The Doomsday argument was proposed in a 1983 lecture by Brandon Carter and elaborated on in John Leslie's 1996 book The End of the World: The Science and Ethics of Human Extinction. The basic idea is to think of your order among humans being born and apply the Copernican principle that you aren't in a special position. If you imagine yourself as the median human in birth-order, that would imply as many people will be born after you as were before. You can extend it to a cumulative probability function quickly, that is you have a 95% chance of being in the last 95% of births and this holds if you swap first with last or replace 95% with a different percent. I first remember hearing about the Doomsday argument in the 2000s. It was framed to me[1] as an argument that humanity might go extinct soon, which seemed counterintuitive given the Fukuyama-esque optimism about humanity that was otherwise in vogue, but in this post I will show that for much of human history, given the number of humans who lived in the past and population growth rates at that time, the Doomsday argument gives generally reasonable estimates and generally predicts that Doomsday is very far in the future. By 'reasonable', I do not mean I am going to dissolve the Doomsday Argument with mind-bending reinterpretations of the philosophy involved[2], I mean that a layman at the time would see a 50% chance of humanity going extinct by a date and accept it at face value. In some cases, I argue that the estimates are still reasonable from our hindsight.
If you're a LessWrong reader[3], then you should already believe that the current time is an extremely strange time in human history, but even ignoring that, the median-birth-rank human to have existed so far is a subsistence farmer around 180 AD[4], so let's step back for a second and consider three people who fit that description.
You are a farmer in Bronze Age Mesopotamia in 2000 BC. Interpolating from PRB, there's around 108 million people alive and 8.6 million born each year. 25 billion humans have been born, which predicts 50 billion humans (and doomsday) for ~219 BC, with the 95% upper bound at 500 billion humans and 4600 AD. For modern humans, predicting that the world should have been destroyed 2200 years ago is alarming, confusing, and falsified, but a farmer hearing the world has 1800 years to live is the opposite of alarmed or surprised. The Sumerian King List has hundreds of thousands of years of mythical kings, an apocalyptic flood, thousands of years of less mythical kings until we get to real history with Enmebaragesiof Kish around 2750 BC. 2000 BC is four years after war destroyed the Third Dynasty of Ur and Mesopotamia will be in a state of chaos for a while. The Sumerian Gods are very real, heavily interventionist, and not very nice about it. From this perspective of lengthy history, occasional apocalypses demonstrated in the form of the Flood and the end of Ur, and capricious gods, "The world may be destroyed in 60 Lifetimes, but almost certainly won't last more than 6,000 years" fits right in.
You grow rice under the Han dynasty. It's 180 AD. Interpolating from PRB, there's around 320 million people alive, 58.3 billion have ever lived, and 19.2 million are born each year. That puts a 50% chance of doomsday 3,030 years away, a thousand years in our future at 3210 AD. Sima Qian's Records of the Grand Historian has recorded history starting in 2700 BC, the time before that being too mythical for him to believe in, which means our prediction lines up nicely with just saying there will be as much history in the future as there was in the past, but Chinese had a very cyclical view. The Chinese Dynastic Cycle and the Five Phases of the Wuxing are not clear beginnings and ends, but lengthy cycles. So, it would make sense to them that the current phase of humanity would have an end to match its beginning, but the idea that this might be a final end and not just an end of a phase might be a stretch.
You are a farmer in Medieval Europe around 1200 AD. There are 450 million humans, 27 million more are born every year, and 81.6 billion have ever been born. This puts probable-Doomsday at 4220 AD, the farthest future date we've seen so far. Ironically, here is when the people might be doomier than you. Early Christian theologians, such as Hippolytus and Africanus divided history into six ages each approximately a thousand years and ending with the second coming of Jesus as a mirror to God creating the world in six days and then resting on Sunday. This theory had been used to predict the apocalypse in 500, 801, and 1000 AD, and people continued to do that[5]. The Cistercian abbot Joachim of Fiore's followers predicted an "Age of the Holy Spirit" would start in 1260 AD based on the 1,260 days mentioned in Revelation 11-12. It would be nice if we had more secular writers, so that we could try to figure out if a non-believer from these cultures would still believe in a near apocalypse, but this one is a bit of a weak point in my argument that people in the past would think its estimates were reasonable.
