The equation · piece 5 of 7 · fi
The share of planets with life on which it becomes intelligent
Given a planet with life, how likely it is that some of that life eventually becomes intelligent in the sense that matters here: able to build technology. On Earth it took about four billion years, most of it spent as single cells, and happened in one lineage out of billions of species, which the biologist Ernst Mayr took as proof that it is a fluke. Others read the steady rise in the complexity of life as a sign that intelligence is close to inevitable given time. There is no second example, and the only new evidence is statistical: reasoning from how late in Earth's habitable life we arrived.
set on 16 October 2026
When the number on the home page is computed, a value for this piece is picked at random from this range each time, and every tenfold step between the two ends is equally likely.
Why that range
Starts from the 2018 paper's span of 0.001 to 1, which they took from the published estimates, and lowers the floor one power of ten to 0.0001 so that Pascal Lee's 0.0002 falls inside it. The top is 1, Drake's and Westby and Conselice's assumption and Conway Morris's direction of travel. Mayr's one in a billion is recorded but not used for the floor: it counts species, not planets, and no one has turned it into a chance per living world. Kipping's weak three-to-two for 'intelligence is rare' argues against bunching the weight at the top but does not say how far down to go. Evenly spread across its powers of ten, as in the 2018 paper.
Rests on: Sandberg and others, 2018.
The published estimates
6 estimates on the record, oldest first. Each says who made it, when, how, and where to find it. A range is set from these by hand, with the reason above, never computed from them: the reason is the arguable part.
| When | Who | Estimate | How it was reached |
|---|---|---|---|
| 1961 | Frank Drake and the Green Bank meetingGreen Bank meeting of November 1961, as recorded in Drake and Sobel, Is Anyone Out There? (Delacorte, 1992), pages 55 to 62 (drake-1961) | 1 | Assumed: the meeting took it that intelligence follows from life given enough time. |
| 1995 | Ernst MayrMayr, 'Can SETI Succeed? Not Likely', Bioastronomy News 7(3) (1995), and his reply to Carl Sagan, reprinted by The Planetary Society as 'Ernst Mayr on SETI' (text read in a blog reproduction on 2026-10-16; the Planetary Society page was not reached). Mayr gives a count, not a chance: the span here is our reading of it | 1 in 50 billion to 1 in 1000 million | Argued from the fossil record: of the billions of species that have lived on Earth, perhaps as many as 50 billion, exactly one developed the kind of intelligence that builds radio telescopes, so the chance per planet is read as between one in 50 billion and one in a billion. A count of species, not of planets, which is why it is recorded but not used for the range's floor. |
| 2005 | Simon Conway Morris, as reviewed by CampbellConway Morris, Life's Solution: Inevitable Humans in a Lonely Universe (Cambridge University Press, 2003), as reviewed by Campbell, 'Human-like intelligence is inevitable' (2005); and Bonner, The Evolution of Complexity by Means of Natural Selection (Princeton, 1988) | 1 | Argued that evolution keeps finding the same solutions (eyes, flight, social behaviour) so that something like human intelligence is close to inevitable wherever complex life has time; a direction rather than a value, recorded as 'approaching 1'. |
| June 2018 | Anders Sandberg, Eric Drexler and Toby OrdSandberg, Drexler and Ord, 'Dissolving the Fermi Paradox', arXiv:1806.02404 (2018), Table 1 (sandberg-2018) | 0.001 to 1 | A span evenly spread across its powers of ten, taken from the published estimates of 0.001 to 1, with the paper's note that this treats the previous factor as the chance of 'evolutionarily competent' life rather than life of any kind. |
| June 2020 | Tom Westby and Christopher ConseliceWestby and Conselice, 'The Astrobiological Copernican Weak and Strong Limits for Intelligent Life', Astrophysical Journal 896, 58 (2020) (westby-2020) | 1 | Assumed: in their approach intelligence follows on any planet with life after four and a half to five and a half billion years, as on Earth. |
| October 2020 | Pascal LeeLee, 'N ~ 1: Alone in the Milky Way', talk to the Mount Tamalpais astronomy programme, 2020-10-24, and to the Kalamazoo Astronomical Society, 2021-03-06 | 0.0002 | Took the one million years since the first humans against the four and a half billion years since Earth formed as the share of a planet's life during which intelligence is present, about 0.0002, and read it as the chance. |
What would move this
The discovery that would narrow the range
A second example of complex or intelligent life anywhere, a change in the fossil record's timeline for the major steps (complex cells, animals, brains), or a published analysis that puts a new number on how often intelligence follows from life.When a paper or a survey of that kind is published, it is logged in the story so far with a note saying whether it moved this range. A move is written as a dated revision below, with the old number, the new one and the reason.
