Wednesday, January 09, 2008

The Doubling Time

Perhaps 15 years ago or so, I was planning a renewable energy gathering and we invited Dr. Albert Bartlett to speak. The then Professor of Physics from the University of Colorado in Boulder gave a remarkable presentation on the arithmetic of steady growth, continued over modest periods of time, in a finite environment.

The title of the presentation was Arithmetic, Population and Energy

Here is a small part of it:

"Well, you say, what's the exponential function?

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 is 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.

I wish we could get every person to make this mental calculation every time we see a percent growth rate of anything in a news story. For example, if you saw a story that said things had been growing 7% per year for several recent years, you wouldn't bat an eyelash. But when you see a headline that says crime has doubled in a decade, you say “My heavens, what's happening?”

OK, what is happening? 7% growth per year: divide the seven into 70, the doubling time is ten years." more

I can't tell you how many times I have used Dr. Bartlett's handy formula.

Once, while working on a long range energy plan, I used the formula to predict energy sales well into the future. The figure was so accurate that the folks in planning thought I had somehow got into their files. If someone tells me that the rate will increase by 2% a year, I immediately know that the rate will double in 35 years. Try it for yourself on the growth rate of your town or on the inflation rate.

The presentation is worth a full read, or you can watch the video.

Towards the end of his talk, Dr. Bartlett said this:

We should remember the words of Aldous Huxley, that “facts do not cease to exist because they're ignored”. We should remember the words of Eric Sevareid; he observed that “the chief source of problems is solutions.” This is what we encounter every day: solutions to problems just make the problems worse. clip

We should remember the words of Galileo; he said, “I do not feel obliged to believe that the same god who has endowed us with sense, reason, and intellect has intended us to forgo their use.”

If there is one message, it is this: we cannot let other people do our thinking for us."

As I listened to the pundits and the politicians last night, I thought about how silly most of it was. No one is thinking well it seems. We listen to dribble and confuse it with the gentle rain of true enlightened human thought.

And we truly should not let these people

do our thinking for us.


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