A good question. I think that Go provides more lessons and better lessons to an aspiring rationalist than do most other games. More lessons even than such worthwhile activities as paperclip manufacturing. The reason has to do with Go's "richness".

I pointed out one aspect of what I mean by "richness" in my comment mentioning "self-organized criticality". Here I will point out one aspect of the game which I think leads to that "richness".

In moving from conceptual high-level to conceptual low-level in your thinking about a game of go, you are forced to switch between binary objective thinking (I want to win!) and quantitative objective thinking (More! More! I want more!). You are forced to switch repeatedly.

For example, I win the game (by three points) because the balance of territory on the left side of the board is 14 points to the good, whereas the balance on the right is only 11 points to the bad. But part of the reason I (black) am 14 points ahead on the left is because that largish eyeless white group is dead, rather than alive. But the reason it is dead is that it has only two liberties, while my opposing black eyeless group has four.