Working papers

Each study is a short paper with its numbers, its limits, its code and the report of the second analysis that tried to break it. Both were run by Claude for this project; no outside expert has reviewed them. The three rounds of criticism of the model, also by separate runs of Claude, are here in full as well.

Original studies

There are twenty-two studies, and all of them have been revised after the second analysis reported. In the summaries below, “the referee” is that second analysis.

How early did life start, and how late did we arrive?I re-derived published calculations of what Earth’s timeline says about how easily life starts. Life’s early start favours an easy origin over a hard one by 13 to 1 (10.2 to 19.2), but only 9, 7 and 6 to 1 if two, three or four improbable evolutionary steps follow, and under 3 to 1 with undisputed fossils alone if any later step is hard (up to 5.7 to 1 if none is). The referee exposed an unstated assumption: how we count our own existence decides whether these dates reveal how common life is.
Stars passing the Sun: a Gaia census and what it means for short-hop settlementFrom Gaia satellite data I counted how often star systems pass within one parsec (about 3.3 light years) of the Sun: 11.1 ± 1.0 per million years. That makes about 21,000 passes (11,000 to 59,000) since oxygen first accumulated in Earth’s atmosphere, or 4,000 to 6,000 since oxygen neared modern levels and plants covered the land. After the referee’s report, my simulated settlers hopping between passing stars cross the Galaxy in 200 to 500 million years, not about 100 million.
How much of a head start did other planets have?From the measured ages of about 8,500 subgiants (stars just leaving the Sun-like phase, whose ages can be measured well), checked against a second catalogue of 17,000, about 70% (64 to 78% across samples and age scales) of the Sun-like stars now in our part of the Galaxy formed before the Sun, by about 4 billion years on average. This reproduces a known result. The referee showed that my first figure, 72.5% (69 to 76%), overstated its precision.
Dimmed elliptical galaxies: a fundamental-plane search for harvested starlightA civilisation intercepting starlight would leave its galaxy too faint for its size and internal motions. Among 114,210 elliptical and lens-shaped galaxies, about 15,000 bright enough to test, with 95% confidence fewer than 0.29% (0.24 to 0.45%; 1.4% on the most pessimistic noise assumption) can have 75% of their light intercepted. The referee made me withdraw my claim to cover star-harvesting generally: enclosing all but the brightest stars removes only about 20 to 36% of the light, barely constrained here.
Dimmed spiral galaxies: a Tully-Fisher search for harvested starlightUsing rotation speed to predict brightness, I tested 9,379 gas-rich spiral galaxies for missing starlight; about 1,800 could show it. None is confirmed as dimmed, but 34 remain unexplained. Counting those as real, with 95% confidence fewer than 2.6% (1.9 to 3.5%) of massive spirals can have 75% of their starlight intercepted, if the energy leaves as heat colder than about 250 kelvin (minus 23 Celsius). The referee made me raise the limit from 1.8% and withdraw “at any temperature”.
Sixty years of radio searches, combinedI combined the major published radio searches into one limit on transmitters in the Galaxy. They allow up to about 400,000 (170,000 to 2.6 million) beacons that broadcast continuously in every direction at 10¹⁷ watts, a bit over half the power of all sunlight striking Earth, at any frequency from 1 to 10 gigahertz. Transmitters like ours are not limited at all. The referee showed I had overcounted distant stars in the telescopes’ view, raising the figure from about 300,000.
How repeatable is the road to intelligence?I re-analysed a published list of 77 evolutionary innovations and brain and body weights for 1,547 living mammal species. Older innovations are more often one-offs (odds up 3.2-fold per tenfold increase in age), but only 1.4 to 2.9-fold once traits inherited together are grouped. Relative brain size within a factor of two of ours arose in three or four lineages, showing that large brains recur, not that human-level intelligence does. The referee made me withdraw my numerical estimates of repeatability.
Red dwarfs and the question of whether we are earlyHumanity looks surprisingly early if planets of long-lived small red stars stay habitable. In published JWST and Spitzer space telescope results I found no thick atmosphere on any of 14 rocky red-dwarf planets with a clear verdict (at most 3 of 17 counting ambiguous results), but none orbits where water could stay liquid. That can remove the puzzle only if intelligence needed a single improbable evolutionary step. After the referee’s report I no longer call it decisive even then.
Does spreading keep going? Real colonisation wavesI used the settlement of the Pacific to test whether spreading keeps going, and where it was possible it was quick. After a pause of about 1,700 to 1,900 years, settlers reached 29 of 50 land units (islands or island groups) in East Polynesia within roughly 250 to 360 years. Of those, 16 were later abandoned. But in every human example the chain of colonies founding new colonies ran for only four to six rounds, which cannot show whether a wave lasts the thousands of rounds a galaxy needs.
How long does a rocky planet stay habitable?I estimated how long rocky planets born with the Sun stay geologically active. I used two tracers of radioactive heating, thorium and europium, measured in Sun-like stars, and four models of how planets cool. The median, or middle value, is 4 to 11 billion years under one rule for when habitability ends, and up to about 21 billion under others. Whether we are early therefore stays open, since humanity could come anywhere from the first 2% of civilisations to later than 70% of them.
Partial Dyson spheres among stars within 100 parsecsOf the 273,856 ordinary stars within about 330 light years, I could search 54% in WISE satellite infrared data for the glow of Dyson swarms, clouds of light collectors around a star. I counted every star with extra infrared light as a possible swarm. With 95% confidence, fewer than one star in 1,400 (1,000 to 2,600 across model settings, not independently checked) hosts a warm swarm intercepting 1% of its star’s light. Swarms colder than about minus 170 Celsius or hotter than about 330 are untested, and the unsearched stars are assumed to be no different.
