The Doomsday Argument is Reasonable and Mostly Points to Longevity

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 thi