Psychic Octopuses

So the big news these days is obvi­ously Paul the Psy­chic Octo­pus. Def­i­nitely inter­est­ing. It was able to main­tain a 100% suc­cess rate in this year’s World Cup (and a much higher suc­cess rate than it had in 2008 where it mis­pre­dicted a whop­ping two matches).

So what’s going on here? Freak coin­ci­dence? Super­nat­ural pow­ers? At a first glance, both sound ridicu­lous to me.

But I want to think about the more “inter­est­ing” expla­na­tion a bit: per­haps Paul really is psy­chic. Per­haps Paul can tell the future.

And then what? What does that really tell us? Does it answer our prob­lem? Say we have a psy­chic octo­pus. It could show us any­thing. It could’ve pre­dicted the finan­cial cri­sis, it could have pre­dicted the death of Michael Jack­son, it could have given us next week’s lot­tery num­bers. And yet this psy­chic octo­pus chose to show us the World Cup results of all things.

Why? Was there some sig­nif­i­cance behind this? Is God telling us that the World Cup is impor­tant? That we should for­get about oil leaks and bank bailouts and cli­mate change, and instead focus on who won the World Cup? That seems unlikely. Why would God, or any­one else, care about that? Or are we back where we started, that it’s just a freak coin­ci­dence that they chose to pre­dict the World Cup, rather than the hun­dreds of other sport­ing events?

Does it mean that our lives are pre­de­ter­mined, that Spain had to win, that we have no free will? Or does it mean that Paul was able to con­trol events? Per­haps Spain could have lost, but Paul exerted his mighty Psy­chic will and gave them the vic­tory. (Is that cheat­ing? Does it count as dop­ing perhaps?)

How did Paul know the results? Read­ing people’s thoughts wouldn’t help, unless some­one else also knew the results. Per­haps he can sim­ply see into the future. But is he intel­li­gent? Is he able to choose what to report back to us? Could he have cho­sen to instead arrange stones at the bot­tom of his aquar­ium into the shape of the next week’s lot­tery num­bers? How did he know what it was we were ask­ing him to pre­dict? All Paul saw from us were two boxes with food in them, and a dif­fer­ent flag on the top of each. How did Paul fig­ure out “they must be ask­ing about who will win the World Cup”? For that mat­ter, how did he deter­mine that we would inter­pret it as “the box I open indi­cates the win­ning team”? He could just as well have meant it was the team that was going to lose (he’s tak­ing their food, after all)

The prob­lem is that in order to explain any­thing, it is not enough to say that Paul has psy­chic abil­i­ties. We have to assume that Paul is an intel­li­gent psy­chic octo­pus, that we live our lives along pre­de­ter­mined paths (unless Paul is able to con­trol us) and that Paul has an inter­est in soc­cer specif­i­cally, and fig­ures that of all the things he could reveal to us, the results of each World Cup match is what mat­ters. And we’re still not able to say any­thing about how he man­ages to make these predictions.

Taken together, those assump­tions makes the “super­nat­ural” expla­na­tion sound at least as unlikely as call­ing it a pure sta­tis­ti­cal coincidence.

I’m gen­er­ally a pretty skep­ti­cal per­son. I don’t believe in Gods, magic, ghosts, spir­its or any­thing super­nat­ural. Not because I’m sure none of it exists, but because it seems so absurdly unlikely for those spe­cific beliefs to be true. Let’s say there really is some­thing to the belief in ghosts. How do we know what it is? When you hear weird noises in an old house, how do you know it is the ghosts of dead peo­ple specif­i­cally? Per­haps instead the house itself is alive. Per­haps it’s the peo­ple who live in it in some alter­nate dimen­sion? Per­haps it’s the Mar­tians remote-controlling lit­tle dust clouds to mess with us. Believ­ing in the super­nat­ural isn’t an easy way to dodge the ques­tions we can’t answer. Instead it just makes the prob­lems big­ger. Instead of explain­ing “Last night, I heard some­one breath­ing even though I was home alone”, we now have to explain why some­how dead peo­ple are able to walk around here with us, and they’re able to make noises and for some rea­son they can think of noth­ing bet­ter to do than breath­ing heav­ily in my house. We have to explain how dead peo­ple come to be here (and that means we have to explain what hap­pens to us when we die), and we have to explain how they can manip­u­late the world of the liv­ing. Some­how, they’re simul­ta­ne­ously insub­stan­tial and invis­i­ble, and at the same time, able to make noises, or flick light switches or throw small objects around?

