Monday, October 6, 2014

The Exponential Function and Ebola

 "The greatest shortcoming of the human race is our inability to understand the exponential function." 
Albert Bartlett, Professor of Physics, University of Colorado
You know the exponential function, the one which starts off so slowly you can hardly see it increasing until it literally takes off with increasing acceleration. It's often called, pejoratively, the hockey stick, when salespeople protest that sales may be small now, but just wait for next quarter!

The exponential function is particularly interesting right now because of the Ebola crisis, which is spreading at an exponential rate. The Centers for Disease Control and Prevention have published that the cases are doubling every 15-20 days in Liberia and every 30-40 days in Sierra Leone and Guinea. It has been clear that the crisis was underestimated in the early days, probably because people didn't understand the inexorable power of the exponential function. There's the same effect in misunderstanding climate change, where feedback mechanisms cause changes to proceed exponentially.

Here's a chart from Wikipedia as of October 16, 2014, showing the number of cases of Ebola. It's a classic case of the Exponential function.

Not all exponentials are bad. I've written in a previous post about Ray Kurzweil. He also adamantly argues that people underestimate the power of the exponential, particularly as related to technological progress, which he considers unilaterally good. Some people might find his conviction that technology to support immortality is just around the corner a bit, well, spooky.

Then there is the Indian legend of the mathematician who did understand the power of the exponential. In fact, he lost his head over it! Here's how Wikipedia reports the legend.

When the creator of the game of chess (in some tellings an ancient Indian Brahmin[1][2] mathematician named Sessa or Sissa) showed his invention to the ruler of the country, the ruler was so pleased that he gave the inventor the right to name his prize for the invention. The man, who was very clever, asked the king this: that for the first square of the chess board, he would receive one grain of wheat (in some tellings, rice), two for the second one, four on the third one, and so forth, doubling the amount each time. The ruler, arithmetically unaware, quickly accepted the inventor's offer, even getting offended by his perceived notion that the inventor was asking for such a low price, and ordered the treasurer to count and hand over the wheat to the inventor. However, when the treasurer took more than a week to calculate the amount of wheat, the ruler asked him for a reason for his tardiness. The treasurer then gave him the result of the calculation, and explained that it would take more than all the assets of the kingdom to give the inventor the reward. The story ends with the inventor being beheaded. (In other variations of the story, the inventor becomes the new king.)

No comments: