Some of these people show signs of being rather high-level rationalists overall, although some don't.

I wouldn't necessarily expect there to be a super-strong connection between not rationalizing and being a "high-level rationalist". There are other ways to go systematically wrong than through goal-directed rationalization. As a possibly overlapping point, your concept of "high-level rationalist" probably sneaks in things like intelligence and knowledge that aren't strictly rationality.

In a word: compartmentalization.

Since that's not helpful, I will say that it doesn't even seem to be possible for there to be people who don't rationalize. (Or enough that you're at all likely to find them.)

Some of these people show signs of being rather

"Some", "signs", "rather". These words all show signs of being rather belief in belief. I notice you don't say, "Some of these people are high-level rationalists," just that they show warning signs of being so. What does this really mean? Are you referring to the "visible aura of competence" Eliezer talked about in his 'the level above mine' sequence on people who are aspiring rationalists? If so, I'd wager this carries very little information, since you're sampling from aspiring rationalists!

Also, could you explain what you mean by "seem to have little clue what Tarski is for"?

It seems introspectively plausible that when you ask people questions like "how do you know when you're rationalizing", they feel like they've been asked a "when did you stop beating your wife" question, and feel initially tempted to react with an "oh yeah, well maybe I don't" regardless of whether it's true.

This description is very plausible, but entirely wrong. It was almost completely the opposite of what you're saying. The Muslim mathematicians used fewer symbols than the Greek tradition they inherited for almost the entire timeline of medieval Arabic/Islamic mathematics. The "first textbook" you're referring too, Al-Khwarizmi's Al-jabr wa'l muqabalah, the one ultimately responsible for the word "algebra", did not use any symbols at all, and wrote everything out in words.

Greek mathematicians started to use something like symbols (abbreviated letters with fixed positional meaning) by the time of Diophantus around 3rd century CE. The Arab mathematicians did not adopt that when they translated the Greek texts, and for the first 500 years of their work, wrote everything out fully. Moreover, it is those texts devoid of any symbolic systems that were translated into Latin and used to help fuel the European tradition in 12th-13th centuries CE. Even though some Islamic mathematicians later did develop the beginnings of a symbolic notation, in 14th-15th centuries, this happened roughly in parallel with the Europeans inventing their own symbols, and did not influence the modern tradition that derives from those European symbols.

To be sure, Muslim mathematicians were much better algebraists than the Greeks. But that was because Greeks never quite reached the idea of decoupling numbers (and unknown quantities) from geometry and manipulating them as separate objects on their own. The Muslim mathematicians were able to do that (and as a result, much more), despite not having any symbolic system at their disposal.

If there were a world in which algebra had been learned only through reading essays, without subskill-by-subskill practice, it would not be surprising if the world’s best algebra practitioners could be outperformed by an ordinary student who worked diligently through the exercises in a standard textbook.

This actually happened. The ancient Greeks weren't very capable algebraists because they didn't develop a symbol system that they could systematically manipulate according to prescribed rules. Their description of formal logical inferences were insane to read: "If the first and the second, or the third, implies the fourth, then the first or the fourth, implying the third...." The reason our word "algebra" comes from Arabic isn't because the Muslims were better algebraists; it was because they used symbol systems (to avoid making icons of Mohammad) in order to encode the material they were reading in the Greek literature. The result was something reasonably close to our modern symbol-manipulation system, which made it possible to train in algebra.

So this isn't just a theoretical example. Really, honestly, the first textbook ("al-jebr..." I don't quite remember the title) absolutely trounced several hundred years of careful, intelligent Greek thought on the topic of numerical reasoning.

Edit: Please see this. There's some question about the accuracy of my statement here.

As a quick addendum: If you're interested in hearing about the Enneagram keys but weren't at the previous meetup, you'll get a lot more out of that discussion if you have some familiarity with the Enneagram beforehand. If you're totally new to it, I'd suggest reading this webpage. Just two caveats:

• You can safely stop after you've read the section on "Levels of Development." I'm pretty sure the material on Directions of Integration and Disintegration is just pretty theory and doesn't quite tie into reality the way an empirical claim should. I also don't talk that much about the Instinctual Variants.
• There's a lot of fluff in Enneagram talk. It started out as a kind of sacred geometry and then went through several layers of having psychological theories woven into it. Despite its origins, though, empirically the system works extremely well in specific domains. Part of my goal in this presentation (if we elect for me to present it) will be to point out exactly how you can test it and precisely what results to expect. It's not subtle. So please don't be too surprised to find mystical language and dualism and other mental traps in Enneagram literature; it's pretty ubiquitous, but unnecessarily so. There really is a rational version of the Enneagram, and that's what I focus on and am offering to share.

I attended the first one in 2010. It was pretty neat. I mean, I met Eliezer there and found out about Less Wrong as a result! The people were really wonderful to get to talk to, and the spirit of connection was very, very strong for many of us there. Lots of new friends as a result, even if we're spread all over creation and stay connected only tangentially via Facebook.

With that said, I found the conference itself often kind of silly. We spent a lot of time doing self-descriptions to everyone and then doing a few dozen ice-breaker activities. But really, almost all the social time occurred after each day of formal sessions when people would hang out in the hot tub or in hotel rooms and just chat. I watched some fantastic plans form for getting cryonics reliably available throughout Europe as part of those after-hours meetings. :-)

I understand that the 2011 one was basically an exact repeat of the one before, which was kind of odd since many people already knew each other or at least of each other and just wanted to chat. If the same person is running it this time, I kind of suspect that'll happen again. But it was certainly worth it for me, at least, to go through those oddball ceremonies to have a chance to chat with so many forward-thinking people. There's something downright relieving about being with a large group of intelligent people who all get that death is bad and life is good! At least if you're of a like mind, that is; I imagine that people who think that immortality would be horrid would feel very sorely out-of-place there.

The tour of Suspended Animation afterwards was really neat, too. Between seeing what they do and talking to several of the scientists who were at the conference, I had to update my beliefs about how important it is to get suspended immediately after death as opposed to minutes or hours later.

And as a sociological thing, it was really, really nice to see so many young people involved with cryonics not being total eggheads. (Bear in mind that I pretty much have to count myself as an egghead. No offense intended!) There were entrepreneurs and lawyers and artists and musicians and adventure-seekers. It was really amazing to see real variety entering the cryonics meme pool!

I plan on going to the next one if I can. I really liked getting to chat with the people there two years ago, so even going through the same introduction scheme and presentations that spell out someone's pet theory on the Singularity would totally be worth it. :-)

Mercurial, thanks for an AMAZING presentation on Enneagrams. I was a "9" in the meet-up, but written tests keep brining me out as a "5" with 9 coming in 3rd or 4th place. Whaddyagonnado. I can't wait to find out what my wife is.

Mike