"We used 10 times as much energy in the 20th century as in the 1,000 previous years"

Mark Jones jones118 at SPAMlineone.net
Mon Jun 26 01:58:22 MDT 2000

Anyone who has any doubts at all about the utter unsustainability of modern
world capitalism and the onset of terminal crisis, should read Albert
Bartlett's original article on the meaning of exponential growth, archived


Below is Bartlett's comments on the 209th anniversary of this classic
prediction of the end of Big Oil.

Mark Jones

"Forgotten Fundamentals of the Energy Crisis"
by Albert A. Bartlett
University of Colorado at Boulder

Around 1969, college and university students developed a major interest in
the environment and, stimulated by this, I began to realize that neither I
nor the students had a good understanding of the implications of steady
growth, and in particular, of the enormous numbers that could be produced by
steady growth in modest periods of time.  On September 19, 1969 I spoke to
the students of the pre-medical honor society on "The Arithmetic of
Population Growth."  Fortunately I kept my notes for the talk, because I was
invited to speak to other groups, and I gave the same talk, appropriately
revised and enlarged.   By the end of 1975 I had given the talk 30 times
using different titles, and I was becoming more interested in the
exponential arithmetic of steady growth.  I started writing short numbered
pieces, "The Exponential Function," which were published in The Physics
Teacher.  Then the first energy crisis gave a new sense of urgency to the
need to help people to gain a better understanding of the arithmetic of
steady growth, and in particular of the shortening of the life expectancy of
a non-renewable resource if one had steady growth in the rate of consumption
of such a resource until the last of the resource was used.

When I first calculated the Exponential Expiration Time (EET) of U.S. coal
for a particular rate of growth of consumption, using Eq. 6,  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

This led to the first version of this paper which was presented at an energy
conference at the University of Missouri at Rolla in October 1976, where it
appears in the Proceedings of the Conference.  In reading other papers in
the Procedings I came to realize that prominent people in the energy
business would sometimes make statements that struck me as being unrealistic
and even outrageous.  Many of these statements were quoted in the version of
the paper that is reprinted here, and this alerted me to the need to watch
the public press for more such statements.  Fortunately ( or unfortunately )
the press and prominent people have provided a steady stream of statements
that are illuminating because they reflect an inability to do arithmetic and
/ or to understand the energy situation.

As this is written, I have given my talk on "Arithmetic, Population, and
Energy" over 1260 times in 48 of the 50 States in the 28 years since 1969.
I wish to acknowledge many constructive and helpful conversations on these
topics I have had throughout the 20 years with my colleagues in the
Department of Physics, and in particular with Professors Robert Ristinen and
Jack Kraushaar, who have written a successful textbook on energy.  (Energy
and Problems of a Technical Society,  John Wiley & Sons, New York City, 2nd
Ed. 1993)

Reflections on the "Fundamentals" Paper Twenty Years Later

As I read the 1978 paper in 1998, I am pleased to note that the arithmetic
that is the core of the paper remains unchanged, and I feel that there are
only a few points that need correction or updating.
1)  When I derived my Eq. 6 in the Appendix, I was unaware that this
equation for the Exponential Expiration Time (EET) had been published
earlier by R. T. Robiscoe (his Eq. 4) in an article, "The Effect of Growth
Rate on Conservation of a Resource."  American Journal of Physics, Vol. 41,
May 1973, p. 719-720.  I apologize for not having been aware of this earlier
derivation and presentation of this equation.

2)  III.  The world population was reported in 1975 to be  4  billion people
growing at approximately 1.9 %  per year.  In 1998 it is now a little under
6  billion people and the growth rate is reported to be around  1.5 %  per
year.  The decline in the rate of growth is certainly good news, but the
population growth won't stop until the growth rate has dropped to zero.

3) VI.  In 1978 I reported that "We are currently importing one-half of the
petroleum we use."  The data now indicate that, except for brief periods,
this could not have been true in 1978.  The basis for my statement was a
newspaper clipping that said that the U.S. had experienced, in 1976,  the
first month in its history in which more oil was imported than was produced
domestically.  However, the imported fraction of the oil consumed in the
U.S. has risen, and in early 1995 the news said that the calendar year 1994
was the first year in our nation's history when we had to import more oil
than we were able to get from our ground ourselves. (Colorado Daily,
February 24, 1995)

4) IX.  The paper reported that by 1973 nuclear reactors (fission) supplied
approximately  4.6 %  of our national electrical power.  By 1998 this had
climbed to approximately 20 %  of our electrical power, but no new nuclear
power plants have been installed in the U.S. since the 1970s.

