I just got a PM with this question: "What would be the minimum intellectual investment necessary to be able to fruitfully take part in the discussion of decision theory on LW?" This is not the first time I've been asked that. Our new discussion section looks like the perfect place to post my answer:
1) Learn enough game theory to correctly find Nash equilibria in 2x2 games all by yourself.
2) Learn enough probability theory to correctly solve Monty Hall, Monty Fall, Monty Crawl all by yourself.
3) Learn enough programming to write a working quine (in any language of your choice) all by yourself.
4) Learn enough logic to correctly solve the closing puzzle from Eliezer's cartoon guide.
Then you're all set. Should take you a few days if you've studied math before, a few weeks if you haven't. No special texts needed beyond Wikipedia and Google.
Do you seriously believe that someone who has never studied math before can understand Loeb's theorem and start solving puzzles in mathematical logic after a few weeks of study?! I can imagine that someone very smart could figure out (1)-(3) from scratch fairly quickly, but (4) strikes me as a much harder step. Also, mathy LW discussions often touch on quantum mechanics, various things in computability theory, and sundry other stuff where I don't see any easy way up (especially for QM).
In any case, here's a neat test for those who'd like to tackle step (1):
http://www.rasmusen.org/GI/_stest1/selftest1.htm
I don't think (4) is much harder than (3). Someone who's never programmed before will find (3) very hard. Still, a few weeks of dedicated work should do it. From my experience teaching math to kids, I think it's actually more difficult to go from zero to (1) and (2) than to go from those to (4), because the hard part is learning how to think rigorously at all.
There is no serious descussion of quantum mechanics (or physics in general) on LW. I'd be glad if there was. Likewise, there's almost no serious discussion of statistical inference (frequentism, Bayesianism and related topics), though we do have a handful of people who understand it.