Chapter 14 of 15
Equations of life
The Drake and Seager equations are ways to organise what we do not know. They are speculative frameworks, not predictions: no number on this page is an estimate of real civilisations or of life.
N = R★ · f_p · n_e · f_l · f_i · f_c · L
Presets: the 1961 Green Bank values and the "commonly quoted set" are repeated in secondary sources; the meeting's own record was not checked. "Data where we have it" uses the measured terms below and leaves the unknown ones where you set them. R★ is stars per year; the measured Milky Way rate of 1.65 ± 0.19 M☉ per year (Licquia & Newman 2015) is a mass, not a count.
| Term | How well we know it | Value and source |
|---|---|---|
| R★ | Measured | 1.65 ± 0.19 M☉/yr star formation (Licquia & Newman 2015); stars per year needs an initial mass function |
| f_p | Measured | ≈ 1: 0.77 small planets per GK star at 50–300 d (Burke et al. 2015); ≈ 2.5 per M dwarf at P < 200 d (Dressing & Charbonneau 2015) |
| n_e | Constrained | η⊕ = 0.37–0.60 for 0.5–1.5 R⊕ in the conservative zone around 4800–6300 K stars (Bryson et al. 2021); 11 ± 4% for 1–2 R⊕ at 1–4 × Earth's flux (Petigura et al. 2013) |
| f_l, f_i, f_c, L | Unknown | No data. Any value is an opinion. |
One number hides the uncertainty. Following Sandberg, Drexler & Ord (2018), each term is drawn from a range instead: R★ 1–100, f_p 0.1–1, n_e 0.1–1, f_i 0.001–1, f_c 0.01–1, L 100–10¹⁰ years, all log-uniform. Their f_l comes from a log-normal model of the rate at which life starts; here f_l is a log-uniform stand-in from 10⁻ᵏ to 1, with k on the slider. Draws are seeded, so the result repeats.
| Quantity | Value | From |
|---|---|---|
| This page, k = 10: median N | 0.036 | 90% of draws between 10^-7.9 and 10^5.0 [calc] |
| This page, k = 10: P(N < 1) | 64% | [calc] |
| Sandberg et al. 2018: median N | 0.32 | with their f_l model; the mean is about 27 million, which is why a single average misleads |
| Sandberg et al. 2018: P(N < 1) | ≈ 52% | their priors |
The Seager equation
N = N★ · F_Q · F_HZ · F_O · F_L · F_S
It counts planets where a biosignature gas could be detected, not civilisations (Seager 2018): stars observed, the fraction quiet, with rocky planets in the habitable zone, observable, with life, and whose life makes a detectable gas.
Starting values: N★ = 30,000 M dwarfs bright enough for JWST, F_Q · F_HZ = 0.15, F_O = 0.001, F_L = 1, F_S = 0.5, giving N ≈ 2. They come from secondary summaries of Seager's talk and paper, not checked against the paper here; F_L = 1 is an assumption, not a measurement. The habitable-zone fraction links to the Population chapter's figures.
Sources
- Sandberg, Drexler & Ord 2018, Dissolving the Fermi Paradox
- Seager 2018, Int. J. Astrobiology 17, 294 (Seager equation)
- Licquia & Newman 2015, ApJ 806, 96 (Milky Way star formation rate)
- Burke et al. 2015, ApJ 809, 8 (Kepler occurrence)
- Dressing & Charbonneau 2015, ApJ 807, 45 (M-dwarf occurrence)
- Bryson et al. 2021, AJ 161, 36 (η⊕)
- Petigura, Howard & Marcy 2013, PNAS 110, 19273