Paranoia runs deep

Andrew Gelman has some thoughts on my thoughts regarding Naomi Wolf and the varieties of stupid experience.

Gelman’s take is that Wolf’s post about how her computer went on the fritz “coincidentally” immediately after she endorsed Donald Trump is that Wolf was at least half-joking, in the classic internet troll kidding on the square way:

I’m guessing that, in promoting these ridiculous claims, Wolf is making what in poker is called a semi-bluff: mostly she doesn’t believe it, she’s just saying it as a kind of joke, she sees herself as a charming imp, demonstrating once again that the people on the other side have no sense of humor, etc etc . . . on the other hand, maybe there really is a conspiracy controlling her cursor! It’s the kidding-not-kidding thing.

My take, based on the totality of her oeuvre in recent years, is that Wolf has gone legitimately bananas, to use the official DSM-V terminology, and isn’t doing any kind of trolly nudge nudge wink wink thing. To put it another way, if I read a similar post by Ann Coulter I’d be inclined to interpret it the way Gelman interprets Wolf’s, because Coulter, although thoroughly loathsome in various ways, doesn’t strike me as fundamentally separated from contact with reality by paranoid fantasies of increasingly baroque dimensions. (Amusingly, or maybe not, at least a couple of Gelman’s commenters think either that Wolf’s suspicions are quite possibly reasonable, and/or that the joke is on me, because she’s “obviously” doing one of those metaphor/analogy thingees to point out how persecuted fine people of good will actually are if they do something as totally innocuous as support Donald Trump).

I do think Gelman’s similar take regarding Harvard Law School professor and convert to the most extreme form of integralist Catholicism Adrian Vermeule is much more accurate:

Wolf’s post reminds me of when “libertarian paternalist” Harvard law professor Adrian Vermeule was promoting discredited election-conspiracy theories. I doubt he really believed these theories, but he probably put a bit of effort into avoiding any evidence against them. It serves his comfort to be able to stay in a hazy state of ignorance about the topic, so he can continue to be a charming contrarian.

Of course the whole kidding on the square schtick is a big part of our neo-fascist dicourse, with Donald Trump’s “jokes” about annexing various friendly allies that appear especially gigantic on the Mercator projection being the most salient example.

In any event, I’ve been thinking a lot about intelligence and stupidity for a book project, and one thing I’m convinced of is that stupidity is every bit as multiple as intelligence, in the sense that people can be very intelligent in one area of cognition and totally hopeless in another. Indeed, somebody can be a flat-out genius in terms of certain kinds of thinking, and still have apparently inexplicable breakdowns and blind spots within that same area of thought.

My current favorite example of this is the inability of the great mathematician Paul Erdos to grasp the solution to the Monty Hall problem. Apparently Erdos was so befuddled by the problem that he wouldn’t accept the correct answer until it was demonstrated to him purely empirically, via a computer simulation of a vast number of trials!

Now how is it that Paul Erdos was both approximately 117,431% better at mathematical reasoning than I’ll ever be, and yet I happen to have immediately seen the solution to the problem when it was first described to me? And this is not some isolated case: the Monty Hall problem is infamous for being something that huge numbers of extremely intelligent people — moreover people who are generally excellent at calculation, statistical reasoning, etc. — find it very difficult or impossible to understand.

As long as we’re having fun with statistics, here’s a problem that I have no idea how to answer, so I look forward to your analyses. A few weeks ago I wrote to Gelman about a statistical question involving a trick coin, that was weighted in such a way as to always land on heads. It turns out he had already published a paper demonstrating that, as a matter of physics, you can’t bias a coin.

So what I should have asked him was this:

Suppose you have a jar with 100 pennies in it. 99 of them are conventional pennies, and one is a trick penny that has heads on both sides. Someone blindly draws a penny out of the jar, in which the trick penny has been mixed in completely randomly.

The odds that this penny is the trick penny are 1%. Here’s the question I was puzzling over: How does each successive flip of the coin move the probabilities in regard to the change from this initial probability? Obviously the first time the coin flip results in tails, the probability instantly drops to zero. But what if it keeps coming up heads? After one flip of heads, what is the probability that it’s the trick coin? What about after two heads in a row? Three? Four? The odds that a normal coin will come up heads consecutively is .5 times each consecutive event, so a coin will randomly come up heads three times in a row on an average of one out of every eight three flip series. So let’s say the coin has done that, which is something that will happen randomly 12.5% of the time. How much have we moved from the initial odds that there’s a 1% chance it’s the trick coin?

Have fun, and remember: there are no dumb questions, just dumb people who ask questions.