I've been reading at about the pace of the Google book scanning project (well, trying to!) on topics of interest, mainly around groups, cooperation, rational and irrational behavior, why people do what they do.
And various concepts pop up: critical mass for stable, self-sustaining groups, choices dependent on what other people will do, logical dilemmas... OK, I think I quite literally took every course in the undergrad catalog that involved the explicit study of logic. But it occurred to me, upon reading a college-level text, that my first introduction to most of these concepts was Sideways Arithmetic from Wayside School. It's a children's book, aimed at elementary schoolers, in the same setting as the Sideways Stories from Wayside School.
And it's actually pretty sophisticated math. About half the book is "alphametics": arithmetic problems written out so that each number is replaced by a specific letter, usually in such a way so that the inputs and outputs spell words (for example, "elf+elf=fool"); the challenge is to determine which numbers the letters must represent. (For example, the "f" must be 1 here.)
The other half is logic problems and puzzles, and not easy ones; at least, ones that even a mathematically-inclined adult would have to take a little time to solve, and a non-mathematically-inclined adult would have to take time to figure out how to solve. I read it when I was 9 or 10 and found it a great challenge. It probably did more to open up the idea of logical problem-solving outside of math textbooks, and the ability to figure out how to approach those problems, than any other book I read. And the word problems were funny. Every bright kid should get a copy. Because by the time I saw those concepts again (I wish I had gotten a really good math education in grade school, but that's another story), they had been a part of my thinking for such a long time that they weren't foreign when I saw them.
Also, despite it being a classroom copy, I got as much time to work through the problems as I wanted, because I finished my "real" classwork in no time, and no one else in my class was interested in reading the book.
(Postscript: Yes, that is Gödel, Escher, Bach in my LJ icon. I first read that -- and carried around a little notebook to work out the problems -- when I was 16. A fitting follow-up, I think.)
