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\section{A lesson from the sky?}  Let's define $n=\frac{N}{V}$ the number density of communicative civilizations in the Galaxy, where $N$ is the total number of such civilizations existing at any given time in the Milky Way and $V$ is the total galactic volume. Assuming an homogeneous distribution across the Galaxy, the average separation $r$ between two neighbour communicative civilization is $r\sim n^{-1/3}$. In order for two civilization to communicate, their separation needs necessarily to be smaller than their communicative phase lifetime $L$. This is assuming communication technology that is limited by the speed of light. We can then ask what would be the minimum value for $L$ such that communication can occur (we call this value $L_c$). That is we impose $r=L$. We then obtain $L\approx (N/V)^{-1/3}$.  Now we can use equation \ref{Drake_simplified} to derive the minimum lifetime of the communicative phase in order for contact to occur. occur  \begin{equation}  L_c \sim \left[\frac{V}{5\,f_l\, f_i\, f_c}\right]^{1/4} f_c}\right]^{1/4}.  \end{equation}  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). Therefor we can further simplify and obtain