Implications of the Pessimistic Lower Limit on the Drake Equation

The observation of life on Earth is generally accepted to be uninformative concerning the probability of life on other Earth-like planets, a belief first formalized by Brandon Carter and based on the selection effect of our existence. In a similar way, the Drake equation is either presented as estimate of the total number of active, communicative, extraterrestrial civilizations in our Galaxy ($n^g_{\rm civ}$), i.e. excluding humanity, or humanity is included in the estimate but judged to be an uninformative data point. Daniel Whitmire has recently challenged the Carter abiogenesis argument, claiming the logic behind it is flawed, as the conditional likelihoods used by Carter in Bayes'theorem are not evaluated prior to the occurrence of the evidence of life on Earth, but posterior. Doing so correctly, the anthropic selection effect is removed and the observation of life on Earth is informative after all. Following this argument, we treat the Drake equation as estimate of all technological civilizations in a statistical counting experiment and include the data point of humanity as informative evidence. This allows one to set a pessimistic lower limit on $n^o_{\rm civ}$ for the observable universe, $n^o_{\rm civ}>0.051$ at 95\% C.L., or $n^g_{\rm civ}>8\times10^{-13}$ at 95\% C.L. for the Galaxy. In particular, this excludes models that predict $n^o_{\rm civ}\ll 1$ for the observable universe and refines the allowable parameter space for hypotheses like Rare Earth. Our analysis substantially reduces the portion of the Drake equation parameter space that predicts humanity is alone; when applying the lower limit this study finds $P(n^o_{\rm civ}>1 |\, {\rm humanity}) = 97.6\%$, making solitude in the observable universe a disfavored outcome. For the low-end estimate of $n^o_{\rm civ}\! =\! 1$ we calculate a probability of 42\% for the existence of other communicating civilizations.