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Exponential Growth

In America growth is seen as American as the flag and apple pie. But there is trouble in paradise. The flag that flies for growth is a noose and the apple pie of expansion is laced with cyanide. But it's not just America that has this unhealthy relationship with growth it's the majority of the world and its economies. As our populations, economies, and resources use grow exponentially, so do our environmental problems and the potential for collapse of the earth's ability to sustain human life. Growth as we know it cannot continue.

As the primary proponent of growth worldwide, business must adjust to the reality of the problems created by growth. Because our current systems of business rely upon continuous growth and development they can not survive in their current form. As Paul Hawken writes in The Ecology of Commerce, "Just as internal contradictions brought down the Marxist and socialist economies, so do a different set of social and biological forces signal our own possible demise. Those forces can no longer be ignored or put aside" (2). The internal contradictions that Hawken is speaking of are creation of waste, unsustainable uses of resources, environmental degradation, a disparity of wealth, and a plethora of other unsustainable business practices.

The most important foundation of all of these problems is exponential growth in human population and resource use. Hawken states, "The problems to be faced are vast and complex, but come down to this: 5.5 billion people are breeding exponentially. The process of fulfilling their wants and needs is stripping the earth of its biotic capacity to produce life; a climactic bust of consumption by a single species is overwhelming the skies, earth, waters, and fauna" (xii). Hawken relates this to business practices by showing that business relies on and creates unsustainable growth. Hawken seeks to answer, as did the United Steelworkers of America (USWA) Task Force on Environment, "What kind of jobs will be possible in a world of depleted resources, poisoned water and foul air, a world where ozone depletion and greenhouse warming make it difficult even to survive." (USWA 14).

What exactly is exponential growth, and is exponential growth in population and resource use really unsustainable? Much of the public and by many of our policy makers do not understand exponential growth. Unfortunately this lack of understanding does not keep exponential population and resource use from being a problem. In fact Dr. Albert Bartlett, a distinguished professor of physics at the University of Colorado at Boulder, claims that the greatest failing of the human race is its failure to understand the exponential function (Forgotten Fundamentals of the Energy Crisis).

Exponential growth is simply growth by a fixed rate, such as compound interest. This is opposed to linear growth which is growth by a fixed number, for example the number of days you have lived grows linearly because every year you add no more days than the last year. The difference between these two types of growth is startling.

The possible origin of chess shows a striking example of exponential growth. Legend has it that chess was invented by a mathematician who asked a king for what seemed to the king like a small price for the game. He asked that the king pay him in wheat. He asked the king to place 1 piece of wheat on the first square of the board, two on the second and that he continue to double the grains of wheat for all the squares on the board. The king agreed to pay the price, but it's quite impossible that he held up his end of the bargain. The amount of wheat needed is enormous. With 64 squares on a chessboard, the king needed 263 grains of wheat to pay the mathematician. This is roughly 400 times the 1990 worldwide harvest of wheat, and could be more wheat than has been harvested in the history of humanity (Forgotten Fundamentals of the Energy Crisis)! This is exponential growth. The king was probably thinking of linear growth, where the number of grains would grow by one for each square, when he made the deal. Linear growth would give 2048 grains of wheat in total. Enough grain for a few meals perhaps, but nothing compared to the amount of wheat harvested in human history.

Many things other than that cunning mathematician's grains of wheat grow exponentially. Human population, resource use, and the waste that accompany them are growing exponentially. While many types of resource use are growing at over 5% per year, the human population is growing at about 1.6% (Miller 9). 1.6% does not seem too like an unacceptable rate of growth to many. In economic terms 1.6% growth is downright horrendous. The Japanese declare their economy is in recession if it grows less than 3% per year.

Although 1.6% does not seem like much to some of the kings and economists of the world, applied to human population it can yield huge numbers. While it took 2 million years for us to reach a population of 1 billion, we will add another billion to the earth's population in just the next 11 years (Miller 9). If we calculate 1.6% growth out to 600 years we find that there would be one person for each square meter of the dry land surface of earth, and in 1800 years the mass of humans would exceed the mass of the earth (Forgotten Fundamentals of the Energy Crisis). Clearly human population growth will stop. But it's not just our population that is growing, it's also our use of natural resources.

Most types of resource use are growing faster than population. Although many associate growth in resource use with population growth, growth in resource use can also be independent of population growth. Resource use can grow even without population growth, although the reverse is hard to imagine. An example of what exponential growth means in resources can be seen with US coal reserves. Coal is the US's most abundant fossil fuel. In 1991 the US Department of Energy reported that at current rate of use US coal reserves could last almost 500 years. But the caveat here is current rate of use. Between 1971 and 1991 the use of coal grew 2.86%. With this rate of growth US coal could last about 94 years if we could use it all, but more likely 72 years of coal would be recoverable (Forgotten Fundamentals of the Energy Crisis).

Lack of understanding of how long coal could last comes from people's lack of knowledge of exponential growth. In 1978, Time Magazine reported that there is "enough coal to meet the country's energy needs for centuries, no matter how much energy consumption may grow" (Forgotten Fundamentals of the Energy Crisis). This is clearly untrue. If we look just at the amount of electrical energy the country uses and its historical growth over the last 40 years, we see that coal could meet that need for just 36 years. Remember, coal is our most abundant fossil fuel. This utter lack of understanding of the results of exponential growth isn't limited to Time -- it's pervasive in our government, media, and general public.

One reason for this is that exponential growth moves so fast. It seems we should not worry with 500 years of coal left, but we need to know how fast use will grow. Exponential growth is deceptive. The ramifications of exponential growth can be better understood if you understand doubling time.

