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.