## The over-population clock

Canto: From time to time I’ve shown my students the world population clock (WPC), because I’ve brought my discourse round to it for some reason, and they’ve been mostly fascinated. And I’ve usually told them that the world’s population will level out at about 9.5 billion by mid-century, because I’ve read or heard that somewhere, or in a few places, but is that really true?

Jacinta: So you’re wanting to investigate some modelling?

Canto: Well yes maybe. I was looking at the WPC the other day, and was shocked at how births are outnumbering deaths currently. What’s actually being done to stem this tide?

Jacinta: Looking at the WPC website, there’s a lot more data there that might enlighten you and calm your fears a bit – if it can be trusted. Ok we went past 7.4 billion this year and you can see that so far there’s 70 milliom births compared to around 29 million deaths, and that looks worrying, but you need to look at long-term trends. The fact is that we’ve added a little over 40 million so far this year, with a current growth rate of about 1.13%. That figure means little by itself, but it’s important to note that it’s less than half of what the growth rate was at its peak, at 2.19% in 1963. The rate has been decelerating ever since. Of course the worry is that this deceleration may slow or stop, but there’s not much sign of that if we look at more recent trends.

Canto: Okay I’m looking at the figures now, and at current trends the projection is 10 billion by 2056, by which time the growth rate is projected to be less than 0.5%, but still a fair way from ZPG. The population, by the way, was two point something billion when I was born. That’s a mind-boggling change.

Jacinta: And yet, leaving aside the damage we’ve done and are doing to other species, we’re doing all right for *ourselves*, with humanity’s average calorie intake actually increasing over that time, if that indicates anything.

Canto: Averages can carpet over a multitude of sins.

Jacinta: Very quotable. But the most interesting factoid I’ve found here is that the current growth rate of 1.13% is well down on last year’s 1.18%, and the biggest drop in one year ever recorded. In 2010 the growth rate was 2.23%, so the deceleration is accelerating, so to speak. It’s also interesting that this deceleration correlates with increasing urbanisation. We’re now at 54.3% and rising. I know correlation isn’t causation, but it stands to reason that with movement to the city, with higher overheads in terms of housing, and with space being at a premium, but greater individual opportunities, smaller families are a better bet.

Canto: You bet, cities are homogenously heterogenous, all tending to favour smaller but more diverse families it seems to me. That’s why I’m not so concerned about the Brexit phenomenon, from a long-term perspective, though we shouldn’t be complacent about it. We need to maintain opportunities for trade and exchange, co-operative innovation, so that cities don’t evolve into pockets of isolation. Ghettoisation. Younger people get that, but the worry is that they won’t stay young, they won’t maintain that openness to a broader experience.

Jacinta: Well the whole EU thing is another can of worms, and I wonder why it is that so many Brits were so pissed off with it, or were they duped by populist nationalists, or are they genuinely suffering under European tyranny, I’m too far removed to judge.

Canto: Well, if there were too many alienating regulations, as some were suggesting, this should have and surely could have been subject to negotiation. Maybe it’s a lesson for the EU, but you’re right, we’re too far removed to sensibly comment. Just looking at the WPC now – and it’s changing all the time – it has daily birth/death rates which shows that the birth rate today far exceeds the death rate – by more than two to one. How can you possibly extrapolate that to a growth rate of only 1.13%?

Jacinta: Ah well that’s a mathematical question, and I’m no mathematician but obviously if you have a birth rate the same as the death rate you’ll have ZPG, no matter what the current population, where as if you have a disparity between births and deaths, the percentage of population increase (or decrease) will depend on the starting population and the end-population, as a factor of time – whether you measure is annually or daily or whatever.

Canto: Right so let’s practice our mathematics with a simple example and then work out a formula. Say you start with 10, that’s your start population at the beginning of the day. And 24 hours later you end up with 20. That’s a 100% growth rate? But of course that could be with 1000 additional births over the day, and 990 deaths. Or 10 more births and no deaths.

Jacinta: Right, which indicates that the total number of births and deaths is irrelevant, it’s the difference between them that counts, so to speak. So let’s call this difference d, which could be positive or negative.

Canto: But to determine whether this value is positive or negative, or what the figure is, you need to know the value of births (B) and deaths (D).

Jacinta: Right, so d = B – D. And let’s set aside for now whether it’s per diem or per annum or whatever. What we’re wanting to find out is the rate of increase, which we’ll call r. If you have a start population (S) of 10 and d is 10, then the end population (E) will be 20, giving a birth rate r of 100%, which is a doubling. I think that’s right.

Canto: So the formula will be: r* = *S – E… Fuck it, I don’t get formulae very well, let’s work from actual figures to get the formula. It’s actually useful that we’re almost exactly mid-year, and the figure for d (population growth) is currently a little under 42 million. That’s for a half-year, so I’ll project out to 83 million for 2016.

Jacinta: So d now means *annual *population growth.

Canto: right. Now if we remove this year’s growth figure from the current overall population we get as our figure for S = 7,391,500,000 and that’s an approximation, not too far off. And we can calculate E as 7,474,500, approximately.

Jacinta: But I don’t think we need to know E, we just need S and d in order to calculate r. r is given as a percentage, but as a fraction it must be d/S. And this can be worked out with any handy calculator. My calculation comes out at 6.6% growth rate.

Canto: Wrong.

Jacinta: Yes, wrong, ok, a quick confab with Dr Google provides this formula. d = ((E – S)/S).100. But we already have that? E-S is 83 million. Divided by S (7,391,500,000), and then multiplying by 100 gives a growth rate annually of 1.1229%, or 1.12% to two decimal places, which is not far off, but significantly less than, the WPC figure of 1.3%. I must have stuffed up the earlier calculation, because I think I used the same basic formula.

Canto: Excellent, so you’re right, my fears are allayed somewhat. Recent figures seem to be showing the growth rate declining faster than expected, but let’s have another look at the end of the year. Could it be that the growth figures are higher in the second half of the year, and the pundits are aware of this and make allowances for it, or are we actually ahead of the game?

Jacinta: We’ll have a look at it again at the end of the year. Remember we did a bit of rounding, but I doubt that it would’ve made that much difference.

**Some current national annual population growth rates (approx):**

Afghanistan 3.02%

Australia 1.57%

Bangladesh 1.20%

Brazil 0.91%

Canada 1.04%

China 0.52%

India 1.26%

Iran 1.27%

Germany 0.06%

Morocco 1.37%

Nigeria 2.67%

Pakistan 2.11%

South Africa 1.08%

United Kingdom 0.63%

(These are not, of course, calculated solely by births minus deaths, as migration plays a substantial role – certainly in Australia. Some surprises here. The highest growth rate on the full list of countries: Oman, 8.45%. The lowest is Andorra with -3.61%, though Syria, with -2.27% on these figures, has probably surged ahead by now).

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