Blog 8. Was Chicken Little right? An exponential tale

After she* was conked on the head by a falling acorn, Chicken Little ran around in panic, crying that the sky was falling. From that story, our children presumably learn not to exaggerate, not to make conclusions without data. Despite the moral of the story, was Chicken Little right? Is the sky falling?

There have always been mythological dooms, like the prediction that the world would end on 12/21/2012, derived by some nut who bounced off the Mayan calendar. There have also been realistic predictions of calamity, as when a few people recognized that the unrestricted proliferation of private debt and paper speculation would lead to the economic collapse that actually happened in 2008.

For the last four decades, environmentalists have sometimes seemed like nutty doomsayers, pointing to buried poisons (Love Canal), air pollution, nuclear power plants, oil spills, and piles of plain old municipal garbage. Today, the environmental stories are more apocalyptic: overpopulation and overconsumption, resource depletion, global climate change, and social collapse. These are bigger things, things too big to be fixed by passage of another clean air act or a subsidy for solar collectors. And this time it isn’t only the banner-waving environmentalists who smell trouble. Jared Diamond, a professor whose several books examine the geopolitics of human progress (or regress) through the centuries, published Collapse, a cool analysis of where we’re going and what happens if we elect to continue the journey. Yet the earth is still here, babies are born, the sun shines, and sometimes we’re surprised when a river gets cleaner rather than dirtier.

What’s different?

The current Big Problems of change: greenhouse gases, polar ice melting, population, rain forest clearing, energy consumption, population …, are linked together and have common features. They are global, and the rate of change is roughly proportional to what exists. For population, that’s easy to understand. The more people there are, the more babies they produce. Until either social sense or calamity limits the population. It’s compound interest: the more money in the account, the faster it grows because all the interest from prior years grows, too.

The behavior of anything for which the rate of change is proportional to the existing amount is called an exponential, as mentioned in Blog 1.   An exponential just grows, the rate of growth becoming faster and faster. It’s why the rich tend to get richer, why change becomes more rapid, why a big problem appears so suddenly.

Think of filling a cup with water. Start with one drop in the cup. The first day add one drop because there is one drop already in the cup. The second day add two drops, because there are two drops already in the cup. Each day gradually add water equal to the amount in the cup (rate of change is proportional to the content—that’s exponential). When the cup is half full, it appears to have plenty of empty space. But it will become full in only one more day. About 6000 drops from a small eyedropper will be required to fill a 8-oz cup.  After four days the bottom of the cup is covered with water; after 11 days the cup is half full.  On the twelfth day, it’s a problem when the cup runneth over.

That’s why the environmental arguments are so alarming.  The rate of environmental damage is roughly proportional to the population and to the consumption per person, and the consumption rate is roughly proportional to the previous technical development of humanity, while technical progress feeds on prior technical progress. It’s gonna end sometime, and today looks like day 11 of the cup experiment. The chicken littles of the world may be onto something this time.  We’ll look at actual data in a later blog.


* Some current authors of Chicken Little stories (CL, aka Henny Penny) portray CL as a he, but when I was a child CL was a she, a hen.  I argue that it is NOT  more politically correct to feature a ditzy he than a ditzy she.  Besides that, it’s insulting to name a rooster Henny Penny.