What does it look like when growth hits physical limits?

 

I've been thinking a lot about the limits to growth recently.  If you look up the non-renewable resources that our economy depends on it quickly becomes apparent that all of them, whether they be fossil fuels or metals like copper, are somewhere between 30% and 70% exhausted.  And the exhausted part is invariably the easiest to get to.  However, it has only recently occurred to me that land is also a non-renewable resource:  they're not making any more of it....

Checking out Our World in Data one can see that nearly 5 billion hectares are currently in use by humans.  That compares with a total available of 13 billion hectares, if you discount the ice covered land.  So, in fact land falls into the same 30-70% exhausted range as everything else.

I downloaded the data and produced a smoothed graph of growth (%) vs year and found something interesting: growth grew more or less exponentially until about 1956 at which point it fell sharply to zero.  So this is exponential growth in growth - itself an exponent.  Or another way to put it is that growth in land use was super-exponential, until it collapsed.

Obviously such growth cannot last that long, and it is interesting to see what happens when a super-exponential hits physical limits.  The answer appears to be a crash out.  This graph also makes it fairly obvious why the world's human population is levelling out now.  Often this is put down to freely available contraception, or better career opportunities for women.  However, looking at this graph above it becomes apparent that one way or another it had to happen, if not now then within a few decades at most.