One of the gems is his simple, but brilliant analysis of the Prisoner's Dilemma. The usual analysis notes that the Nash equilibrium is for both players to defect. Hofstadter notes (correctly) that if both players are rational, then because the game is symmetrical, both players will choose the same strategy. So, the only choices are for both to cooperate or both defect. Since both cooperating has a higher payoff than both defecting, the rational strategy is to cooperate. The Nash equilibrium isn't relevant because it considers pairs of strategies which are impossible if both players are rational, i.e., the pairs where one player defects and the other cooperates.

Hofstadter notes that many people when presented with the above argument still say that they would defect. His descriptions of his attempts to reason with his friends and the results of the lottery he conducted (he told readers of his column they could send in entries for the lottery, but the more that entered, the smaller the prize would be) are, as he says, amusing, disturbing, and disappointing.

Some parts are really bad. In chapter 5 he wonders why one can judge the intellectual content of magazines by their cover, not seeing the obvious solution that these magazines try to attract different audiences. He spends some time discussing the prisoners dilemma and he get's it completely wrong. He argues that a rational person would know that other rational persons would think along the same lines and therefore act the same way. So a rational person can use this knowledge to influence another person. This is complete bogus of course. People are rational when they act rational, if I cooperate in the prisoners dilemma, I am not changing the definition of rationality, I'm simply irrational. Hofstadter also discusses Axelrod's famous computer tournaments. A more realistic view on the topic is provided by a review of Axelrod's book by Ken Binmore. That review can be found on the web.

The book is still valuable for the good parts, but one should read the book with a sceptical eye. Hofstadter is a layman on many things he discusses, and sometimes this shines through. Another problem is that some issues like the cold war anren't really interesting anymore. People who like Hofstadter will surely like it and find enough pearls to make the buy worth it though.