All About Growth

When I was growing up, there was a series of books, many of which found their way into our elementary school libraries, called the All About books. When I was in 2nd grade I discovered and became fascinated with Dinosaurs. So of course I read All About Dinorsaurs and every other book on the subject that I could get my grubby little hands on. Eventually, I exhausted the school library’s supply of such titles and, casting about in desperation, ran across another All About book: All About Early Mammals. I thumbed through the pages. Okay, I thought, they’re weird looking; some of them are almost as big as a dinosaur; I’ll give it a try. Reading the book in 3rd grade reading class, I discovered that much of our information on the subject came from fossils found in the La Brea Tar Pits. As I recall, the book went into some detail about the horrors of getting stuck in the tar pits; they were a regular prehistoric abbatoir. I became so engrossed, I forgot where I was. Gazing into space, the better to picture to myself the scenes of slaughter, I happened to hear one of the girls in my class reading from the day’s lesson: “Mary and Sue went down to the beach to play in the water.” “NO!” I corrected. “They were TAR pits!” Much hilarity ensued, along with a note to the parents, etc.

The only point to this little vignette is that the All About books were never totally satisfying because they fell far short of their title’s promise. They always left me a little disappointed. I was certain there was more. Fair warning Today’s subject is big. It involves strange and monstrous behaviors. And you can be certain that there is always more.

When we think about growth in ecological terms, especially in terms of human ecology, we’re looking at the idea in two separate but interconnected dimensions: growth in population, and growth in consumption. The more individuals there are, the more food, water, shelter, jobs, and entertainment they will require. Consumption, though, can also grow along a different axis, the axis of the individual. Consumption increases with population, but the appetites of the indiviual can increase as well. It’s important, here, to mention the canonical yet very important distinction between quantity and quality when it comes to the products we consume. The very first Europeans to arrive in the “New World” found themselves somewhat dwarfed by the indigenous people. The simplified diet of the “civilized” world couldn’t compete with the nutritional variety and quality inherent in the array of offerings from which the indigenes could choose. Another interesting factoid relates to the population density of the Americas circa 1491 – 1520. To illustrate, early Spanish explorers of Florida reported that the life expectancy of a Spanish soldier landing alone on some arbitrary stretch of beach on the southern Florida coast was around 3 minutes. Apparently the natives of those parts had gotten wind of the habits and intentions of the European explorers. Apparently my childhood history texts seriously underestimated the population density of the “New World” in 1491.

The distinction between quality and quantity will become very important when we begin to consider what kind of growth might be sustainable.

In 1798 a curate of the Church of England named Thomas Malthus published a paper entitled An Essay on the Principle of Population predicting food shortages by the end of the coming 19th century. His argument was based on the idea that the demand for food would outrun the supply because population grows faster than our abilty to increase agricultural yield. The rate of population growth increases with the number of people. The more people there are the more people there are to get down to the business of reproducing. So not only does the number of people increase with each generation, but the rate at which the number of people increases with each generation increases with each generation. Increased agricultural yield, on the other hand, depended on human effort:

man is a lazy animal, who would lead a satisfied life and procreate as long as his family was well fed. However, as soon as human population would feel constraints in food supply due to increase in population, he would again work hard to provide enough for his family. This might lead to an increase in agricultural production to provide for all, but at the same time man would be back to his complacent stage, where all his needs would be fulfilled. This would start the cycle of overpopulation and food shortage, all over again.

Of course, and as always, there were food shortages for the poor and the displaced. There were food shortages caused by agricultural policy, as in the Irish Potato Famine. But the full extent of his dire predictions did not come to pass within the timeframe of his theory. So his ideas are largely ignored these days. But while his predictions were falsified, his essential insight is still with us and stubbornly refuses to go away.

In the early 20th century quite a number of people began to wonder “how long can this go on.” The Great Depression was a great catalyst for such questioning. The great depression was a great example of poverty in the midst of plenty. Of course in certain parts of the country drought worked together with poor soil management to produce the dust-bowl shortages. But by and large the US was a country rich in natural resources and economic potential. Yet people went hungry all across the land. Looking back you could say that the depression represented a crisis of distribution, a problem in the financial system. You might say that the dynamics of the system were producing the very effects that the system was “designed” for. Of course the system’s design was not entirely intentional; it was the result of myriad decisions, political and economic over many decades. Nevertheless some people began to wonder. How long can this go on? What kinds of things actully limit growth, and how can we avoid these effects so that a catastrophe of this type doesn’t happen again?

So, alright let’s get to the meat. What is this thing called growth? Growth is an increase in quantity or size over time. In can also imply development, complexification, self-organization, a process of elaboration and refinement. It can be qualitative as well as quantitative.

