Doubling Time

In mathematics, exponential trends go on forever. 

In real life, they inevitably end.

Teaser for Forbes article, The Seduction of the Exponential Curve by Alex Knapp

Time comes in different flavors.

If we're speaking of the formation of galaxies, stars and planets, we might speak in terms of Deep Time. Of the drift of tectonic plates, the rise and fall of mountains and sedimentary stratification, it all plays out in Geologic Time. The onset and progress of Life is measured in Evolutionary Time. Periods and Centuries toll our history in Chronologic Time. Our own lives flit in decades, years, months, days, minutes... heartbeats.

But there's another kind. Doubling Time.

Doubling Time pertains to things which grow. Fire. Explosive fission. Life. Capital. Economies. It has its own language. Exponential growth, compounded growth, rate of growth, positive feedback, doubling period, exponential curves with horizontal, transitional and vertical portions.

A simple rule of thumb governs the relation between the rate of growth and the period required for doubling. The Rule of 69 goes thus: Divide 69 by the percentage rate of growth to find the doubling period. Sixty-nine, divided by an annual, average growth rate of 3% yields a doubling period of 23 years (currently the annual average growth rate of the global economy).

But growth must be fed - it must consume resources in order to grow - and has a dark corollary. Decline.

Exponential decline has its own language as well. Limited resources, non-renewables, diminishing returns, depletion, exhaustion. Peak Oil. Peak anything. Peak everything.

As an economy grows, it consumes resources, reserves of which diminish proportionately. In the course of each doubling period, all the the resources consumed since the onset of growth are consumed. Finite resources fall before exponential growth at a mind-boggling rate.

Now let's add a reality check. How about, "Growth is limited by that necessity available in the least amount." Obvious, innit?

I mean, we can't build a billion widgets if we've run out of widgetium.

Some argue that the free market will provide. As supplies of widgetium dwindle in the face of increased demand, it's cost skyrockets - runs the argument. The reward for replacing widgetium will be so enticing, that some, enterprising scientist will rise to the bait and find a way to replace it with a synthetic formed by heating landfill Pampers, their contents and Red Bull. Brilliant! Why didn't I think of that?

From Calvin and Hobbes by Bill Watterson

Here's the problem. The financial incentives to replace widgetium are already vast beyond imagining. Consider cold fusion, a real world example. With how much financial incentive and for how long has its solution attempted to lure the world's lazy, indolent scientists? How many rabbits can be pulled out of an empty hat?

So what does this mean, in Doubling Time? Answer: If we don't have an amount of every necessity in reserve equal to all we've used to date, growth ends this doubling period.

What are the necessities? No one's absolutely sure, but cheap energy, fresh water, arable land and living oceans are safe bets, for starters. How much of them do we have in reserve? Again, amounts are debatable, but few would argue that our reserve in any of these fields equals the amount we've used to date.

We in the business of spreading the gloomy word are often scorned for having our prophecies go unfulfilled. We go awry by thinking and prophesying  in Chronological Time, rather than Doubling Time. In this, we are like those we wish to persuade that trouble is coming, and steps might be taken.

Let's try a thought experiment:

Prophet A has appeared at Times Square every New Years Eve for 2,000 years with his sign, "The End Is Near!" After all that time, folks dismiss him... oh sure, the End has come and gone several times in that span, but it's never been global. We judge him wrong x 2000. Boooo! Even he's a bit discouraged. But in that span, the world has been growing - saturating the planet and globalizing into one, inter-woven economic machine.

Prophet B has appeared at Times Square on New Years Eve for 2,000 years with his sign, "The End Is Near!" The difference is that he only shows up on years that are a power of two. Year 0, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024... we only booo him 12 times, and with less conviction. In 512, after all, conquistadores and smallpox were bringing TEOTWAWKI to the New World. But 1024 was kind of quiet... not much going on... a few Bogomils burned, but who cares? BOOO!

He doesn't need to show up again until 2048. What's the forecast for then?

Mmm. It's not looking so good for energy, arable land, fresh water or oceans, now... and, at the current rate of growth we're due to double our economy/consumption by 2035. That's based on the optimistic assumption that growth can continue at the current rate. More is considered better; much less is considered catastrophic by the Bean Counters. As in, cessation of growth implies a full on collapse into global depression.

Damned if we do; damned if we don't.

Now I'm not going to point at that particular date, 2035, but I would wager that we don't make it that far. One thing is certain, in doubling time, it's late in the day.

And the bet I'm laying down is preparation.