17 November 2005


Paul is at it again, making me and others think about statistics, and analytic philosophy. Damn him, doesn't he know that if I wanted to think all the time I would have wasted the last decade or more trying to be an intellectual?

I've never studied the Doomdsday Argument, because I've never done serious analytic philosophy but more importantly because (after looking at the argument) I think I got a better training in statistics than all that. In other words, it seems to me that one does not need to make a philosophical critique of the argument, because it's based on an utterly invalid application of Bayesian statistics. Bayesian theory tells us that we can revise prior probabilities in light of new information. Like most probability theory it relies heavily on the idea a random sample. This paper that Paul linked to is actually much clearer than the link above. It gives the example of balls in an urn: if we don't know if there are 10 balls in the urn or 100, then our prior probability is .5 for each possibility (10 or 100). If we then pick one ball out of the urn and it turns out to be numbered 1 through 10, we can revise the probability of there being only 10 balls upward (since the chances of picking 1-10 if there are only 10 is much higher than picking 1-10 if there are 100). Fine by me. Go Mr. Bayes.

The Doomdsday argument says we can apply this reasoning to the population of the species. If you sample US - that is, the human population today - we seem to be the 1-10 balls, increasing the chances that there are only going to be 10 or so balls, ever. But we aren't a random sample of the entire history of the human species! I don't know if it's bad philosophy, but it's awful statistics. If we went to the end of time, when the human species was extinct, then sampled from all of human history and picked one of us that would tell us that there's a good chance humans didn't live very long. But we are not at the end of time, we are in time and we always will be. Sometimes we want to freeze things to look at statical samples, but we can never do that with humanity as a whole and certainly not with the future history of humanity.

Part of the problem with applying statistical theory more broadly - to thinking about human problems, politics, history, the world, etc. - is that it has no space for a sense of temporality. It is either completely static, or it moves through points in time in the most fixed and linear sense possible. Statistical reasoning is almost always very contrained by its prior assumptions of a random sample (and others). And the world we live in is filled with patterns and choices that make it only rarely a random sample. The world (and us) is marked by a temporality that will always thwart our own efforts to fix that world in place with logic.


Rev. Mr. T. Bayes said...

Dr. Chambers is clearly right. Let's take the balls-in-an-urn example. Let's assume that the balls are drawn out sequentially rather than randomly (just as people are born, unless we are coming from Plato's afterlife). Let's assume that Ball No. 7 is drawn. All that tells you is that you are in Time No. 7. It tells you nothing about what will happen at Time No. 11, unless you felt about in the urn when you were drawing and know there are only ten balls.

Transient Gadfly said...

Yeah, but it's still a little trickier than that. Just to clarify something, the argument does not contend that drawing the time = seven marble tells you about the existence of marble time = 11, what it tells you is that if there are two choices, ten time marbles or a hundred time marbles, you are (much) likelier to be in the former case.

It seems obvious to you, and me, and the pseudonymous Rt Honorable Bayes, that we are not truly random humans. It seems like you're saying, "hmm...let me pick a person totally at random throughout all of time and space to be the subject of this experiment, I'll flip a coin, roll the d20, consult the I Ching, and...pick...myself." Doesn't seem very random.

It's this tricky time thing that seems to be the hang-up. It's the fact that we are, as we'd say in mathematical analysis, "well ordered." This argument pre-supposes a) that you can look at all of time that humans occupy as a "bag," and b) You being Here Now is equivalent to picking a random ball out of that bag. While a) seems at least okay-ish, it immediately seems like b) is not true.

Quoting myself here, again: it's 2005 and I'm alive on the earth. What are the odds I'm American? Do the math and you'll come up with an answer that's around 1 in 24, or about a 4% chance. And you're wrong, the Odds Are One™, I am in fact American. Bayes says I should bet on me being not American, but if I were to do so, I'd lose. Don't get me wrong, I think the Doomsday Argument is totally, utterly invalid, but I don't think it lies in deciding whether you're a random human or not, because it seems very difficult to show that this isn't the case, just as it's difficult to show that it is. I think the answer is really more Platonic than that--you and I can't be defined as random human number 60-billion-and-some-odd, because we cannot be separated from our 20th century-ness, our American-ness, our iPod-having-ness. You could bet on you having many other, much more likely attributes (non-American, born before 1950, not having an iPod), but you'd lose. Not because of the odds, but because You Do Not Exist Apart From Those Things. That is Who You Are.

(by the way, no, I still don't have an iPod).

Transient Gadfly said...
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