I edited my post “Immortality and reproduction are incompatible in the long term future“. Unfortunately, I had made a math error, and the conclusion is wrong unless we make additional assumptions.

What was the mistake? A simple math error. The original post had two key points:

Assuming no one ever dies:
1. The total resources available to humanity grow less than t³ with time.
2. Even 1% of people reproducing grows the population exponentially with time.

These two points taken together imply exponentially decaying resources per person.

However, the second point is clearly wrong! I’m going to explain why; but first we have to define one of humanity’s final bosses: the Total Fertility Rate, and how population growth works in terms of it.

Modeling population growth in terms of TFR

The key term in analyzing population growth is the Total Fertility Rate (TFR); which means “average number of kids a woman has over her lifetime”.

Modeling the population growth in terms of TFR is a tiny bit complex without additional assumptions; I’m going to spare you the details and just show you the plots.

footnote: You need to model both the distribution of birth years over a woman’s lifetime; and how the average age of women in the population changes over time. To make it simple for the immortality case, here we do the simple thing and assume all women who give birth sort of give birth at the same year of their life, which yields a simple model of growth.

Let’s first look at how it works in the real world, when everyone dies eventually.

Note three different curves depending on the TFR:

• TFR > 2 kids/woman: the population grows exponentially;

• TFR = 2 kids/woman: the population remains sort of constant;

• TFR < 2 kids/woman: the population goes extinct.

This is sort of concerning, given that many TFRs of societies in the developed world are between 0.8 and 1.5. Here are the numbers from Wikipedia:

Now, with immortality, it is kind of obvious that it’s not the case that the population goes extinct. But what are the population dynamics in terms of TFR?

Again, there are three regimes:

• TFR > 2 kids/woman: the population grows exponentially;

• TFR = 2 kids/woman: the population grows linearly;

• TFR < 2 kids/woman: the population converges.

One simple way to see why the population converges when TFR < 2 is that, in discrete time, it is a geometric series:

1. If there are W women in a generation, there are (TFR / 2) * W women in the next generation;

2. Extrapolating to the N-th generation, the number of new women born is (TFR / 2) ^ (N - 1) * W;

3. The sum of the geometric series is W * (1 + (TFR / 2) + (TFR / 2) ^ 2 + ... + (TFR / 2) ^ (N - 1)) = W * (1 - (TFR / 2) ^ N) / (1 - TFR / 2).

In any case, whatever that final term is, it is finite for TFR < 2; and we can see that in the TFR=1 case, the population never makes it to double the original population.

LLMs did not catch the bug

Having a simple math bug in such a short post was surprising to me. Not because I am particularly good at it (I wrote it without checking from my head, and I am so much better on paper); but because I do have a protocol to avoid such mistakes. I never really post anything without an LLM commenting on it first.

However, this time I only ran it by Claude Opus 4.1, which did not catch the mistake in the original post. OpenAI Deep Research turned up several related sources without telling me my original thesis was wrong. Gemini 2.5 Deep Think and GPT 5 Thinking did catch the mistake; but I forgot to run the original post by all the models.

Further, I severely overestimated how confident I should be in 2025 LLMs to not make this type of mistake.

For instance, for the plots in the post, both Claude Code and GPT 5.1 Thinking made completely wrong plots! The mistake they are both making in their code is implementing constant TFR as implying a “constant birth rate per woman per year”. This is obviously wrong if people never die, as any constant birth rate per year would make a single person produce infinitely many children in the long run.

P.S. I was also wrong about the marketing game of pronatalists and the Don’t Die folks

In the original post, I claim that the longevity movement seems to have better marketing than the pronatalist movement.

However, I’ve been told that pronatalist content is extremely popular on parts of the Internet that I do not frequent; especially short-form video apps. Keywords include “Nara Smith”, “Ballerina Farm”, “trad wife”, and so on.

Bryan Johnson’s antics are popular; but only as a “health hack” thing, not as an explicit anti-death meme, as in e.g. the Fable of the Dragon Tyrant.