By popular demand (well, Stephen asked for it, and he’s a popular guy)
here’s the text of my recent speech, which expands on the ideas presented
in the original exponentials post.
Mr. Toastmaster, my fellow Toastmasters and guests, our story begins with the
invention of a game called Chaturanga in India some 1400 years ago. Chaturanga
is the precursor to the game we call chess; it’s played on a board similar to
the one used today for chess, checkers, and backgammon. The ruling prince of
the region where the game was developed was so taken with Chaturanga that he
summoned the game’s inventor and offered to reward him for his genius.
Now the man who invented Chaturanga was, indeed, a genius. He asked the prince
that he be given only a very modest reward. Just one grain of rice placed in
the first square of the Chaturanga board. That’s all. Oh, and then two grains
of rice in the second square and four in the third and eight in the fifth and
so on, doubling until all 64 squares were filled.
Well,
the prince was pretty shocked that his subject should ask for such a paltry
reward, but he felt he had to comply. So he dispatched one of his stewards to
fulfill the order. It took the steward a while to report back, and when
he did the news was not good. Although harvest was just completed, the gift
was going to completely exhaust the royal granaries. And they were only on the
40th square!
In fact, it turns out that if you were to keep doubling until you reached the
64th square, you would have an amount of rice greater than the total
yield of every rice crop in the history of the planet earth. The inventor of
Chaturanga had trapped the prince with what mathematicians call a geometric
progression. As we follow the progress of the rice as it doubles with each step,
we’re witnessing what’s called an exponential increase.
As the example with the rice grains shows, any time we witness an exponential increase, we’re in for quite a show. Things start out small and get
crazy really quickly. Let’s look at a few exponential trends that are unfolding in our world today. (My first three examples come from an article
by Rodney Brooks that appeared recently in MIT Technology Review.)