The amount of time it takes for the amount of something that is growing exponentially to double can be approximated by dividing 70 by the rate of growth. So the human population doubles at 70/1.6 which equals about every 43 years. Doubling time is important because it's easier to conceptualize than a percentage. Also in exponential growth the growing item during any doubling time is greater than the entire amount that came before. For example the last square of the chessboard will contain more wheat than all the other squares combined. Hence in the next 25 years, the doubling time of coal use, if we increase the use of coal by our current rate of 2.86% we will use more coal than we have used in the history of humankind. This is deceptive because when we have reserves of a resource that are greater than all of that resource previously used, people tend to think the resource will last a great while longer. For example, if a nonrenewable resource has been used for centuries, and almost half of it remains, people will generally believe they have a lot of time before they have to adjust; however, as we have seen, they may not have enough for the last doubling time which will require more than has ever been used before. What may seem like huge amounts of resources can be decimated in short periods of time when we apply linear growth to a question when the thing in question grows exponentially.

Some people, however, argue that growth can continue because of humanity's incredible propensity for change, technological innovation, and our historical ability to find new resources and processes. Chief among these proponents of growth is economist Julian L. Simon. Simon argues, "Raw materials have been getting less scarce instead of more scarce throughout history, defying the common sense notion that if one begins with an inventory of a resource and use some up, there will be less left. This is despite, and indirectly because of, increasing population" (Miller 24-25). Simon is right that we have historically found new ways to manipulate our environment and hence have increased the diversity of raw materials we have available. But Simon doesn't seem to recognize the power of exponential growth, and that until the industrial revolution the earth's population wasn't growing exponentially.

Contrary to what Simon says, discovery of new resources will not be enough. A discovery of a natural resource with the energy generating capacity of the nation's coal, for example, would be truly astounding. But how much more time would it buy? Thinking linearly, it would give us 500 more years of the energy coal currently provides. But resource use isn't growing linearly. We saw that at the current rate of use, US coal will last about 72 years. Simon's newly discovered resource would not. Remember use is continuing to grow. The new resource, with all the capacity of current coal reserves, would last for less time than the doubling time of the growth of use of coal -- less than 25 years. After that 25 years of use, an entirely new resource twice as large would have to be found to maintain growth. To support our rate of growth in the use of the energy coal provides we need to find a resource that is 15 times as large as our coal reserves just to support another century of growth after the coal runs out. Although Simon claims that these resources can be found he doesn't suggest what they may be. But the issue goes far beyond just availability of resources.

The earth's capacity to maintain human life is being degraded by consumption of natural resources. Take coal again, for example. We've already seen that our huge reserves aren't that large after all, but what of the environmental effects of burning coal? According to G. Tyler Miller, "Coal is by far the dirtiest fossil fuel to burn" (383). Each year in the US burning of coal causes at least 50,000 cases of respiratory disease, kills thousands of people (estimates range from 5,000 to 200,000), and causes billions of dollars in property damage (383). This is just from burning it. Since 1900 underground mining has killed more than 100,000 miners and permanently disabled at least 1 million. And another 250,000 retired US miners suffer from black lung disease (382). Coal burning is also a major cause of acid rain. Acid rain causes much of the property damage noted above, weakens and sometimes kills forests, and severely impacts lakes and riparian life. All of these problems come from the amount of coal we burn now; if we follow the advice of Simon and continue on the current path, in just 25 more years we will be burning twice as much coal -- in 50 years 4 times as much. As the rate of coal burning increases exponentially it's prudent to assume that the environmental problems associated with it will also.

Coal is just one example of the larger issues surrounding resource use. No one knows if we'll be able to discover enough resources to maintain our level of growth, or if the social, human, and environmental costs of using these resources will be too high to use them if they are found. If one understands the way exponential growth works it becomes clear, as it is to most that study the issue, that population and resource use growth cannot continue (Miller 31). The manor in which these will stop is unknown. We seem to have two basic choices: we can decide how to stop the growth of population and resources use, or we can let nature do it for us.

The latter choice isn't very appealing to those who know how nature takes care of exponentially growing populations. In 1910, 26 reindeer were introduced to one of Alaska's Pribilof islands. The reindeer quickly overshot the ability of their environment to sustain them -- also known as carrying capacity. By 1935 their population was up to 2,000. The reindeer population grew exponentially then it crashed in the same way. By 1950, only eight reindeer remained (Miller 170). Humans have also experienced this type of population crash: in the 1845 potato blight in Ireland; Easter Island; and many other areas. Up until now, these population crashes have been local and small, but our world is much different now. Our resources are being depleted on a global scale and unlike the reindeer on the island we can move to other areas and deplete the resources there. Although a crash in human population would affect areas differently, there is little doubt that it would be worldwide.

We are at a unique point in human history. Proponents of growth are offering us quite a deal. Just play the game they say, and surly we'll be able to find enough grain to pay. The game here is not chess, but continued growth of population and material wealth. The Simple Simons of the world tell us that doubling the amount of grain on each square cannot ever be too much, and it sure is a nice game, they say. But prudence would dictate following the advice of a simple piece of math called the exponential function.

Works Cited

Hawken, Paul. The Ecology of Commerce: A Declaration of

Sustainability. New York: HarperCollins, 1993.

Forgotten Fundamentals of the Energy Crisis. Dir. and Perf. Dr. Albert A. Bartlett, Professor Emeritus, Dept. of Physics, University of Colorado at Boulder, 1986.

Miller, Tyler G. Living in the Environment. New York: Wadsworth Publishing Company, 1996.

United Steelworkers of America Task Force on the Environment. Our Children's World: Steel Workers and the Environment. Pittsburgh, PA: USAW, AFL-CIO, August 1990.


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