Sunday, January 3, 2010

Exponential Growth

If you ask, most people would probably say exponential growth is "out of control" growth. That's not what it means. Technically, it means that growth is regular, predictable, and under control.

Well, maybe not "under control" -- but definitely regular and predictable.

Regular doubling. If something doubles regularly, that's exponential growth. Doubling every two years, doubling every 10 years, doubling every 50 years -- these are fast, medium, and slow rates of growth. All of them are exponential growth rates, because they double in known time frames. Regular and predictable.

Wikipedia's Doubling Time article says the concept has many uses:

It is applied to population growth, inflation, resource extraction, consumption of goods, compound interest, the volume of malignant tumours, and many other things which tend to grow over time.

There is even a rule of thumb you can use to figure the doubling time. The Rule of 72 says: Divide the number 72 by the growth rate, and it tells you how long it will take for a given quantity to double. Regular, and predictable.

Of course, this all depends on the growth rate being stable. It sounds like something the scientists would make up. Not something that could happen in real life. But stable growth rates do occur in real life. I'll give you an example, from my 12-page PDF:

"The Debt per Dollar ratio rose ... to $8.05 (in 1973) and rose to $12.12 (in 1983) and rose to $16.65 (in 1990) and $24.86 (in 2000) and $32.78 (in 2006)."

Check it out: From $8 to $16 in 17 years. From $12 to $24 in 17 years. From $16 to $32 in 16 years. As I point out in that paper: Debt per Dollar has been doubling every 16 or 17 years. This is exponential growth. It's not just an abstract notion. It happens.

Debt has been growing exponentially since the end of World War II. The growth of debt is not under control. But since the end of World War II, it has been regular and predictable. It depends on mathematical forces or, let's say, on the mathematical consequences of economic forces. It does not depend on who wins the election.

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