Below is a table summarizing the previous three "normal human" entries, before I go on to what are more exceptional times.
Era
Cum Pop
Cur Pop
Birth Rate
Estimated Doomsday
Local Opinion of Estimate
2000 BC
25 billion
108 million
8.6 million
219 BC
Seems reasonable
180 AD
58.3 billion
320 million
19.2 million
3210 AD
Framed as a cycle, seems reasonable.
1200 AD
81.6 billion
450 million
27 million
4220 AD
Much too far in the future.
Out of all the humans that have existed so far, those were pretty average ones, but now let's go for the stranger cases.
Let's consider early Homo Sapiens. Modern science now has anatomically modern humans around 300,000 years ago, whereas PRB's estimated the species' beginning at 190,000 BC, so we have less firm ground for our math to stand on, but the conceptual argument works just as well. If we approach these early humans quickly after they become a new species, then we would predict a rapid death, which has surely happened to many newly evolved species which turned out to be marching into an evolutionary dead end. If we approach these humans after 200,000 years, when they are still behaving like clever monkeys and not humans, we would then expect them to survive until 100,000 AD.
It's not clear that early Homo sapiens could understand these concepts given that behavioral modernity came much later than the beginning of the species, but the Homo genus has a plentiful graveyard. Homo habilis, erectus, heidelbergensis, neanderthalensis,longi (Denisovans), antecessor, floresiensis, luzonensis, naledi, and rudolfensis all demonstrate that species like ours aren't immortal, but a four hundred thousand year lifespan would fit in just fine.
Now let's move to much more recent times. The Cuban Missile Crisis avoided nuclear war due to individual commanders on Soviet submarines armed with nuclear torpedoes deciding not to use them[6]. Paul Ehrlich popularized the idea that unchecked population growth would create worldwide famines and social unrest[7]. Scientists were beginning to raise the alarm about how extreme global warming from burning fossil fuels could become.[8] This seems like a pretty scary time, but what does the doomsday argument say? If you're standing in 1965 and assume population continues growing exponentially, we get median in 2085 and 95% confidence at 2230[9]. Big yikes, huh.
This is when the Doomsday Argument has the nearest doomsday and the vibes match, but that exponential growth assumption is doing a lot of the work to make it so and is coming in a brief window where humans are no longer crushed by Malthusian population limits, but the global fertility bust has not yet gone global. Still a 50% chance of human extinction between 1965 and 2085 has not been falsified and even from today's perspective, I would not be surprised if a reasonable person thought there was a 50% chance of doom by 2085.
As we return to 2005 where we started, we see the end of rapid population growth makes a big difference DA-wise. With 114 billion people born, 6.5 billion alive, and 137 million annual births, that gives us a 50% chance of lasting to 2835 AD which is much less frightening and hilariously backs up the Fukuyama-esque vibes and pushes back against those who sold me the Doomsday Argument as evidence that we might go extinct soon.
What about today? DA now predicts 50% doom by 2919, 95% by 19010 AD, and 8% by 2100[10]. Coincidentally, the domain experts in the 2022 Existential-Risk Persuasion Tournament concluded that there was a 6% chance of human extinction by 2100 [11]. This close match seems almost reassuring, but if you check the report, you will see the experts were aware of and to some extent influenced by the DA's estimate. Regardless, those seem like very optimistic projections when compared to contemporary AI-Doomers. There are of course lots of loopholes where humans stop having births or AI doom happens without it being a bad thing. Human brains could be uploaded and run as emulations, AIs could be worthy successors, Homo sapiens could be replaced with a genetically engineered Homo superior. I will end this essay by leaving you with those strange possibilities, but I would like to think that I have made my point. The Doomsday Argument is not actually that pessimistic and the dates it suggests seem reasonable if you actually consider them.
