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\section*{A lesson from the sky?}  Let's define $n=N/V$ 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 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{eq:Drake_simplified} to derive the minimum lifetime of the communicative phase in order for contact to occur \begin{equation}  L_c \sim \left[\frac{4\,V}{ f_i}\right]^{1/4}.  \end{equation} 
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Since we are discussing the second hypothesis, $f_i$ is not a small number. Let's assume, as Frank Drake did in his estimates, that $f_1=1$.   %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). Therefore we can further simplify and %obtain   \begin{equation}  %L_c \sim \left(\frac{V}{L_c}\right)^{1/3} = V^{1/4}  L_c \sim (4V)^{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 scales with the volume of the galaxy to the power 1/4. Note that at the same time this number This  is also the scaling for then  minimum communicative phase lifetime required for contact. The absenece absence  of a contact message  then allows to assess estimate  that in our Galaxy $LThe galactic volume can be estimated as 10^{12}-10^{13} cubic light years: therefore in our Galaxy $L  The galactic volume can be estimated as 10^{12}-10^{13} cubic light years: therefore in our Galaxy $L  It also means that at this time in our Galaxy  there can be at max $N\approx 250...1000$actively  communicative civilizations in our Galaxy. civilizations.  and %and  the lifetime of such civilizations is also usually shorter than 1000\...3000 years. This does not necessarily necessaril%y  mean that the number of intelligent civilizations in the Galaxy is limited to this number, it just implies that %that  their communicative phase is limited to a short time. There could be different reasons for this, including transition %transition  to more efficient forms of communication than electromagnetic signals, loss of interest, singularity etc. %etc.  (many of these possibilities have been extensively discussed in the context of the \href{http://en.wikipedia.org/wiki/Fermi_paradox}{Fermi \href{http://en.wikipedi%a.org/wiki/Fermi_paradox}{Fermi  paradox}). Nevertheless self-annhilation / destruction of natural resources is a realistic %realistic  possibility. Overall the absence of contact tells us that there should be an important transition in the %the  characteristic of human civilization occuring in a timescale shorter than about 1000\...2000 years.