Introduction:

Many have asked me to elaborate on what I mean when I talk about the underpopulation crisis and so rather than continue to respond to a great many people via direct message I decided it warrants a dedicated post. If you too have this problem perhaps you can share this post with your friends when they ask you about it.

This post does not seek to be an entirely comprehensive discussion, this is because I have other more interesting topics I want to focus on and I have a lot of other projects, as well as work and tutoring which are taking up an unfortunate quantity of my time but also because the subject matter is straight-forward. To anyone who can suspend their emotions and ideological precommitments to view the subject rationally, it is obviously a serious problem—which is the main reason I am bothering to spend the time addressing it.

Laying the Groundwork,

Addressing the question of how to prioritise what the human species ought to care about is to smuggle in the assumption of the continued existence of the species itself. Why be concerned about prioritising anything if you think the entire enterprise is meaningless? Therefore if you care about the future of the human species, then before that you care about its survival. The same logic goes for the project of human civilisation, before you talk about what civilisation should do civilisation needs to exist.

First, the goal is to look at the system and broadly classify its solvability on the basis of experience, if one concludes there is no method of understanding the system dynamics by axiomatic deduction, mathematical reducibility or emergent principles of complexity then one decides to analyse the boundaries, extrema or constraints, in fact, this is almost always a good idea for any system. This type of analysis is performed in a lot of fields and is given different names, although it is the tendency of people to not generalise it to all types of problems. One might ask in materials science or civil engineering how wide a range of temperature variation is permissible in order for the device or structure to remain unaffected or experience negligible distortion for the application at hand. That is to say, we ask how far can the base parameters which seem to play a role in the dynamics of the system be changed before the system breaks down.

The Issue

If we ask this in the case of civilisation the answer is fairly clear, the answer is obviously that in order for civilisation to persist a human population must exist. This is all just to say that before we worry about anything else we have to worry about the continued survival of the species and before we worry about liberty we need to worry about whether a society that can support liberty is capable of sustaining itself under certain conditions.

When it comes to analysing the population, you can have two extrema, 0 and saturation. Saturation is when a population utilises its resources to sustain the maximum population, this is the Malthusian Trap, no matter how much more food you are able to produce eventually the population will expand to reach saturation. Population growth is generally sigmoidal, that is to say, it has the typical S-Curve shape. When the population is low and it has access to lots of resources it grows quickly, nearly exponentially, when a population has nearly consumed all resources then growth becomes negligible.

This is all assuming that populations will continue to expand to saturation, however, if the situation is reversed, which it now appears to be for humans, then instead of the fated progression toward saturation, you will have a fated progression toward 0. Obviously, the dynamics are more complicated than this, but once you start heading down just like you get aggressive sigmoidal/exponential growth on the upswing, on the downswing you can get sigmoidal/exponential collapse. We will talk more about this shortly, for now, let us take a look at some population pyramids to visualise what the problem is and why people are talking about it.

Population Pyramids, Examples of Demographic Collapse

Population pyramids show the population on the x-axis, each bar up the y-axis represents a year of age or set of years, often split into male and female on the left and right. They are called population pyramids because typically they look like a pyramid, with the vast majority of the population being young. Throughout history people would die from all causes at a higher rate, provided we consider age irrelevant to the probability of dying from all causes, this turns out to be a less bad assumption than one might immediately assume, then we get the memoryless property, so our survival function is a negative exponential, that is to say, that the probability of being alive exponentially declines as we age.

Modern medicine has changed this, it has a tendency to push everybody through, up until the age that most get cleaned up by diseases of aging that medicine has failed to solve. With people living older than they have in the past, the pyramids, stop looking like pyramids, if you look at the top of most though you can see a return to a much more aggressive exponential decay. That is not the only effect at play, however. People are also having fewer children in every industrialised nation, this is not a problem that has gone entirely unnoticed but since it runs counter to the Cathedral’s narrative, namely that population growth is unsustainable, its implications have been ignored.

To build a bit of intuition for how the negative exponential dynamics of decline work, not age-related mortality, in fact entirely ignoring that for the minute, let us make the following assumptions; if we say there are 4 generations alive at a time and over the course of the last 4 generations there has been a birth rate of 1.5 births per woman then that means we have a ratio of 3/4 for the population of the younger generation to that of the preceding generation since we assume women are roughly 50% of the population. Therefore for replacement, we would need 2.0 births per woman, 1 to replace themselves and another 1 to replace the male population, actually in general people say 2.1 is a preferred number due to some individuals dying before they are able to reproduce and due to infertility in some.

A Mathematical Diversion

If our ratio is 3/4 or 1.5 births per woman, which is higher than most Western countries and is certainly higher than the birthrate of the native populations in almost every Western Population, then this is the base of our exponential, giving us the following rough description of generations,

If we say each generation is 20 years in length and people die spontaneously when they reach 80 and then we choose an n and add up the terms for n, n+1, n+2 and n + 3, with the caveat here that because we have decided to only worry about n as an element of the natural numbers that we always start when the oldest individual in the oldest generation has just turned 80 and is dying and there is a new person about to be born which will be the first member of a new generation.

If we assume that the G2 is responsible for looking after G0, then already G2 is half of G0, this places a fairly extreme expected workload upon those who are in the younger generation, facing up to the reality that the old are not productive one has to wonder how such a system will function, continuous economic depression appears the only result, indeed this is what is occurring in the case of Japan, 20 years of stagnation and the only thing preventing complete collapse is the nation’s insane work ethic.

In the above equation, Sn gives us the total number of people born in the generations up to and including Gn, where here a = G0 and r = 3/4. The number of people currently alive we could call Pn, and it is Sn+3 minus Sn-1 which is Gn + Gn+1 + Gn+2 + Gn+3, so Pn gives you the population of generation n to generation n+3 inclusive, so P0 is G1 + G2 + G3 + G4. Say if we want to know the population for the first set of 4 generations since birthrate began being 1.5 then we obtain P0 = S3 - 0 = (175/64)*G0 ~ 2.734*G0, of course, if we had perfect replacement we would expect 4*G0. So what does the population look like one generation later at P1?

My phone is not working so I can’t take a photo of my working out but if you do 5 or 6 steps with the algebra you will arrive at:

Substituting in our value of r = 3/4, we obtain after some simplification:

or if you prefer

So now we can ask how quickly does population decline, with the help of mathematica we can produce a table,

The second row of the first column begins with n = 0, and indeed we can see we got ~2.734 as in above calculation of P0.

If we want we can smuggle our (175/64) into P0 and rewrite the equation like this, we just need to remember that for P0 there have already been 3 generations of 1.5 births per woman, since P0 = G0 + G1 +G2 + G3.

This little mathematical excursion was mainly to point out that decline compounds even if one just assumes a constant birth rate of 1.5. Although my contention is once you get this ball rolling it can compound in other ways too, reduced capacity in the system leads to cutting corners which causes further breakdown in a cycle, a fall and all the monsters from the edge of the world come roaming about. We’ll continue this apocalyptic discussion in the next instalment of this post!

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