Excess Kurtosis of Unusual Size? I don’t believe it exists.

The Princess Bride, like many fairy tales of its ilk, relies on a narrative built from dashed expectations. Buttercup expects Westley to return, Inigo expects revenge, Vizzini expects normal humans to be unable to scale the Cliffs of Insanity, &c &c. The classical heroic tropes are interesting because they exceed ordinary human probability distributions. 

There’s no swashbuckling in the 95% interval.

Each of Westley’s achievements, from charming the Dread Pirate Roberts, to tailing Vizzini in thick fog, to scaling the cliffs, to besting a fencer who’s trained his entire adult life, to choking out Andre the Giant, to outwitting a Sicilian when death is on the line speaks of a character who lives in the fat tails of his distributions. Even when he’s recently recovered from being mostly dead, The Man in Black sweet talks Humperdink into surrender without raising anything apart from the tone of his voice.

The hero triumphs because he was underestimated. Vizzini found his actions “inconceivable” because models are more tractable when they employ normal distributions. Inigo’s model, one based on heuristics and experience brought by many years of practical training, was perhaps less precise, but certainly more accurate. Acknowledging uncertainty, acknowledging non-ergodicty grants robustness, flexibility, and wu-wei (to borrow a quip from Drew) to your model of the world. The death of Vizzini is a metaphor for the perils of hubris.

At EE today, I asked if exchange with a robot could be euvoluntary. In a world governed by normal probability distributions, the future of automation looks scary indeed. It’s very difficult to imagine what people might do with their time once robots have pushed us out of meaningful employment. But I have a hunch that if you’d have asked 14th c. farmers the same question about the development of the thresher or the gas-powered tractor or the combine, they’d have been equally at loggerheads to imagine a world of word processors and dubstep. Just because we can’t imagine life in the long tails doesn’t imply that such life doesn’t exist.

Don’t be Vizzini. Let your father’s sword guide you.

Bayesian Inference atop the Cliffs of Insanity

It appears I haven’t updated my priors since 1987. When Vizzini, Inigo, and Andre the Giant stand at the top of the Cliffs of Insanity and see the Man in Black below them slowly ascending, Vizzini claims against the evidence of his own senses that such effort is “inconceivable.” In one of the more oft-quoted lines of the film, Inigo retorts “you keep using that word–I do not think it means what you think it means.”

When I first watched the film as, gosh, I guess I was 13 at the time, I interpreted it as a dig at Inigo’s lack of sophistication. To me, it was a simple pun: “inconceivable” can also mean “unable to conceive [a child].” Ha ha, snare drum, cue curtain, and scene.

The more apt interpretation wouldn’t have occurred to a 13 year old me: Inigo was criticizing Vizzini’s Bayesian processing. “Inconceivable” means that the mind is incapable of imagining the outcome. Well, clearly the evidence presented refutes Vizzini’s prior beliefs about the Man in Black’s abilities. It’s not “inconceivable” unless Vizzini is unwilling or unable to update his beliefs given the currently available evidence. To Inigo, “inconceivable” means that the posterior probability is 0. To Vizzini, “inconceivable” means that the prior probability is 0. The difference in opinion over the use of the word contrasts the simple (Hayekian) humility portrayed beautifully by Mandy Patinkin against the technocratic arrogance portrayed (again, beautifully) by Wallace Shawn.

And a few scenes later [spoiler alert], Vizzini’s hubris leads to his untimely demise. Is The Princess Bride a paean to libertarianism? Eh, probably not. But the political intrigue is catnip for public choice scholars, for sure.

Why is this relevant to Sweet Talk? Well, the unfortunate truth about people is that they tend to be pretty awful Bayesians. In some circumstances, they have resolutely, irrationally immobile priors. In others, they update too much based on weak or misleading evidence. This intemperate tendency should favor biasing institutions towards robustness against the vagaries of popular opinion. Presume Chestertonian fences.

And never go up against a Sicilian when death is on the line.