When I criticize, I'm a genius. I can go through a book of highly-referenced scientific articles and find errors in each of them. Boy, I feel smart. How are these famous people so dumb?

But when I write, I suddenly become stupid. I sometimes spend half a day writing something and then realize at the end, or worse, after posting, that what it says simplifies to something trivial, or that I've made several unsupported assumptions, or claimed things I didn't really know were true. Or I post something, then have to go back every ten minutes to fix some point that I realize is not quite right, sometimes to the point where the whole thing falls apart.

If someone writes an article or expresses an idea that you find mistakes in, that doesn't make you smarter than that person. If you create an equally-ambitious article or idea that no one else finds mistakes in, then you can start congratulating yourself.

Yesterday I was using the Global Terrorism Database to check some suprisingly low figures on what percentage of terrorist acts are committed by Muslims. (Short answer: Worldwide since 2000, about 80%, rather than 0.4 - 6% as given in various sources.) But I found some odd patterns in the data for the United States. Look at this chart of terrorist acts in the US which meet GTD criteria I-III and are listed as "unambiguous":

I'm reading George Steiner's 1989 book on literary theory, Real Presences. Steiner is a literary theorist who achieved the trifecta of having appointments at Oxford, Cambridge, and Harvard. His book demonstrates an important Dark Arts method of argument.

So far, Steiner's argument appears to be:

1. Human language is an undecidable symbol-system.
2. Every sentence therefore carries with it an infinite amount of meaning, the accumulation of all connotations, contexts, and historical associations invoked, and invoked by those invocations, etc. Alternately, every sentence contains no meaning at all, since none of those words can refer to things in the world.
3. The meaning of a sentence, therefore, is not finite or analyzable, but transcendent.
4. The transcendent is the search for God.
5. Therefore, all good literature is a search for God.

The critics quoted on the back of the book, and its reviews on Amazon, praise Steiner's rigor and learning. It is impressive. Within a single paragraph he may show the relationship between Homer, 12th-century theological works, Racine, Shakespeare, and Schoenberg. And his care and precision with words is exemplary; I have the impression, even when he speaks of meaning in music or other qualia-laden subjects, that I know exactly what he means.

He was intelligent enough to trace the problems he was grappling with out past the edges of his domain of expertise. The key points of his argument lie not in literary theory, but in information theory, physics, artificial intelligence, computability theory, linguistics, and transfinite math.

Unfortunately, he knows almost nothing about any of those fields, and his language is precise enough to be wrong, which he is when he speaks on any of those subjects. How did he get away with it?

Answer: He took a two-page argument about things he knew little about, spread it across 200 pages, and filled the gaps with tangential statements of impressive rigor and thoroughness on things he was expert in.

My take on some historical religious/social/political movements:

• Jesus taught a radical and highly impractical doctrine of love and disregard for one's own welfare. Paul took control of much of the church that Jesus' charisma had built, and reworked this into something that could function in a real community, re-emphasizing the social mores and connections that Jesus had spent so much effort denigrating, and converting Jesus' emphasis on radical social action into an emphasis on theology and salvation.
• Marx taught a radical and highly impractical theory of how workers could take over the means of production and create a state-free Utopia. Lenin and Stalin took control of the organizations built around those theories, and reworked them into a strong, centrally-controlled state.
• Che Guevara (I'm ignorant here and relying on Wikipedia; forgive me) joined Castro's rebel group early on, rose to the position of second in command, was largely responsible for the military success of the revolution, and had great motivating influence due to his charisma and his unyielding, idealistic, impractical ideas. It turned out his idealism prevented him from effectively running government institutions, so he had to go looking for other revolutions to fight in while Castro ran Cuba.

The best strategy for complex social movements is not honest rationality, because rational, practical approaches don't generate enthusiasm. A radical social movement needs one charismatic radical who enunciates appealing, impractical ideas, and another figure who can appropriate all of the energy and devotion generated by the first figure's idealism, yet not be held to their impractical ideals. It's a two-step process that is almost necessary, to protect the pretty ideals that generate popular enthusiasm from the grit and grease of institution and government. Someone needs to do a bait-and-switch. Either the original vision must be appropriated and bent to a different purpose by someone practical, or the original visionary must be dishonest or self-deceiving.

The recent OKCupid blog, which gwern mentioned in Media Open Thread, investigated the impact of three different factors on users' perceptions of each other: authority (reported match %), profile text (present or absent), and looks.

I just read this in the Wikipedia article on the Mattaponi River and it really tickled me. If only all language were so rational!

• The Mat River and the Ta River join in Spotsylvania County to form the Matta River;
• The Po River and the Ni River join in Caroline County to form the Poni River;
• The Matta River and the Poni River join in Caroline County to form the Mattaponi River.

I'm reading The Last Intellectuals: American culture in the age of academe by Russell Jacoby (1987). It contains many interesting and important observations and insights, but also much stupidity. By the last chapter, I was as interested in the question of how a person can be so smart and stupid at the same time as in the author's actual arguments.

The official story: "Fifty Shades of Grey" was a Twilight fan-fiction that had over two million downloads online. The publishing giant Vintage Press saw that number and realized there was a huge, previously-unrealized demand for stories like this. They filed off the Twilight serial numbers, put it in print, marketed it like hell, and now it's sold 60 million copies.

The reality is quite different.

A friend recently posted a link on his Facebook page to an informational graphic about the alleged link between the MMR vaccine and autism. It said, if I recall correctly, that out of 60 studies on the matter, not one had indicated a link.

Presumably, with 95% confidence.

This bothered me. What are the odds, supposing there is no link between X and Y, of conducting 60 studies of the matter, and of all 60 concluding, with 95% confidence, that there is no link between X and Y?

Answer: .95 ^ 60 = .046. (Use the first term of the binomial distribution.)

So if it were in fact true that 60 out of 60 studies failed to find a link between vaccines and autism at 95% confidence, this would prove, with 95% confidence, that studies in the literature are biased against finding a link between vaccines and autism.

Consider some disputed proposition X. Suppose there appeared to be a limited number of ways of proving and of disproving X. No one has yet constructed a proof or disproof, but you have a feeling for how likely it is that someone will.

For instance, take Fermat's Last Theorem or the 4-color problem. For each of them, at one point in time, there was no proof, but people had some sense of the prior probability of observing the lack of a counterexample given the space searched so far. They could use that to assign a probability of there being a counterexample (and hence a disproof) [1]. Later, there was an alleged proof, and people could estimate the probability that the proof was correct based on the reputation of the prover and the approach used. At that point, people could assign values to both P(will_be_proven(X)) and P(will_be_disproven(X)).

Is it reasonable to assign P(X) = P(will_be_proven(X)) / (P(will_be_proven(X)) + P(will_be_disproven(X))) ?

If so, consider X = "free will exists". One could argue that the term "free will" is defined such that it is impossible to detect it, or to prove that it exists. But if one could prove that the many worlds interpretation of quantum mechanics is correct, that would constitute a disproof of X. Then P(will_be_proven(X)) / (P(will_be_proven(X)) + P(will_be_disproven(X))) = 0.

Is it possible for this to happen when you know that X is not undecidable? If so, what do you do then?

1. The computation is not as simple as it might appear, because you need to adjust for the selection effect of mathematicians being interested only in conjectures with no counterexamples.