Is there a mathematical argument for the end of the world? Developed by Astrophysicist, Brandon Carter, the Doomsday argument or “The Carter Catastrophe” is a probabilistic argument that claims to predict the number of future members of the human species (the longevity of our civilization) using the number of humans born so far. In a nutshell, it concludes that human extinction is far more closer than we’d previously thought.

Imagine a giant urn that either contains a few balls (numbered 1-10) OR many balls (numbered 1-1,000,000). You don’t know which of the two scenarios is the case, but if you randomly pulled a ball from the urn and drew one numbered “4”, then which of the two scenarios is more likely? That the urn has many balls, or just a few? The one ball you drew is evidence in favor of the “10 Ball” condition.

Now imagine yourself, a human, as a numbered ball, your birth number. It’s probably 60 billion, judging by the number of humans who came before you. Just like the number 4 ball, you are a random sample of all humans that will ever live. The doomsday argument points out that from 200 billion people, there’s a 50 percent chance that a human like you will be born in the first 100 billion. Whereas if there were 10 trillion humans that could possibly exist, your existence is only a very unlikely 1% chance that a human would be born in the first 100 billion.

Either you are extremely lucky to be born as early as you were or, the more disturbing scenario; there are only very few humans and extinction is coming sooner rather than later…


The Carter Catastrophe (championed by academics like Richard Gott, John Leslie and Nick Bostrom) is a case that predicts the end of humanity somewhere in the next few thousand years (and that’s if we are lucky and the Earth’s population stabilizes). The whole calculation centers on the “principle of mediocrity”.

If you are at the halfway point of all humans that have ever lived, then you are much more likely to be born at “the end” than the beginning. Denoting by “N” the total number of humans who were ever or will ever be born, the Copernican principle suggests that humans are equally likely to find themselves at any position “P” of the total population. Assume that our fractional position f = P/N is uniformly distributed on the interval [0, 1] prior to learning our absolute position, there is a 95% chance that f is in the interval (0.05, 1), that is f > 0.05.

In other words, this assumes that we could be 95% certain to be within the last 95% of all the humans ever to be born. 60 billion humans have been born so far, so it can be estimated that there is a 95% chance that the total number of humans (N) will be less than 20 × 60 billion = 1.2 trillion (using “Leslie’s figure”). Hopefully, if people stop having too many children, the world population will stabilize at 10 billion and life expectancy at 80 years. If we are successful, it can be estimated that the remaining 1140 billion humans will be born in 9120 years.

This puts the maximum number of time until “Doomsday” at roughly about 9000 years.

Depending on the projection of world population in the forthcoming centuries, estimates may vary, but the main point of the argument is that it is unlikely that more than 1.2 trillion humans will ever live on Earth. If you are the Trillionth human to be born, you are statistically way more likely to be part of the “doom soon” group.


JUST TO BE CLEAR, the Doomsday argument DOES NOT say that humanity cannot or will not exist indefinitely. It does not put any upper limit on the number of humans that will ever exist, nor provide a date for when humanity will become extinct. Don’t confuse probability with certainty. The argument’s conclusion is there is a 95% chance of extinction within 9,120 years, HOWEVER, it gives a 5% chance that some humans will still be alive at the end of that period.

In essence, the Doomsday Argument suggests that human extinction is FAR more likely to occur sooner rather than later. This means we have grossly underestimated how easy it is for humanity to destroy itself and that we should probably take DRAMATIC precautions to prevent extinction.


If the universe is so vast and high-tech intelligent aliens exist, then why do we not see evidence of them? If you are familiar with the fermi paradox, you might see why the Carter Catastrophe might explain why high tech alien civilizations so rare. This is because the vast statistical majority kill themselves off (thus making it hard for us to detect them).

The Doomsday argument is a fascinating statistical analysis of human beings that seems silly when you first hear it (>Blah blah blarmageddon) but it slowly brings to light just how far we’ve statistically underestimated the probability of human extinction and the reason we don’t see other civilizations. It is more likely to find someone born at the end of civilization (where there are billions of inhabitants) than early in civilization, which is what makes the existence of high-tech civilizations so brief. It is more probable to be born at a later point in time, leaving the window for detection of your high-tech civilization very small.

Think of yourself as a randomly selected observer, a sample of all humans that have ever lived. In your case, around 60 billion people have historically come before you, yet we are approaching an age in history where a mind-blowing 10 billion humans can live on earth all at the same time. By this measure, more humans live at the end than at the beginning, so you are statistically more likely to be closer to a doomsday scenario. Even if some premises of the Carter Catastrophe are wrong, would it still not remind us to be more careful of our actions?