Sun-like stars that are too dim for their typeA light-collecting swarm would make its star fainter than its spectrum (its light split by colour) predicts, however cold the waste heat. Following Zackrisson and colleagues (2018), I used survey spectra and distances from the Gaia satellite to test 790,783 Sun-like stars within 3,300 light years. With 95% confidence, fewer than one in 26,000 is 90% dimmed (21,000 to 33,000 across model settings). Swarms of dust that change a star’s colour are untested, and the limits for lighter dimming are much weaker.
Waste heat from quiet elliptical galaxiesA civilisation capturing part of its galaxy’s starlight would give it off again as infrared heat. I looked for that in WISE satellite measurements of 113,158 red, quiet galaxies (ones forming few new stars) from the Sloan survey. With 95% confidence, fewer than one in 5,800 (1,700 to 7,500 across analysis choices) turns at least 30% of its starlight into room-temperature heat. For 1% there is no limit at all, spiral galaxies are untested, and the final range was not independently checked.
How well has the Solar System been searched for artefacts?I estimated whether an inert alien object parked in the Solar System would already be known, from images, asteroid catalogues and a simulation. A 1 to 10 metre object is 20 to 36% likely to be catalogued if such objects mostly sit near Earth. If they sit in the asteroid belt or beyond, it is about 2%. The chance that it is also recognised as not of human making is 0.01 to 0.6%, which rests on assumed values. The revised figures were not independently checked.
Small bodies with unexplained accelerationsSunlight shifts the orbit of a light sail or empty hull far more than a rock’s. I tested for such a push in public position measurements of 19,192 near-Earth objects and found no sail-like object. With 95% confidence, among catalogued objects tracked well enough to show such a push, fewer than 0.3 to 1.1%, depending on size, can be sail-like. Dense probes would look like rocks, and this search was not independently checked.
Would a past presence on Earth have left a trace?From 47,525 land fossil collections in the Paleobiology Database I measured how much ancient land has been inspected. Take a 100 square kilometre site occupied for 10,000 years in the last 500 million. It would be known from buried rock about 1 time in 40,000 (1 in 500,000 to 1 in 3,000). Only the fossil coverage is measured. The rest is assumed, and the range in brackets was not independently checked.
Fully enclosed stars: a census by gravity aloneA star inside a complete shell is invisible but still has gravity. Gravity near the Sun allows up to 42% of the mass in stars to hide this way (29 to 50% across measurements, about 60% if no unseen dark matter lies nearby). If shells give off the starlight as heat, infrared counts tighten this to 5% of Sun-like stars at 40 kelvin (minus 233 Celsius), and far less at 100. Those counts were not independently checked. Below about 35 kelvin (45 for small, dim red dwarfs, which are most stars) only the gravity limit applies.
When was Earth last sterilised?I simulated giant impacts on early Earth, timed from 30 dated basins (giant craters) on the Moon, to see whether they shortened the time life had to start. If only an impact that melts the whole surface (an impactor of about 2,000 km) sterilises the planet, Kipping’s (2025a) 13 to 1 for an easy origin is unchanged. That threshold is my reading of the literature and is not settled. Every sterilising size is larger than the biggest body that hit the Moon, so the number of giants is assumed, and the revised figures were not checked again.
Stars salted with artificial elementsMarking a star by adding an element nature makes sparingly is an old idea. Whitmire and Wright (1980) noted that dumped nuclear waste would do it unintentionally. I searched GALAH survey spectra (starlight split by colour) of 408,000 Sun-like stars and found no convincing salted star. With 95% confidence, fewer than about one star in 4,500 to 8,000 carries at least ten times its natural amount of the element neodymium. Weaker marks and the 18% of stars with unreliable spectra are untested.
How long between oxygen and intelligence?Complex cells, animals and humans may each have needed a rare lucky step, or may only have had to wait for oxygen. I compared their published dates with dated oxygen rises, and the dates do not separate the two. On three dates for complex cells, they are 1.2, 1.9 or 2.3 times as likely under waiting as under luck. On a fourth date the figure is 28. Across 48 analysis choices it runs from 0 (waiting ruled out) to 28. The main unknown is when animals first had enough oxygen.
Cold objects crossing in front of starsOpaque shells built around stars would sometimes hide distant stars for months. In 221,801 brightness records from the OGLE-II survey towards the Galaxy’s centre I found no such disappearance. If every star had a shell ten Earth to Sun distances in radius, I would have expected 130 to 480. With 95% confidence, under about 2% of stars there have shells that size or larger. The limit is 0.6% on optimistic assumptions and about 5% at worst. Shells under about two such distances go unseen.
How hard have we looked for a second origin of life?I judged how thoroughly Earth and the Solar System have been searched for a second origin of life, using public databases and mission records. If life starts easily, the searches had a 3 to 25% chance of revealing one. They shift my model’s 78% chance that our Galaxy never held another civilisation by between about 2 percentage points down and 3 up. Any fall depends on one unresolved Mars rock. My scores are judgements and none is a measurement.

The model and its critics

Red team, round 1: the first modelThe critics’ reports in full, including the objections that were not resolved.
Red team, round 2: the rebuilt modelThe critics’ reports in full, including the objections that were not resolved.
Red team, round 3: the model and the main pageThe critics’ reports in full, including the objections that were not resolved.
Result tablesEvery number on the main page, with the runs behind it.
How the model worksPriors, likelihoods, classes and known weaknesses.
Model source codeThe model, the scripts that run it and the scripts that build the tables and the page’s data, as plain text files.cells4.py chain4.py cosmo_tables.py leverage4.py model4.py run4.py scan4.py build_data.py make_tables.py