deletions | additions       diff --git a/Derive L.tex b/Derive L.tex  index a1d8eb8..1583d1b 100644  --- a/Derive L.tex  +++ b/Derive L.tex 
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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 $Lcan not be higher is smaller  than 10^8-10^9. a few thousands.  Also the lifetime of such civilization civilizations  is usually shorter than 1000-2000 years. This does  not longer necessarily means that the number of intelligent civilizations in the Galaxy is limited to this number, it just implies that their communicative phase is limited to a short time. There could be different reasons for this, including transition to more efficient forms of communication than electromagnetic signals, loss of interest (e.g. singularity). Nevertheless self-annhilation / destruction of natural resources is another 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 XXX about 1000-2000  years.