Photo: Flickr/IFPRI-IMAGES

A couple of questions for you to ponder over your morning coffee:**What’s the sustainable long-term growth rate for the world population?**

And, relatedly…

**What’s the sustainable long-term growth rate of the world economy?**

Go ahead–take some guesses.

2% annual population growth?

4%-5% economic growth?

That sounds reasonable, right? Not asking too much? We’ve all gotten used to growth rates like those, and they’re baked into just about every projection countries and economists make. It seems perfectly sane to imagine that we can sustain 2% population growth and 4%-5% global economic growth pretty much forever. Because even though we’re currently sustaining ourselves in part by consuming the finite resources of our planet, our big brains and innovation and productivity improvements will always save us in the end.

Well, if you’re planning for us to grow our population and economy at 2% and 4%-5% respectively forever, you’d better pray that we soon figure out how to travel at warp speed, live forever in space, and find hundreds of other habitable planets to live on, because otherwise we’ll soon cover every inch of the Earth and then some.

A few years ago, investment manager Jeremy Grantham gave a presentation to some highly sophisticated traders and mathematicians in which he gave examples of why and how our current conceptions of sustainable growth are completely misguided.

So much of a part of conventional thinking are these conceptions, however, that even the mathematicians had trouble grasping this.

To see why a 4%-5% economic growth rate isn’t sustainable, read on.

In the meantime, if a 4%-5% long-term economic growth rate isn’t sustainable, what is?

1%?

Nope.

Photo: Wikipedia

Even a 1% growth rate sustained over thousands of years would result in inconceivably humongous numbers.Even a 0.1% growth rate would probably doom us in the end.

Basically, given the reality of finite space and resources, the only growth that is truly sustainable over the long-term is no growth.

So *that’s* something to think about over your coffee.

Four years ago I was talking to a group of super quants, mostly PhDs in mathematics, about finance and the environment.

I used the growth rate of the global economy back then – 4.5% for two years, back to back – and I argued that it was the growth rate to which we now aspired. To point to the ludicrous unsustainability of this compound growth I suggested that we imagine the Ancient Egyptians (an example I had offered in my July 2008 Letter) whose gods, pharaohs, language, and general culture lasted for well over 3,000 years.

Starting with only a cubic meter of physical possessions (to make calculations easy), I asked how much physical wealth they would have had 3,000 years later at 4.5% compounded growth.

Now, these were trained mathematicians, so I teased them: “Come on, make a guess. Internalize the general idea. You know it’s a very big number.” And the answers came back: “Miles deep around the planet,” “No, it’s much bigger than that, from here to the moon.”

Big quantities to be sure, but no one came close.

In fact, not one of these potential experts came within one billionth of 1% of the actual number, which is approximately 10 to the 57th power, a number so vast that it could not be squeezed into a billion of our Solar Systems.

Go on, check it.

If trained mathematicians get it so wrong, how can an ordinary specimen of Homo Sapiens have a clue? Well, he doesn’t.

So, I then went on. “Let’s try 1% compound growth in either their wealth or their population,” (for comparison, 1% since Malthus’ time is less than the population growth in England). In 3,000 years the original population of Egypt – let’s say 3 million – would have been multiplied 9 trillion times! There would be nowhere to park the people, let alone the wealth.

Even at a lowly 0.1% compound growth, their population or wealth would have multiplied by 20 times, or about 10 times more than actually happened. And this 0.1% rate is probably the highest compound growth that could be maintained for a few thousand years, and even that rate would sometimes break the system.

**The bottom line really, though, is that no compound growth can be sustainable.** Yet, how far this reality is from the way we live today, with our unrealistic levels of expectations and, above all, the optimistic outcomes that are simply assumed by our leaders.

It’s the mathematical reality of compound growth, in part, that makes Grantham so bearish about the future of humanity (if wildly bullish on commodity prices).

For more on the latter, read the following…

**SEE ALSO: JEREMY GRANTHAM: We’re Headed For A Disaster Of Biblical Proportions**

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