Exponential Growth is Counterintuitive

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.)

Failures of Intuition

Ed Moses begins the new Long Now Seminar talking about the BP oil spill, saying, basically, that there’s a 30″ hole, one mile down, that’s leaking about a million barrels of oil into the Gulf of Mexico every week. Keep in mind, though, he says, that the US burns a million barrels of oil an hour.

Oh… right.

It reminded me of an “Oh… right” experience I had the morning of September 11, 2001, when my friend Biko told me there had been terrorist attacks. It turned out that the early death-toll estimates were way higher than they turned out to be–we had heard that it was tens of thousands–but even then, Biko said, “Well, to keep this in perspective, a lot more people than that die of starvation every day.”

It’s amazing to me how relatively small-scale catastrophes grab my attention and get my emotions going, as long as they are dramatic in some way, while global-scale catastrophes can be easy to ignore.

This also reminds me of a lecture I attended last year by Paul Slovic about how our moral intuition fails when it comes to large-scale problems like genocide. He presented an experiment in which (among other things) one group of participants were shown a profile of a starving child and were given the opportunity to give some of the money they’d earned by participating to help the child. Another group of participants had the same experience except they were shown two children. The people who saw two profiles gave way less money than those who saw only one. It’s worse than diminishing returns. It’s not just that more people in trouble get less money per person, they get less money in total. It seems that bigger problems become more abstract, and so become less emotionally pressing.

The question is, how can we motivate ourselves and others to do what is right in situations where moral intuition routinely misleads us? The person who answers that question could really change things. Imagine a world in which the recent earthquake in Haiti was not that big of a deal because we had helped them out before it hit. After all, we all knew they had been desperately poor and vulnerable for our entire lifetimes. We just didn’t care that much.

[First published on Nathen’s Miraculous Escape, July 6, 2010.]