VIII.  A WORD OF CAUTION 

We must note that these calculations of the EET of fossil fuels are not predictions of the future.  They simply give us first-order estimates of the life expectancies of known quantities of several fuels under the conditions of steady growth which our society and our government hold sacred.  These estimates are emphasized as aids to understanding the consequences of any particular growth scenario that the reader may want to consider or to evaluate. 

The rate of production of our mineral resources will not rise exponentially until the EET is reached and then plunge abruptly to zero, as modeled in these calculations and as shown in curve A of Fig. 5 even though our national goals are predicated on uninterrupted growth.  The rate of production of our nonrenewable mineral resources will not follow the classical S-shaped transition from an early period of exponential growth to a horizontal curve representing a constant rate of production, curve B.  Such a curve can be achieved in the production of renewable resources such as food, forest products, or the production of solar energy, provided the rate of production of the renewable resource is not dependent on fossil fuels.  Reference has already been made to the dependence of modern agriculture on petroleum, and as long as this dependence continues, the curve of agricultural production would be expected to follow curve C, (the curve for nonrenewable petroleum) rather than curve B.  Although the rate of production of mineral resources has been growing  
  
 

  
exponentially, one knows that at some time in the future the resource will be exhausted and the rate of production will return to zero.  The past history, this one future datum and a careful study of the rate versus time of production of resources that have expired has led Dr. M. King Hubbert to the conclusion that the rate of production of a nonrenewable resource will rise and fall in the symmetrical manner of a Gaussian error curve as shown in curve C of Fig. 5.  When he fits the data for U.S. oil production in the lower 48 states to a curve such as C, Hubbert finds that we are now just to the right of the peak.  We have used one-half of the recoverable petroleum that was ever in the ground in the U.S. and in the future the rate of production can only go downhill.  However, our national demand for petroleum has continued to grow exponentially and the difference between our demands and our production has been made up by imports.  Bold initiatives by the Congress could temporarily reverse the trend and could put a small bump on the downhill side of the curve.  Alaskan oil can put a little bump on the downhill side of the curve.  The downhill trend on the right side of the curve was noted clearly by Deputy Energy Secretary John O'Leary under the headline, "U.S. Energy ‘Disaster' Inevitable by 1985,"³⁴ 
 

Although U.S. oil and gas production hit their peak several years ago and are declining by about 8 percent per year, O'Leary said, the nation has avoided serious problems by using more foreign oil...We are walking into a disaster in the next three or four years with our eyes wide open.

The most dramatic conclusion that Hubbert draws from his curve for the complete cycle of U.S. oil production is that the consumption of the central  80 % of the resource will take place in only 67 yrs.! 

It is very sobering to face the downhill side of the curve and to note that in the past the rise in our annual per capita consumption of energy has gone hand-in-hand with the increase of our standard of living.  It is more sobering to note the close coupling between our production of food and our use of petroleum.  It is even more sobering to note that on March 7, 1956 (over 22 years ago) Dr. Hubbert, addressing the conference in San Antonio, Texas, of a large group of petroleum engineers and geologists said: 
 

According to the best currently available information, the production of petroleum and natural gas on a world scale will probably pass its climax within the order of half a century, while for both the United States and for Texas, the peaks of production can be expected to occur within the next 10 or 15 years. (i.e., between 1966 and 1971)

Pazik tells³³ of the shock this statement and the related analysis caused in oil industry circles and he tells about the efforts that were made by the "experts" to ignore this and the other results of the analysis made by Hubbert. 
  

IX.  WHAT DO WE DO NOW? 

The problems are such that we have rather few options.  All of the following points are vital: 

(i)  We must educate all of our people to an understanding of the arithmetic and consequences of growth, especially in terms of the earth's finite resources.  David Brower has observed that, "The promotion of growth is simply a sophisticated way to steal from our children." 

(ii)  We must educate people to the critical urgency of abandoning our religious belief in the disastrous dogma that "growth is good," that "bigger is better," that "we must grow or we will stagnate," etc., etc.  We must realize that growth is but an adolescent phase of life which stops when physical maturity is reached.  If growth continues in the period of maturity it is called obesity or cancer.  Prescribing growth as the cure for the energy crisis^{28, 29} has all the logic of prescribing increasing quantities of food as a remedy for obesity.  The recent occasion of our nation's 200th anniversary would be an appropriate time to make the transition from national adolescence to national maturity. 

(iii)  We must conserve in the use and consumption of everything.  We must outlaw planned obsolescence.  We must recognize that, as important as it is to conserve, the arithmetic shows clearly that large savings from conservation will be wiped out in short times by even modest rates of growth.  For example, in one or two dozen years a massive federal program might result in one-half of the heat for the buildings where we live and work being supplied by solar energy instead of by fossil fuels.  This would save 10 %  of our national use of fossil fuels, but this enormous saving could be completely wiped out by two years of  5 %  growth.  Conservation alone cannot do the job!  The most effective way to conserve is to stop the growth in consumption. 

