Saturday, October 16, 2010

Is Heinlein a Bayesian?

Brad DeLong had a post yesterday about Robert Heinlein, who I read extensively as a teenager and enjoyed tremendously. The subject was The Moon Is A Harsh Mistress, which I thought was a great story. I like Brad's blog a lot, and learn a lot about economic issues from him, but I thought the post so wrong as to make me question whether he is as knowledgable on other topics as he seems to be.

DeLong says "Heinlein [has a] failure to understand the Law of the Reverend Thomas Bayes," and then approvingly quotes another writer who complains that you can't compute the odds for an event and come up with different answers at different times. But of course this is the whole point of Bayes. If you understand nothing else about the issue, you should realize that what Bayes makes possible is to update probabilities as new evidence becomes available.

So I decided to say something in a comment, nicely I thought. I'm quite mystified to find my comment has been deleted a few hours later. I'll shrug my shoulders and go on, but I am shocked, shocked, first, that Brad DeLong is clueless about Bayes, second, that a whole string of commenters has missed the central point, and then finally that a polite comment pointing this out should be thought subversive. Very weird indeed, and disheartening.

[UPDATE: Perhaps it's just a misunderstanding. The original post says:

I have two problems with Mike. One is the figuring the odds for the revolution. I’d have bought it if he did it once. It’s the complex refiguring and odds changing and—no. People complain about the Dust hypothesis in Permutation City that you can’t calculate things out of order, and this is worse. You can’t work out odds of 7 to 1 against and then say they will keep getting worse until they get better.

The statement about "complex refiguring and odds changing and—no" is just wrong. And you can calculate in any order you like.

But it turns out Brad's objection and maybe this poster's is that they read Heinlein as saying " [the odds] will keep getting worse until they get better." You can't keep getting installments of bad news and say things are looking up.

But that's not how I remember the book. Mike knows things, everything public anyway. Some events break the revolutionists' way early, but a thousand small unmentioned things change the balance. And time is running out. Read the book, and judge for yourself. One of Heinlein's best, along with my favorite, Stranger in a Strange Land.]


I dug into it a little bit and I am convinced that I'm right. The original post is a very nice review of the book. Great story, but lots of not-PC stuff, characteristic Heinlein. However, it is clear that (1) Jo Walton does not understand Bayes (hence the first part of the quote above) and (2) Heinlein does, at least to the extent he knows how to bet on a horse race, and can appropriately update odds when in possession of new information.

I looked through an online version of the book (pdf) and read all the pages where the word "odds" appears, and nearby. For an example showing Heinlein's understanding, you might read the discussion about the comparative advantage of various strategies depending on the selected time frame (p. 57-58).

The sequence that Brad DeLong thinks damning, that the revolutionists' odds of success are improved after the trip to earth, is just unclear. We're never told what Mike has been "thinking" during this time, or much about what's been happening overall. The evidence used to update the odds is not given to us.

The only counterargument that I could find against my interpretation is based on this dialog on p. 110:

As soon as Stu went Earthside, Mike set odds at one in thirteen. I asked him what in hell? “But, Man,” he explained patiently, “it increases risk. That it is necessary risk does not change the fact that risk is increased."

This doesn't make any sense. But I think Heinlein was probably just seduced by the fact that it sounds a good line. And maybe he is thinking about the time-frame dependence.

The whole rest of the book makes perfect sense from a Bayesian perspective.

Now, I'm not defending Heinlein's political philosophy. There is a lot to complain about (just look at the wikipedia entry for this book). But it's still a great story. Three things irritated me (from most to least important):

• the post held up as a model of correctness was itself wrong on the fundamentals
• DeLong wrongly criticized Heinlein as a mathematical simpleton
• he deleted my comment pointing this out

Too bad no one will ever know. ]

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