Over on SciBlogs Aimee has started a discussion around the apparent psychic powers of Paul, the octopus who's claimed to have predicted the results of several games in the just-ended soccer World Cup. (Actually, if he could predict the outcomes of games, this would make him prescient, not psychic. Once a pedant, always a pedant, alas!)
This octopode seer has supposedly picked the correct outcome for (if I remember rightly) 7 games in a row. The odds of getting this by chance are 1 in 128, which sounds rather good really. But 'runs' of 7 in a row are not actually unusual if you toss a coin often enough. They just look spectacular if they happen when you begin tossing (or picking mussels in a box) - & even more special if you then stop tossing while you're ahead...
But I wonder if we're not looking at an example of the 'clever Hans' effect. Clever Hans was a horse who amazed German audiences in the 1890s with his ability to count. If his trainer/owner, Wilhelm Von Osten, asked Hans for the sum of 3 + 4, the horse would tap his forefoot on the ground 7 times; no more, & no less. Apparently he could also tell the time, & identify people by name... Anyway, Von Osten - & those in the audience - firmly believed that the animal was the Mastermind of the equine world, not least because Clever Hans performed just as well when his trainer was out of the room. However, psychologist Oskar Pfungst eventually demonstrated (on the basis of careful experimentation) that Hans was instead responding to unconscious cues from those asking the questions. For instance, when those present didn't know the answer to a question, the horse was equally stumped. It turned out that the animal was responding to changes in posture or expression: the questioner would tense up as Hans's foot-tapping approached the correct answer, & relax when he reached it. The horse was certainly intelligent, but not a mathematician :-)
Now, cephalopods are also intelligent. The 'clever Hans' effect is a much more parsimonious explanation for Paul's apparent predictive powers than the suggestion that a tentacled mollusc with a completely different brain (&, presumably, experience of the world) might be capable of predicting the outcome of a game played by a bunch of ball-kicking bipeds :-)