Exponential Growth for Doomies

A whirlwind tour of growth versus limits

The problem is, exponential growth patterns 

don't give you an early warning sign.

Because the dangers really speed up at the end, 

when it's too late to do anything about it.

-- Dr. Kent Moors 
  

Exponential Growth for Doomies:       
      Double, Double, Toil and Trouble

We all think we're familiar with growth.

If we can earn $1000 a week, that's $4000 a month and $48,000 a year. Nice, neat and linear, right? Most of what we count in our everyday lives is like that.

But exponential growth aka geometric growth aka non-linear growth aka compounded growth isn't as intuitive. Even if one is familiar with it, this kind of growth can ambush us.

If something is growing exponentially, each dollop added to the heap is proportional to (a fraction of) the heap that's already there. The bigger the heap, the bigger the dollop, the bigger the heap the bigger the dollop... a dash, a pinch, a dollop, a handful, a bucket.....

We typically say the heap is growing at some percent rate per unit of time, say 5% annually (that is, 5% of the total heap size added to the heap every year... the amount added gets bigger each year).

Or we might think in terms of doubling rate, or doubling time (the time it takes the heap to double in size). Each doubling period... tick, tick, tick... doubles the entire heap.

The rate of change may stay the same, but the increment of change - the dollop of change - gets bigger. And bigger. And BIGGER! As we go from the more horizontal portion of an exponential curve to the more vertical portion, any given stretch of time - a year; a decade; a lifetime - spans an astonishing increase. Each stretch encompasses an ever more fantastic volume of change.

An exponential curve is sometimes called a 'hockey-stick'. Things are flattish for a while, there is a transitional middle, then things get steep.

Things might look nearly flat for a long, long time (like my father before me, time out of mind; as if nothing will ever change). It took us millions of years to learn to control fire, for example.

Then things pick up to an exciting time of change for the better (that old woman saw the first automobile AND the first moonshot).

Things pick up more, and things get a little scary (That kid born in 2000 is now looking at super bugs, cyber warfare and an ice-free arctic).

In a finite system (the only kind we know of), nothing continues doubling forever. Most systems can be described in boom / bust cycles. Exponential growth for a giddy while, then crash. Sometimes repeat. Sometimes not.

Rule of 69 or 70

The Rule of 69 (or 70) is a handy rule-of-thumb which allows a rough estimation of doubling time given the percent rate of growth per unit of time. Using 70 is slightly less accurate than 69, but the math is often slightly easier.

Doubling-Rate = 70 / %Rate-of-Growth 

If our average rate of growth is 5% per year, then 70/5 = 14 years... our heap will double in 14 years. If the rate of growth is quarterly, say, it would double in 14 quarters.

Let's say an economy grows at 2.5% per year on average. By our rule of 70,  70/2.5 = about 30 years. At that rate, the economy will double in 30 years. If this rate is sustained, it will double every 30 years.

Consequences

In rough terms, the global, industrial economy - the world's heap of goods, services and assets; its pollution, environmental impact, its footprint - has been doubling every 25 years for the last two hundred (give or take).This means today's global economy is roughly 256 times that of 1800. Double the economy of 1990. Next stop, 512x!

At every doubling, close to twice the resources are consumed. Twice the waste produced. Twice the 'footprint' is required, as it were. The next doubling is due about 20 years from today according to the IMF.

A 'next doubling' assumes nothing happens big enough to derail that juggernaut. It has mass. It has momentum. If it hits a wall or leaves the tracks it'll make one hell of a wreck.

My friends, we live in a time when the now vast human world is doubling every few decades.

 
We Doomies think that, coming somewhere soon-ish along the economic curve, something's gotta give. We'll hit the limits our planet can support. And then the trend will break. Break bad.

Now here's the thing: Just before that last doubling - the one that can't fit within limits and brings down the house  of cards - the world looks to have half of its reserves left. We've taken all of human history to saturate the world to today's level, only those few decades (if that) to double it. Or go bust.

How many more doublings have we got?

For further consideration, I suggest the Crash Course, free from the team at Peak Prosperity. Episode #3 focuses on exponential growth.