"R" == Rich  <someone@somewhere.com> writes:

R> And how can one derive probabilties from a sample size of zero (or
R> one if you count the earth)? This is what I want to know.

I've already posted this as part of my illustration of the scientific
method, but it clearly got lost there so let me be a bit more
specific.  I'll cast it in terms of SETI, though the idea is far more
general than SETI.

We'd like to know how many radio transmitting ET civilizations there
are in the Galaxy.  For simplicity, take the Galaxy to be a disk of
diameter D.  (This is actually a fairly good approximation.)  The
total area in which there could be ET civilizations is then
\pi*(D/2)^2.

Now suppose we search for radio transmitting ET civilizations.  We
don't find any[*] within a region of diameter d.  The area we've
searched is \pi*(d/2)^2.

There are now numerous ways to state this result.  

 - The density of radio transmitting ET civilizations is, on average,
   no more than 1 civilization per \pi*(d/2)^2.

 - The fraction of the total Galaxy that we've searched is (d/D)^2.

 - The total number of radio transmitting ET civilizations in the
   Galaxy can be, on average, no more than about (D/d)^2.



[*] By "any" of course I mean that we find no radio transmitting ET
civilizations transmitting above a certain power level.

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