## Bayes, Sober, dice, intelligent design

I’m teaching Bayes’ theorem this week in my discrete math course, and that reminds me of an interesting puzzle related to the “argument by design” for God’s existence. The argument goes something like this: the probability that the universe would, by pure chance, have the physical constants “fine-tuned” in such a way as to allow intelligent life is spectacularly small. The probability that God would create the universe in this way, though, seems pretty high. So, according to Bayes, whatever prior degree of belief we might have in the existence of God should be much amplified by the fact that the universe is so hospitable to human life.

Objection to this argument: if the physical constants of the universe weren’t fine-tuned to permit our existence, we wouldn’t be here to notice! So the observation that the constants are fine-tuned carries no information, and shouldn’t be allowed to affect our beliefs.

Objection to the objection: Then suppose you were blindfolded in front of a firing squad, you hear twenty shots ring out, and you find yourself alive and unharmed. Quite naturally, you’re drawn to the conclusion that the firing squad must have missed you on purpose. Now a philosopher wanders by and objects: “But if you’d been killed, you wouldn’t be here to make that observation, so the fact that you survived carries no information and shouldn’t affect your beliefs about the intentions of the firing squad!”

At this point your confidence in philosophers would be shaken.

Elliot Sober handles this version of the argument by design, along with many others, and their corresponding objections and counter-objections, in a very thorough and clearly-written paper (.pdf file). So rather than try to unravel this knot in a blog post, I’ll give you one more puzzle.
Suppose you roll a die 20 times and get

6-4-1-5-1-2-1-3-3-1-6-2-4-1-5-1-3-2-4-5

A person sitting next to you now pipes up and says, “Well, there you have it, very strong evidence of the existence of God.”

You: “How so?”

Person: “Any God I can conceive of would certainly have arranged for those dice to fall 6-4-1-5-1-2-1-3-3-1-6-2-4-1-5-1-3-2-4-5. So the probability of that outcome, conditional on God’s existence, is 1, while the probability conditional on God’s nonexistence is 6^(-20). So you and I both have to drastically increase our degree of belief that God exists.”

How similar is this to the argument by design for God’s existence? To the firing squad argument that the shooters must have missed on purpose? Which of the three arguments are right and which are wrong?

## Human(itie)s, aliens, and autism: Ian Hacking and Elliot Sober at Fluno Center tomorrow

Humanities at Wisconsin are said to be underfunded and demoralized, but you’d never know it from the excellent “What is Human?” symposium the Center for Humanities is holding tomorrow at Fluno Center. At 1:45, Ian Hacking will speak on “Humans, aliens, and autism” — perhaps he’ll expand on some of the material in this 2006 essay from the LRB. Hacking’s two books on the development of probability theory, The Emergence of Probability and The Taming of Chance, are probably the best I’ve read on the history of mathematics; to stay bound to the theme of this post, he is one of the only people writing really humanely about mathematical practice. (The late Thomas Tymoczko was another.)

Speaking at 11:15 is our own Elliot Sober, who is that most powerful of creatures, a philosopher who knows Bayes’ Theorem. (See also: Adam Elga, K. Anthony Appiah.) Sober’s title is TBA, but he may well talk about (or, more likely, against) the “design argument” against Darwinism. (He’s definitely giving a talk on that subject at 7:30 this Thursday night, in 1315 Chemistry.) A very vulgar version of the design argument looks like this. The probability that intelligent life would arise, if there were no divine guidance, is nonzero but spectacularly small. The probability that intelligent life would arise, if a divine being created it, is 1. Now Bayes says you should think that divine origin of human life is very likely, even if it was very unlikely in your prior. Sober’s new book, Evidence and Evolution, takes on the design argument and its many more sophisticated variants, and more generally tries to work out what we mean by “evidence” about the origins of life. Bayes flies everywhere.

Sober is also credited with the following joke:

A boy is about to go on his first date, and is nervous about what to talk about. He asks his father for advice. The father replies: “My son, there are three subjects that always work. These are food, family, and philosophy.”

The boy picks up his date and they go to a soda fountain. Ice cream sodas in front of them, they stare at each other for a long time, as the boy’s nervousness builds. He remembers his father’s advice, and chooses the first topic. He asks the girl: “Do you like potato pancakes?” She says “No,” and the silence returns.

After a few more uncomfortable minutes, the boy thinks of his father’s suggestion and turns to the second item on the list. He asks, “Do you have a brother?” Again, the girl says “No” and there is silence once again.

The boy then plays his last card. He thinks of his father’s advice and asks the girl the following question: “If you had a brother, would he like potato pancakes?”

(This philosophy joke, along with many others, appears here.)