The last reading
Once a week the records are read against the news, each against the test above. Open a line to see what that week held. Every reading ever made of this record is on the reading page.
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2026-10-16 Logged, no change By hand
No second example of intelligent life and no new number for this piece. Three results bear on its test and were not in the log: Mills and others (Science Advances, 2025-02-14) argue the long wait for intelligence on Earth needs no improbable steps, only windows of habitability opening in turn; Bernabeu and others (Nature, 2026-06-10) find the complex cell arose through a long succession of microbial partnerships rather than one freak capture; and Rueda-Alaña and others (Science, 2025-02-13) find birds and mammals built similar sensory brain circuits by separate routes, read as complex cognition evolving at least twice. All three lean toward the optimistic end of a range that already reaches 1; none gives a number, so the range stays.
Mills, 2025Bernabeu, 2026Rueda-Alaña, 2025 source 1source 2source 3
How the range has moved
| Date | What | From | To | Why |
|---|---|---|---|---|
| 16 October 2026 | estimate (Carl Sagan, 1980) | value 0.1, 'a round guess, one tenth' | removed | Checked against Cosmos (1980), chapter 12, on 2026-10-16: Sagan writes 'let us choose fi x fc = 1/100' and gives no value for the intelligence factor alone. The range is untouched. |
| 16 October 2026 | estimate (Ernst Mayr, 1995) | value 1e-9 (the Wikipedia article's rendering) | low 2e-11, high 1e-9 | Checked on 2026-10-16 against a reproduction of Mayr's essay and reply: he counts billions of species, perhaps as many as 50 billion, one of them intelligent, and gives no chance of his own. The range is untouched (its floor is 0.0001); the published pessimistic extreme in the headline's estimate table moves with this. |
| 17 October 2026 | range.status | first-pass | reviewed | The outside review of the seven ranges ran on 2026-10-17 and John ruled on every item the same day (docs/reviews/2026-10-17-rulings.md). |
The explanations that lean on this piece
An explanation for the silence is, in the end, a claim about one or more of the seven pieces. 7 explanations say this piece is smaller than it looks.
