Passive SETI Detection Probability (new) · Civiletti 2025
Formalising the null: P(≥1 detection) as a function of N
Civiletti (2025, arXiv:2505.00062) derived the geometrical probability that at least one EM signal from N communicating civilisations, each broadcasting for duration δ years, passes through Earth's location: P(≥1 detection) = 1 − (1 − 0.6δ/R)𝑥, where R is the Milky Way radius in light-years. The factor 0.6 comes from the geometry of a uniform spherical source distribution.
With R = 50,000 ly the per-civilisation term is p₁ = 0.6δ/R. Try the Sandberg 2018 preset (N = 10, δ = 100 yr): p₁ = 1.2×10−3 and P(detection) = 1.2%, so the great silence is expected. Now try the Drake (1961) point estimate (N = 20,000, δ = 1,000 yr): p₁ = 0.012 and P(detection) is indistinguishable from 100%. Under this framework the Drake point estimate is not merely unlucky, it is excluded by the null result. The silence becomes hard to explain well below N = 106: at δ = 100 yr, P passes 50% at N = 577 and 90% at N = 1,918.
Step payoff
The Civiletti framework converts "we heard nothing" into a likelihood. Combined with the threshold N values from the tool (N = 57 for P = 50% at δ = 1,000 yr, or N = 577 at δ = 100 yr), you can state: "the null result constrains N to fewer than ~X civilisations, given these signal-duration assumptions." That is a far sharper statement than "we found nothing."