I'm new to the list and so don't know if this has been pointed out here before.
As presented in SETI's web site, N is the number of civilizations in our
galaxy whose radio emissions are detectable. This particular definition of N
then leaves out of consideration all the advanced civilizations whose
methods of communication have long since surpassed that stage and rendered
radio-wave communication obsolete.
If the typical length of time spent in the radio-wave emission stage is two
centuries, say, while the typical lifetime, L, of a civilization is, for
example, a hundred thousand years, then this definition of N omits 99.8% of
the advanced civilizations. Although this line of argument assumes that
science and technology continue to advance without halting just beyond our
own level of development, that is a plausible assumption, which is
incorporated within Dyson's work, for example. Sometimes it requires a new
development to make us realize that science does continue onward while a
civilization endures, and one that could be pertinent at this time,
regarding communications, is the "teleportation of a photon" (as might be
developed a few centuries from now).
The SETI website's definition of N also emits all those civilizations that
are still in a stage of radio-wave communication but whose emissions, due to
distance from us in the galaxy, are too weak for us to detect.
However, as I understand the origin and ordinary use of Drake's equation,
its estimates of L can run up into the millions of years, while Rx involves
the rate of star formation within the whole galaxy.
The recent innovation of an optical SETI may alleviate the above objections,
but only somewhat. In any case, shouldn't the SETI website definition of N
be corrected?
Jim Deardorff
Research Professor Emeritus
Oregon State University