{
const lam = p.q * p.N;
const Ts = d3.range(0.5, 13.55, 0.25).map(t => { const c = LC.planetCeiling(p, t); return {x: t, y: isFinite(c) ? Math.min(c, 1e12) : NaN}; });
const yMin = 10 ** Math.floor(Math.log10(Math.min(...Ts.map(d => d.y).filter(isFinite), lam, 1e-12))), yMax = 1e12;
return chart({
width: 680, data: Ts, ylog: true, xdom: [0.5, 13.5], ydom: [yMin, yMax],
xticks: [1, 4.6, 8, 12], yticks: decTicks(yMin, yMax, Math.log10(yMax / yMin) > 16 ? 6 : 4),
yfmt: t => pow10(Math.log10(t)), xtitle: "time to emerge T (Gyr)", ytitle: "largest qN an empty sky allows",
color: "var(--planet)", forbid: "above", markers: [{x: p.T, y: lam, label: "your qN", left: p.T > 9}],
tip: d => `T ${d.x.toFixed(2)} Gyr · qN ≤ ${sci(d.y)}`
});
}The Long Lineage
I’ve been playing around recently with a less appreciated explanation of the Fermi Paradox. It comes up every now and then as a throwaway line in a paper or blog post, but you rarely see anyone give it much airtime. I have some ideas about why that might be, and why the epistemic ground is shifting.
The Fermi Paradox (FP) (Sandberg, Drexler, and Ord 2018), also known as the Great Silence (Brin 1983), asks why, given the fact that life can evolve and apparently alters its environment in highly conspicuous ways, do we see no evidence of it elsewhere in the galaxy. It gets harder and harder to understand as we detect more planets in habitable zones (Bryson et al. 2021).
Sandberg, Anders, Eric Drexler, and Toby Ord. 2018. “Dissolving the Fermi Paradox.”
Brin, G. David. 1983. “The ‘Great Silence’: The Controversy Concerning Extraterrestrial Intelligent Life.” Quarterly Journal of the Royal Astronomical Society 24: 283–309. https://articles.adsabs.harvard.edu/full/1983QJRAS..24..283B.
Bryson, Steve, Michelle Kunimoto, Ravi K. Kopparapu, et al. 2021. “The Occurrence of Rocky Habitable-Zone Planets Around Solar-Like Stars from Kepler Data.” The Astronomical Journal 161 (1): 36. https://doi.org/10.3847/1538-3881/abc418.
Drake, Frank D. 1961. “Project Ozma.” Physics Today 14 (4): 40–46. https://doi.org/10.1063/1.3057500.
Dyson, Freeman J. 1960. “Search for Artificial Stellar Sources of Infrared Radiation.” Science 131 (3414): 1667–68. https://doi.org/10.1126/science.131.3414.1667.
Olson, S. Jay, and Toby Ord. 2021. “Implications of a Search for Intergalactic Civilizations on Prior Estimates of Human Survival and Travel Speed.” https://arxiv.org/abs/2106.13348.
Back in the 60s when Frank Drake famously made a start on related calculations, he thought about detecting life as hearing their radio signals (Drake 1961). Some contemporaries were already expecting life to make more noise than that, most famously Freeman Dyson (Dyson 1960). This view didn’t become central to the field until the 70s, but nowadays people who work on FP expect life to move beyond its starting planet and dim its star, and spread to neighboring stars and do the same (Hanson et al. 2021; Olson and Ord 2021). Whether we have any right to expect this, from where we are sitting today, is a good question and one of the first objections often raised against this kind of work. One of the results that fell out of my calculations, completely unexpectedly, was a way to put a numerical value on this objection– and the objection is strong. I will give that objection its own section, alongside all other objections of the form ‘how would we know, what would we see, what would make us confident in an observation’.
But first, let me get to the model and its assumptions.
