Is There Intelligent Life On Earth?
Richard Gott, III and the Copernican Principle
This is based on J.R. Gott, "Implications of the Copernican principle for our future prospects," Nature 363, 315-319 (1993). Assume we are living within a 95% confidence interval for our civilization's lifetime and that this civilization has existed for 200,000 years. Let
Past = Time thus far (200,000 years)
Future= Time from now to extinction
Then if the distribution function for X={Future/Past} is
(1) F(x)=x/(x+1),
a 95% confidence interval for time to extinction (Future ) would be : [(1/39)Past, (39* Past] = [5 thousand, 8 million] years.
Assumption (1) can be justified in more than one way. It would be correct, for example if
(2) "Past" and "Future" behave like independent exponential random variables,
and the exponential is somewhat plausible as a lifetime distribution. But (2) is not a necessary assumption for (1) (just sufficient).
Now suppose you take as a definition of intelligence: "the ability of a species to live on its planet for Z years after achieving radio technology. " (The justification for this type of definition might be that a species must at least be capable of interstellar communication for a certain period, Z, if it is to be deemed intelligent. Otherwise, even an interstellar neighbor, within Z light years, could not be aware of our alleged intelligence while we were still extant!) What is the probability that we will ever qualify as intelligent if Z=1 million,10 million, or 1billion years? Equation (1) implies that
P[Future> f] = 1/(5f+1), approximately, where f is measured in millions of years, so the probability that we will eventually qualify as an intelligent species is:
17% if the requirement is that we survive 1 million years;
2% if it's 10 million years;
and only 0.1% if it's 1 billion years !!