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## June 07, 2002

### Rare Earth and Statistics

Thinking back to Rare Earth, I found another way to express my disatisfaction with their approach. The focal point of their attack is the Drake Equation, which attempts to assign probabilities to various conditions which would be needed to support intelligent life. People like Carl 'billions and billions' Sagan argued from the Law of Large Numbers that even tiny probabilities in each of the variables would result in a respectable number of civilizations due to the vast number of stars:

The Law of Large Numbers says that in repeated, independent trials with the same probability p of success in each trial, the chance that the percentage of successes differs from the probability p by more than a fixed positive amount, e > 0, converges to zero as the number of trials n goes to infinity, for every positive e.

In our terms, each star system is an independent trial, and the proportion of star systems which have a given attribute should approach the probability p for that attribute. So a law of statistics is used in tandem with the large number of stars in the universe to plead for the ubiquity of life.

That's a tough, if somewhat specious argument to beat. And it is an arbitrary target, as Carl Sagan, Frank Drake and the authors of **Rare Earth** *all* admit. The numbers assigned to all the probability variables are *guesses*. Most of the earlier contributors are willing to live with that, and class the Drake Equation as an interesting thought experiment.

But the authors of **Rare Earth** take the bait, and make it their mission to try to push as many of the variables as possible to darn near zero, even introducing *new* variables which they have a better chance of assigning probability zero to in order to achieve their goal. But it's just a game. And it's this aggressive attack of what is clearly just a game, and clearly just a parlor trick at that, which makes the book annoying. Lots of the topics discussed were fascinating, but that they were all directed to destroying an admittedly offhand, back-of-the-envelope thought experiment just irked me no end.

Posted by dpwakefield at June 7, 2002 10:12 AM