How Long Will the Human Race Last? Reframing the Doomsday Argument
There’s a strange argument in philosophy called the Doomsday Argument. It attempts make a probabilistic prediction of the total number of humans who will ever live based on the number of people who have already lived. This sounds weird on the face of it, and indeed the argument is contentious, as you will see if you read the Wikipedia page on the subject. In this article I want to propose a way of reframing the argument that makes it self-evidently clear that, in spite of being counter-intuitive, the argument is indeed valid, while also providing parameters for understanding its limits.
To understand the basic premise of the argument, let us imagine I present you with a hat full of numbered pieces of paper, from one up to some number you don’t know. I ask you to pull out a number, then tell me how many numbers you think are in the bag. You pull out the number five. What’s your best guess at the number of pieces of paper? Around ten, right? It’s very unlikely you would pull out the number five if the hat contained a million pieces of paper, for example. (The odds of pulling out the number five or under from a million numbers are, obviously, five in a million, or one in 200,000.)
This is an example of the so-called “mediocrity principle”, which is the principle that we should assume that our observations are typical rather than exceptional. If you had never met another human being, you should assume you are more or less average in most respects, even if, in reality, you may be exceptional in a few ways. This principle tells us that even a single observation carries some statistical information about the entire population from which it is sampled.
The Doomsday Argument applies this principle to the human population in a novel and surprising way. It imagines that each person is assigned a birth sequence number from 1 for “Lucy”, the first human, to n for the birth number of the very last person who will live.
If we consider that your birth sequence number is effectively random, like the number pulled from the hat, then it should follow that we can say, with 90% certainty, that no more than ten times that number of humans will ever live. Our best guess at the total number of humans who have lived so far (and therefore your rough birth sequence number) is about one hundred billion. Therefore, we can be around 90% confident that the total number of people who will ever live is no more than one trillion.
We can also be 50% confident that we are already more than halfway through the total history of the species! Note, we are talking about the number of humans born here, not the amount of historical time. Given the massive population of the world today compared to earlier historical epochs, we would likely expect the total time of the second half to be much shorter than the first half, unless humans die out over the course of a very long period of decline after the current peak.
At this point you are probably thinking, “Whoa! That can’t be right!” Some immediate objections come to mind. For example, you might think that if Lucy’s children had made this argument, they would have been wildly wrong. A second argument that people tend to raise is that it seems impossible that our birth number could tell us anything about events that have yet to happen. In the case of the numbers in the hat, all the pieces of paper are already in the hat before you draw your number, whereas it seems weirdly precognitive for our birth number to tell us something about events in the future!
There has been a lot of debate on the Doomsday Argument among philosophers. For example, Nick Bostrom in his paper on the Simulation Hypothesis, which I roundly criticise in another Medium article here, says that the Doomsday Argument asks us to reason as if we were randomly selected members of the human species, when we know ourselves to be humans living at the start of the 21st century. In other words, Bostrom seems either to reject the randomness of our birth number, or to argue that we have more information about the likely longevity of the human species than the Doomsday Argument accounts for. There are many more objections that have been raised which go beyond the scope of this short article. I am choosing to gloss over these here because of the reasoning I am about to introduce, which cuts through these objections by framing the argument in different, clearer terms.
Let’s consider the matter this way. Imagine that at birth, every human being makes the bet that they are in the first 90% of all those who will live. They are forced to do so blindly, regardless of what they know or don’t know about how many people have come before them, or anything else. How many win the bet? Obviously, 90% do. This is true over the whole population even if at the time they are born and make their bet, the final population number has yet to be determined, and even if they don’t even know their own birth number.
So what is the probability of you winning your compulsory bet? Well, you know that 90% of people do win the bet, so that’s reassuring! It sets the base probability. Now of course, in 10% of cases, the bet fails, and it may be obvious to you, as a given individual, that yours is a losing bet. For example, you may look up and see a planet-destroying asteroid on track to hit the planet in three days’ time. In that case, the additional information given by your circumstances is sufficiently strong to let you know the bet is almost certainly lost. Note however that the “power” of this evidence needs to be strong in inverse proportion to the strength of the bet. If, for example, the bet was that you are in the first 99.99% of the population (a very weak bet), it would require relatively very strong evidence of imminent doomsday to override that base probability.
This argument makes the picture clear. Unless we have strong evidence against the base probability of a given “bet”, where the strength of evidence required is inversely proportional to the bet odds, we must accept the verdict of the Doomsday Argument. Of course we should note that the predictive power of the argument is fairly weak; the upper end 90% confidence level for the total number of humans to live is around 1 trillion, but this obviously allows for the human future to play out in many ways.
I would argue that current evidence of the state of the world suggests that, if anything, the Doomsday Argument prediction is likely optimistic rather than the reverse. It’s a sobering thought, but we don’t have forever. Probably.
