to write. Perhaps there are dozens of other octopod clairvoyants who even now toil away in obscurity, their comparatively spotty track records condemning them to mass media disinterest. I might even feel a twinge of pity for them, if I wasn’t so sure they wanted to stick their tentacles in my ears and work me like a podgy meat-puppet.

The important point here is that, so far as I can tell, the press – the international press, at any rate – only took an interest in Paul after he already had three successes under his belt (not that octopuses wear belts, though I guess they could make one from their own tentacles to hold up trousers made from human skin). If an Alaskan grizzly had done as well by savaging specially marked salmon, or a tree sloth had eaten the right sequence of painted leaves over an eighteen hour period, the articles would have been about them instead. I’ve no idea exactly how many of these bizarre alternatives to coin tosses were carried out (don’t any of these fauna-aided purveyors of precognition have real jobs?), but you’d only need eight of them before you’d expect at least one to get through the group phase with perfect accuracy.

This means, of course, that by the time the eyes of the world were focussed on Paul’s murky aquarium he needed to predict only four more results correctly in order to be crowned the world’s most miraculously prescient mollusc (Mystic Moll?). So whilst - to return to a previous column - you could model this situation using a binomial distribution, with seven trials (the seven matches), and fixed probability of success each time (1/2, unless Paul really does have some kind of access to the space-time continuum, and further is prepared to waste that gift by alternately placating and enraging the German people), it doesn’t really apply here. What we’re interested in is how far the octopus gets before he makes his first mistake. This is modelled by what we call a geometric distribution; you keep running the trials one by one, until the first failure. Only here, you have who knows how many of those processes running at the same time, but you only get to hear about the one that’s been delivering the goods.

One of the big mistakes people make when considering probability is a generalised version of this issue. They’re told how many times something has happened and are amazed by the figure, without stopping to think about how many times it would need to have happened before anyone bothered to tell them about it in the first place. Or perhaps they’ll focus on the specific event they’ve witnessed, rather than all the other similar events that would incur the same reaction. Have you ever travelled to a new city, miles from home, only to run into someone you knew? Did it strike you as strange, or even uniquely unlikely? “What were the chances of meeting Pete here?”, you might have asked yourself. Well, probably pretty small, but you’d also be asking that question had you met Sally, or Dave, or Anna, or anyone from the hundreds of people you know or at least recognise.

Paul is just one predictor amongst tens of thousands. In fact, given the way he was presented with his choices, it’s just as likely something else was doing the selecting in any case. A soccer-savvy aquarium cleaner, maybe. Hell, they might actually have been using coin tosses the whole time after all, but were smart enough to realise “Coin comes down heads seven times in a row” isn’t something anyone could give the faintest damn about.

Just think about that for a second. Seven successful coin tosses is a total non-event. Seven random surely, surely random – predictions by an octopus are enough to encourage national mourning and Argentinian death threats. There are more serious and depressing examples of the media’s ability to manipulate the way people conceive of randomness and probability, but I’m not sure there’s a clearer one.

In summary, then: sometimes it’s important to not get too carried away. Now, if you’ll excuse me, I need to check my car is still where I left it.

* I’m cheating here, since there are three possible results in a group game. On the other hand, I’m cheating under the assumption that Paul’s keepers would have cheated too. If there had been a draw, one imagines they would have pointed to, say, ball possession as a way of arguing one team had the best of it.