As we consider the absolute urgency of conservation we must recognize that some powerful people are hostile to the concept of conservation.  One of our great multinational oil companies has advertised that conservation is: "Good for you–but not if there's too much."  And in the same ad they noted that: "Conservation does no harm."³⁵ 

In his message to the American people President Carter proposed a tax on large "gas guzzling" cars.  General Motors Chairman Thomas Murphy had the following reaction to this proposal to conserve energy: Murphy calls the excise tax on big cars, coupled with rebates on small cars "one of the most simplistic irresponsible and short-sighted ideas ever conceived by the hip-shooting marketeers of the Potomac."³⁶ 

Big labor is hostile to this same conservation measure.  Leonard Woodcock, President of the United Auto Workers said of the tax: "I respectfully suggest that the proposal is wrong. 
It is not properly thought through and should be withdrawn."³⁷ 

Congress is not enthusiastic about conservation: "Look for Senate leaders on both sides of the aisle–including Chairman Russell Long of the Finance Committee and Minority Leader Howard Baker–to gang up on Carter's energy package.  The two influential lawmakers want more stress on the production of oil, not so much on conservation."³⁸ 

Closer to home we can note that our governors don't show much enthusiasm for conservation: "The nation's governors told President Carter that the federal government is placing too much emphasis on conservation and not enough on developing new resources."³⁹ 

With all this influential opposition one can see how difficult it will be to launch major national programs of energy conservation. 

(iv) We must recycle almost everything.  Except for the continuous input of sunlight the human race must finish the trip with the supplies that were aboard when the "spaceship earth" was launched. 

(v) We must invest great sums in research (a) to develop the use of solar, geothermal, wind, tidal, biomass, and alternative energy sources; (b) to reduce the problems of nuclear fission power plants; (c) to explore the possibility that we may be able to harness nuclear fusion.  These investments must not be made with the idea that if these research programs are successful the new energy sources could sustain growth for a few more doubling times.  The investments must be made with the goal that the new energy sources could take over the energy load in a mature and stable society in which fossil fuels are used on a declining exponential curve as chemical raw materials and are not used as fuel for combustion.  One great area of responsibility of our community of scientists and engineers is vigorous pursuit of research and development in all these areas.  These areas offer great opportunity to creative young people.  

Perhaps the most critical things that we must do is to decentralize, and consequently humanize, the scale and scope of our national industrial and utility enterprises.⁴⁰ 

(iv) We must recognize that it is exceedingly unscientific to promote ever-increasing rates of consumption of our fuel resources based on complete confidence that science, technology, and the economics of the marketplace will combine to produce vast new energy resources as they are needed.  Note the certainty that characterizes this confidence.  

Coal could help fight a rear-guard action to provide time for scientific breakthroughs which will move the world from the fossil fuel era of wood, gas, oil, and coal to the perpetual energy era of infinitely renewable energy resources.⁴¹  The supply (of coal) is adequate to carry the U.S. well past the transition from the end of the oil and gas era to new, possibly not discovered sources of energy in the 2000s.⁴² 

There seems to be an almost complete absence of the caution that would counsel us to stop the growth of our national energy appetite until these "unlimited energy resources" are proven to be capable of carrying the national energy load.  We must recognize that it is not acceptable to base our national future on the motto "When in doubt, gamble." 

Fusion is most commonly mentioned as being an unlimited energy source.  The optimism that leads some people to believe that fusion power will be ready whenever it is needed should be balanced against this opening statement in a report on fusion from MIT.  "Designing a fusion reactor in 1977 is a little like planning to reach heaven: theories abound on how to do it, and many people are trying, but no one alive has ever succeeded."⁴³  

If the generation of electric power from fusion was achieved today, we could ask how long would it then be before fusion could play a significant role in our national energy picture.  The time-constant for the replacement of one major energy source by another can be estimated from the fact that the first nuclear fission reactor was operated in December 1942.  Even though the recent growth of nuclear energy in the U.S. has been spectacular, it was not until around 1972 that annual energy consumption equaled our annual energy consumption from firewood!  By 1973 nuclear energy had climbed to the point where it supplied  1.3 %  of our U.S. total annual energy consumption and  4.6 %  of our electrical power.⁴⁴ Thus in 31 years nuclear energy has grown to provide only a small fraction of our energy needs.  Had there been no growth of our national electrical needs since 1942, today's nuclear plants would be supplying  41 %  of our national electrical power. 

