New trends in physics teaching, v.4; The ... - unesdoc - Unesco

New Trends in Physics Teaching IV
Forgotten fundamentals of the energy crisis
ALBERT A. BARTLETT
“Facts do not cease to exist because they are ignored”. Aldous Huxley.
What are the fundamentals of the energy crisis? Rather than travel into the sticky abyss of
statistics it is better to rely on a few data and on the pristine simplicity of elementary mathematics.
With these it is possible to gain a clear understanding of the origins, scope and implications
of the energy crisis.
BACKGROUND
When a quantity such as the rate of consumption of a resource is growing by a fixed percentage
per year, the growth is said to be exponential. The important property of the growth is that the
time required for the growing quantity to increase its size by a fixed fraction is constant. For
example, a growth of 5 per cent (a fixed fraction) per year (a constant time interval) is exponential.
It follows that a constant time wil be required for the growing quantity to double its size
(increase by 100 per cent). This time is called the doubling time T2, and it is related to P, the
percentage growth per unit time, by a very simple relation that should be a central part of the
educational repertoire of every person.
As an example, a growth rate of 5 per cent/year wil result in the doubling of the size of the
growing quantity in a time T2 = 70/5 = 14 years. In two doubling times (28 years) the growing
quantity wil quadruple in size. In four doubling times it wil increase sixteenfold (24 = 16);and
so on. It is natural then to talk of growth in terms of powers of two.
THE POWER OF POWERS OF TWO
Legend has it that the game of chess was invented by a mathematician who worked for an ancient
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