Anthropic Reasoning
The Doomsday Argument
You are the 100 billionth human ever born. This is evidence that humanity will go extinct soon.
Approximately 100 billion humans have ever existed. You are one of them. You have a birth rank: you are roughly human number #100,000,000,000.
This number alone, according to a controversial probabilistic argument first formalized by Brandon Carter in 1983, provides evidence about humanity's future - specifically, evidence that we will go extinct sooner than you might expect.
The argument asks: why should you expect to be special?
If humanity will eventually number in the trillions, it would be remarkably unlikely for you to be among the first 100 billion.
This is the Doomsday Argument. It uses your birth rank as evidence about the total number of humans who will ever exist - and therefore, about how much time humanity has left.
“There is no way you could have found yourself to be an early human if in fact you were going to be a late one.”- John Leslie
Where Do You Fall on the Timeline?
Imagine laying out all humans who will ever exist on a timeline, from the first to the last. Where do you fall? Adjust the slider to see how your position changes based on different assumptions about total human population.
Your Rank
#100B
Total Humans
200B
Your Position
50.0%
If 200B humans will ever exist, your birth rank is roughly in the middle. This seems more plausible.
If trillions of humans will exist, you are among the very first 0.01%. Does that seem likely?
The Probability of Being This Early
The core of the Doomsday Argument is a simple probability calculation. If you are randomly sampled from all humans who will ever exist, what is the probability of being born in the first 100 billion?
Probability of being born at position #100B or earlier:
50.00%
If 200B humans will ever exist, the probability of being born in the first 100B is 1 in 2.0.
The larger the total population, the less likely it is that you would find yourself this early. Under the Self-Sampling Assumption (SSA), this low probability counts as evidence against scenarios with very large total populations.
Updating Your Beliefs
The Doomsday Argument is fundamentally Bayesian. You start with prior beliefs about different possible futures for humanity, then update those beliefs based on the evidence of your birth rank.
Bayes' theorem tells us:
P(Doom Soon | Birth Rank) = P(Birth Rank | Doom Soon) × P(Doom Soon) / P(Birth Rank)
Prior Beliefs
After Birth Rank Evidence
Notice how the birth rank evidence always shifts probability toward doom scenarios. Even with optimistic priors, learning you are human #100B makes near-term extinction more likely than before.
The key insight: under every scenario, learning your birth rank shifts probability toward earlier doom. The only question is how much.
The Copernican Principle
The Copernican Principle states that we should not assume we occupy a special position in the universe. Applied to the Doomsday Argument: you should not assume you are unusually early or late among all humans.
This principle lets us construct confidence intervals. If you assume you are randomly located, you can calculate bounds on the total number of humans with any desired confidence level.
The Copernican principle assumes you are not special - you are a typical human randomly sampled from all humans who will ever exist.
Lower Bound
103B
humans total
Upper Bound
4.0T
humans total
With 95% confidence, total humans will be between 103 billion and 4.0 trillion.
At 95% confidence, humanity probably ends before reaching 4.0 trillion people - that is only about 40x more humans than have already existed.
See It In Action
To build intuition, let's simulate many possible worlds and see what happens. In half the worlds, doom comes early (200B total humans). In half, doom comes late (2000B total).
Among all observers who find themselves at position #100B, what fraction come from early-doom worlds?
Simulate 1000 possible worlds. Half have early doom (200B humans total), half have late doom (2000B total). Among observers who find themselves at position #100B, how many come from early-doom worlds?
Why This Might Be Wrong
The Doomsday Argument has been debated by philosophers for decades, and there is no consensus. Many brilliant thinkers have proposed objections. Here are the most important ones:
The Doomsday Argument is controversial. Here are the main objections:
The Reference Class Problem
Who counts as "human"?
Self-Indication Assumption (SIA)
Your existence is evidence of more observers
The Presumptuous Philosopher
SIA has its own problems
Selection Effects
We can only observe from here
Population Dynamics
Growth patterns matter
Information Hazard
Does learning this change anything?
The debate continues. Nick Bostrom, who has written extensively on anthropic reasoning, notes that “the Doomsday Argument is either one of the most important discoveries in the history of human thought, or it is a subtle mistake.”
What Should We Conclude?
Whether or not the Doomsday Argument is correct, engaging with it reveals deep questions about probability, reference classes, and what it means to reason about our place in the universe.
If the argument is valid...
We should take existential risks more seriously than our intuitions suggest. Our prior estimates of human extinction probability should be revised upward.
If SIA is correct...
Your existence is evidence for large populations, canceling the Doomsday shift. But this leads to other counterintuitive conclusions about infinite universes.
If the reference class is wrong...
The argument may not apply to us specifically. Perhaps we should compare ourselves only to biological humans, or only to Earth-bound humans, changing the calculus.
Regardless of its validity...
The Doomsday Argument reminds us that our intuitions about probability and self-location can be deeply unreliable. We should reason carefully about existential questions.
The fundamental question:
Can you learn anything about the world from the mere fact that you exist, and when you exist? The Doomsday Argument says yes. Many disagree. The debate touches the deepest questions in philosophy of probability.
You are human #100 billion. What does that tell you about the humans yet to come?
Explore More Paradoxes
The Doomsday Argument is one of many counterintuitive results in probability and philosophy. Explore our other interactive explainers.
References: Carter (1983), Leslie (1996), Bostrom (2002)