1. The Lineage
At conception an egg fuses with a sperm cell and starts the miracle of ontogenesis. That egg was formed early in the development of the mother, while she was in the womb, going through her own ontogenesis, from her own egg, which was inside her mother. And on and on, through many as-yet poorly understood evolutionary leaps and bounds back to LUCA, the last universal common ancestor. Take note of one simple thing here– the egg never dies. The cell never dies. Individual cells can die, individual lineages can be cut. But the egg from which you grew was the descendant of an unbroken lineage of simple cells, multiplying and reproducing, back deep into pre-history. Until when exactly? That is the question, and we can pick two bounds quickly. The Earth formed about 4.6 billion years ago (4.6 Gya) and the Big Bang happened around 13.8 Gya.
The first bound, the origin of the Earth, is taken as the default hypothesis. The statement ‘after the Earth cooled and liquid water appeared in large quantities life evolved and reached the level of bacteria by 3.7Gya, possibly earlier’ (Nutman et al. 2016) could be a summary of the most common position. Moody et al. (2024) used phylogenetic analysis to date LUCA at 4.2 Gya.
Nutman, Allen P., Vickie C. Bennett, Clark R. L. Friend, Martin J. Van Kranendonk, and Allan R. Chivas. 2016. “Rapid Emergence of Life Shown by Discovery of 3,700-Million-Year-Old Microbial Structures.” Nature 537: 535–38. https://doi.org/10.1038/nature19355.
Moody, Edmund R. R., Sandra Álvarez-Carretero, Tara A. Mahendrarajah, et al. 2024. “The Nature of the Last Universal Common Ancestor and Its Impact on the Early Earth System.” Nature Ecology & Evolution 8: 1654–66. https://doi.org/10.1038/s41559-024-02461-1.
There is an unbroken lineage of cells going back for around 4 billion years. The reason this lineage is unbroken is that counterfactual lineages that form spontaneously out of nothing have not been observed. The miracle of life earns its epithet– it is a remarkably improbable phenomenon. LUCA is estimated to have had 2.5 million base pairs. The greatest unanswered question in evolutionary theory is, how did something so complex emerge spontaneously on the early Earth so quickly?
My preferred answer is that it simply didn’t. The lineage didn’t start on Earth, it came from outer space. This is known as panspermia, the seeding of life on planets through meteors or other means (Kawaguchi et al. 2020; Adams and Napier 2022). Panspermia strikes a lot of people as wacky at first glance, because it invites the first mover question. Who sent the seeds, some alien civilization? In which case, per the above, why don’t we see any other evidence of them? But the version I follow is not so exotic. It is simply that the accumulation of enough chemical complexity for hereditary ecosystems to kick-start must have taken billions of years, and could have happened anywhere with the right combination of starting materials and temperature, pressure, and energy flow. The pre-Earth part of the story is long, boring, and spread out across the galaxy in a vast number of pockets, large and small (Sharov and Gordon 2013).
Kawaguchi, Yuko, Mio Shibuya, Iori Kinoshita, et al. 2020. “DNA Damage and Survival Time Course of Deinococcal Cell Pellets During 3 Years of Exposure to Outer Space.” Frontiers in Microbiology 11: 2050. https://doi.org/10.3389/fmicb.2020.02050.
Adams, Fred C., and Kevin J. Napier. 2022. “Transfer of Rocks Between Planetary Systems: Panspermia Revisited.” Astrobiology 22: 1429–42. https://doi.org/10.1089/ast.2021.0187.
2. The Start
How does this help with the Fermi Paradox? Surely the fact that life’s precursors were around before Earth and are presumably relatively common in the universe should mean we would see more life, everywhere, not less of it? That is true, and is one of the testable differences between the long lineage and the hard steps model. But more on that later.
The main problem the hard steps model solves is that, if life evolved on one planet from a standing start, it could have done so on earlier planets. 75% of the planets in the galaxy are older than ours, many by billions of years (Lineweaver, Fenner, and Gibson 2004). Anything expanding from one of those planets would have had enough time by now to take over and transform the entire galaxy. The hard steps model solves this by making life on any given planet exceedingly unlikely. Indeed, it has to be so unlikely that there would only be one surviving lineage every million galaxies (Hanson et al. 2021).