Let’s look at quantitative growth. The type of growth I’m interested in is what you might call steady growth. In terms of steady growth the two relevant types are linear growth and exponential growth. Linear growth is interesting because it seems to be how humans are wired to think. We are very good at extrapolating trends in a linear fashion. Of course if you think of growth you have also to think of decrease or depletion, since mathematically depletion is just growth with a negative sign. Or, as one of my favorite comic strips, Pogo, says, “If you gonna talk about life an’ everthin’ else then that everthin’ else gotta be death. Seems like that makes life a perty risky business.” News reports are full of linear extrapolations. They usually begin with phrases like, “at present rates of consumption,” and then go on to predict that a given resource will last some number of years, usually in the hundreds. Linear growth is called linear growth because if you were to make a graph of your periodic measurements, annually, quarterly, whatever, the graph would be a line. Sure, the line could have a very steep slope, indicating rapid growth. But the rate of growth would never change. The slope of a line is always the same. And because we think naturally in terms linear growth, even linear growth that you might consider to be catastrophically rapid, would never surprise us. As soon as we see the growth rate, we know that it will be constant, and we can plan or adjust accordingly. Exponential growth is anothet kettle of fish, one that no one seems to like to smell much.

The really annoying thing about exponential growth (and decay) is that the rate is constantly changing. Now that’s great if you have a couple of hundred thousand dollars in the bank collecting compound interest but more difficult if you’re trying to figure out how many lanes to add to your local bypass so that you don’t have to do it again in 3 or 4 years. Dr. Albert Bartlett’s description of this frustration is illuminating:

When I first calculated the Exponential Expiration Time (EET) of U.S. coal for a particular rate of growth of consumption, … I used my new hand-held electronic calculator, and the result was 44 years. This was so short that I suspected I had made an error in entering the problem. I repeated the calculation a couple of more times, and got the same 44 years. This convinced me that my new calculator was flawed, so I got out tables of logarithms and used pencil and paper to calculate the result, which was 44 years. Only then did I begin to realize the degree to which the lifetime of a non-renewable resource was shortened by having steady growth in the rate of consumption of the resource, and how misleading it is for leaders in business and industry to be advocating growth of rates of consumption and telling people how long the resource will last “at present rates of consumption.”

So what type of steady growth is he talking about? Because linear growth seems to be steady, since the rate is constant, equal to the slope of the line.

The Power of Two

Since I’m feeling lazy, I’m going to quote Dr. Bartlett one more time:

Legend has it that the game of chess was invented by a mathematician who worked for an ancient king. As a reward for the invention the mathematician asked for the amount of wheat that would be determined by the following process: He asked the king to place 1 grain of wheat on the first square of the chess board, double this and put 2 grains on the second square, and continue this way, putting on each square twice the number of grains that were on the preceding square. …We see that on the last square one will place 2 exp(63) grains and the total number of grains on the board will then be one grain less than 2 exp(64).

How much wheat is 2 exp(64) grains? Simple arithmetic shows that it is approximately 500 times the 1976 annual worldwide harvest of wheat? This amount is probably larger than all the wheat that has been harvested by humans in the history of the earth! How did we get to this enormous number? It is simple; we started with 1 grain of wheat and we doubled it a mere 63 times!

The point he stresses is that “exponential growth is characterized by doubling, and a few doublings can lead quickly to enormous numbers.” Usually this type of growth is expressed as an annual percentage: 3% percentage annual growth in GDP, or some such. Three Percent? That ain’t shit! You might say. Well, actually, a steady annual growth rate of 3% will double the original quantity in 23 years and 4 months (give or take a couple of days). To get the approximate doubling time in this fashion, apply the rule of 70: T =(approximately) 70/r, where T is the doubling time and r is the percentage growth rate. If you want a more accurate number, do the math.

Imagine you are a healthy, reasonably well-off and respected bacterium in a nice jar of rice culture. You have a job as what passes for a city planner in bacteria culture, and there have been some rumblings among the masses concerning the dangers of overpopulation. What you don’t know is that the population is growing at a rate that causes it to double every day, at this rate the jar will be full in 30 days, and it’s now day 29. How does this look from your perspective? Well, you say, we have as much unused space as we have used in the entire history of our civilization. Therefore, you reason in your linear fashion, we can go on as we are for 29 more days. Remember, 29 days is a long time for a bacterium, think in the thousands of years range. Pretty funny, huh? The joke is on him. This is exactly how people think.

Tomorrow, back to peak oil and whatever else might be peaking.