The earth and its biological inhabitants comprise an evolving system in which various of its components change in magnitude with time. To describe these changes we may use the term "growth'' in a generic sense as being synonymous with change. Thus a given quantity may be said to exhibit positive growth if its magnitude increases with time, negative growth if it decreases with time, and zero growth if it remains constant.
Two terms applicable to an evolving system are of fundamental importance. These are steady (or stationary) state and transient state. A system is said to be in a steady state when its various components either do not change with time, or else vary cyclically with the repetitive cycles not changing with time. A system in a transient state is one whose various components are undergoing noncyclical changes in magnitude, either of increase or decrease.
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The growth phenomena with which we are at present concerned are almost exclusively of the transient kind. Three types of transient growth are illustrated in Figure 1. This figure is drawn with a time base extending from the year 1800 to beyond 2100 during which some quantity is assumed to grow in one or the other of the three modes shown.
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Another fundamental property of uniform exponential growth is the following. If the logarithm of the quantity is plotted graphically as a function of time, or if the quantity is plotted on semilogarithmic paper, the resulting graph will be a straight line whose slope is proportional to the growth rate. Conversely, a straight-line graph of the growth of a quantity, when plotted on semilogarithmic paper, indicates a uniform exponential growth.
A second type of growth is that shown in Curve II of Figure 1. Here the growing quantity increases exponentially for a while during its initial stage, after which the growth rate starts to slow down until the magnitude of the quantity finally levels off to some fixed maximum quantity. After this the growth rate becomes zero, and the quantity attains a steady state.
Examples of this kind of growth are afforded by biological populations and by the development of water power in a given region. The population of any biologic species, if initially stationary, will respond to changed conditions in a manner indicated by Curve II, or conversely by its negative analog. That is, the population in response to a disturbance will either increase exponentially and then level off to a stable maximum, or else decrease negative-exponentially and finally stabilize at a lower level, or perish.
A third type of transient growth is that represented by Curve III in Figure 1. Here, the quantity grows exponentially for a while. Then the growth rate diminishes until the quantity reaches one or more maxima,
and then undergoes a negative-exponential decline back to zero. This is the type of growth curve that must be followed in the exploitation of any exhaustible resource such as coal or oil, or deposits of metallic ores.
Transition From Steady State To Transient State Due To Fossil Fuels
By about 2 million years ago biological evolution had advanced to where the ancestors of the present human species had begun to walk upright and to use crude stone tools. At that stage this species must have existed as a member of an ecological complex and competed with the other members of the complex for a share of the local solar energy essential for its existence.
The energy utilizable was almost exclusively the food supply derived by the biological system from solar energy by the mechanism of photosynthesis. During the subsequent million or more years the human species progressively devised means of capturing an ever larger supply of the available energy. This resulted in a slow change in the ecological relations and to an increase in density and geographical spread of the human population, but the energy per capita changed very little.
Although the pace quickened about 8,000 to 10,000 years ago with the domestication of plants and animals, a rapidly changing transient state of evolution was not possible until the large supplies of energy stored in the fossil fuels began to be utilized -when the mining of coal as a continuous enterprise was begun near Newcastle in northeast England about 9 centuries ago. This was followed as recently as 1857 in Romania and in 1859 in the United States by the exploitation of the second major source of fossil-fuel energy, petroleum.
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What is most strikingly shown by these complete-cycle curves is the brevity of the period during which petroleum can serve as a major source of energy. The peak in the production rate for the United States has already occurred three years ago in 1970. The peak in the production rate for the world based upon the high estimate of 2100 billion barrels, will occur about the year 2000.
For the United States, the time required to produce the middle 80 percent of the 170 billion barrels will be approximately the 67-year period from about 1932-1999. For the world, the period required to produce the middle 80 percent of the estimated 2100 billion barrels will be about 64 years from 1968 to 2032. Hence, a child born in the mid-1930s if he lives a normal life expectancy, will see the United States consume most of its oil during his lifetime. Similarly, a child born within the last 5 years will see the world consume most of its oil during his lifetime.
A better appreciation of the epoch of the fossil fuels in human history can be obtained if the complete production cycle for all the fossil fuels combined -- coal, oil, natural gas, tar sands, and oil shales--is plotted on a time span of human history extending from 5000 years in the past to 5000 years in the future, a period well within the prospective span of human history. Such a plotting is shown in Figure 13. This Washington Monument-like spike, with a middle 80-percent span of about three centuries, represents the entire epoch.
On such a time scale, it is seen that the epoch of the fossil fuel can be but an ephemeral and transitory event-an event, nonetheless, that has exercised the most drastic influence so far experienced by the human species during Its entire biological existence.
Other Sources of Energy
It is not the object of the present discussion to review the world's energy resources.
Therefore, let us state summarily that of the other sources of energy of a magnitude suitable for large-scale industrial uses, water power, tidal power, and geothermal power are very useful in special cases but do not have a sufficient magnitude to supplant the fossil fuels. Nuclear power based on fission is potentially larger than the fossil fuels, but it also represents the most hazardous industrial operation in terms of potential catastrophic effects that has ever been undertaken in human history.
For a source of energy of even larger magnitude and without the hazardous characteristics of nuclear power, we are left with solar radiation. In magnitude, the solar radiation reaching the earth's surface amounts to about 120,000 × 1012 watts, which is equivalent, thermally, to the energy inputs to 40 million 1000-megawatt power plants. Suffice it to say that only now has serious technological attention begun to be directed to this potential source of industrial power.
However, utilizing principally technology already in existence there is promise that eventually solar energy alone could easily supply all of the power requirements for the world's human population.
