When Einstein was asked what is the most powerful force in the universe, he reputedly answered "exponential numeration". Compound growth is perhaps a more familiar term. Any number x growing exponentially for n periods means x is multiplied by itself n times. The mathematical expression is:
xn = x * x * x * x * x * x (where n = 6)
Since x can be any number, it is easy to understand that xn can be huge if we start with x equal to a fairly big number. For example, if x = 1,000 then x2 = x * x = 1,000,000. We move from a thousand to a million in one iteration.
But what if x is a small number like two? In this case, each time we multiply x * x the quantity doubles in size. The Rule of 72 reveals how to determine the percent growth per unit of time for a quantity to double:
Percent growth per unit of time = 72 / Time to double
Thus an investment that doubles in twelve years is growing at a 6% compound rate (72 / 12 = 6).
How deceptive is exponential growth? It is hard to believe that a piece paper 1/32 of an inch thick and folded over (doubled) fifty times would be more than 277 million miles thick!
The real deception is believing that we can see a high magnitude of exponential growth coming at us in sufficient time to react. Just as a killer virus can replicate and a plague can sweep through a population faster than any attempt to isolate it, so too the human population can overrun the earth's resources before the seriousness of the crisis is understood.
Suppose it takes 25 years (one average generation in which two parents have four children) for the earth's population to double. If there is a maximum number of people that the earth can support, when will the earth be half full?
The earth will be half full exactly one time period (one generation, or 25 years) before it doubles to become entirely full. The earth will be one quarter full just two iterations before it is totally full. Suppose we don't realize we are getting over crowded until the earth is 75% populated? The realization may come after it is too late to do anything.
War and disease can slow the growth of population, but what if the human race succeeds in eliminating war and disease? It took over a million years of reproduction and evolution to reach a population of one billion people in 1810. In spite of two world wars and many other catastrophes, the world population tripled to three billion people by 1960. (A mere 150 years.) In a little over one generation, the world population has now doubled again to an estimated six billion people! The rate of population growth is accelerating, and the time interval between doubling is shrinking. What are we going to do with the next six billion people due to arrive in the near future?
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