In his new lecture for the Long Now Foundation, Geoffrey West asserts that part of the problem humans face is that we tend not to understand exponential growth. An economy growing at a miserable 2%, for example, is still growing exponentially. And economic growth is still largely a measure of the acceleration of entropy–how much faster are we turning resources into pollution. He advises figuring out ways that periods of slow or no growth OK, because it will have to be.
Exponential growth really is counterintuitive. Here’s the way he describes it:
Imagine you are going to grow a test tube of a bacteria, starting with one bacterium at 8 AM and ending with a full test tube precisely at noon. The bacteria grow by doubling–a kind of exponential growth–each second. So at the end of one second we have two, after two seconds we have four, after three seconds we have eight, and so on. That being the case, at what time will the test tube be one-half full?
Right. Precisely one second before noon. And two seconds before noon it’s a quarter full. Three seconds is an eighth, four seconds a sixteenth. At 11:59.55 AM, the tube is only 1/32 full. Imagine being a bacterium in the tube at five seconds to noon. It would seem more crowded than usual, but look at all that space to go, and we’ve been doubling like this for almost four hours! There may be a problem in the next few days, but certainly not in the next few seconds–exponential growth is probably also counterintuitive for bacteria.
(Published first on Nathen’s Miraculous Escape as “Exponential Growth,” August 21, 2011.)