- A hostile galaxy: exploding stars and bursts of radiation have kept resetting life almost everywhere, and only recently stopped They were never there says this piece is smaller than it looks
- Complex cells are rare: life may start easily but then stay simple forever, because the one step that made big cells happened only once They were never there says this piece is smaller than it looks
- Rare Earth: simple life may be common, but a planet that can carry complex life needs a long list of lucky breaks They were never there says this piece is smaller than it looks
- Rare intelligence: evolution has no goal, and of the billions of species that have lived on Earth only one built anything They were never there says this piece is smaller than it looks
- The Great Filter is behind us: somewhere on the road from dead matter to a galaxy-spanning civilisation there is a step almost nothing passes, and we have already passed it They were never there says this piece is smaller than it looks
- There is no paradox: once you admit how little we know about each factor, an empty galaxy is the expected result, not a surprise They were never there says this piece is smaller than it looks
- We are early: the universe has barely started making civilisations, and we are among the first They were never there says this piece is smaller than it looks
The papers that bear on it
- Gene ancestries reveal diverse microbial associations during eukaryogenesis 10 June 2026 Moisès Bernabeu, Saioa Manzano-Morales, Marina Marcet-Houben, Toni Gabaldón · logged; moved no range
- A reassessment of the "hard-steps" model for the evolution of intelligent life 14 February 2025 Daniel B. Mills, Jennifer L. Macalady, Adam Frank, Jason T. Wright · logged; moved no range
- Evolutionary convergence of sensory circuits in the pallium of amniotes 13 February 2025 Eneritz Rueda-Alaña, Fernando García-Moreno, and colleagues · logged; moved no range
- If Loud Aliens Explain Human Earliness, Quiet Aliens Are Also Rare December 2021 Robin Hanson, Daniel Martin, Calvin McCarter, Jonathan Paulson · logged; moved no range
- The Timing of Evolutionary Transitions Suggests Intelligent Life Is Rare March 2021 Andrew E. Snyder-Beattie, Anders Sandberg, K. Eric Drexler, Michael B. Bonsall · logged; moved no range
- The Astrobiological Copernican Weak and Strong Limits for Intelligent Life 15 June 2020 Tom Westby, Christopher J. Conselice · logged; moved no range
- An objective Bayesian analysis of life's early start and our late arrival 18 May 2020 David Kipping · logged; moved no range
- Dissolving the Fermi Paradox 6 June 2018 Anders Sandberg, Eric Drexler, Toby Ord · moved a range
- A New Empirical Constraint on the Prevalence of Technological Species in the Universe May 2016 Adam Frank, Woodruff T. Sullivan III · logged; moved no range
- Eternity in six hours: Intergalactic spreading of intelligent life and sharpening the Fermi paradox August 2013 Stuart Armstrong, Anders Sandberg · logged; moved no range
- Fermi's Paradox: The Last Challenge for Copernicanism? June 2009 Milan M. Ćirković · logged; moved no range
- Rare Earth: Why Complex Life Is Uncommon in the Universe January 2000 Peter D. Ward, Donald Brownlee · logged; moved no range
- The Great Filter – Are We Almost Past It? 15 September 1998 Robin Hanson · logged; moved no range
- The anthropic principle and its implications for biological evolution 20 December 1983 Brandon Carter · logged; moved no range
- The 'Great Silence': the Controversy Concerning Extraterrestrial Intelligent Life 1983 Glen David Brin · logged; moved no range
- Extraterrestrial Intelligent Beings do not Exist 1980 Frank J. Tipler · logged; moved no range
- An Explanation for the Absence of Extraterrestrials on Earth 1975 Michael H. Hart · logged; moved no range
- The Drake Equation, as written for the Green Bank conference on extraterrestrial intelligent life November 1961 Frank Drake, and the Green Bank meeting: Dana Atchley, Melvin Calvin, Su-Shu Huang, John Lilly, Philip Morrison, Bernard Oliver, Carl Sagan, Otto Struve, J. Peter Pearman · logged; moved no range
Books and films that take it up
- 2001: A Space Odyssey 1968 Film · Stanley Kubrick (film); Arthur C. Clarke (novel and the 1951 story 'The Sentinel')
- A Fire Upon the Deep 1992 Book · Vernor Vinge
- Blindsight 2006 Book · Peter Watts
- Childhood's End 1953 Book · Arthur C. Clarke
- Children of Time 2015 Book · Adrian Tchaikovsky
- Dragon's Egg 1980 Book · Robert L. Forward
- Life Beyond (chapters 1 to 3) 2019 Video · John D. Boswell (melodysheep, YouTube channel)
- Project Hail Mary 2021 Book · Andy Weir
- Roadside Picnic 1972 Book · Arkady and Boris Strugatsky
- Solaris 1961 Book · Stanisław Lem (novel); films by Andrei Tarkovsky (1972) and Steven Soderbergh (2002)
