"Since after extinction no one will be present to take responsibility, we have to take full responsibility now." ― Jonathan Schell, The Fate of the EarthWhen will the last person be born? The question is simple; the answer is difficult. J.R. Gott tried to answer this question using Bayes' theorem and simple statistics. The number of people who will be born is likely to be large. But is it more likely that there will be one trillion people or two trillion? We expect larger numbers to be less likely than smaller numbers. We write $\text{Pr}(N) = k/N$ and $\text{Pr}(n) = k/n$, where N is the number of people that will ever be born and n is the number of people already born. Furthermore, we'll assume that there is nothing special about our position in human history. We were as likely to be born as the billionth or the hundred billionth person. Mathematically, this is written $\text{Pr}(n|N)=1/N$.
The likelihood that there will be N people, given that we know there have been n people already—$\text{Pr}(N|n)$—is obtained from Bayes' theorem:$$\text{Pr}(N|n)=\frac{\text{Pr}(n|N) \times \text{Pr}(N)}{\text{Pr}(n)} = \frac{n}{N^2}$$From this, we can calculate the probability for upper bounds on the number N: $\text{Pr}(N \leq z)= \frac{z-n}{z}$. The first modern census was not conducted until the 18th century, but we can estimate the number of people who have lived on Earth—it's on the order of 100 billion. We can be 95% confident that there will be fewer than 2 trillion people. Given that there are four births every second, this person will be born in 15 thousand years.
There are a number of objections that can be made against the doomsday argument on mathematical grounds; however, the biggest problem is that it fails to address the physical causes of extinction. Genetic mutations will continue to accumulate in human populations, perhaps causing h. sapiens to differentiate into new species. Disasters may contribute to an early human extinction. A 2008 report by the Future of Humanity Institute estimates a 1 in 5 chance of humans extinction before the year 2100. Though, the methodology of this study is questionable. The doomsday argument may be flawed, but it raises questions in mathematical inference, and has opened the door to managing the risks we face as a species.
Dustin,
ReplyDeleteI'm not sure the assumption of our unspecialness is valid. The onset of free-market capitalism in the early 1800's caused birthrates to fall (demographic transition) but population growth to skyrocket. It's not clear that we not in a special phase of human history. Furthermore, what happens when, in the next 1000 - 10000 years, we begin spreading throughout the galaxy? We will no longer be vulnerable as a species to a single disaster. Is there a reason to see any end to the number of human descendants?
This assumption doesn't say anything about when people will be born--only the order in which they are born. I'm inclined to agree that the doomsday argument isn't the best, but it has some interesting mathematics and can get people thinking about the risks society faces.
DeleteAlso, if people begin to colonize other planets--though, this is a pretty big if--those populations are likely to evolve to their new environments relatively quickly. After even 1,000 years on Mars, for example, people may adapt to the conditions and become reproductively isolated from people on Earth.