Thursday, November 13, 2008

Exponential Growth

This bit from the Wired article on Ray Kurzweil really grabbed my attention because Phil has our class thinking about the origin of GrameenPhone.
Kurzweil had a special confidence that grew from a habit of mind he'd been cultivating for years: He thought exponentially. To illustrate what this means, consider the following quiz: 2, 4, ?, ?.

What are the missing numbers? Many people will say 6 and 8. This suggests a linear function. But some will say the missing numbers are 8 and 16. This suggests an exponential function. (Of course, both answers are correct. This is a test of thinking style, not math skills.)

Human minds have a lot of practice with linear patterns. If we set out on a walk, the time it takes will vary linearly with the distance we're going. If we bill by the hour, our income increases linearly with the number of hours we work. Exponential change is also common, but it's harder to see. Financial advisers like to tantalize us by explaining how a tiny investment can grow into a startling sum through the exponential magic of compound interest. But it's psychologically difficult to heed their advice. For years, an interest-bearing account increases by depressingly tiny amounts. Then, in the last moment, it seems to jump. Exponential growth is unintuitive, because it can be imperceptible for a long time and then move shockingly fast. It takes training and experience, and perhaps a certain analytical coolness, to trust in exponential curves whose effects cannot be easily perceived.

Iqbal Quadir, the founder of GrameenPhone, recognized early on that cell phones would serve as the tool to level the information playing field. But the phones were expensive in the early 1990s and the key to making this work was Iqbal's recognition of Moore's Law, which is what the quote above is really talking about. Having the insight that a product that is not currently feasible soon will be is a very valuable insight. Few of us naturally think along these lines and it is powerful to see smart people apply these ideas. Analytical coolness, indeed.

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