Three-Toed Sloth

Where Are They?

Christopher Genovese of Signal + Noise is, appropriately enough, meditating on interstellar communication and has just been introduced to the Fermi paradox. Which goes somewhat as follows. (This is the version I use when teaching physics, i.e., I have no idea whether it's historically accurate.) Imagine it's, oh, about 1950, and you're Enrico Fermi, hanging around Los Alamos with Oppenheimer, von Neumann, Ulam, Teller, Morrison, Szilard and the rest of the gang, and somebody --- perhaps one of the younger physicists who reads pulpy science fiction magazines --- brings up the question of whether there's intelligent life Out There. Now, for some odd reason, you have super-critical branching processes on your mind, and this leads you to make a quick calculation about how long it would take a space-faring species to colonize the galaxy; with any reasonable-looking set of parameters, you conclude that they should've been here long since: this is the paradox. There are a number of possible resolutions.

1. There are no other intelligent space-faring species; we are, for some reason, the first. Somebody has to be. Or: conditions became right for the evolution of intelligent life only very recently, and colonization is slow, so while we're not necessarily the first, nobody else has much of a head start on us. But it's hard to see why intelligent life couldn't possibly have evolved, say, 65 million years ago, which should be plenty of time. The most satisfying scenario along these lines is that the evolution of intelligent species with a cumulative technology is extraordinarily improbable; we're it.
2. Intelligent space-faring species don't live very long (see "super-critical branching processes" supra), so the colonization process dies out if it ever gets started. Or: intelligent space-faring species get beyond the crude desire to spread themselves hither and yon. Problem: In both cases it takes only one greedy species which isn't quite vicious enough to blow itself up to set off the branching process.
3. We have been contacted. The nicest version of this is the one attributed to Szilard: "Maybe they're already here, only you call them Hungarians". Other candidates have been suggested. None, and I say this with all due respect for my Magyar colleagues, are plausible.
4. We're in a zoo or nature preserve, and will not be contacted until we're ready for it/sufficiently marinated/a galactic Republican administration guts the park service.

Now, my favorite solution is "none of the above". It is instead to return to the back of the envelope and reconsider what happens to the branching process when one takes into account the fact that it's got to move across space. Quite standard growth processes, even if supercritical, will tend to produce huge voids and gaps, where nobody goes for no particular reason, and these gaps will persist for a very long time. (Technically: the distribution of gap sizes and lifespans has power-law tails.) This was first suggested by the Brazilian physicist Osame Kinouchi, in one of the cleverest physics papers I've ever read. I'll quote from the beginning, before he gets into the math:

I live in Brazil, and sometimes I wonder about such exotic places like New York or Paris and the curious customs of their inhabitants: they do not make gestures when speaking and mix sweet food with salty food! Some people drink warm beer and even do not like soccer! And their women use very large bikinis! Very irrational behavior, indeed! However, I must recognize that there are also a lot of exotic places (and even populations) inside Brazil, which are almost never visited or contacted by the global civilization. Suppose that you are a member of a lost Amazonian tribe that has never been contacted. Now, it is obvious that a technological civilization able to perform travel by air at 1000 km/hour certainly had time to colonize the entire globe. But since they have not reached you (remember, you are a member of a undiscovered Ianomani tribe), should you conclude that there is no such global civilization?

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