How Many Are There? The Number of Communicative Civilisations Computed as a Count, in Time, and on the Past Light Cone

Fermi's question asks for a count; the Drake equation returns an expectation. This paper removes three modelling choices hidden in the product: it converts the expectation into an actual count (Poisson mixture; median 5 other civilisations, P(alone) = 0.352 in the product's own form), shows that the lifetime range read as variation between civilisations rather than ignorance of one constant raises the median expectation to 387, and recomputes the answer as a birth-death process over the Galaxy's star-formation history with a 0.5-5 Gyr emergence delay (median 830 others alive now, P(alone) = 0.0245; a median of 2.17 million civilisations over all Galactic history). The nearest neighbour is typically thousands of light-years away; the population whose signals are arriving now equals the population alive now to within 0.01%; and the observed silence shifts the probability of being alone by about one part in ten million. All numbers are conditional on the stated guess ranges for the four unmeasured factors and are not evidence that extraterrestrial life exists.