And from the title of Leslie's book alone, we can see it was intentional on his part! Not to mention the book's chapter length argument in favor of the Doomsday Argument!
The standard trick here is that the Doomsday Argument relies on the self-sampling assumption, but if you go with the self-indication assumption instead, then the fact that you exist at all is evidence that the number of people to exist will be very large which cancels out the DA's argument that the number of people to exist will be smaller than you might expect. (Dieks 1992, Olum 2002)
Landes, [“The Fear of an Apocalyptic Year 1000: Augustinian Historiography, Medieval and Modern”](https://www.bu.edu/history/files/2011/10/11.Fear-of-an-Apocalyptic-Year-1000-Speculum.pdf), *Speculum* 75, no. 1 (2000): 97–145.
Assume 60 billion have been born (this is Leslie's number), annual births are 120 million, and grow 2% a year: Cumulative future births after t years would be (120M/0.02)(e^0.02t − 1) = 6B(e^0.02t − 1), which can be solved algebraically for t=120 (50%/2085) and t=263 (95%/2230). If we use a more modern estimate of 109 billion, that moves our 50% to 2112 and 95% to 2257, but I think using the period's estimate helps you get into the mindset of the period better.
The Doomsday argument was proposed in a 1983 lecture by Brandon Carter and elaborated on in John Leslie's 1996 book The End of the World: The Science and Ethics of Human Extinction. The basic idea is to think of your order among humans being born and apply the Copernican principle that you aren't in a special position. If you imagine yourself as the median human in birth-order, that would imply as many people will be born after you as were before. You can extend it to a cumulative probability function quickly, that is you have a 95% chance of being in the last 95% of births and this holds if you swap first with last or replace 95% with a different percent. I first remember hearing about the Doomsday argument in the 2000s. It was framed to me[1] as an argument that humanity might go extinct soon, which seemed counterintuitive given the Fukuyama-esque optimism about humanity that was otherwise in vogue, but in this post I will show that for much of human history, given the number of humans who lived in the past and population growth rates at that time, the Doomsday argument gives generally reasonable estimates and generally predicts that Doomsday is very far in the future. By 'reasonable', I do not mean I am going to dissolve the Doomsday Argument with mind-bending reinterpretations of the philosophy involved[2], I mean that a layman at the time would see a 50% chance of humanity going extinct by a date and accept it at face value. In some cases, I argue that the estimates are still reasonable from our hindsight.
If you're a LessWrong reader[3], then you should already believe that the current time is an extremely strange time in human history, but even ignoring that, the median-birth-rank human to have existed so far is a subsistence farmer around 180 AD[4], so let's step back for a second and consider three people who fit that description.
You are a farmer in Bronze Age Mesopotamia in 2000 BC. Interpolating from PRB, there's around 108 million people alive and 8.6 million born each year. 25 billion humans have been born, which predicts 50 billion humans (and doomsday) for ~219 BC, with the 95% upper bound at 500 billion humans and 4600 AD. For modern humans, predicting that the world should have been destroyed 2200 years ago is alarming, confusing, and falsified, but a farmer hearing the world has 1800 years to live is the opposite of alarmed or surprised. The Sumerian King List has hundreds of thousands of years of mythical kings, an apocalyptic flood, thousands of years of less mythical kings until we get to real history with Enmebaragesi of Kish around 2750 BC. 2000 BC is four years after war destroyed the Third Dynasty of Ur and Mesopotamia will be in a state of chaos for a while. The Sumerian Gods are very real, heavily interventionist, and not very nice about it. From this perspective of lengthy history, occasional apocalypses demonstrated in the form of the Flood and the end of Ur, and capricious gods, "The world may be destroyed in 60 Lifetimes, but almost certainly won't last more than 6,000 years" fits right in.
