The Fermi Paradox

Fermi's question was not the Fermi paradox. This matters for the history and it matters for the argument.

Eric Jones, at Los Alamos, wrote in 1985 to the three surviving lunch companions — Emil Konopinski, Edward Teller and Herbert York — and printed their recollections in a laboratory report. What they remember is a conversation about flying saucers and faster-than-light travel, and Fermi asking Teller for the probability that we would obtain evidence of superluminal travel within ten years. Teller said one in a million; Fermi said more like one in ten. Then, later in the meal, out of nowhere: "Where is everybody?" York recalled that Fermi went on to make a rapid estimate, in his characteristic style, and concluded that we should have been visited long ago and many times over.

Their memories differ in detail, and they were recalling a lunch thirty-five years earlier. What is clear is that the topic was whether interstellar travel is feasible, and that Fermi published nothing about it and appears never to have returned to it.

Hart deserves the credit. The argument as it is now used — the timescale calculation, the systematic elimination of alternatives, the treatment of absence as evidence — is Michael Hart's, from 1975. Robert Freitas made this point explicitly in a 1985 Icarus paper pointedly titled "There Is No Fermi Paradox", and some authors write "the Fermi–Hart paradox" for this reason. The habit of naming it after Fermi has had a real cost: it lends the argument the authority of a great physicist who never made it, and it obscures that the argument has specific, examinable premises which are Hart's.

Is it even a paradox? By the standards used on this site, not in the strict sense — nothing contradicts anything. It is classified here as an open problem because the disagreement is real and current, and because presenting any single resolution as settled would be false. It is worth noticing that the label "paradox" itself does some of the persuasive work: calling something a paradox implies that a resolution is owed, and part of what Sandberg, Drexler and Ord argue is that no resolution is owed, because the expectation was never justified.

The methodological quarrel underneath. Two camps have been arguing past each other for fifty years.

The astronomical camp treats the question as one about physical processes: how likely is abiogenesis, how likely is complex life, how fast can you actually travel. Progress comes from telescopes and laboratories, and the honest answer is that we do not yet know enough.

The probabilistic camp treats it as a question about inference under deep uncertainty: how should a reasoner update on a null observation, how do you handle a quantity uncertain over two hundred orders of magnitude, what does your own existence entitle you to conclude. Progress comes from being careful about priors.

The 2018 paper is the clearest statement of the second view, and its central claim — that much of the apparent force of the paradox comes from treating uncertain quantities as though they were known — is now hard to ignore even for people who reject its conclusion.

Why nobody should be confident. Every proposal here requires an assumption about the motives, longevity or technology of beings we have never observed. The sample size is one, the observer is inside the sample, and the search has been shallow. The appropriate epistemic state is genuine uncertainty, and the entries that claim otherwise — in either direction — are claiming more than the evidence supports.

Summer 1950. The lunch at Los Alamos. Fermi with Emil Konopinski, Edward Teller and Herbert York.

1959. Giuseppe Cocconi and Philip Morrison publish "Searching for Interstellar Communications" in Nature, proposing that microwave frequencies near the 21-centimetre hydrogen line would be the natural channel. Modern SETI begins as a research proposal.

1960. Frank Drake conducts Project Ozma, pointing an 85-foot dish at Tau Ceti and Epsilon Eridani. Nothing.

1961. Drake writes his equation on a blackboard at Green Bank, not as a predictive formula but as an agenda for a three-day meeting — a way of organising what would need to be known.

1973. John Ball publishes the zoo hypothesis in Icarus.

1975. Michael Hart's paper appears in the Quarterly Journal of the Royal Astronomical Society. It is the first rigorous statement of the argument, and its conclusion is blunt: there are no extraterrestrial civilisations in the Galaxy, and searching for radio messages is probably futile.

1980. Frank Tipler, in the same journal, adds von Neumann probes under the title "Extraterrestrial Intelligent Beings Do Not Exist".

1983. Carl Sagan and William Newman reply with "The Solipsist Approach to Extraterrestrial Intelligence", arguing that the colonisation models assume exponential growth that real populations do not sustain. Also in 1983, David Brin's survey "The Great Silence" catalogues the possibilities and introduces the deterrence-based reasoning that later became the dark forest.

1985. Eric Jones publishes the recollections of the lunch. Robert Freitas publishes "There Is No Fermi Paradox" in Icarus.

