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The given definition of L does not say that, guys. It specifies the length of time one civilization exists, period. It's not enough to assume that two sufficiently long-lived civilizations will necessarily overlap just because they are long-lived. That overlap is another variable outside of L, and should be stated as such.
Of course, the whole equation is incredibly generalized anyway, so I suppose we could just break it all down to one variable Ue (for extremely unlikely)...
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