If there is a holy grail in the domain of pop economics it must be economic growth. By all reports keeping a national economy growing at a steady annual rate eventually cures all ills. Deficits vanish, everyone is estatic and all fiscal difficulties are but a memory consigned to text books for future economics students to digest.
The unfortunate problem is such a solution in perpetuity is a fantasy. Before getting into the details of why compound growth can't continue indefinitely let's consider some definitions. Imagine a very simple economy that produces only widgets. In this economy we'll consider economic growth to have occurred on any year in which more widgets were produced than in the previous year. So if a thousand widgets were produced last year and a thousand and ten were produced this year we can claim our economic growth was 1%.
Given our sample economy we'll now establish a mechanism of production. Again to keep it simple we'll just assume we have a magic box called a factory. You simply pour inputs of production into it and the factory spits out widgets and heat. Even better, factories are free, take up zero space and are available upon request to everyone. Thus essentially we are left with only two obstacles between us and economic growth. One, we must come up with more or better inputs each year and two we must get rid of the waste heat somehow.
In this simple case let's say that our inputs of production are simple energy and labor. Since our factories take up zero space we can't very well have people working inside them, but we'll just assume that someone standing near a factory not doing anything else increases it's production by a small margin. Given that people take up physical space it's academic to show that there is a finite amount that can fit on our planet. Further, anything that has a hard limit can not be a source of compound growth indefinitely. Thus we can conclude that increasing labor is not a viable way to continue compound economic growth.
Energy is similarly constrained. In the long term the only viable energy sources are renewable in nature. Essentially that boils down to solar power. Given that only a fixed amount of sunlight strikes the earth each day, total energy inputs are limited by solar output striking the earth times the efficiency of our gathering apparatus. While this is an immense amount of energy it is still limited and thus can not support compound growth indefinitely.
If neither of our inputs are as limitless as we'd hoped perhaps we can simply use what we have better. Or in other words perhaps technological gains can deliver us to the promised land. However, even here the are boundaries we can not cross. In our simplified example we're converting energy to matter. Physics demands a certain quantity of energy for each widget we produce and no technological improvement can bypass this restriction. In a more practical sense at the point that you're gathering all of the energy that strikes the planet (impossible) and converting it to useful work without losses (also impossible) you can't get any further improvements.
Nor do the problems end there. Our example also included one unavoidable and undesirable waste product: namely heat. The earth only radiates heat into space at a given rate. Once your heat production exceeds the rate of radiation things begin to heat up. Each year more waste heat is produced and each year the earth can radiate a smaller proportion of that heat away into space. Eventually the oceans boil away, though not before that everyone has died anyway.
These problems seem like abstractions. Reading about it likely feels similar to having a museum guide inform you, with a conspiratorial wink, that a meteor like the one that killed the dinosaurs will one day be headed for earth... but probably not tomorrow. While the end of compound economic growth isn't quite so dire a catastrophe it's also a lot closer to hand.
Looking at the primary difficulties we can examine how close we already are to our limits. Researchers currently estimate that the world population will peak at around ten billion persons somewhere around the end of this century. So in terms of that input we have approximately a hundred years of growth.
Currently the world population utilizes around five hundred exajoules of energy annually. By the time we reach peak population and bring everyone up to a reasonable standard of living that number will easily exceed a thousand exajoules. Total solar input on the earth is approximately four million exajoules. If energy inputs are increased at a rate of 1% per year in order to continue economic growth than we'd have approximately eight hundred years of that free ride until we reached our limit. However, it's important to note that the practical limit is far far shorter unless we develop 100% efficient solar cells and cover every surface of the planet with them. A more reasonable assumption would assume approximately five hundred years of possible gains. Of course the problem worsens as the rate of growth rises. At a 2% growth rate we start running into problems in approximately two hundred and fifty years.
The problem of heat is equally dire. The point of heat generation that causes oceans to boil likely seems remarkably far off. However, given current energy growth rates and the laws of thermodynamics it's likely that the earth would heat to the point of boiling water in under five hundred years. Clearly well before that things will begin to grow uncomfortable. Obvious changes begin to occur again around the two hundred and fifty year mark and accelerate rapidly from there. Note this phenomenon is completely separate from (though would be exacerbated by) any global warming effects due to green house gases.
It seems that we've got at most a quarter millennium to get our finances in order before the miracle of compound growth is forced to a screeching halt. In practical terms growth will slow over time until we reach a relatively steady state. However, the idea of simply growing out of any fiscal difficulties has an eventual expiration date. And it's not all that far off in historical terms.
A couple hundred years may seem like a long time, but given the rate of progress in Washington D.C. I'm not sure it's long enough.
A bit of an addition set apart from the main body of the post: I'm well aware that there are possible solutions to the problems presented above. In this posting I've treated the earth as a closed system for reason of simplicity. You could conceivably move industrial production off planet in order to mitigate problems of heat and energy (as you wouldn't be pumping heat into the planet's environment nor using it's surface area to gather energy). The point is not to propose a certain date at which point economic growth must halt. Rather it's to demonstrate that compounded growth must halt at some point. To carry it further, if all economic activity requires some energy then energy input must grow at a compound rate as well. If that is the case then given current energy expenditure growth rates how long until we're consuming the entire annual output of the sun? How long until we're consuming the annual energy output of the galaxy for that matter. Doing the math on such questions still leads to dates measured in historical, not geological terms. The fact is our society as it exists now can not support the current growth model indefinitely.