1996–1998. Robin Hanson formulates the Great Filter, initially in response to claims about fossil life in the Martian meteorite ALH84001.

2000. Ward and Brownlee's Rare Earth.

1995 onward. The exoplanet era. 51 Pegasi b in 1995; the Kepler mission from 2009 establishes that planets outnumber stars and that small planets are the most common kind. One of the Drake equation's seven factors moves from unknown to measured.

2008. Liu Cixin's The Dark Forest is published in Chinese, reaching English in 2015 and putting one particular hypothesis into general circulation far more effectively than any academic paper had.

2015. Breakthrough Listen begins, the largest and best-funded SETI programme so far.

2018. Sandberg, Drexler and Ord post "Dissolving the Fermi Paradox".

It is the only argument that turns a non-observation into a claim about our own future. If the Great Filter framing is right, then the silence of the sky is data about how often civilisations like ours survive their own technology. That makes an astronomical question into a question about existential risk, and it is why the Fermi problem is taken seriously by people who have no professional interest in aliens.

It shaped how the search is done. Hart's argument is the standing objection to optimistic Drake numbers, and it is why the field's centre of gravity has shifted from listening for deliberate radio beacons towards looking for technosignatures — unintended industrial byproducts that would be visible whether or not anyone wants to be found. Richard Carrigan's search of the IRAS infrared catalogue for Dyson spheres, and Jason Wright's Glimpsing Heat from Alien Technologies survey, both exist because of it.

It made "we haven't found any" a technical quantity. How much of the search space has actually been covered, and what a null result licenses you to conclude, are now questions with published answers rather than rhetorical positions. That is a real methodological improvement, and it came from taking the paradox seriously enough to try to dissolve it.

It is the reason METI is controversial. Whether humanity should deliberately broadcast its position is a live policy dispute, and every position in it — Stephen Hawking's caution, the dark-forest argument, the counter-argument that our radio leakage has made the question moot — is an argument about which resolution of the Fermi problem you believe.

Exoplanets have removed one excuse. In 1975 Hart had to assume that planets existed around other stars. They do, in enormous numbers, and rocky planets in temperate orbits are common. Every year of exoplanet results makes the astronomical premises stronger and pushes the uncertainty further into biology and sociology, where it is much harder to reduce.

Biosignature searches are about to test the first factor. The James Webb Space Telescope can attempt atmospheric characterisation of some rocky exoplanets, and the next generation of extremely large ground-based telescopes will do better. If oxygen-rich atmospheres turn up on nearby worlds, the probability of abiogenesis moves from "unknown over two hundred orders of magnitude" to something measurable — and, on Hanson's reasoning, the news will be worse for us the better it looks.

Grabby aliens. Hanson, Daniel Martin, Calvin McCarter and Jonathan Paulson published a model in the Astrophysical Journal in 2021 that inverts the usual approach: instead of asking how many civilisations there are, it asks what distribution of expanding civilisations is consistent with humanity appearing as early in cosmic history as it has. Their answer is that if loud, expanding civilisations exist, they must be rare and we are unusually early. It is a good example of the paradox generating testable structure rather than just a list of possibilities.

'Oumuamua and the evidential bar. The first confirmed interstellar object passed through the Solar System in 2017 with an unusual shape and a small non-gravitational acceleration. Avi Loeb argued publicly that artificial origin should be on the table; most of the field disagreed, favouring exotic but natural explanations. The episode is instructive independently of who is right: it demonstrated how quickly the Fermi question turns any anomaly into a contested one, and how badly the field needs agreed standards of evidence in advance.

It is a stress test for reasoning under deep uncertainty. The Fermi problem is now used as a worked example well outside astronomy — in forecasting, in risk analysis, in the study of how to handle parameters uncertain across many orders of magnitude. The 2018 dissolution paper is cited as often for its methodology as for its conclusion, and that may end up being its more durable contribution.

The Drake equation and what it is for

$$N = R_* \cdot f_p \cdot n_e \cdot f_l \cdot f_i \cdot f_c \cdot L$$

where $R_*$ is the rate of star formation, $f_p$ the fraction with planets, $n_e$ the mean number of habitable planets per such system, $f_l$ the fraction on which life arises, $f_i$ the fraction of those on which intelligence arises, $f_c$ the fraction that become detectable, and $L$ the mean duration of detectability.