You grow rice under the Han dynasty. It's 180 AD. Interpolating from PRB, there's around 320 million people alive, 58.3 billion have ever lived, and 19.2 million are born each year. That puts a 50% chance of doomsday 3,030 years away, a thousand years in our future at 3210 AD. Sima Qian's Records of the Grand Historian has recorded history starting in 2700 BC, the time before that being too mythical for him to believe in, which means our prediction lines up nicely with just saying there will be as much history in the future as there was in the past, but Chinese had a very cyclical view. The Chinese Dynastic Cycle and the Five Phases of the Wuxing are not clear beginnings and ends, but lengthy cycles. So, it would make sense to them that the current phase of humanity would have an end to match its beginning, but the idea that this might be a final end and not just an end of a phase might be a stretch.
You are a farmer in Medieval Europe around 1200 AD. There are 450 million humans, 27 million more are born every year, and 81.6 billion have ever been born. This puts probable-Doomsday at 4220 AD, the farthest future date we've seen so far. Ironically, here is when the people might be doomier than you. Early Christian theologians, such as Hippolytus and Africanus divided history into six ages each approximately a thousand years and ending with the second coming of Jesus as a mirror to God creating the world in six days and then resting on Sunday. This theory had been used to predict the apocalypse in 500, 801, and 1000 AD, and people continued to do that[5]. The Cistercian abbot Joachim of Fiore's followers predicted an "Age of the Holy Spirit" would start in 1260 AD based on the 1,260 days mentioned in Revelation 11-12. It would be nice if we had more secular writers, so that we could try to figure out if a non-believer from these cultures would still believe in a near apocalypse, but this one is a bit of a weak point in my argument that people in the past would think its estimates were reasonable.
Below is a table summarizing the previous three "normal human" entries, before I go on to what are more exceptional times.
Era
Cum Pop
Cur Pop
Birth Rate
Estimated Doomsday
Local Opinion of Estimate
2000 BC
25 billion
108 million
8.6 million
219 BC
Seems reasonable
180 AD
58.3 billion
320 million
19.2 million
3210 AD
Framed as a cycle, seems reasonable.
1200 AD
81.6 billion
450 million
27 million
4220 AD
Much too far in the future.
Out of all the humans that have existed so far, those were pretty average ones, but now let's go for the stranger cases.
Let's consider early Homo Sapiens. Modern science now has anatomically modern humans around 300,000 years ago, whereas PRB's estimated the species' beginning at 190,000 BC, so we have less firm ground for our math to stand on, but the conceptual argument works just as well. If we approach these early humans quickly after they become a new species, then we would predict a rapid death, which has surely happened to many newly evolved species which turned out to be marching into an evolutionary dead end. If we approach these humans after 200,000 years, when they are still behaving like clever monkeys and not humans, we would then expect them to survive until 100,000 AD.
It's not clear that early Homo sapiens could understand these concepts given that behavioral modernity came much later than the beginning of the species, but the Homo genus has a plentiful graveyard. Homo habilis, erectus, heidelbergensis, neanderthalensis, longi (Denisovans), antecessor, floresiensis, luzonensis, naledi, and rudolfensis all demonstrate that species like ours aren't immortal, but a four hundred thousand year lifespan would fit in just fine.
Now let's move to much more recent times. The Cuban Missile Crisis avoided nuclear war due to individual commanders on Soviet submarines armed with nuclear torpedoes deciding not to use them[6]. Paul Ehrlich popularized the idea that unchecked population growth would create worldwide famines and social unrest[7]. Scientists were beginning to raise the alarm about how extreme global warming from burning fossil fuels could become.[8] This seems like a pretty scary time, but what does the doomsday argument say? If you're standing in 1965 and assume population continues growing exponentially, we get median in 2085 and 95% confidence at 2230[9]. Big yikes, huh.
