I’m listening to “Against the Grain: A Deep History of the Earliest States”, a new book exploring recent findings on the 97% of our past as human beings before writing, tax collectors, cities, and modern states.

One surprising finding: from ten thousand BC to five thousand** **BC, the total population of us human beings (homo sapiens sapiens) world wide went from about 4 million souls to 5 million — according to one estimate by Macevedy & Jones. (There are other estimates: https://www.census.gov/data/tables/time-series/demo/international-programs/historical-est-worldpop.html )

That was rather slow growth, the author noted. But *how* slow, this retired math teacher wondered?

So I got out a pencil and my notebook and wrote an equation. I used G for the annual growth factor, and wanted to see how close to 1.0000000 it was.

(Note: If G is exactly 1, then the population never changes; if G is less than 1, the population shrinks with exponential decay. If G=2.0, then the population doubles every year, which obviously can’t happen in any human population anywhere nor at any time. Though it certainly can for some of our commensal pests like mice…)

So, Macevedy & Jones’ initial population estimate of 4,000,000 (assuming smooth exponential growth over five millennia — a useful mathematical fiction) gets multiplied by G, whatever that might be, five thousand times (ie by G raised to the 5,000th power) to produce 5,000,000 people.

Or, 4000000*G^5000 = 5000000

Dividing both sides by four million I get

G^5000 = 1.25

The only way I know to solve that is to take the logarithm of both sides. Doing that with base ten and using the special laws of logs, I get

5000*log (G) = log (1.25)

Then I divide both sides by 5000 and I get

Log(G) = log(1.25) /5000

Then I exponentiate both sides using the original log base (ten), and I get

G =10^( log(1.25) / 5000)

At this point I use a calculator on my phone, typing in exactly the stuff on the RH side of the equals sign. And I get

10^(log10(1.25)/5000) = 1.00004463

Which is very, very close to unity. How close? Let us subtract one from that. We get

0.0000463 or 4.463e-05 in scientific notation. Or roughly 45 parts in a million. Mind you, there were a grand total of four million of our ancestors on the planet then, so we can multiply that 45 by four, and we get 180.

But what does that mean?

It means that on average, out of the ENTIRE HUMAN POPULATION ON THE PLANET AT THAT TIME, there was a net increase of people of only 180 souls per year.

That’s all.

On the whole planet!!!!

They had nearly achieved zero population growth!

But during the next five thousand years our population really exploded, to some hundreds of millions of people. Doinfg the same calculation, I found that the annual growth rate was about 1.00074, or 0.074%, or 74 additional net humans per year per hundred thousand, or about 74 thousand net new humans per year total, world-wide, once they got up to about a hundred million people.

That’s just up to the year 0 BC/AD.

Let us remember always that this planet right here is the only one we humans can possibly live on or get to in any numbers. We are as a species have done incalculable damage. Here in North America, think of the thoughtless and greedy extermination (or near-extermination) of the passenger pigeon; the American chestnut, elm, hemlock and ash; the buffalo; almost all of old-growth forests; most anadromous Atlantic fish; and Chesapeake bay oysters — all of which used to be plentiful beyond belief.

Some species are now recovering, such as deer, beavers, skunks, rabbits, foxes and coyotes.. Why is that? If you look at photos of Virginia countryside from 90 to 150 years ago, you see very, very few trees. Lumber companies and plantation owners and small farmers had cut them all down to plant grain and cash crops. Plowed land erodes quickly from both wind and rain. Those formerly fertile fields became uneconomical to farm, and so field after field (including ones I played or worked or hunted on as a kid and young man) have been allowed to regrow brush and then trees or housing developments, shopping centers, and pavement. So East of the Mississippi, there has been a dramatic increase in percentage of tree canopy over the last century.

However, some countries are repeating America’s mistakes and are cutting down primeval firsts as fast as they can…