Republican presidential contender Tim Pawlenty has put forth a plan in which he hopes the US economy will grow at 5% a year for decades.

Such growth, Pawlenty suggests, will solve all of our problems. (And in the meantime, in Pawlenty's plan, we'll get to enjoy lower taxes to boot!)

Over the short-term, economies certainly can grow 5% a year, or even faster. And Pawlenty's projected growth rate seems achievable in part because, in 2006 and 2007, the global economy grew at 4.5% a year. Thanks to that happy growth spurt, in fact, economic growth of 5% a year seems not just achievable but normal.

But lest we all become too enamored of the idea that we can grow at 5% a year forever, it's worth pointing out that we can't. Over the long term, this growth rate is not just unlikely--it's impossible.

Nothing can grow at 5% a year for long without eventually overwhelming everything else. Corporate profits, for example, cannot grow at 5% a year (real), without eventually exceeding corporate revenues (which have been growing about 3% a year, real). Economies cannot grow at 5% a year for long without dominating the entire world economy. And populations cannot grow 5% a year for long before they gobble up all the finite resources available to them.

Economies and populations, in fact, can't even grow 3% a year for very long. And they certainly can't grow 3% a year in perpetuity.

Investor Jeremy Grantham of GMO illustrates this in his recent apocalyptic commodity analysis with an anecdote about ancient Egypt, which was one of the most successful civilizations in human history.

Grantham asked a group of mathematicians how big Ancient Eqypt would have gotten if its economy had growth 4.5% a year for the 3,000 years the civilization lasted.

The mathematicians were directionally correct: Very big.

But not one of them came even remotely close to the actual number (which is mind-boggling).

Grantham then went on to show that Egypt would have become impossibly huge with even 1% growth or 0.1% growth--growth rates that we would consider not just unacceptable, but pathetic.

And then he pointed out that our current growth expectations are not just unsustainable. They're impossible.

Here's the anecdote:

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, 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 raised 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.

So don't go thinking that global economies are going to grow 5% a year forever. They aren't.

Especially, as Grantham also points out, now that we're running out of natural resources.

See Also: JEREMY GRANTHAM: We're Headed For A Disaster Of Biblical Proportions