I think it was a lot sim­pler to explain back when it was just “I heard a weird breath­ing noise and I have no clue what it was”

Just like I’d rather have to come up with a plau­si­ble expla­na­tion for an octo­pus through ran­dom chance man­ag­ing to pre­dict World Cup matches, than hav­ing to do the same for the idea that the octo­pus can tell the future, is intel­li­gent, cares about soc­cer, and cares about let­ting us know the result of soc­cer matches. Oh, and that the future is fixed and we can do noth­ing to change it.

Cor­rectly guess­ing the out­come of 8 matches is pretty unlikely. Assum­ing it has a 50/50 per­cent chance of cor­rectly guess­ing the out­come of each match (which sounds likely, given that octo­puses prob­a­bly don’t know much about soc­cer), the odds of this are 0.39%.

That’s low, very low, but not impos­si­ble. Sta­tis­ti­cally, one out of 256 octo­puses should man­age such a 8/8 suc­cess rate. Pretty lucky then that it hap­pened to be Paul who got it right.

But that’s not quite right. Sta­tis­tics don’t work like that. Paul made a num­ber of pre­dic­tions before he got famous, which were what brought him to our atten­tion in the first place. The mir­a­cle here isn’t that he pre­dicted 8 matches. Paul only really became famous when he pre­dicted that Ger­many would beat Eng­land. If he can keep guess­ing cor­rectly, we might start won­der­ing if there’s some­thing going on. But of course it’s going to look mirac­u­lous if we include past results. If you roll a die long enough, you’re going to get, say, four 6’es in a row. It’s bound to hap­pen sooner or later. And once that hap­pens, it’s hardly a mir­a­cle if you roll another 6. There’s a 16.6% chance that it’ll hap­pen. We can’t include the first 4 rolls and say “I rolled five 6’es in a row! The odds of this hap­pen­ing are 0.013%,! It’s a mir­a­cle! This die is mag­i­cal!”, because you cheated: you waited until you’d got the first four rolls right. The real coin­ci­dence is just that the final die roll came up a 6 as well.

So we only really started won­der­ing about Paul’s pre­dic­tive abil­i­ties after England’s defeat. Since then he’s made four pre­dic­tions: the odds of that are much bet­ter. Even by a ran­dom coin toss, you’d have a 12.5% chance to get 4 matches right.

So now it’s no longer a super­nat­ural phe­nom­e­non, but “just” a curi­ous coin­ci­dence. But there’s another inter­est­ing thing to note: take a look at the results¹ listed on Paul’s Wikipedia page. In par­tic­u­lar, take a quick look at the flags.

Notice any­thing?

They don’t look very ran­dom. If you don’t look care­fully, you won’t even notice that the flag in the “pre­dic­tion” col­umn var­ied in a few matches. They’re gen­er­ally dom­i­nated by yel­low and red. Nearly all the losers had flags with a lot of blue in them. Per­haps Paul just likes red and yel­low bet­ter than blue. Ser­bia is really the only odd­ity then.

The trend is even more pro­nounced if we look at the results from 2008: Paul guessed that Ger­many would win every sin­gle match, regard­less of the out­come of the actual match.

So per­haps Paul just likes the col­ors. Or per­haps he’s just real­iz­ing that when­ever peo­ple show him a Ger­man flag, there’s food under­neath it.

Tags: statistics, supernatural

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