Lineweaver, Charles H., Yeshe Fenner, and Brad K. Gibson. 2004. “The Galactic Habitable Zone and the Age Distribution of Complex Life in the Milky Way.” Science 303: 59–62. https://doi.org/10.1126/science.1092322.
It’s worth dwelling for a moment on this value, \lambda = qN. It combines the number of lineages in the galaxy with their probability of expansion. In the left, there are sliders for q and N, but under the default settings they are incompatible– hence we also show \lambda, the combined number that is forced by the empty sky.
Figure 1 · How long did the lineage take?
By contrast, if it simply takes life much longer than the lifetime of the planet to get started, the fact that we are emerging now is not so remarkable. In this view, we are emerging now and apparently alone because we are essentially synchronized with all other lineages.
Here the other bound comes in, the lifetime of the universe. If you work through the geometric calculation, as Hanson does in the grabby aliens model (Hanson et al. 2021), you realize that we must be synchronized not only within our galaxy, but also between galaxies. If there is such a thing as a galaxy-transforming civilization, the light from its distant now-transformed galaxy would have reached us by now.
Figure 2 · The head-start cap
What could synchronize the start of different lineages across such enormous scales? It has to be something very early. There are a few candidates, such as the habitable epoch in the early universe, the so-called goldilocks epoch around 17 million years after the Big Bang (Loeb 2014). However there was nothing at that time capable of retaining information, no carbon to form structure. The first carbon showed up between 100 and 200 million years in (Bromm 2013; Stacy and Bromm 2014), and that is the time that I have chosen to start my clock. That is the time when structure started to form, when the first rocky bodies started to form (the first stars went supernova in only a few million years, so there would have been rocky bodies forming throughout that era).
Loeb, Abraham. 2014. “The Habitable Epoch of the Early Universe.” International Journal of Astrobiology 13: 337–39. https://doi.org/10.1017/S1473550414000196.
Bromm, Volker. 2013. “Formation of the First Stars.” Reports on Progress in Physics 76: 112901. https://doi.org/10.1088/0034-4885/76/11/112901.
Stacy, Athena, and Volker Bromm. 2014. “The First Stars: A Low-Mass Formation Mode.” The Astrophysical Journal 785: 73. https://doi.org/10.1088/0004-637X/785/1/73.
Another thing that draws me there is the remarkable coincidence between the age of Earth and the age of the universe. We could plausibly have woken up on a planet orbiting a red dwarf a trillion years from now. Then we would have good reason to be surprised by the empty sky! But our planet is about 1/3 the age of the entire universe. Jumping from 4 billion years of evolution to 13 billion years of evolution is, from a certain perspective, quite a small step.
3. The Race
Extending the history of our evolutionary lineage to the start of the universe is simple enough, and does help limit the population of the sky. But surely over the last 13 billion years there must be some variance in the speed of evolution. This is true, and we can make some guesses about how much that might be, or at least model different estimates. If, for example, we allow the speed of evolution to vary by 1% (Hair 2011) and we believe there is one lineage per habitable planet, and we suppose that we have evolved at an average speed, then there would be 30 other lineages emerging from their planets per year right now in this galaxy, and there would already have been 5 billion lineages that emerged over the last 850 million years.
Hair, Thomas W. 2011. “Temporal Dispersion of the Emergence of Intelligence: An Inter-Arrival Time Analysis.” International Journal of Astrobiology 10: 131–35. https://doi.org/10.1017/S1473550411000024.
In this example, the typical lineage is still about a billion years from emerging. We belong to a thin first wave, arriving around now in galaxy after galaxy.
Figure 3 · Durations that vary: the first flush
The number of emerging lineages in this result is of the order of N, the total number of lineages in our model. These are the aliens we are racing against. The fact that the sky is empty means we can’t have been sitting around– we can’t be in the middle of the pack, or we would see the evidence of the leaders all around us. If you picture us as a random lineage, the chance of being this far ahead is about one in a hundred billion — roughly one over the number of lineages.