The SIA (self-indication assumption) suggests that you are more likely to exist if there are a huge number of humans on the planet at that time (say, 7 billion), as compared with 99% of human history where we numbered in mere millions. You are more likely to exist in a “Doom late” universe than a statistically improbably “doom soon” universe, as are the many potential alien civilizations in the night sky.

This may be incredibly disturbing and depressing for some. Luckily, there are some counterarguments to the Doomsday argument.


The doomsday argument “feels wrong” because it doesn’t seem to involve any physical experimentation, more just statistical postulating. As such, there have been a lot of attempts to explain why the doomsday argument fails.

It assumes that we will never become immortal (a population crash with a small number of humans who go on to live for millions of years), it assumes that technology will never dramatically change the human race, it assumes that humans will always think in the same way, and that there is nothing wrong with the statistical analysis used. Here are a few counterarguments:

1) Argument from a posteriori (dominant species are unlikely to go extinct) : Extinction level events are rare could be offered as evidence that the Doomsday Argument’s predictions are implausible. It doesn’t consider the fact that humans may also develop ways to resist existential threats.

Typically, extinctions of a dominant species happens less often than once in a million years (dinosaurs, etc.). Therefore, it is argued that human extinction is unlikely within the next ten millennia. Overall, if you change the calculation’s reference class from “people” to “years” then you get a different answer.

2) Argument from a priori (we are the first 5%) :

If one agrees with the statistical methods but still disagrees with the Doomsday argument, they can imply that:

a) The current generation of humans are within the first 5% of humans to be born.

b) This is not purely a coincidence.

For example, if one is certain that 99% of humans who will ever live will be cyborgs, but that only a negligible fraction of humans who have been born to date are cyborgs, one could be equally certain that at least one hundred times as many people remain to be born as have been.

3) Argument from Reference Class: Heavily tied in with the doomsday argument is “the Anthropic Principle” (also developed by Brandon Carter), that in order to observe the universe there must be conditions inside that permit observers to exist in the first place (you can’t observe how likely or how unlikely your existence is if you don’t exist).

Are you REALLY a random sample of all humans that will ever be born? There is no reason to think of yourself as a random set of observers. For all we know, the expectation of the human population is actually infinite.

4) Argument from Transhumanism: First we have to define what a “human” even is in the context of post-human states and immortality. That cyborgs, mind-uploads, or planetary computers is not a human. Some might argue otherwise, but in that sense “humanity” does become extinct if your biological form is abandoned. So the doomsday argument would hold. Even with immortality, finite resources could be exhausted entirely and endanger the new civilization.

If humanity ever becomes something beyond our contemporary definition of “human”, then we are not “typical observers” and Carter’s Catastrophe is invalided.

5) Argument from Civilization: Humans have had varying intelligence and civilizational capabilities throughout their lifetimes. If doomsday argument advocates suggest counting transhumans is “unfair”, why then at what point do we BEGIN counting how many humans have lived? If we sample humans from the beginning of evolution rather than the beginning of civilization then we get a very different calculation…

Did we begin at the Roman Empire? Cavemen? Why can’t we begin at Homo Sapiens? Australopithacus? Why not bonobos, chimps, or dolphins? In this sense, perhaps the right reference class is something that only includes “Contemporary humans”, which may be difficult to pinpoint.


If the Doomsday Argument is correct it means that the probability of us becoming a civilization spanning trillions of years and thousands of worlds across the galaxy is extremely unlikely.  Many religious preachers often say “we are living in the end times”, surely a ridiculous notion? After all, so many in the ancient times, the Dark Ages, and the Renaissance believed the end times were upon them, yet they passed along without incident. However, THIS TIME, by pure accident of birth and place in history, these doomsayers may be inadvertently correct in a statistical sense.

Overall, the conclusion of the Doomsday Argument is as follows: whatever the prior probability of “doom soon” vs “doom late”, after reflecting on this argument, you should update your probability of a “doom soon” scenario. We as a species have underestimated just how likely we are to be destroyed, yet we go about our lives without even a second thought and undervalue prevalent threats to our existence.

We may be on thin ice, but while this is the fate of millions of dice rolls it doesn’t HAVE to be our fate. We do control our own destiny, regardless of how small our chances of survival are. Perhaps we humans should significantly elevate our sense of caution and take care of how we behave on this Earth, lest it bring about an unexpected extinction.

If we can transition to world peace and combat existential risk we can treat the Carter Catastrophe not as our inevitable fate, but as a wake-up call. A warning. A call to action…