Constraints on Growth
Returning now to the problem of sustained growth, it would appear that with an adequate development of solar power it should be possible to continue the rates of growth of the last century for a considerable time into the future. However, with regard to this optimistic view attention needs to be directed to other constraints than the magnitude of the energy supply. These constraints may be broadly classified as being ecological in nature. For more than a century it has been known in biology that if any biological species from microbes to elephants is given a favorable environment, its population will begin to increase at an exponential rate. However, it was also soon established that such a growth rate cannot long continue before retarding influences set in. These are commonly of the nature of crowding, pollution, food supply, and in an open system by adjustments with respect to other members of the ecological complex.
In our earlier review of the rates of production of the fossil fuels it was observed that for close to a century in each case the production increased exponentially with doubling periods within the range of 8 to 16 years. The same type of growth rates are characteristic of most other industrial components. Figure 14 is a graph showing the exponential growth of the world electric generating capacity. The solid part of the curve since 1955 shows a growth rate of 8.0 percent per year with a doubling period of 8.7 years. The dashed part of the curve shows approximately the growth since 1900. In the United States during the last several decades electric power capacity has been doubling about every 10 years. The world population of automobiles and also passenger miles of scheduled air flights are each also doubling about every 10 years.
In Figure 15 a graph is shown of the growth of the world's human population from the year 1000 A.D. to the present, and an approximate projection to the year 2000. This is important in that it shows the ecological disturbance of the human population produced by the development of technology based upon the fossil fuels, the concomitant developments in biological and medical science, and expansion into the sparsely settled areas of the newly discovered geographical territories. Note the very slow rate of growth in the human population during the 500 year period from the year 1000 A.D. to 1500, and then the accelerated growth that has occurred subsequently. Were it possible to plot this curve backward in time for a million years, the curve would be barely above zero for that entire period. The flare up that has occurred since the year 15M is a unique event in human biological history.
It is also informative to contrast the present growth rate of the human population with the average that must have prevailed during the past. The present world population is about 3.9 billion which is increasing at a rate of about 2 percent per year, with a doubling period of about 35 years. What could have been the minimum average doubling period during the last million years? This minimum would occur if we make a wholly unrealistic assumption, namely that the population a million years ago was the biological minimum of 2. How many doublings of this original couple would be required to reach the world's present population of 3.9 billion? Slightly less than 31. Hence, the maximum number of times the population could have doubled during the last million years would have been 31. The minimum value of the average period of doubling must accordingly have been 1,000,000/31, or 32,000 years.
To be sure the population need not have grown smoothly. Fluctuations no doubt must have occurred due to plagues, climatic changes, and wars, but there is no gainsaying the conclusion that the rate of growth until recently must have been so extremely slow that
we may regard the human population during most of its history as approximating an ecological steady state.
The same kind of reasoning may be applied to the other components of any ecological system. It is known from geological evidence that organic species commonly persist for millions of years. Consequently, when we compute a maximum average growth rate between two finite levels of population at a time interval of a million years, we arrive at the same conclusion, namely that the normal state that is the state that persists most of the time is one of an approximate steady state.
The abnormal state of an ecological system is a rapidly changing transient or disturbed state. Figure 16 illustrates the behavior of the populations of three separate species of an ecological complex during a transient disturbance between two steady states. In such a disturbance all populations are effected, some favorably, some unfavorably.
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Cultural Aspects of the Growth Problem
Without further elaboration, It is demonstrable that the exponential phase of the industrial growth which has dominated human activities during the last couple of centuries is drawing to a close. Some biological and industrial components must follow paths such as Curve II in Figure 1 and level off to a steady state; others must follow Curve III and decline ultimately to zero. But it is physically and biologically impossible for any material or energy component to follow the exponential growth phase of Curve I for more than a few tens of doublings, and most of those possible doublings have occurred already.
Yet, during the last two centuries of unbroken industrial growth we have evolved what amounts to an exponential-growth culture. Our institutions, our legal system, our financial system, and our most cherished folkways and beliefs are all based upon the premise of continuing growth. Since physical and biological constraints make it impossible to continue such rates of growth indefinitely, it is inevitable that with the slowing down in the rates of physical growth
cultural adjustments must be made.
One example of such a cultural difficulty is afforded by the fundamental difference between the properties of money and those of matter and energy upon which the operation of the physical world depends.
Money, being a system of accounting, is, in effect, paper and so is not constrained by the laws within which material and energy systems must operate. In fact money grows exponentially by the rule of compound interest.
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In particular, if the industrial growth rate a and the average interest rate i have the same values, then the ratio of money to what money will buy will remain constant and a stable price level should prevail. Suppose, however, that for physical reasons the industrial growth rate a declines but the interest rate i holds steady. We should then have a situation where i is greater than a with the corresponding price inflation at the rate (i-a). Finally, consider a physical growth rate a=0, with the interest rate i greater than zero. In this case, the rate of price inflation should be the same as the average interest rate.
Conversely, if prices are to remain stable at reduced rates of industrial growth this would require that the average interest rate should be reduced by the same amount. Finally, the maintenance of a constant price level in a nongrowing industrial system implies either an interest rate of zero or continuous inflation.
Time Perspective of Industrial and Cultural Evolution
The foregoing example has been discussed in detail because it serves as a case history of the type of cultural difficulties which may be anticipated during the transition period from a phase of exponential growth to a stable state. Since the tenets of our exponential-growth culture (such as a nonzero interest rate) are incompatible with a state of nongrowth, it is understandable that extraordinary efforts will be made to avoid a cessation of growth. Inexorable, however, physical and biological constraints must eventually prevail and appropriate cultural adjustments will have to be made.
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