Yesterday’s post, as well as being mistitled, was probably quite depressing, although that depends on your view of human extinction since many people don’t consider that to be a bad thing. As a kind of antidote, I’ve decided today to offer a more encouraging view of our future, assuming that you consider the continued existence of the human race as positive. I’ve covered the Doomsday Argument before, but did it in quite an idiosyncratic manner, concentrating on my own thoughts about its possible flaws. This post is more an outline and survey of the Doomsday Argument and its rebuttals.
The Doomsday Argument has its origins in the astrophysicist Richard Gott’s visit to the Berlin Wall in 1969. The Wall began to be built in 1961 and Gott visited it eight years later. After speculating about how long it would be there, he did a quick calculation, and I get the impression this was mental arithmetic, and reached the conclusion that it would be demolished some time between 2⅔ and two dozen years after that date in 1969. In fact it came down in 1991, twenty-one years later. This provoked him to publish his calculation in a scientific paper in 1993 where he applied the same calculation to the history of the human race, concluding with 95% confidence that we would cease to exist between twelve and eighteen millennia from 1993. This is of course quite a big range, but it’s notable to me that the Berlin Wall came down towards the end of that period.
The Berlin Wall version of the argument is the original and has also succeeded in predicting its demise, and is therefore worth looking at closely. A random visitor to the Berlin wall will be there at some point in its history. It’s likely that Gott visited the Wall some time between 25% and 75% of the way through its duration, because that’s half of its history, so a steady stream of visitors would put them somewhere in that interval half of the time. If they then make a prediction about when it will come down, the most confident period would be that it would last between a third and three times as long as it had been in existence, because they can believe fairly confidently that they’re between a quarter and three-quarters of the visitors in chronological order (more than 50% probability) and therefore it will last somewhere between a third as long again (if they’re at 75%) and three times as long again (if they’re at 25%).
Now apply that to human history. It might at first seem that it predicts that if anatomically modern humans came into existence around 300 000 years ago, we would continue to exist for between a hundred millennia and getting on for a million years, again with 95% confidence, which should be taken as read from now on. This doesn’t work quite the same way though. Visitors to the Berlin Wall were assumed, fairly reasonably, to have occurred at a roughly constantly frequency according to Gott’s argument, but the same doesn’t apply to the whole human population, which increases exponentially. Therefore it isn’t about where in history you are chronologically so much as the order of your birth among all the human births that will ever be. The figures I use for my version of the argument are the population of the planet in about 1970, my own birth in 1967, the figure of all human lives up until 1970 quoted at the time and a thirty-year doubling time. The population at that time was around 3000 million and the estimate at that time was 75 000 million. Given that figure of 3 000 million, 6 000 million would be the population by 2000, 12 000 million by 2030, 24 000 million by 2060 and 48 000 million by 2090. It reaches 96 000 million by 2120 at this rate of doubling, meaning that the last birth could be said to occur by that time at 50% probability assuming that everyone born in 1970 was still alive, but earlier than that otherwise because there would’ve been more human lives. We can assume, for example, that almost everyone born in 2000 would be dead by 2120, the figure only needs to go as high as 150 000 million in toto anyway, and so on. But the figures work out as between 25 000 million and 225 000 million further births after 1967 given these rather inaccurate figures, which place the earliest time before 2060 and the latest before the end of next century. You will gather from my vagueness that I can’t do calculus. Or look at it this way: if everyone who ever lived considered the question of whether they were in the first or second half of the number of human births which will ever be, almost half will be correct. (It’s possible that there is an exact “middle” birth if the total number of people who will ever live is odd rather than even.)
Most people agree that this argument is flawed, and I’ve previously mentioned my own objections to it, but there are superficial and deeper causes of the flaws. The superficial reasons for the above figures are that they’re sloppy and inaccurate. Population doubling time has been quoted at between twenty-eight and thirty-five years during the period it was widely considered a major concern, and adjusting for those moves the dates to between 2054 and 2225. It also turned out that the doubling rate fell recently and that economic development reduces the size of families, so it’s been estimated, and again this is an old figure, that the world population will stabilise at eighteen millard (thousand million) in the mid-twenty-second century, which gives us centuries to go. A rather less superficial argument is based on selecting my own birthdate, because the argument can be made for anyone who has ever had this thought, and therefore there could easily be a prediction thousands of years ago that puts us way beyond the latest 95% confidence limit today. The argument is equally valid no matter whose life you use as an example. The date changes as time passes. If someone had made the prediction about the Berlin Wall in 1990, the lower bound of their confidence interval would’ve been in 2000.
But there are other problems with the argument which are not to do with these details or even applying it to human extinction. Before I go into them, I want to make two observations. Firstly, there’s a tendency for people who do believe in its validity to dismiss other’s (go on, ask me about that apostrophe, I dare you!) arguments as indicating that they haven’t understood it properly. Secondly, although it’s widely agreed that it’s invalid, the reasons are multiple, and people who believe it’s invalid for one reason often don’t agree with the other reasons given. This complicates things.
