I had the great pleasure a few nights ago to see Derren Brown‘s new illusionist / mentalist, hypnotist show Svengali. It’s fantastic, and highly recommended. If you’ve seen any of Derren’s previous shows on TV, then some of the routines will be familiar. This fails to make them any less baffling. If you’re unfamiliar with his work, here’s a sample:
(Here’s a bit more). One of the main themes of much of Brown’s work is his ability to recreate the “powers” of psychics, mind-readers and spiritualists without the pretence of supernatural intervention or paranormal activity. For example, in 2004 he performed a seance “live” on channel 4, and in 2011 trained a member of the British public to become a faith healer.
There is an important and quite general lesson to be learned from Brown’s abilities. In the course of last night’s performance, Brown did a number of things which, if they had been performed by someone claiming psychic powers, would seem, if not totally convincing, at least on the way to suggesting psychic powers. I remain at a complete loss as to how Brown seems to read the minds of audience members and anticipate their seemingly free choices.
Suppose that Connie claims to be a witch – a real, proper, supernatural witch – and as proof of her powers, performs a great feat of mind-reading. Being the mathematical nerds that we are, we decide to formalise our inference that Connie is a witch (and should thus be burned). Help us, Rev. Bayes!
= Connie is a Witch
= Connie totally just Read that girl’s mind.
Now, what is the probability that Connie is a witch, given that she just read that girl’s mind:
Three of these factors are fairly straightforward.
- is the prior probability that Connie is a witch, that is, how likely was it that Connie was a witch before we saw her totally really that girl’s mind. We’d probably set that number to be small.
- is the probability that Connie could read that girl’s mind, given that she really is a witch. We’ll assume that witches can do that kind of thing, so this number is fairly high.
- is “not-W” i.e. Connie is not a witch. Thus, was set when we set the prior, since .
Here’s the important bit: the other term! is the probability that Connie could appear to read that girl’s mind given that she is not a witch. This factor is not determined by the other ones. We have to ask the question: how good are charlatans? What can non-witches do?
Here, then, is the Bayesian utility of Derren Brown. If I had to guess what is on the basis of our own mind-reading abilities, I’d probably set it to be very low. That is, I might be tempted to think that because I’d just have to guess what that girl was thinking, it’s practically impossible for a non-witch to read that girl’s mind. Brown shows us that, in fact, a talented but thoroughly non-supernatural bloke can perform such feats with relative (though baffling) ease. This shows that , and Connie’s performance has made it no more likely that she is a witch. We’re simply left with our initial skepticism, .
I’m not a fan of “skepticism” as a rational slogan. Of course, these terms are open to interpretation, but skepticism struggles to distinguish itself from denialism, the idea that not-believing is somehow the superior intellectual pose. I do, however, support the following principle – call it a form of skepticism if you like. Given the claim “evidence E supports/proves the hypothesis H”, one must consider alternatives to H. One must be skeptical of H, assume for a moment that it is false, and see if some other way of explaining the evidence E is available and plausible. The fact that all the evidence fits with my favourite theory H is not sufficient to show that the evidence makes my theory probable.
(There is a loophole, you may have noticed. Perhaps Brown really is a witch, but is just pretending to be an illusionist. We’ll need some scales, and a duck …)