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The "L" Paradox
by Dr. Charles Rubin, Duquesne University

As Frank Drake tells it, the number N of detectable civilizations in space is highly correlated with the longevity L of civilizations capable of interstellar communication: N~L . But we know no more about the value of L today than Drake did at Green Bank 35 years ago. SETI scientists have always hoped for a very large L, not only because they are well wishers of intelligent civilizations, including our own, but because it appears to improve the chances of ETI contact. Yet as L grows, it poses a problem for SETI.

A short L reduces the odds that civilizations will overlap in time. If Planet A is "on the air" for 100 years, how likely is it that Planet B, with a correspondingly short L, will be in a receiving mode for the 100 years in which A's signal will pass by? Longer Ls increase the odds that multiple senders and multiple receivers will overlap. As L gets very long, should we not expect an ever increasing accumulation of broadcasting or leaking civilizations, hence an ever artificially brighter radio sky?

SETI results thus far do not suggest that such a bright sky exists. Thus Fermi's Paradox takes on meaning not just for interstellar travel, but also for communication. If L is very large, where are their signals? The explanation might be purely technical. Even very large Ls produce a small number of civilizations relative to interstellar distances. Speed of light lag and signal attenuation reduce the chance that, at any moment, one civilization will get wind of another.

Another possibility is conceptually more interesting, for it has important implications for SETI even if the technical explanation is correct. The assumption of mediocrity is essential to the plausibility of SETI. Yet routine assertions that civilizations to be contacted are likely far in advance of our's violate that assumption. It is true we could hardly contact a civilization much less advanced than ours. Still, thinking this point through in connection with mediocrity produces bad news for SETI. Are we standing at one tail of the L distribution, expecting to contact somebody at the other tail? Then we lose the advantage of the large L, because we are saying we are only likely to hear from a small fraction of N.

Is it not more consistent with the assumption of mediocrity to say that (terrible thought) our present age is the mean for L, i.e., life spans are extremely short? Or, assuming a different scale for mediocrity, perhaps life and intelligence developed on roughly the same schedule everywhere, so that cosmically speaking intelligence and technical civilizations are mostly as young as we are. Are we close to the mean for the universe's current technological level?

Practically speaking, these considerations point in the same direction. SETI had best plan for the long term--assuming we have a long term. The evidence for ETI is not yet obvious. This should remind us what a big place the universe is, or perhaps suggest that most of our prospective partners are about as new to SETI as we are.

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