(vii) We can no longer sit back and deplore the lack of "leadership" and the lack of response of our political system.  In the immortal words of Pogo "We have met the enemy, and they's us."  We are the leaders, we are vital parts of the political system and we have an enormous responsibility.  

The arithmetic makes clear what will happen if we hope that we can continue to increase our rate of consumption of fossil fuels.  Some experts suggest that the system will take care of itself and that growth will stop naturally, even though they know that cancer, if left to run its natural course, always stops when the host is consumed.  My seven suggestions are offered in the spirit of preventive medicine. 
  

X. CONCLUSION 

The preceding calculations are offered as guideposts which must be understood by those who would deal constructively with the energy crisis.  The role and limitations of science in analyzing and in solving our problems was beautifully expressed by Gustav Lebon (1841-1931). 

"Science has promised us truth; an understanding of such relationships as our minds can grasp.  It has never promised us either peace or happiness."

Perhaps the most succinct conclusion that is indicated by the analysis above is taken from the immortal words of Pogo, "The future ain't what it used to be!"  The American system of free enterprise has flourished for 200 years with spectacular achievements.  Until recently it flourished in a world whose energy resources were essentially infinite.  Whenever one fossil fuel came into short supply, another could always be found to take its place.  We are now close enough that we can see the end of the world's total supply of fossil fuels.  The challenge that we must meet is set forth clearly in the question, "Can free enterprise survive in a finite world?"  President Carter observed (April 18, 1977) that: "If we fail to act soon we will face an economic, social, and political crisis that will threaten our free institutions." (See Fig. 6) 

  
XI.  A POSTSCRIPT FOR SCIENCE TEACHERS 

For decades physics teachers throughout the world have discussed the  RC  circuit and the decay of radioactive atoms and have thus introduced the simple differential equation that gives rise to exponential decay of the charge on the capacitor or of the number of remaining radioactive nuclei.  These provide a wonderful opportunity for us to digress and to point out that exponential arithmetic has great value outside of these two special examples in physics and to show our students that exponential arithmetic is probably the most important mathematics they will ever see.  It is especially important for students to see how the change in the sign of the exponent can make an enormous difference in the behavior of the function.  But we will need to do more.  We must integrate the study of energy and of the exponential arithmetic into our courses as has been done, for example, in one new text.⁴⁴   In addition, we have an even larger task.  As science teachers we have the great responsibility of participating constructively in the debates on growth and energy.  We must be prepared to recognize opinions such as the following, which was expressed in a letter to me that was written by an ardent advocate of "controlled growth" in our local community: "I take no exception to your arguments regarding exponential growth. I don't think the exponential argument is valid on the local level." 
  
  

    
We must bring to these debates the realism of arithmetic and the new concept of precision in the use of language.  We must convey to our students the urgency of analyzing all that they read for realism and precision.  We must convey to our students the importance of making this analysis even though they are reading the works of an eminent national figure who is writing in one of the world's most widely circulated magazines.  (The emphasis in the following quotations is in the original. 
 

The simple truth is that America has an abundance of energy resources... An estimated 920 trillion cubic feet of natural gas still lies beneath the United States.  Even at present consumption rates, this should last at least 45 years... About 160 billion barrels of oil still lie below native ground or offshore.  That's enough to last us into the next century at present rates of consumption.⁴⁵

When students analyze these statements they can see that the first statement is false if "abundance" means "sufficient to continue currently accepted patterns of growth of rates consumption for as long as one or two human lifetimes."  An evaluation of the second and third statements show that they are falsely reassuring because they suggest the length of time our resources will last under the special condition of no growth of the rates of use of these resources.  The condition of no growth in these rates is absolutely contrary to the precepts of our national worship of growth.  It is completely misleading to introduce the results of "no growth:" unless one is advocating "no growth." 

If it is true that our natural gas reserves will last 45 yrs. at present rates of consumption ( R / r₀  =  45 yrs.), then Eq. (6) shows that this amount of gas would last only 23.6 yrs. at an annual growth rate of  5 % / yrs., and only 17 yrs. at an annual growth rate of  10 % / yrs..  When the third statement is analyzed one sees that the given figure of 160 x 10⁹  barrels of reserves is roughly 60 % larger than Hubbert's estimate.  This amount would last 49 yrs. if oil was produced at the 1970 rate of  3.3 x 10⁹  barrels / yrs., held constant with no growth.  However, our domestic consumption is now roughly twice the rate of domestic production, so this amount of oil would satisfy domestic needs for only about 25 yrs. if there was no growth in these domestic needs.  If   R / r₀  =  25 yrs., then Eq. (6) shows that this amount of oil would last only 16.2 yrs. if production grew 5 % / yrs. and only 12.5 yrs. if it grew  10 % / yrs.. 

