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A pleasantly lulling subject for speculation (at least for those of us who grew up reading science fiction) is the following: if the universe is very big and very old, and multicellular life is not vanishingly unlikely, then where are they? That is, where are all the otherworldly, intelligent species who should have contacted us?

This problem was most perfectly expressed by the great Italian physicist Enrico Fermi. In its most succint formulation, the “Fermi Paradox” goes: The commonly held belief that the universe has many technologically advanced civilizations, combined with our observations that suggest otherwise, is paradoxical, suggesting that either our understanding or our observations are flawed or incomplete.

In the middle 1940s, when Fermi was working on the Manhattan Project at Los Alamos, he and other scientists debated the problem late into the night. The scientists came to no conclusions of course, but they did sketch some intriguing possibilities:

1. Extraterrestrials exist, but we missed them.
2. They exist, but for obscure reasons of their own choose not to communicate with us.
3. They exist and they communicate, but we cannot hear them.
4. They existed or they will exist, but our existence does not overlap with theirs: we are either too late or too early.
5. They never existed.

(There was a final possibility, itself perhaps a variation of No. 4, suggested by Edward Teller, the inventor of the Hydrogen Bomb: intelligence is not a useful adaptation. Civilizations tend to blow themselves up.)

The problem, in fact, is an essentially mathematical one: how common is intelligent life in the universe? An astronomer called Frank Drake formulated an equation that allowed scientists to quantify the uncertainty of the factors which determine the number of civilizations in our galaxy. The Drake Equation states:


N = R* fp ne fl fi fc L

Where:

N is the number of extraterrestrial civilizations in our galaxy with which we might expect to be able to communicate

and

R* is the rate of star formation in our galaxy
fp is the fraction of those stars which have planets
ne is average number of planets which can potentially support life per star that has planets
fl is the fraction of the above which actually go on to develop life
fi is the fraction of the above which actually go on to develop intelligent life
fc is the fraction of the above which are willing and able to communicate
L is the expected lifetime of such a civilization

The problem, which is obvious when stated in this form, is that scientists cannot agree on values for the Drake Equation. Drake himself thought that intelligent life was common (that is, N > 1) despite all evidence to the contrary. But that’s because Drake used wildly optimistic figures for the frequency with which planets develop life, the frequency with which that life becomes intelligent, and the length of time that civilizations cohere.

More gloomy values produce a lower sum. Indeed, Michael Shermer, the founder of the Skeptics Society, once argued in an article in Scientific American that L = 304 years, based on the length of time that societies since the Roman Empire have managed to survive. Using some conservative values (stolen from Wikipedia), we might say:

R* = 10/year, fp = 0.5, ne = 2, fl = 0.33, fi = 1×10-7, fc = 0.01, and L = 304 years

N = 10 × 0.5 × 2 × 0.33 × 1×10-7 × 0.01 × 304 = 10.032×10-7 = 0.0000010032

In other words, the probability of an intelligent civilization communicating with us is fantastically unlikely. Of Fermi’s possible explanations of why we have never heard from aliens, the correct answer is something like No. 4. We are alone with our day. No one is coming to help. We have no one to talk to.

The Drake Equation is obviously incomplete, really little more than a kind of mathematical joke, but it possesses one famous curiousity: using conservative values, the Equation will produce a sum that contradicts our observations. However improbably, there is at least one human-like civilization in the universe with whom we can communicate.

UPDATE: 6.18.2005: I expressed this last thought differently, and badly, in my initial post. The fact that we now exist, and that we communicate with each other, does not of course mean that N = 1. I was making a poor kind of joke, but I seemed to fall into the “observer fallacy. ”

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