I’ll talk about luck more below, but it’s worth thinking about the rest of the players in the race. To make the model simple, I have chosen to assume that there is one evolutionary lineage per habitable planet. But that wraps a lot of assumptions up into one. First, we don’t really know what that means, and we are changing our model of it all the time. Some people are stricter about what constitutes a goldilocks zone, some say a planet needs a moon and a nice stable star. And perhaps the seeds, perhaps LUCA, is not so common that every planet gets seeded at exactly the right moment, or other planets are more prone to destabilizing catastrophes than ours. The number of other lineages N, that is, the number of our contemporaries, the number of our competitors in the race for the front, varies a lot model to model.
Changing the number of competitors changes our luckiness and the number of contemporaries we would expect to meet in our galaxy, but several other parts of the models are insensitive to it, such as the number of lineages ahead of us in our galaxy and the spread in time. The empty sky still needs an explanation, even if there are only a hundred or less surviving lineages per galaxy.
Figure 4 · The sky fixes the count, not the share
4. Luckiness
However fondly you may think of our lineage, however proud you may be of the cyanobacteria that transformed the atmosphere or the plucky archaea that first swallowed up a prokaryote and formed our domain, we do still seem to have been the beneficiaries of some remarkable rolls of the dice. Every model of the Fermi Paradox has to do it– to guesstimate our luck. Let’s start with that, and then think about ways we might make it a little firmer.
There are two broad ways to portion out the luck. The first is the hard-steps lottery, going back to Brandon Carter (Carter 1983; Watson 2008; Snyder-Beattie et al. 2021), which models evolution as a series of improbable events, events that normally don’t happen in any given lineage– the origin of life, eukaryotes, sex, multicellularity, language, etc. (Maynard Smith and Szathmáry 1995) These transitions are modelled as inherently unlikely, so unlikely that any given planet might not pass even one of them. A planet such as ours has passed through a series of major flukes to get where it is today.
Carter, Brandon. 1983. “The Anthropic Principle and Its Implications for Biological Evolution.” Philosophical Transactions of the Royal Society A 310: 347–63. https://doi.org/10.1098/rsta.1983.0096.
Watson, Andrew J. 2008. “Implications of an Anthropic Model of Evolution for Emergence of Complex Life and Intelligence.” Astrobiology 8: 175–85. https://doi.org/10.1089/ast.2006.0115.
Snyder-Beattie, Andrew E., Anders Sandberg, K. Eric Drexler, and Michael B. Bonsall. 2021. “The Timing of Evolutionary Transitions Suggests Intelligent Life Is Rare.” Astrobiology 21: 265–78. https://doi.org/10.1089/ast.2019.2149.
Maynard Smith, John, and Eörs Szathmáry. 1995. The Major Transitions in Evolution. Oxford University Press.
Mills, Daniel B., Jennifer L. Macalady, Adam Frank, and Jason T. Wright. 2025. “A Reassessment of the ‘Hard-Steps’ Model for the Evolution of Intelligent Life.” Science Advances 11: eads5698. https://doi.org/10.1126/sciadv.ads5698.
Hard steps was built to explain a coincidence on Earth: we turned up fairly late in the Sun’s habitable lifetime, which is what you’d expect if the path here ran through several long shots. It has since become the standard way to keep the sky empty. But a recent review by Mills and colleagues (Mills et al. 2025) argues that the case for any particular step being hard is weak. Several of the ‘steps’ waited on the planet changing, not on biological luck, and when you look closely each one breaks down into smaller pieces that each pay their way. Take language for example. Vocal cords evolve because communication of any sort over distance is beneficial to a community of genetically related individuals. Memory benefits any organism that has to interact with a sometime-predictable world. As memory develops, an organism can learn things within a lifetime that might benefit its offspring or cousins, so more advanced forms of communication and instincts for copying evolve. All the parts of advanced language are beneficial individually, and it’s easy to understand how it could have progressed, becoming more and more powerful as it evolves.