We can conclude that the author is probably advocating growth in the rate at which we use fossil fuels from the following imprecise statement, "The fact is that we must produce more energy."  Therefore the author's statements about the life expectancy of resources at current rates of use are irrelevant.  When they are offered as reassurance of the lack of severity of our energy problem they are dangerously and irresponsibly misleading. 

Students should be able to evaluate the same author's statement about coal, "At least 220 billion tons of immediately recoverable coal–awaits mining in the United States."  This "could supply our energy needs for several centuries."  Students can see that the size of the coal reserves given by the author is significantly smaller than either of the two estimates given by Hubbert.  They can see that it is imprecise and meaningless to suggest how long a resource will last if one says nothing about the rate of growth of production.  In addition to encouraging our students to carry out their responsibility to analyze what they read, we must encourage them to recognize the callous (and probably careless) inhumanity of a prominent person who is perhaps in his fifties,⁴⁵  offering reassurance to younger readers to the effect, "don't worry, we have enough petroleum to last into the next century," The writer is saying that "There is no need for you to worry, for there is enough petroleum for the rest of my life."  Can we accept the urgings of those who advocate unending expansion and growth in the rates of consumption of our fossil fuel resources and who say "Why worry, we have enough to last into the next century." 

We must give our students an appreciation of the critical urgency of evaluating the vague, imprecise, and meaningless statements that characterize so much of the public debate on the energy problem.  The great benefits of the free press place on each individual the awesome responsibility of evaluating the things that he or she reads.  Students of science and engineering have special responsibilities in the energy debate because the problems are quantitative and therefore many of the questions can be evaluated by simple analysis. 

Students must be alert not only to the writings in the popular press but to the writings in college textbooks.  In the bookstore of a school of engineering I purchased a book that was listed for one of the courses, possibly in political science.  Here are a few interesting statements from the book:⁴⁶ 
 

Our population is not growing too rapidly, but much too slowly... To approach the problem ("the population scare") from the standpoint of numbers per se is to get the whole thing hopelessly backward... Our coal supply alone, for example, is sufficient to power our economy for anywhere for 300 to 900 years–depending on the uses to which it is put–while gas and oil and coal together are obviously good for many centuries... So whatever the long-term outlook for these energy sources, it is obvious (that) natural shortage cannot account for the present energy crunch.

Dr. Hubbert, speaking recently, noted that we do not have an energy crisis, we have an energy shortage.  He then observed that the energy shortage has produced a cultural crisis. (See Fig. 7.) 

We must emphasize to our students that they have a very special role in our society, a role that follows directly from their analytical abilities.  It is their responsibility (and ours) to become the great humanists. 

Note added in proof: 

Two incredible misrepresentations of the life expectancy of U.S. coal reserves have been called to my attention recently.  Time (April 17, 1978, p.74) said: 
 

Beneath the pit heads of Appalachia and the Ohio Valley, and under the sprawling strip mines of the West, lie coal seams rich enough to meet the country's power needs for centuries, no matter how much energy consumption may grow."  (emphasis added) 

In reply to my letter correcting this, Time justified their statement by saying that they were using the Citibank estimate of U.S. coal reserves which is larger than the estimate used by Hubbert. 

A beautiful booklet, "Energy and Economic Independence" (Energy Fuels Corporation of Denver, Denver, 1976) said: "As reported by Forbes magazine, the United States holds 437 billion tons of known (coal) reserves.  That is equivalent to 1.8 trillion barrels of oil in British Thermal units, or enough energy to keep 100 million large electric generating plants going for the next 800 years or so." (emphasis added)   This is an accurate quotation from Forbes, the respected business magazine (December 15, 1975, p.28).  Long division is all that is needed to show that 437 x 10⁹ tons of coal would supply our 1976 production of  0.665 x 10⁹ tons per year for only 657 years, and we probably have fewer than 500 large electric generating plants in the U.S. today.  This booklet concluded, "Your understanding of the facts about "energy and economic independence' issue is of great importance." 

A very thoughtful comment on fusion was made to me recently by a person who observed that it might prove to be the worst thing that ever happened to us if we succeed in using nuclear fusion to generate electrical energy because this success would lead us to conclude that we could continue the unrestrained growth in our annual energy consumption to the point (in a relatively few doubling times) where our energy production from the unlimited fusion resource was an appreciable fraction of the solar power input to the earth.  This could have catastrophic consequences. 

Richard Stout, columnist for the New Republic, noted (Time, March 27, 1978, p.83) that in America, "We consume one third of all the energy, one third of the food and enjoy one half of the world's income.  Can a disparity like this last?  I think that much of the news in the next 50 years is going to turn on whether we yield to the inevitable graciously or vindictively."