If the population falls the circumstances that created the low birth rate will change. This seems like the equivalent of an economist extrapolating a high inflation situation into the future and determining that only billionaires will be able to afford tomatoes.

I don't think the claim "if human population is only 560M a minor disaster could be enough to wipe out humanity" stands under scrutiny. There can be all kind of different arangement that these number of people live, wth different levels of fragility.

Imagine a universe with only 560M humans spreaded through the galaxy. Say there are only about a hundred people on every inhabited planet. However there are also bilions of aligned robots ensuring the wellbeing of these humans and capable to repopulate the humans if they die out.

Such arangement seems more protected from disasters than tens of billions of humans living on Earth in high density.

Any population argument that stretches centuries in the future needs to contend with whether humans will attain clinical, biological, or some other form of immortality or amortality in that time. If we increase the lifespan to 300 or 1000 or 10000 years of healthy life, that both forestalls population decline and enables those who do want children to have more of them over the course of their lives.

I take issue with the authors here:

Won't the Amish or some other high-fertility, perhaps religious, sub-population expand to be as many as we need? For several reasons, no.

...

First, fertility in a high-fertility sub-group would have to be high enough (certainly above two, for example). We've already seen above that the "high fertility" of high fertility subgroups has been declining over the decades. High fertility used to mean 6 children per woman. Now it means 2.5. Before long, it may mean 1.8. Second, the children of high-fertility parents would have to be very likely to remain in their high-fertility cultural group.

I grew up in a small-town homeschooling community where large families were fairly normal, but many of the children did not go on to have many children, or homeschool their own children.

In contrast to that, I am now a member of a church where 4 children is considered a small family, and 12 children is considered a large family.

Many of the families are second-generation, and one of the topics of conversation is how to pass on a worldview that involves passing on that worldview recursively through the generations.

We're not Amish, but the Amish do seem to be doing a good job of this – per https://en.wikipedia.org/wiki/Amish#Population_and_distribution their numbers have been impressively consistent over the years. I don't know why the authors think that their next 100 years of growth would change from the last 100.

Now, it's going to take a while for their numbers to affect the global population. But it doesn't seem crazy to me that in a few centuries the world's population will be comparably large, and even more dominated by a few Islamic and Christian sects than it is now.

I can imagine humanity going voluntary extinct in the future. Making children is just one possible activity among many, and the number of possible activities and their attractiveness is probably going to grow, so at some moment most people may go "meh, too much effort". Or there can can be some weird economical effect where most people won't be able to afford children -- not because of meaningful resources such as food, but because of some bullshit reason (something that becomes infinitely expensive for some stupid reason, such as university education, will be considered a basic human right and you are not allowed to have kids if you can't afford to buy it for them). Or there could be a passively-aggressively unfriendly AI which can't hurt or defy humans openly, but may subtly discourage them from reproducing, because it is allowed to destroy humanity as long as it happens voluntarily and nonviolently. All of this seems possible to me, and yet the article seems needlessly alarmist.

The combination of technological progress and population decline could make children much cheaper. Just ask people how many children they would have, if they had universal basic income, affordable housing, affordable robotic nanny, and affordable robotic tutors. (As opposed to today, when often both parents need a job, stuff is expensive, and yet most people choose to have kids.)

I am curious about the specific details of "minor disasters" that can wipe out a population of 500M, but cannot wipe out a population of 8000M. Fewer people would probably still be distributed across the planet. For example, lower population density and more time spent online would reduce the risk of pandemics.

IMO I think the most important takeaways from this work are the following:

1. Assuming you both have a view where certain humans are positive EV in your book and you think the long term matters, extinction risk reduction may look far less valuable, and in particular we can no longer assume that mere global catastrophes are survivable for the human race, like nuclear war or bioweapons, since we can no longer assume that humans will breed back from a mere catastrophe. Thus, extinction risk no longer looks that special in the grand scheme of things, and global catastrophic risks look more valuable for prevention.

2. It imposes a deadline on long-termism, and in particular means that we can no longer appeal to very long-term projects. This type of reasoning was implicit in some arguments against making advanced AI like Geoffrey Miller's arguments, and while I think it could be salvaged somewhat, I do think that most reasoning related to hundreds to thousands of years long feedback loops or more needs to address the paper seriously, or it has 0 expected value in my book.

3. For those who believe that certain humans have positive EV in your book, then becoming grabby soon (as in the next few centuries) is very important, and that it's plausible that the actions taken in the next few centuries determine pretty much the whole expected value of the future, and depending on whether infinities are supported, may be the difference between a future where the expected value is 0, and a future where the expected value is +infinity or -infinity.

4. While I don't believe that this model will always be robust in all situations, I do think it's central conclusions are probably going to hold up assuming a non-grabby humanity in the next few centuries, and a humanity that doesn't get rocked by any global catastrophes, because of the essential uniformity of fertility and the inability of cultures to get out of the low fertility state once they get into it, combined with poor at best transmission of high fertility genetics.

I don't see any reason how the population can stabilize at the arbitrary level of 560 million. Either it will start to increase again at some point (due to cultural shift, natural selection or some other reason), or it will decline until the collapse of the industrial civilization. But in that case, with no universal education anymore, the demographic transition will reverse, and the population starts growing again to limits imposed by pre-industrial agriculture (which is somewhere around 2 to 3 billion, not half a billion).