Saturday, 9 February 2013

Arithmetic, Population And Energy - Sustainability 101

The chessboard has 64 squares. According to legend, chess was invented by Grand Vizier Sissa Ben Dahir, and given as a gift to King Shirham of India. The king was so delighted that he offered him any reward he requested, provided that it sounded reasonable. The Grand Vizier requested the following:

"Just one grain of wheat on the first square of a chessboard. Then put two on the second square, four on the next, then eight, and continue, doubling the number of grains on each successive square, until every square on the chessboard is reached."

The king thought this a very modest request, promised it, and asked for a bag of wheat to be brought in. However the bag was emptied by the 20th square. The king asked for another bag, but then realized that the entire bag was needed for the next square. In fact, in 20 more squares, he would need as many bags as there were grains of wheat in the first bag!

The number of grains in the last square can be calculated by multiplying 2 times itself 63 times. If you include the grains on the first 63 squares, the sum is about twice as large.

The amazing feature of this problem is that with just 64 steps, each one quite modest (you are only doubling) you get a huge number. This type of rapid growth is called exponential growth.

Albert Bartlett, professor in nuclear physics from the University of Colorado, Boulder explains the concept of compound growth in this 1 hour video.

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