*Professor Albert Bartlett has died at the age of 90.*

Albert Bartlett might have been another obscure physics professor had he not put together a now famous lecture entitled "Arithmetic, Population and Energy" in 1969. The lecture, available broadly on the internet, begins with the line: "The greatest shortcoming of the human race is our inability to understand the exponential function."

The logic is surprisingly simple and irrefutable. Exponential growth, which is simply consistent growth at some percentage rate each year (or other time period), cannot proceed indefinitely within a finite system, for example, planet Earth. The fact that human populations continue to grow or that the extraction of energy and other natural resources continues to climb does not in any way refute this statement. It simply means that the absolute limits have not yet been reached.

Bartlett, who died this month at age 90, gave his lecture all over the world 1,742 times or on average once every 8.5 days for 36 years to audiences ranging from junior high students to seasoned professionals in many fields. His ability to stay on message for so long about something so important should make him the envy of every modern communications professional.

His favorite shortcut is the doubling time, the time it takes to get to twice the original number at a constant rate of growth. The formula is 70 divided by the percentage rate of growth per year (or other period). Just a 2 percent growth rate doubles the rate of use of a resource or the size of world population in 35 years. Actual world population growth is about 1.2 percent per year today, which seems benign; but, it implies the next doubling within 58 years to 14 billion. (U.N. forecasts project world population will reach 10 billion by 2070–57 years from now–and continue to grow through 2100.)

In his lecture Bartlett relates that in his hometown of Boulder, Colorado, city council members once stated publicly their preferences for population growth rates ranging from 1 percent to 5 percent per year. In the course of 70 years, roughly one lifetime, the 5 percent rate would make Boulder’s population (about 100,000) some 32 times larger or about 3.2 million, which would make it the third largest city in the country behind Los Angeles and in front of Chicago. A city that size could not possibly fit in the valley now home to Boulder, Bartlett explains. Attempting to do so would inevitably eliminate all open space, something highly prized by Boulder residents.

Has Bartlett made a dent in our habitual ways of thinking about growth? Maybe. There were others back when Bartlett started giving his lecture who asked the same questions in a different form. One manifestation of that questioning was the groundbreaking study *The Limits to Growth* which, despite what its detractors have said, made no predictions. Rather the study models resource use over time given a large range of conditions including an endowment of resources that was twice what anyone imaged they might be at the time. The troubling conclusion of the study was that nearly all scenarios led to the crash of industrial civilization at some point.

The key observation in that study aligns with Bartlett’s, namely that exponential growth in the consumption of finite resources is unsustainable. At some point growth in the rate of extraction will cease. And, given the dependence of the economy on continuous growth of resource inputs including energy, this leads to instability and finally decline.

Let me help you envision what exponential growth means. If you receive 10 percent interest on $100, after one year, your $100 will turn into $110. In the second year, at the same interest rate, your money will turn into $121. At the end of year 50, the amount will be $11,739, a considerable sum. At the end of year 100, the amount will be $1,378,061. By year 200 your heirs will have almost $19 billion.

If we dial down the rate to, say, just 2 percent, the corresponding figures are $269 for year 50, $724 for year 100 and $5,248 for year 200. Clearly, rate matters a lot! But, even so, if these numbers represented the rise in the rate of resource consumption, even at two percent after 50 years, we’d be consuming resources at 2.7 times the original rate. At 100 years it would be 7.2 times, and at 200 years, 52 times.

Now money is a social invention which can be created by electronic keystrokes these days in any amount. Eons of geologic transformation and concentration are not required. But finite natural resources by definition have a limit. We cannot say with precision what that limit is, but we know it is there.

The rejoinder to Bartlett and others like him is that technology will overcome any limits, and that we’ll use substitutes for resources that run low. It’s hard to imagine what might be a good substitute for uncontaminated, potable water; but, in the cornucopian’s mind anything is possible. It’s also hard to imagine a modern technical society without metals. But, we’ll think of something, right? However, please don’t say that that something is made out of materials derived from oil, natural gas or coal which are also finite.

The problems posed by exponential growth mean we’ll have to think of "something" at increasingly short intervals given the ever rising rates of consumption and the broad range of finite materials we depend on–especially fossil fuels (oil, natural gas, coal) and much of the periodic table of elements including the usual suspects such as iron, copper, aluminum, zinc, silver, platinum, and uranium and the more exotic ones such as lithium, titanium, the so-called rare earth elements, and helium.

It’s not just one substitute we’ll have to find. And, we may be faced with having to find many all at once. The idea that technological innovation will always and everywhere stay ahead of an ever increasing rate of depletion may be true or not true. But we cannot know this ahead of time.

In fact, if it were true, why hasn’t technological innovation brought oil prices down to where they were in the 1990s before the run-up of the last decade? There’s no commodity more central to the functioning of our economy; and, there’s been huge spending by the oil industry and deployment of revolutionary new techniques. Yet, the price remains stubbornly high. The glut that was promised year after year has failed to materialize. The problem is not that technological innovation has ceased; it’s that it may not be enough.

And so, we are assuming huge risks by taking it on faith that all hurdles to the continuance of our technical civilization as it stands can be overcome in time and forever by technological advances. We are taking it on faith, essentially, that we will never screw up so badly that our highly-efficient, just-in-time economy will cease to grow and finally decline until it reaches a level that can be sustained by a much simpler and less technically advanced set of practices, probably for a much smaller population.

It stands to reason that even the RATE of technological advancement must have a limit. Humans are not infinite in their powers of reason. Even with computers, we cannot innovate at infinite speeds.

It is the rate issue that Albert Bartlett spent the last half of his life trying to bring to the fore in the minds of the public and policymakers. While many in the scientific community have now come to understand his message, the broader public and policymakers still seem largely in the dark. Rates, and particularly exponential growth, are clearly not easy to grasp; otherwise, so many more human beings would have grasped these concepts.

But we have Albert Bartlett to thank for relentlessly reminding us that we should pay attention to the simple math that refutes our notions of endless growth. He asks in his lecture the following question:

Can you think of any problem on any scale, from microscopic to global, whose long-term solution is in any demonstrable way aided, assisted or advanced by having larger populations at the local level, the state level, the national level, or globally?

So far, I can’t think of any.