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On the other hand our discussion of the Drake equation led to the conclusion that, roughly speaking, $N \sim L$ (meaning the denominator in previous equation is $\sim$ 1) (but see the \href{http://en.wikipedia.org/wiki/Rare_Earth_hypothesis}{rare Earth hypothesis} for a different conclusion). And so we can further simplify and write   $L_c \begin{equation}  L_c  \sim \left(\frac{V}{L_c}\right)^{1/3}$ = V^{1/4} \end{equation}  Which states that at any given time the minimum value for the number of galactic communicative civilizations in order to achieve contact is given by the volume of the galaxy to the power 1/4. Note that at the same time this number is also the minimum communicative phase lifetime required for contact. The absenece of a contact (also discussed as FERMI paradox) then allows to assess that in our Galaxy $L