This is when the Doomsday Argument has the nearest doomsday and the vibes match, but that exponential growth assumption is doing a lot of the work to make it so and is coming in a brief window where humans are no longer crushed by Malthusian population limits, but the global fertility bust has not yet gone global. Still a 50% chance of human extinction between 1965 and 2085 has not been falsified and even from today's perspective, I would not be surprised if a reasonable person thought there was a 50% chance of doom by 2085.
As we return to 2005 where we started, we see the end of rapid population growth makes a big difference DA-wise. With 114 billion people born, 6.5 billion alive, and 137 million annual births, that gives us a 50% chance of lasting to 2835 AD which is much less frightening and hilariously backs up the Fukuyama-esque vibes and pushes back against those who sold me the Doomsday Argument as evidence that we might go extinct soon.
What about today? DA now predicts 50% doom by 2919, 95% by 19010 AD, and 8% by 2100[10]. Coincidentally, the domain experts in the 2022 Existential-Risk Persuasion Tournament concluded that there was a 6% chance of human extinction by 2100 [11]. This close match seems almost reassuring, but if you check the report, you will see the experts were aware of and to some extent influenced by the DA's estimate. Regardless, those seem like very optimistic projections when compared to contemporary AI-Doomers. There are of course lots of loopholes where humans stop having births or AI doom happens without it being a bad thing. Human brains could be uploaded and run as emulations, AIs could be worthy successors, Homo sapiens could be replaced with a genetically engineered Homo superior. I will end this essay by leaving you with those strange possibilities, but I would like to think that I have made my point. The Doomsday Argument is not actually that pessimistic and the dates it suggests seem reasonable if you actually consider them.
And from the title of Leslie's book alone, we can see it was intentional on his part! Not to mention the book's chapter length argument in favor of the Doomsday Argument!
The standard trick here is that the Doomsday Argument relies on the self-sampling assumption, but if you go with the self-indication assumption instead, then the fact that you exist at all is evidence that the number of people to exist will be very large which cancels out the DA's argument that the number of people to exist will be smaller than you might expect. (Dieks 1992, Olum 2002)
And if you're not, I'd like to know where you're reading this.
Interpolation from https://www.prb.org/news/how-many-people-have-ever-lived-on-earth/ is my source for this and many later calculations here.
Landes, [“The Fear of an Apocalyptic Year 1000: Augustinian Historiography, Medieval and Modern”](https://www.bu.edu/history/files/2011/10/11.Fear-of-an-Apocalyptic-Year-1000-Speculum.pdf), *Speculum* 75, no. 1 (2000): 97–145.
https://www.theguardian.com/world/2022/oct/27/cuban-missile-crisis-60-years-on-new-papers-reveal-how-close-the-world-came-to-nuclear-disaster
Ehrlich, P. R. (1968). The population bomb. Ballantine Books.
https://www.theguardian.com/environment/climate-consensus-97-per-cent/2018/jan/01/on-its-hundredth-birthday-in-1959-edward-teller-warned-the-oil-industry-about-global-warming
Assume 60 billion have been born (this is Leslie's number), annual births are 120 million, and grow 2% a year: Cumulative future births after t years would be (120M/0.02)(e^0.02t − 1) = 6B(e^0.02t − 1), which can be solved algebraically for t=120 (50%/2085) and t=263 (95%/2230). If we use a more modern estimate of 109 billion, that moves our 50% to 2112 and 95% to 2257, but I think using the period's estimate helps you get into the mindset of the period better.
118 billion ever born, 8.3 billion alive, 132 million annual births
https://forecastingresearch.org/pdf/existential-risk-persuasion-tournament.pdf
https://files.cercomp.ufg.br/weby/up/410/o/Our_Final_Hour_%E2%80%93_A_Scientist's_Warning_._2003_._Martin_Rees_c%C3%B3pia.pdf
This is me copying from IRB who estimates that the birth rate was 80 per 1000 in 1 AD, but went down to 60 per 1000 in 1200 AD.