On 1/8/99 Anders Sandberg wrote:
>Is the Strong Anthropic Principle Too Weak?
>to appear in Il Nuovo Cimento B
Their abstract reads:
We discuss the Carter's formula about the mankind evolution probability following the derivation proposed by Barrow and Tipler. We stress the relation between the existence of billions of galaxies and the evolution of at least one intelligent life, whose living time is not trivial, all over the Universe. We show that the existence probability and the lifetime of a civilization depend not only on the evolutionary critical steps, but also on the number of places where the life can arise. In the light of these results, we propose a stronger version of Anthropic Principle.
I finally looked this paper over carefully, and I think they misinterpret their main result. Their main result is equation 15 on page 7, which they interpret as showing "that the expected living time of a civilization increases with the number of earth-like planets in the Universe." They contrast this with the suprisingly short living time obtained in Carter's original calculation. What Feoli & Rampone actually calculate, however, is the expected *maximum* living time among all the planets.
Carter got his result by conditioning on a planet having reached the civilization level sometime during the planet's fixed time window of t0. Feoli & Rampone, in contrast, condition on at least one of N planets achieving civilization during its t0 window.
Equation 9 gives the probability P'(t) (for t in [0,t0]) that at least one of the N planets will have reached civilization level by the time that planet is t old. This can be thought of as a CDF over the PDF describing the actual time when the earliest planet reaches civilization level.
Equation 10 differentiates this CDF, obtaining the PDF, and takes the expectation of this PDF. Equation 10 is then reworked to obtain equation 15, which is the main result. Thus the main result is just the expected time duration after civilization arrives on the *earliest* planet on which civilization arrives.
This time obviously should increase as N increases. However, unless we have some reason for believing that we are the earliest planet (relative to when our planet formed), this should give us no comfort about the expected time our planet will remain viable. If there is a conflict between Carter's result and observations about our planet, Feoli & Rampone do not help us resolve it.