“The Waltz of Reason” and a paradox of book reviewing

I was sent a copy of the above-titled book by retired mathematician Karl Sigmund, who is described on the book jacket as one of “the pioneers of evolutionary game theory.”

The book is good. Much of it is a historically-oriented collection of topics in mathematics—the first chapters are called Geometry, Number, Infinity, Logic, etc.—and then it gets into some of the mathematical social science of the 1950s-1980s (Nash equilibrium, prisoner’s dilemma, cooperation, etc.). I was pleased to see that, although Sigmund mentioned certain aspects of game theory and cognitive psychology, he did not get bamboozled by naive or overly-excited applications of these ideas such as the misapplication of the prisoner’s dilemma to trench warfare or the hot hand fallacy fallacy.

My two absolute favorite books of this genre are Selected Topics in the History of Mathematics by Aaron Strauss (1973) and Mathematics: The Loss of Certainty by Morris Kline (1980). Also Proofs and Refutations by Imre Lakatos (1964) but that’s a little different because it’s not intended for general audiences.

Given my background and interests, I’m well qualified to review this new book by Sigmund; on the other hand, given my background and interests, I’m not part of its target audience, as I’m already familiar with much of the material. This is not at all intended to be a negative comment: the book is intended for some version of a general audience; it is not a research monograph.

But it’s an interesting paradox, that the people best qualified to review a book are not part of its audience. This is not always the case! A theater reviewer will want to see a new play for its own sake, similarly for reviewers of novels or films. Even for a highly broad-audience commercial film, there will be reviewers who have worked on such movies and absolutely love them. Pop-science books is another story, which makes them difficult to review. Sometimes reviewers miss the point by asking for a level of detail that would not be appropriate given the audience; other times academics will give gushing reviews because they’re reviewing the researchers’ body of work rather than the project at hand; other times non-academics will give adulatory reviews because they are intimidated by the topic. It can be tricky.