Uncertainty in the Probability of this Crazy Extraterrestrial Life

Over the past 50 years, quite a few fascinating discoveries have been made, changing the direction and the assumptions of scientific inquiry. In his book, Probability 1, Amir Aczel, an associate professor of statistics at Bentley College, uses the question of whether there is intelligent life elsewhere in the universe as a frame for the discussion of a selection of these discoveries. He presents, in a clear and easily accessible narrative format, topics ranging from organic chemistry to chaos theory to the recent discovery of extrasolar planets.

Aczel's treatment of the majority of the topics in the book is accurate, easily understandable and skillfully interlaced with the personal stories behind the scientific discoveries that he discusses. But when, toward the end of the book, Aczel turns to statistics to argue in favor of the existence of extraterrestrial life, he moves onto shaky ground. The statistical constructs that Aczel presents are valid, but the conclusions that he makes based on those constructs are much more speculative than Aczel admits.

For example, Aczel explains that if a bus arrives at a bus stop, on average, every 10 minutes, and you arrive at the bus stop at a random time, you will, on average have to wait more than five minutes for the bus. This is because if you arrive randomly, you are more likely to arrive during a long interval between buses than you are to arrive during a short interval between buses due to the fact that there are more total minutes in the long intervals than there are in the short intervals. The problem comes when Aczel extends this argument to the discussion of life in the universe. He says that if "God creates you and randomly sends you...to live on some planet...a longer-living civilization has a higher chance of receiving you than one that has existed for a short time," and uses this observation, in concert with the fact that we all happen to have been "received" by Earth, to conclude that, "It is very likely that, as galactic civilizations go, we are on the above-average development level, and possibly way up there among the most advanced." But even using Aczel's own logic, we have no idea how many people have been "received" by other civilizations, so we don't know whether we just happen to be the equivalent of the few lucky people who arrive at the stop in the short interval between buses.

In further support of his claim that we are probably one of the most advanced civilizations around, Aczel points out that a 30-year-old has a higher average life expectancy than a newborn because a 30-year-old can no longer die at an age younger than 30. He extends this argument to say that if life on Earth has survived as long as it has, it has a longer life expectancy than life in the universe in general. This is a reasonable statement, when applied to life in general. But Aczel is talking about intelligent life, and in particular, intelligent life that can communicate through space. On both of these counts, we are the cosmic equivalent of newborns, making Aczel's conclusion flawed.

And Aczel's final calculation, leading to the number 1 for the probability of intelligent life elsewhere in the universe, uses a watered down version of Drake's equation to compute the probability of intelligent life evolving around a particular star. Drake's equation, a description of the factors involved in calculating the number of civilizations in the galaxy capable of communicating with each other, is useful in concept. But the equation is not a very practical tool for performing actual calculations because its factors include numbers like the percentage of planets in their stars' habitable zones that contain all of the environmental conditions necessary to life. Any estimates of these numbers that we make range from extremely rough approximations to wild guesses. Aczel, however, does not even attempt to give values for all of the variables in his calculation. Instead, he gives rough approximations for two of the variables in the equation and then lumps the remaining terms together in an arbitrarily chosen, "extremely remote," one in a trillion probability for intelligent life occurring on a planet that lies within its star's habitable zone.

Included in this choice are all of the questions that we began with in trying to determine the probability of the extraterrestrial life. Aczel gives no convincing reason why we should choose one in a trillion as our base probability, and we really have no way of knowing whether his number is correct even to a few orders of magnitude. With so many uncertainties involved, Aczel's statistical argument is attractive, but it does not warrant his unqualified conclusion that, "The probability of extraterrestrial life is 1.00, or a number that for all purposes is 1.00. We are not alone."

Yes, there are lots and lots of stars in the universe; yes, this means that the probability of life forming on one of them can be extremely small, while the probability of life forming on at least one of them is extremely large; and yes, this implies that since we know that life can form (we exist), it probably has formed elsewhere. But while this is a reasonably convincing intuitive argument for the existence of extraterrestrial life, it is, in essence, simply a mathematical restatement of Ellie's comment in Contact--"The Universe is a pretty big place...so if it's just us, seems like an awful waste of space." The argument makes sense. It's conclusion is probably even correct. But Aczel's calculation does not answer any of the key questions that have existed, and that continue to exist, in the search for extraterrestrial life.