There’s Nothing Special About X

In the discussion about my spinoffs of Nick Bostrom’s simulation argument somebody came up with the Mediocrity Principle as one way to look at the argument. My take is quite different from Wikipedia’s—I think I’m talking about the same thing, but I won’t complain if you disagree.

I don’t like the term “Mediocrity Principle” because it conceals the nature of its own argument. It’s simple probability. Better to call it There’s Nothing Special About X, which has the same number of syllables.

I ran a short sequence about it in the Daily Whale (26 October 2009 and 27 October 2009; the following day is also relevant). The main form of the argument is “There are lots of X and p(X) holds for few of them. There’s nothing special about X1, so p(X1) is probably false.”

The argument is (1) Extremely general, since there are lots of things we can count or measure and use to calculate probabilities. (2) Weak, since all it tells us is a probability, and in practice often a rough one. (3) Tricky to get right when it matters, that is, in cases where we know so little that it becomes a valuable argument. All you have to do is define X and p(X) and count them both, but when talking about something as unknown as “alien life forms” or “the long-term future of humanity” that’s tough.

I tend to think of all the probabilistic arguments as alike, so here’s a different but related one. (A) “you are alive now, so it’s unlikely that the human population will remain at its current level or above for centuries to come,” because if it did you’d probably live in the future. In other words, (A’) “human civilization is probably going to crash soonish.”

(A) is a valid argument (you can turn it into a precise Bayesian analysis over models of the time-evolution of the human population), but only gives us a weak probabilistic constraint on the future. (A’) does not follow from (A) because there are other possibilities, but there are people who accept (A’) because of (A). As one of my Daily Whale readers pointed out, a good reason to reject (A’) is that if people accept it, it could be self-fulfilling.

Now consider (B) “Nearly all living things on Earth are microscopic, so humans are almost certainly microscopic.” That doesn’t hold because there is something special about humans. (A’) and (B) show us that probabilistic arguments break easily when abused. Bearing that in mind, consider (C) “There is probably no vast galaxy-spanning alien civilization of trillions of individuals, anywhere in the universe in space or time, because if there were, you would probably be part of it.” This is a valid argument and can be generalized considerably and cast in many different forms, but it tells us nothing about the existence and only a tiny bit about the nature of any alien civilizations. We can choose any definition we like of “individuals” but we can’t know whether it makes sense for aliens. We’re trying to count something before we know what it is.

Original version, April 2010.
Updated and added here November 2011.