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$L_c \sim \left(\frac{V}{L_c}\right)^{1/3}$ = V^{1/4}  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 $Linterest (e.g. singularity). interest, singularity etc. (many of these possibilities have been extensively discussed in the context of the \href{http://en.wikipedia.org/wiki/Fermi_paradox}{Fermi paradox}).  Nevertheless self-annhilation / destruction of natural resources is another a realistic  possibility. Overall the absence of contact tells us that there should be an important transition in the characteristic of human civilization occuring in a timescale shorter than about 1000-2000 years.