I've been reading this book, and finding it really interesting, engaging, and full of great content. However, I also constantly hit little nuggets ground up in the feed that make me not just choke, but spit up almost reflexively. Yeah, gag. On the one hand, you have someone from the Math/Science camp coming out and saying ‘hey maybe there are better ways to learn math, to have it explained, to see what it‘s good for/how it fits in,‘ but then on the other, the same silly chest pounding Nietzsche‘s Gnat routine is just below the surface. To the point of some patently absurd conundrum-inducing silliness. For instance, the whole premise that math is the language nature is written in. Dude, that‘s like Science‘s equivalent of saying ‘everything in the gospels happened exactly.‘ It‘s so silly. No, math is a MADE UP language, dude, and if you are wanting to talk about everything including nature being its spawn, you are a madman. Math and Science guys go completely nuts when they find people who have disregarded a single established finding (like evolution), yet they all talk as if relativity never happened, as if Nietzsche never lived. As if we still didn‘t know what the hell goes on in the mind (we don‘t, but we know more).
Then there is another little bone I have to pick with this book. He does some history of science in here and some of it is most unsatsifying. His depiction of the history of games makes Bayes seem like a really minor player. He doesn‘t talk about La Place hardly at all, and nothing about how it is that Frequentism took over and dominated for a century, only to be rightly pushed aside (messy details of nonlinear noise). Furthermore, he doesn‘t say anything about probability in the 20th Century: Cox, Keynes (yeah, the childless hater of the future in Niall Ferguson‘s dystopian tirade), or Jaynes.
I did like the fact that he sees games as a hugely important part of the emergence of math in the modern age, and seems to see the heuristic advantages. If I were going to teach a kid about math, I might be inclined to start with games, e.g. let‘s throw a die. How do we know what is going to happen? We don‘t. Do we know anything about what might happen? How.. ? And after one thing happens, what does that mean about it happening again, or in unison with other things?
Math and science guys would not go this route because they are so bound up in the worship of their god, they make decisions about what route to take based on when they will have to pull out how much stuff. Bad idea. The guiding principle should be which way to the light, period.
One other bone, after doing a real hopscotch job on the probability stuff, I read the section on the development of Calculus. Have read about this before, but I liked this part of the book. Was pretty great. Newton was a complete maniac. It‘s so weird that Halley had to force him to publish and Bayes ordered his stuff burned, but his paper was published posthumously (and in another coincidence, his discovery was also discovered at the same time elsewhere (by LaPlace)).
Anyway, but then I came upon a session about finding patterns even in words. Ok, here‘s where you bring in Bayes right? Wrong. He goes into the story about the 2 mathematicians who developed a program to figure out who wrote the 19 Federalist Papers whose author was unknown. Not only does he not talk about Bayes, but then as he describes the problem, he mentions the fact that word counts were critical and certain words were determinative and others weren‘t. He leaves the reader with the impression that these smart mathematicians had to pore over the data to figure out which pieces to use to make their case. That is if not wrong, pretty close to it. In fact, in Bayes, when you do text analysis, you are always looking at word frequencies in a document vs. frequencies in the language at large (or a complete body of documents). This is what the likelihood ratio is. Then you don‘t have to pick features. One of the most magical part of Bayes is that because each feature is a ratio, if a feature is non-deterministic, it‘s because the individual (e.g. Hamilton) and the group distribution is similar or the same, in which case the ratio will come out to 1 and it will not move the score in either direction.
So on the whole, worthwhile book, but it‘s a little scary that this is the view from the inside all this time later. Science is just another religion, but my prediction is that as was the case in the Christian Era, we are about to see a Reformation in which the priests are going to lose control of their rectory.