deletions | additions       diff --git a/Derive L.tex b/Derive L.tex  index 40809f4..74c8676 100644  --- a/Derive L.tex  +++ b/Derive L.tex 
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which states that at any given time the minimum value for the communicative phase lifetime required for contact to occur scales with the volume of the galaxy to the power 1/4. This is also the scaling for the maximum number of communicative civilizations in the Galaxy. The absence of a message implies $L  The galactic volume can be estimated as 10^{12}-10^{13} cubic light years: therefore in our Galaxy $Lfew couple  thousand years}. It also means that at this time in our Galaxy there should be less than $N\approx 350...625$ communicative civilizations.  Note that the calculation above does not include "relic communications", messages received by one communicative civilization but sent by a no longer communicative one. So the estimate above represents an upper limit to $L$ and $N$.