- Star Maker 1937 Book · Olaf Stapledon
- Stellaris 2016 Game · Paradox Development Studio
- The Sparrow 1996 Book · Mary Doria Russell
Notes
Kipping's 2020 Bayesian analysis (kipping-2020) found a weak preference, three-to-two, for intelligence rarely emerging, from the fact that it took almost all of Earth's habitable lifetime to appear; the paper strongly excludes intelligence arising quickly (in much less than a billion years) on an Earth-like world, and gives no single value for this factor. Frank and Sullivan (2016, Astrobiology 16, 359) turned the question round: for Earth to be the only technological species ever in the observable universe, the combined chance of life, intelligence and technology per habitable planet would have to be below 2.5 in ten to the 24, and below 1.7 in ten to the 11 for the galaxy. Hanson and colleagues' 2021 'grabby aliens' model (hanson-2021-grabby) constrains the product of this factor and the next from the other end: if expanding civilisations exist and we are early among them, quiet civilisations that never expand can be at most a few thousand times as common as loud ones, else we would have seen a loud one by now. Checked 2026-10-16 against the sources: Carl Sagan's one tenth was removed (Cosmos, chapter 12, gives only the product of this factor and the next, one in a hundred); Mayr's point value of one in a billion was replaced by the span his own counts give, 2 in 100 billion to 1 in a billion (the range is unchanged, and its floor of 0.0001 stays well above it); Westby and Conselice's assumption of 1 is borne out (their section 2.2; the strong version only requires 4.5 to 5.5 billion years). Lineweaver (2009, 'Paleontological tests: human-like intelligence is not a convergent feature of evolution', in From Fossils to Astrobiology, arXiv:0711.1751) argues from the fossil record that human-like intelligence is not convergent, and gives no number, so it is not an estimate; the 'Planet of the Apes' label belongs to the opposite view, which he argues against. Written 2026-10-16. Outside review, 2026-10-17, ruled by John the same day: lowering the floor from 0.0001 to one in 10 billion or below, to include the hard-steps conclusions (item 12), was declined. The hard-steps papers (Carter 1983; Snyder-Beattie and colleagues 2021) conclude that intelligence is rare but give no chance per planet, so there is no published number to put the floor at; the only published figure below 0.0001 is Mayr's count of species, which is kept above and not used. Worth keeping visible because the floor is the one place the site's judgment, not a measurement, decides the headline: at one in 10 billion the chance we are alone in the galaxy would be 77% (scratch copy) against 59%, and if the published pessimist is to be covered the principled step is Mayr's top, one in a billion (75%), not one in 10 billion. The reviewer's suggestion to add Barrow and Tipler (1986) as an estimate (item 13) was declined: their figure counts one genome rather than giving a chance of intelligence per living planet, and is named here among the arguments without a usable number. A survey of living planets against a silent sky (item 14) bounds this factor only together with its neighbours and is not added to the test line.
Claims still to be checked
These were written from memory and have not yet been checked against a source. A later pass clears each one.
- Barrow and Tipler (The Anthropic Cosmological Principle, Oxford University Press, 1986) are said, second-hand only, to put the chance of the human genome evolving at about one in ten to the 24 million; the book has not been read, and the figure, if it is theirs, counts one genome and is not a chance of intelligence per living planet. Raised 2026-10-17 by the outside review (item 13); open.
- Pascal Lee's figure of 0.0002, from a 2020 talk, is quoted from the Wikipedia article on the Drake equation, which cites recordings of the talks; check it. Tried 2026-10-16 and still open: the recordings could not be reached. The only source found is a Centauri Dreams post (2023-10-18) reporting a talk at the Interstellar Research Group symposium in Montreal, which gives 0.0002 and derives it from the median duration of Homo erectus (about a million years) over the age of Earth, not from 'the first humans', and also gives his detectable factor as 0.1 and his lifetime as 10,000 years; so the number is supported second-hand but the talk, date and derivation in the record are not confirmed.
Think the range should move? Argue it, with a source. Spotted an error on this page? Say so. Or read how disagreement gets folded in.
The record itself is data/factors/intelligence.toml in the public repository.