From: Robin Hanson (hanson@econ.berkeley.edu)
Date: Fri Jan 15 1999 - 14:01:23 MST
On 1/8/99 Anders Sandberg wrote:
>
>Is the Strong Anthropic Principle Too Weak?
>A.Feoli, S.Rampone
>to appear in Il Nuovo Cimento B
>http://xxx.lanl.gov/abs/gr-qc/9812093
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.
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