One objection to the argument is that it assumes nothing is known about where one is in human history. It seems to make sense to flip a coin if one is asked the question “was your birth in the first or second half of the total number of human lives?” and go with that answer only if one believes the coin to be fair. If one knows it isn’t fair and will always come up heads, it’s no longer rational to choose tails. If anything relevant can be known about our place in history, it changes the odds. For instance, it could be discovered that there was a correlation between the prevalence, lethality and spread of pandemics on the one hand and the level of population on the other which would make it very likely that a population above ten billion would lead to human extinction within an average human lifespan, in which case as soon as it hit that number and stayed there for seventy years or so, our demise was guaranteed. I don’t personally like this argument because I can’t think of anything which is that reliable which is relevant to human survival. I believe that we are in fact in ignorance, partly because measures might be taken to prevent the apocalypse once its likelihood had been calculated. On the other hand, that might be optimistic given how keen everyone seemed to be, for example, on ignoring the finding that pandemics were in fact much more likely to happen in current circumstances.
There’s also a converse argument which goes like this. The more intelligent life forms which will ever exist, the more likely it is that I exist. There are various ways in which my existence, like everyone else’s, is improbable, and the combination of traits which lead to someone like me existing becomes increasingly probable the more people there will ever be. If there are going to be 200 thousand million people, the chances of someone like me existing might be ten percent – nine out of ten possible worlds with 200 thousand million people in their history don’t have me in them. But if there are going to be 200 billion in that scenario, a thousandfold greater, each world would end up having around a hundred examples of someone like me in its history somewhere.
Here’s another argument, and I may have got this wrong. The Doomsday Argument is an early example of other similar arguments. One of these is the argument that the human species will never substantially settle anywhere off Earth because if there were, for instance, fifty million habitable worlds in the Galaxy and each had a population of a million with a life expectancy of a century for a millennium, all of which are very conservative assumptions, the probability of living before that era is only 0.015%. There are other similar arguments. Therefore there is a sense in which those who are aware of this argument are early adopters. They’re like the people who bought the bug-prone version of a new gadget who were used as guinea pigs by the manufacturer, and therefore the argument they accept is likely to be less sophisticated and more flawed than its successors. We could be working towards a more successful predictor of the future than this argument, and since we’re aware that it only has a short history, we probably have the wrong one. This sounds peculiar to me, which is why I think I might have got it wrong.
We could also be early humans. It might be that the fact that we’re human-basic rather than transhuman is an argument for us not being very advanced in history. We don’t currently augment our bodies much internally, but the technology to make that possible is already in its infancy and will become more advanced. The fact that we don’t download music directly to our brains yet, unlike practically everyone who will be born more than two centuries from now, is evidence that we are unusual.
The fact that mass extinctions only seldom happen has also been used. This is again a probabilistic argument, and can be modified to refer to individual dominant biological taxa. But there seem to have been six mass extinction events in the past 540 million years, so the chances of us being in one are small. Whereas I think that’s valid, it clearly isn’t true because we are in fact in the middle of one right now, probably related to our activity. But dominant species are said only to go extinct about once in a million years, so that’s another odds-based argument for this not being a threat.
Another objection is based on the St Petersburg Paradox. Suppose you bet on a coin coming up heads, and every time the coin is flipped and doesn’t, your winnings double. The expected winning is infinite even though intuition suggests that it will in fact be small compared to how much you put in, because the probability of losing halves with every flip. The rational choice would therefore appear to be to place all your money on the game. I may not be following this argument correctly, but it seems to relate to each generation of human existence being a toss-up between being the last and not being the last, and in the same way, the expected number of human beings is infinite. To be honest this makes no sense to me and I’m not sure I’ve expressed it correctly.
Carlton Caves has offered this example as a rebuttal. Imagine you encounter someone whose fiftieth birthday is today. By the logic of the Doomsday Argument, they have a one in three chance of living to one hundred and fifty. I see this as referring to the idea of having special knowledge, because we know that nobody seems to have lived more than about ten dozen years.
A little like the early adopter argument, there is a self-referential counter-argument. The Doomsday Argument was thought of fairly recently. Including the Berlin Wall calculation, it’s currently four dozen and two years old. Therefore, it is likely to be refuted some time between sixteen and one gross and a half dozen years from now, in other words 2037 and 2171. However, if this argument for its refutation works, it means the Doomsday Argument is valid, which is a paradox. This, though, is problematic because it assumes that the argument can be disproven, which may not be so.
I haven’t found this to be a particularly satisfactory post because I’m not feeling on top of the arguments. Attempts to disprove the Doomsday Argument are very popular and the whole field is rather confusing to a non-mathematician such as myself. That said, if you look at my other post on this topic, you’ll see my own reasons for doubting it. Unfortunately though, or perhaps unfortunately, merely disproving the argument itself doesn’t prevent the possibility that we will soon be extinct. Tomorrow I plan to talk about that.
A Box Of Chocolates 