The Doomsday Argument

The Doomsday Argument

The end is near. Human extinction will occur sooner you thought. At least, according to the Doomsday Argument, it will.

The Doomsday Argument claims to predict the number of future members of the human race given an estimate of the total number of humans born since the beginning of time. It asserts that there is a 95% chance that the human species will become extinct after 9,120 years.


This isn’t some cracked conspiracy theory; it is supported by sound principles of probability. In fact, it has yet to be unproven by mathematicians. Let me explain it to you. Imagine this scenario:

There are two black bags in front of you. They are exactly identical. In one bag, there are ten spheres, numbered 1, 2, 3, 4, … 10. In the other, there are 100 spheres, also numbered. You have to guess how many spheres each bag holds. You’re also allowed to randomly take one sphere from any bag you wish to help you decide. So, you pick one from the right bag. (By the way, you can’t tell how many spheres there are by feeling around in the bag.) The sphere that you chose has the number 7 written on it. From that, you should guess that the right bag has ten spheres.

Okay, I know what you’re thinking. You’re saying that I’m incorrect, because there’s a 50/50 chance of each bag holding ten spheres. Well, that would have been true if you hadn’t chosen a sphere from the bag. But, because you did, we can apply Bayes’ Theorem (a formula that describes how to find the probability of a hypothesis, given evidence). Then, we find that the probability of the right bag holding ten spheres is 91%.

Now, we can apply this reasoning to prove the Doomsday Argument. Let’s say that there are two possible outcomes: early destruction of humanity (ED), or late destruction (LD). In ED, there are 100 billion homo sapiens born, in total. This outcome corresponds to 10 spheres in the bag, from the previous experiment. In LD, there are 10 trillion homo sapiens born (corresponding to 100 spheres in the bag). Suppose you found out that you are the 70 billionth person to be born. Thus, it is much more likely that ED will happen than LD.

Is this making sense so far?

You kept reading, so I’ll assume it did. Let’s continue. According to the Copernican Principle, if each human occupies a random spot in a “timeline” of births, it is likely that each one is about halfway in the timeline. To clarify, if we randomly chose a human, chances are, the human would NOT be among the first 5% of homo sapiens who have ever lived. So, if that human isn’t in the first 5%, then he/she must be in the last 95%, right?

John Leslie used this thought process to calculate the Doomsday Argument. He reasoned that we can be 95% sure that we are among the last 95% of humans to be born. Then, by using 70 billion as an estimate for the number of humans born so far, he calculated that there was a 95% chance that no more than 1.4 trillion humans would be born in the future. Looking at the rate of population growth (or NIR, if you’ve learned AP Human Geography), Leslie estimated that the population would reach that amount, and therefore become extinct, in approximately 10,000 years.


So, that’s the Doomsday Argument. If you’re still here (I wouldn’t blame you if you stopped reading), thanks for visiting my blog and reading this post! In case you’re confused about this concept, you can ask me for any clarifications by commenting, or emailing me. And if you’re scrambling to warn your friends and family about impending disaster, rest assured: humanity will be obliterated, but not during our lifetime.


  • “A Primer on the Doomsday Argument.” Anthropic Principle. N.p., n.d. Web. 16 May 2017.
  • “Doomsday Argument.” Wikipedia. Wikimedia Foundation, 03 May 2017. Web. 16 May 2017.
  • Bostrom, Nick. “The Doomsday Argument: A Literature Review.” The Doomsday Argument: A Literature Review. N.p., 20 Oct. 1998. Web. 16 May 2017.
  • Dvorsky, George. “Can the Doomsday Argument Predict Our Odds of Survival?” Io9., 10 Apr. 2013. Web. 16 May 2017.

8 thoughts on “The Doomsday Argument

  1. Haha I love this post, not only because my own blog concerns Human Extinction. Although this applies advanced and abstruse concepts that may take a bit of time to comprehend, the overall argument and theory is fascinating. I never would’ve thought that mathematics could explain human extinction and this inspires me to look deeper into the exciting possibilities of math.


    1. Yeah, I never would have thought it either. To be honest, I don’t completely understand this concept either. I’m still trying to wrap my brain around it – like, I understand the different methods that mathematicians used to prove the argument, but how do they fit together? I’m working on it. Anyway, go forth with your newfound inspiration, young padawan! Go explore “the exciting possibilities of math.”


  2. I’m still trying to understand the sphere part, but I get the 5% and 95% part. It’s basically probability. But, I have a question: So if 70 billion humans have already been born, and we are the later 95% of that, then wouldn’t the 140 trillion that are added in the future also be taken into account in the 95% of all humans? Then you would have to add in another number of humans, then you do the equation all over again, resulting in a paradox. Or I’m probably not understanding the complex math behind it. I really liked this post as it made me think.


    1. Ok, good question. So first: there will be 1.4 trillion humans added in the future, not 140 trillion. Second, that’s exactly what John Leslie did: knowing that 70 billion people have already been born, assuming that 70 billion was 5%, he calculated that 1.4 trillion were going to be born in the future. Then, looking at population growth rates, he figured that we would reach that in about 10,000 years. I hope that clears up your question. It is a pretty complex concept, but it’s really cool (in my opinion). I’m glad this post made you think! Thanks for commenting, and I hope to see you later, in my next post!


  3. This post is very interesting. Human extinction is something no one can imagine in the near future and it seems like it will never happen. While I still don’t fully comprehend the mathematics behind this prediction, I am still intrigued by the idea that theorems and formulas can be used to calculate human extinction.


    1. I didn’t realize all of the the uses of math until I started writing this blog. I never imagined human extinction to occur so soon, either. There are many different proofs for this theorem, which I tried to combine in this post. It is a confusing concept, but I am working on elucidating it. Thanks for showing interest in math, and I hope you’ll revisit my blog!


  4. Hi Ananya,
    Ok, I’m confused. To be honest, I read this post 3 times over, and it still doesn’t make any more sense than the first time through. I did understand some of the logic. But overall, isn’t this basically biology? I mean the carrying capacity of a region stops a species from growing past a certain point. If this post is referring to this, then I have to say that humans are somewhat of an exception. The human population has been extending the carrying capacity along with their growth, so for now, human extinction and termination has been postponed, but I guess it is still inevitable.


    1. Well, you are correct. Human population might reach the carrying capacity of Earth and plateau before 1.4 trillion more people are born (although, yes, it does seem like humans are out stepping their limits). But I am not entirely sure whether this argument takes this into account – I haven’t researched in depth. Your comment was very interesting. Good thinking! Anyway, thanks for being a frequent commenter! I’ll see you in my future posts!


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