Exponentials and You
I finally saw Dr. Al Bartlett’s famous talk on population last night at the University of Colorado. Dr. Bartlett is a Professor Emeritus at CU in the Physics Department. He begins and ends his talk with the sad assertion that the greatest failing of the human race is our inability to understand the exponential function. You might think that if that is our greatest failing we’re doing pretty well. But that is exactly the problem. Exponential growth of any kind against a finite resource leads to a rather dramatic and unhappy conclusion. One example in Bartlett’s talk is a colony of bacteria that doubles in population every minute. Consider the bacteria in a sample dish that starts growing at 11:00 a.m. and fills the dish one hour later. If it doubles every minute, then that means the dish is half empty at 11:59 a.m., and only 1/16-th full at 11:56 a.m. In other words, four short doubling times before the bacteria are completely out of space, they would look around their dish and see only 6.25% of it occupied. It is unlikely they would be worried about space or resources. This is the consequence of growth at a steady rate (sounds friendly) which is the same as exponential growth (sounds scary): at 3.5% annual growth, things double in 20 years.
The U.S. population is just about to break 300 million and the world population is over 6.5 billion. The current world population growth rate is 1.14% according to the U.S. Census Bureau. If that rate held steady we would see a doubling to over 13 billion people by 2066. However, the Census Bureau projects a continuing decline in the growth rate due to lower fertility rates. Women, on average, need to have 2.1 babies in order for the population to remain stable. The current global fertility rate is 2.6. However, even if it immediately dropped to 2.1 the population would continue to grow for a generation or so as a large population of women matures into child-bearing age.
I found the population numbers overall less alarming than the fossil fuel inventory in Bartlett’s presentation. Here we have a clear case of exponential growth against a finite resource. There’s only so much oil, and usage continues to rise. According to Bartlett we now have reliable means of estimating the quantity of undiscovered oil reserves, those undiscovered reserves are factored into projections of oil consumption and reserves in the future. The production of oil in the U.S. peaked in 1971 and will continue to decline until we are out. Drilling in the Arctic National Wildlife Refuge, for example, will supply the U.S. with, get this, one extra year of oil consumption at the current rate. That’s kind of like those bacteria getting another second or so of growth past noon. Some projections of the oil production in the world can be found in this Wikipedia article. We may be at the world peak production right about now. Check out these projections (no longer available at the Department of Energy website; draw your own conclusions). I suppose it’s dangerous to link to a Wiki site that is by definition a moving target, but a search for “Hubbert Peak” should give you the same general picture: we’re running out of oil, and in a hurry. The world oil consumption is a little less than 2 liters per day per person. That’s about a half a gallon. Americans of course use far more than that on average.
I have to say I came away from the talk a little bit daunted. Driving less is a good idea, but we’re going to need a more radical change in the way we generate and use energy over the course of the next century. Ultimately, the Sun is our main viable long-term power source. Oil is merely a fancy way of storing solar energy (grow some plants, have dinosaurs eat the plants, die, decay and create a nice hydrocarbon reservoir for us). We need to start implementing some simpler dinosaur-less schemes for harvesting large amounts of all that free energy raining down on us from the Sun. It’s going to be interesting.