I ran across an interesting YouTube video of a lecture by Albert Bartlett, emeritus professor of physics at the University of Colorado – Boulder. The title of the lecture is "Arithmetic, Population, and Energy." Bartlett's thesis is that any kind of growth in population and the exploitation of finite resources can be shown to be ultimately unsustainable by simple mathematics. He claims, "The greatest shortcoming of the human race is our inability to understand the exponential function."

Here is Prof. Bartlett's explanation of steady growth and the exponential function:

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This is a mathematical function that you'd write down if you're going to describe the size of anything that was growing steadily. If you had something growing 5% per year, you'd write the exponential function to show how large that growing quantity was, year after year. And so we're talking about a situation where the time that's required for the growing quantity to increase by a fixed fraction is a constant: 5% per year, the 5% is a fixed fraction, the “per year” is a fixed length of time. So that's what we want to talk about: its just ordinary steady growth.

Well, if it takes a fixed length of time to grow 5%, it follows it takes a longer fixed length of time to grow 100%. That longer time's called the doubling time and we need to know how you calculate the doubling time. It's easy. You just take the number 70, divide it by the percent growth per unit time and that gives you the doubling time. So our example of 5% per year, you divide the 5 into 70, you find that growing quantity will double in size every 14 years.

Well, you might ask, where did the 70 come from? The answer is that it's approximately 100 multiplied by the natural logarithm of two. If you wanted the time to triple, you'd use the natural logarithm of three. So it's all very logical. But you don't have to remember where it came from, just remember 70.

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I am accustomed to using the Rule of 70 (or the more familiar approximation called the Rule of 72) for interest calculations. Right now I am getting roughly 0.7% interest on my credit union CDs. At this rate I will double my money in 100 years. This is a miserable state of affairs. (What's worse is that during the past 100 years, inflation has reduced the purchasing power of the dollar by about 95%. It makes a man throw up his hands, say "to heck with it!" and dissipate his small hoardings on wine, women, and song. )

But enough about me and my financial and character deficiencies. Let's look at what Bartlett has to say about population growth:

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A few years ago, one of the newspapers of my hometown of Boulder, Colorado, quizzed the nine members of the Boulder City Council and asked them, “What rate of growth of Boulder's population do you think it would be good to have in the coming years?” Well, the nine members of the Boulder City council gave answers ranging from a low of 1% per year. Now, that happens to match the present rate of growth of the population of the United States. We are not at zero population growth. Right now, the number of Americans increases every year by over three million people. No member of the council said Boulder should grow less rapidly than the United States is growing.

Now, the highest answer any council member gave was 5% per year. You know, I felt compelled, I had to write him a letter and say, “Did you know that 5% per year for just 70 years [...] means Boulder's population would increase by a factor of 32? That is, where today we have one overloaded sewer treatment plant, in 70 years, we'd need 32 overloaded sewer treatment plants."

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Bartlett's thinking was greatly influenced by his University of Colorado colleague Kenneth Boulding, an economist and social philosopher (and poet and Quaker and peace activist and ...). Boulding expounded three theorems in 1971:

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First Theorem: "The Dismal Theorem" If the ultimate check on the growth of population is misery, then the population will grow until it is miserable enough to stop its growth.

Second Theorem: "The Utterly Dismal Theorem" This theorem states that any technical improvement can only relieve misery for a while, for so long as misery is the only check on population, the [technical] improvement will enable population to grow, and will soon enable more people to live in misery than before. The final result of [technical] improvements, therefore, is to increase the equilibrium population which is to increase the total sum of human misery.

Third Theorem: "The moderately cheerful form of the Dismal Theorem" Fortunately, it is not too difficult to restate the Dismal Theorem in a moderately cheerful form, which states that if something else, other than misery and starvation, can be found which will keep a prosperous population in check, the population does not have to grow until it is miserable and starves, and it can be stably prosperous.

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The First Theorem is nothing more than a restatement of the Thomas Malthus (1766-1834) analysis that societal improvements result in population growth which eventually gets checked by famine and disease. I think of this theorem as the "Welcome to Los Angeles" scenario.

I find the Second Theorem utterly dismal and depressing. It claims that heroic efforts to benefit the health and well-being of mankind (e.g., Norman Borlaug's Green Revolution that provided food for a billion people in India and its neighboring countries) will only delay and exacerbate the inevitable misery.

I find only faint cheer in the Third Theorem. No doubt the population trends in the coming century will be driven by both misery and changes in reproductive behavior.

Albert Bartlett assembled his own set of theorems and laws concerning growth, sustainability, and exponential use of finite resources. (See his website www.albartlett.org for his articles and lectures.) Here are his laws that I found most striking.

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First Law: Population growth and/or growth in the rates of consumption of resources cannot be sustained.

Second Law: In a society with a growing population and/or growing rates of consumption of resources, the larger the population and/or the larger the rates of consumption of resources, the more difficult it will be to transform the society to the condition of sustainability.

Fifth Law: One cannot sustain a world in which some regions have high standards of living while others have low standards of living.

Seventh Law: A society that has to import people to do its daily work ("we can't find locals who will do the work") is not sustainable.

Ninth Law: The benefits of population growth and of growth in the rates of consumption of resources accrue to a few; the costs of population growth and growth in the rates of consumption of resources are borne by all of society.

Tenth Law: Growth in the rate of consumption of a non-renewable resource, such as a fossil fuel, causes a dramatic decrease in the life-expectancy of the resource.

Thirteen Law: The benefits of large efforts to preserve the environment are easily canceled by the added demands on the environment that result from small increases in human population.

Seventeen Law: If, for whatever reason, humans fail to stop population growth and growth in the rates of consumption of resources, Nature will stop these growths.

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Albert Bartlett summed up his thinking with his Great Challenge: "Can you think of any problem in any area of human endeavor on any scale, from microscopic to global, whose long-term solution is in any demonstrable way aided, assisted, or advanced by further increases in population, locally, nationally, or globally?"