We’ve seen the Drake equation in many forms, none of them very impressive. They all share the same failing, as we’ll see.
Two fellows, Frank and Sullivan, have another go. The lite version is (appropriately) in the New York Times with the title “Yes, There Have Been Aliens“. The full version is the peer-reviewed paper “A New Empirical Constraint on the Prevalence of Technological Species in the Universe” in Astrobiology. From the Times:
Instead of asking how many civilizations currently exist, we asked what the probability is that ours is the only technological civilization that has ever appeared. By asking this question, we could bypass the factor about the average lifetime of a civilization. This left us with only three unknown factors, which we combined into one “biotechnical” probability: the likelihood of the creation of life, intelligent life and technological capacity.
You might assume this probability is low, and thus the chances remain small that another technological civilization arose. But what our calculation revealed is that even if this probability is assumed to be extremely low, the odds that we are not the first technological civilization are actually high. Specifically, unless the probability for evolving a civilization on a habitable-zone planet is less than one in 10 billion trillion, then we are not the first.
You can already see that abuses of probability are coming up. From the paper:
We define the “A-form” of the Drake equation, which describes the total number of technological species that have ever evolved anywhere in the currently observable Universe:
A = [N* fp np][fl fi ft]
…where N* is the total number of stars, fp is the fraction of those stars that form planets, np is the average number of planets in the habitable zone of a star with planets, fl is the probability that a habitable zone planet develops life, fi is the probability that a planet with life develops intelligence, and ft is the probability that a planet with intelligent life develops technology (of the “energy intensive” kind such as that of our own civilization).
After this comes manipulations of the equation which aren’t especially interesting. There are no insurmountable problems in the leading elements of this or the modified equation. But there is a universe of trouble in the second terms in the brackets, [fl fi ft].
All of these elements are said to be probabilities. Skip whether we can discover unique numbers for each probability and instead focus on probability’s Golden Rule: All probabilities are conditional. From that simple and honest truth flows everything, including the proof that the Drake equation, modified or no, is meaningless.
To prove that, pick the element ft, “the probability that a planet with intelligent life develops technology (of the ‘energy intensive’ kind such as that of our own civilization).” That probability does not exist—no probability does—without premises, assumptions, givens, or conditions. And what might these premises be?
The point of the Drake equation is to count on or, in the modified form, to put a probability to the proposition “Rational creatures on other planets exist”. Yet a main element, fi, is very nearly that same probability. You might argue that it isn’t precisely the same, in an attempt to save Drake from circularity, but fi surely smacks of assuming what it set out to prove.
Even if circularity is missing, fi has no meaning. None. No probability in that equation is sensible. All probabilities need evidence, and these have none. The best we can do is infer the propositions of fi and so on are contingent, and therefore have any number between 0 and 1, which means, thus the final result (in the modified Drake) is itself between 0 and 1, and which is nothing more than knowledge that “Creatures exist” is itself contingent. Nothing has been gained.
In order to calculate fi, we need a list of accepted premises that unambiguously lead to a unique number, or at least to a tight interval. None exist: none that are acceptable and agreed to by all, I mean. Plentiful premises exist that might be used, of course. You might say, “7 out of 10 planets with life develop rational creatures” and thus fi = 0.7. But who would agree to these premises?
Since nobody has any idea of how life began (on Earth) nor do any know of rationality arose, premises which can fix fi just don’t exist. And that same is true for the other probabilities. The Drake equation leads nowhere.