– Chris Lee

I like the dialogues. You can have a lot of fun with them if you have the same characters appear repeatedly, with their own distinctive personalities - illustrating different cognitive tendencies, or different aspects of your own thinking. Done right this sort of thing is very engaging, since we’re hard-wired to be fascinated by real people and their conflicts.

It’s a real art to bring a taste of “real life” into such dialogues without distracting attention from the points you’re trying to make. Ideally, the characters’ personalities can be very helpful in presenting different points. For example, it makes sense to have a mathematician named Matt (cute) who is good at rigorous reasoning but a bit naive when it comes to epistemology: he can help out when math is needed, but also serve to illustrate the dangers of certain kinds of naivete. You could have a frequentist and a Bayesian to carry out two sides of that battle… after all, I think part of your book is about the limitations of “subjective Bayesianism”. Sonya shouldn’t be just “a scientist”, but some specific kind of scientist: you may want a number of different kinds: biologists, computer scientists, physicists and so on — each with their own strengths and weaknesses. Since you’re a Renaissance man, you could use quite a cast of characters.

You write: “Most of us have learned about mathematical logic, theorems and proofs in math class.” Ah, if only that were true! It depends who your audience is, I guess.

Using the Monte Hall paradox to introduce Bayes’ law is good, but maybe you should start with an easier example, like: “if the probability that you die of cancer given that you smoke is 20%, and the probability that you smoke is 10%, and… then… ?”. In other words, a simple “plug and chug” example, just to illustrate the formula and nail down the concepts in the simplest possible way.

But, you can probably find a real-world example that seems quite striking! People tend to get mixed up between “the probability that P, given Q” and “the probability that Q, given P”, and get shocked when these are drastically different. Getting over this seems to be crucial to getting good at statistical reasoning.

(Lisa and I have been in Paris for most of the summer, but will return to California tomorrow.)

Don’t succumb to math envy! Or if you do, imitate those mathematicians who explain things using words rather than equations.