To my eye, the hard-steps lottery looks like it’s backfilled into the data once the uncompromising geometry of our situation is recognized. But the only thing that forces it is the assumption that life began on Earth, which gives other planets billions of years of head-start. If you drop that assumption, the starting clock seems more intuitive.
And the luck backs it up. The frame I use for the calculation is called Full Non-Indexical Conditioning (Neal 2006), and it asks what is the chance of finding an observer in a given situation. For the hard-steps model, what are the odds that there is a lineage on a planet observing an empty sky after having passed through such and such of a number of hard steps after evolving there for 4 billion years. For the process clock model, what are the odds that there is a lineage on a planet observing an empty sky after having evolved for 13 billion years.
Neal, Radford M. 2006. “Puzzles of Anthropic Reasoning Resolved Using Full Non-Indexical Conditioning.” https://arxiv.org/abs/math/0608592.
There are two ways to count luck here. The first is personal: what are the odds that our lineage, out of all of them, ended up this far ahead? That depends heavily on how many lineages there are. With a million lineages in our galaxy, the process clock needs us to be about one in 30 million. The hard-steps lottery needs us to be about one in ten trillion. Change the number of lineages and both numbers move, but the hard-steps one is always about a million times worse.
The second is the one that matters for choosing between theories: how often does a universe like this produce anyone in our position, emerging now under an empty sky? That one barely cares how many lineages there are, and here the process clock beats hard steps by a factor of ten million to a billion. The reason is timing. The process clock bunches its arrivals into a wave a few tens of millions of years wide, so it only has to keep the sky quiet for that long. The lottery spreads them over billions of years, so it has to keep them rare the whole time.
Figure 5 · Two ways to count luck
With regard to the process clock, you might be tempted to make our situation less unlikely by changing the number N. Indeed, you could imagine a synthesis of the hard-steps and process models, along the lines of ‘life is very unlikely, takes a great deal of environmental fortune, and so there are only a handful of surviving lineages per galaxy’. In this scenario we are not particularly lucky at all, it is simply the case that life takes 13 billion years to evolve, and there are only a handful of habitable zones in the galaxy that have happened to be seeded by the right stuff at the right time. There is something quite pleasant and parsimonious about this. And it feels like it takes on the important conceptual lessons from the hard-steps model– let’s not throw out the baby with the bathwater.
On the other hand, someone has to be first, and it might as well be us. Probability can help us select between competing hypotheses, but it can’t stop us from looking out at the empty sky and finding ourselves surprised. I would rather think that N is high, there are many lineages out there, and we will meet them someday than believe that the galaxy is essentially barren.
But there is one last thing that has to be contended with. We must deal with doom.
5. The Filter
In 2010, Katja Grace informed us that the filter is ahead (Grace 2010). That is to say, when observing an empty sky, the chances are you will not live to colonize it.
Grace, Katja. 2010. “SIA Doomsday: The Filter Is Ahead.” Meteuphoric (blog). https://meteuphoric.com/2010/03/23/sia-doomsday-the-filter-is-ahead/.
With our default scenario, an observer like us is about a billion times more likely in a world with a hard filter than without, and for the hard-steps model it’s about a million billion or more.
This value essentially prices all the standard objections to the model. The typical late filter framing imagines that building Dyson spheres is the default outcome, and some catastrophe must stop us from going through with it. However there are many scenarios that should be combined here. In Diaspora (Egan 1997), Greg Egan has a society of artificial entities set out on a galactic mission in a ship the size of a grain of rice. The ‘doom tax’ really covers all of these scenarios– not only the probability that we won’t ever blot out the sun due to catastrophe, but also the probability that we will simply choose not to, or find a more efficient way to run society, or escape into a pocket dimension where we will enjoy unlimited energy and resources forever. By reflection, it also models the chance that there are already other advanced civilizations, that are simply invisible to us or unrecognizable.
Egan, Greg. 1997. Diaspora. London: Millennium. https://www.gregegan.net/DIASPORA/DIASPORA.html.
This was the biggest surprise that fell out of the model, for me. The fact that the most common intuitive objections to this entire enterprise show up, here, at the end, when we try to work out our luck.