Drake wrote it as a meeting agenda, not a prediction. Used as a prediction it is badly behaved, for a reason that has nothing to do with astronomy.

Why multiplying point estimates fails

Write $X = \prod_{i=1}^{n} x_i$ and take logs:

$$\ln X = \sum_{i=1}^{n} \ln x_i .$$

If the $\ln x_i$ are independent with means $\mu_i$ and variances $\sigma_i^2$, then $\ln X$ has mean $\sum \mu_i$ and variance $\sum \sigma_i^2$, and $X$ is approximately log-normal. For a log-normal,

$$\mathbb{E}[X] = \exp!\left(\textstyle\sum\mu_i + \tfrac12\sum\sigma_i^2\right), \qquad \mathrm{median}(X) = \exp!\left(\textstyle\sum\mu_i\right).$$

The ratio is $\exp\left(\tfrac12\sum\sigma_i^2\right)$, which for factors uncertain over many orders of magnitude is astronomically large. The mean and the typical value are not remotely the same number.

What you want is not $\mathbb{E}[N]$ but

$$P(N < 1) = \Phi!\left(\frac{-\sum\mu_i}{\sqrt{\sum\sigma_i^2}}\right),$$

the probability that the Galaxy contains nobody but us. Plugging in point estimates and multiplying computes something like the first quantity while the argument requires the second. Sandberg, Drexler and Ord's contribution is to carry distributions through the calculation from literature-derived priors for each factor. Because the uncertainty in $f_l$ alone spans on the order of two hundred orders of magnitude, $\sum\sigma_i^2$ is enormous and $P(N<1)$ comes out substantial.

This does not prove we are alone. It shows that "we should expect company" was never a licensed inference from the numbers we actually have.

Colonisation as a front

Model expansion as a travelling wave. With hop distance $d$, cruise speed $v$ and settling time $\tau$ per hop, the effective front speed is

$$v_{\text{front}} = \frac{d}{d/v + \tau} = \frac{v}{1 + v\tau/d}.$$

Crossing a galaxy of diameter $D$ takes $T = D/v_{\text{front}}$. For $D = 10^5$ ly, $d = 10$ ly, $v = 0.01c$ and $\tau = 10^3$ yr:

$$v_{\text{front}} = \frac{0.01c}{1 + (0.01)(1000)/10} = \frac{0.01c}{2} = 0.005c, \qquad T = 2\times 10^7\ \text{yr}.$$

Twenty million years against a Galactic age of $1.3\times10^{10}$ years, a ratio of about $1.5\times10^{-3}$. The conclusion is robust to enormous changes in the inputs: to stretch $T$ beyond the age of the Galaxy you need $v_{\text{front}}$ below about $10^{-5}c$ — three metres per second — sustained by nobody, ever. This insensitivity is why Hart's argument is hard to defeat by tweaking parameters, and why the interesting objections attack the premise that anyone expands at all.

The Great Filter, formally

Let $p$ be the probability that a given star produces a visibly expanding civilisation, factored into steps:

$$p = \prod_{i} p_i .$$

Observationally, the Galaxy's $N_* \approx 10^{11}$ stars have produced no visible expanding civilisation, which bounds

$$p \lesssim \frac{1}{N_*} \sim 10^{-11},$$

with the exact bound depending on how confident you are in Fact A. Some product of the $p_i$ must therefore be very small: that is the Great Filter.

The inferential structure is the part that matters. Partition the steps into those already behind us, with product $p_{\text{past}}$, and those ahead, with product $p_{\text{future}}$. The constraint is on the product, so

$$p_{\text{past}} \cdot p_{\text{future}} \lesssim 10^{-11}.$$

Evidence that raises $p_{\text{past}}$ — finding independent abiogenesis on Mars or Europa, finding oxygen atmospheres on nearby exoplanets, finding that eukaryogenesis is easy — must, to preserve the bound, lower $p_{\text{future}}$. Good news about the past is bad news about the future, and the relationship is not rhetorical but arithmetical.

The escape from this conclusion is exactly the 2018 argument: if the observational bound on $p$ is weak, or if our prior on $p_{\text{past}}$ already sits many orders of magnitude below $10^{-11}$, then no filter needs to be posited at all, and nothing follows about our future. Which of these is the case is not known, and this entry does not pretend otherwise.