But one more thing is worth mentioning. I said earlier that our luck really tracks the number of other lineages in our galaxy. If we are the only one, we don’t have to be so lucky. Well, the doom tax, the idea that our situation is likelier if there is a great filter coming up, also tracks N. And it therefore gives us an easy way out of it– just suppose we are alone in the galaxy, and the doom shrinks from a billion to a factor of 20.
Figure 6 · The doom tax
This is convenient, but to me it is unsatisfying. I would rather attack the doom tax with better priors. If we take it as a measure of our uncertainty that we will build a Dyson sphere we can point at Starlink and say, look, we are already launching solar-powered infrastructure into space in significant quantities. We only need to keep to the exponential for a century and we’re there. In this framing, I might excuse myself for watching the Starship launches so avidly, as each one constitutes a Bayesian update against great filter doom.
Conclusion
I entirely credit Sharov and Gordon’s Life Before Earth (Sharov and Gordon 2013) with inspiring this work. I had heard about panspermia before, read it in some Hanson blogs, in some science fiction stories. But Life Before Earth really jarred me and changed the way I thought about evolutionary history. In the years since, other sources fed into this frame of mind, Chaisson’s ERD papers (Chaisson 2011), England’s dissipative adaptation (England 2015), and most recently Assembly Theory (Sharma et al. 2023). Hanson’s Grabby Aliens model (Hanson et al. 2021) inspired me to take the empty sky seriously as an observation, and think about what you could derive from there.
Sharov, Alexei A., and Richard Gordon. 2013. “Life Before Earth.” https://arxiv.org/abs/1304.3381.
Chaisson, Eric J. 2011. “Energy Rate Density as a Complexity Metric and Evolutionary Driver.” Complexity 16 (3): 27–40. https://doi.org/10.1002/cplx.20323.
England, Jeremy L. 2015. “Dissipative Adaptation in Driven Self-Assembly.” Nature Nanotechnology 10: 919–23. https://doi.org/10.1038/nnano.2015.250.
Sharma, Abhishek, Dániel Czégel, Michael Lachmann, Christopher P. Kempes, Sara Imari Walker, and Leroy Cronin. 2023. “Assembly Theory Explains and Quantifies Selection and Evolution.” Nature 622: 321–28. https://doi.org/10.1038/s41586-023-06600-9.
Hanson, Robin, Daniel Martin, Calvin McCarter, and Jonathan Paulson. 2021. “If Loud Aliens Explain Human Earliness, Quiet Aliens Are Also Rare.” The Astrophysical Journal 922: 182. https://doi.org/10.3847/1538-4357/ac2369.
Ponfilenok, Oleg. 2026. “The Critical Path of Evolution.” Zenodo. https://doi.org/10.5281/zenodo.21008110.
While I was working on this intensely in the last couple of weeks, one of my searches turned up Ponfilenok (2026), an independent researcher who uploaded a remarkably similar preprint just a couple of months ago, drawing inspiration from all the same sources as me. His model and his aims are slightly different from mine, and his scholarship is more thorough, so I happily acknowledge his precedence. It will take me a while to fully digest his paper, but I will try to write a note detailing exactly where we differ and by how much. More interesting though is where he has gone further into the possible mechanism and the thermodynamics.
The premise of this work is quite simple, take a few observations and assumptions and grind them through the machinery of statistics until something comes out the other end. But really, the reason ideas like this come around is because of all the mass of circumstantial and partial glancing lines of reasoning and evidence that push you towards them. All the things that you can’t fit into the model. All the lines of evidence that relate to this topic are getting richer and making progress all the time. Every asteroid we touch, every other planet we probe and sample, every distant star system or galaxy we observe adds evidence and allows us to sharpen up the numbers one way or another.
Indeed, research into evolutionary history, molecular biology, sociology on Earth can also often be folded into it. This is the real fun of Fermi thinking. Understanding the evolution of complex life folds in all our endeavours, and speaks to each of them.
Per Ardua, ad Astra.
See you, space cowboy.