5)  A table that I wish I had included in the original paper is one that
would give answers to questions such as, "If a non-renewable resource would
last, say 50 years at present rates of consumption, how long would it last
if consumption were to grow say 4 % per year?"  This involves using the
formula for the EET in which the quotient  ( R / r0 )  is the number of
years the quantity  R  of the resource would last at the present rate of
consumption,  r0 .  The results of this simple calculation are shown in
Table I.

Lifetimes of non-renewable resources for different rates of growth of
consumption. Except for the left column, all numbers are lifetimes in years.

0 %    10   30  100  300  1000   3000   10,000

1 %    9.5  26   69  139   240    343      462

2 %    9.1  24   55   97   152    206      265

3 %    8.7  21   46   77   115    150      190

4 %    8.4  20   40   64    93    120      150

5 %    8.1  18   36   56    79    100      124

6 %    7.8  17   32   49    69     87      107

7 %    7.6  16   30   44    61     77       94

8 %    7.3  15   28   40    55     69       84

9 %    7.1  15   26   37    50     62       76

10 %   6.9  14   24   34    46     57       69

Example 1.  If a resource would last  300 years at present rates of
consumption, then it would last 49 years if the rate of consumption grew  6
% per year.
Example 2.  If a resource would last  18  years at  5 %  annual growth in
the rate of consumption, then it would last  30 years at present rates of
consumption. (0 % growth)

Example 3.  If a resource would last  55 years at  8 %  annual growth in the
rate of consumption, then it would last  115 years at 3 % annual growth

6)  In the end of Section VIII of the 1978 paper I quoted Hubbert as writing
in 1956 that "the peak of production of petroleum"  in the U.S. would be
reached between 1966 and 1971.  The peak occurred in 1970.  Hubbert
predicted that "On a world scale [oil production] will probably pass its
climax within the order of half a century...[2006]"  My more recent analysis
suggests the year 2004, while Campbell and Laherrere predict that the world
peak will be reached before 2010, (Scientific American, March 1998, pp.
78-83)  Studies by other geologists predict the peak within the first decade
of the next century.  Hubbert's analysis appears thus far to be remarkably

7)  The "Fundamentals" paper was followed by a paper titled, "Sustained
Availability: A Management Program for Non-Renewable Resources."  American
Journal of Physics, Vol. 54, May 1986, pp. 398-402.  This paper makes use of
the fact that the integral from zero to infinity of a declining exponential
curve is finite.  Thus, if one puts production of a non-renewable resource
on a declining exponential curve, one can always find a rate of decline such
that the resource will last forever.  This is called "Sustained
Availability," which is somewhat analogous to "sustained yield" in
agriculture.  This paper explores the mathematics of the options that this
plan of action can give to a resource-rich nation that wants to divide its
production of a resource between domestic use and exports.

8)  Many economists reject this sort of analysis which is based on the
assumption that resources are finite.  A colleague in economics read the
paper and later told me that "It is all wrong."  When I asked him to point
out the specific errors in the paper, he shook his head, saying, "It is all

9)  The original paper dealt more with resources than with population.  I
feel that it is now clear that population growth is the world's most serious
problem, and that the world's most serious population problem is right here
in the U.S. The reason for this is that the average American has something
like 30 to 50 times the impact on world resources as does a person in an
underdeveloped country.   (A.A. Bartlett, Wild Earth, Vol. 7, Fall 1997, pp.

We have the jurisdiction and the responsibility needed to permit us to
address our U.S. population problem, yet many prefer to focus their
attention on the population problems in other countries. Before we can tell
people in other countries that they must stop their population growth, we
must accept the responsibility for working to stop population growth in the
United States, where about half of our population growth is the excess of
births over deaths and the other half is immigration, legal plus illegal.
This leads me to offer the following challenge:

Can you think of any problem, on any scale, From microscopic to global,
whose long-term solution is in any demonstrable way, Aided, assisted, or
advanced by having larger populations At the local level, the state level,
the national level, or globally?
Horror Stories
Here are more recent horror stories to add to those that were recounted in
the original paper.

1)  The Rocky Mountain News of October 6, 1993 reported that: Shell Oil Co.
said "... it planned to spend $1.2 billion to develop the largest oil
discovery in the Gulf of Mexico in the past  20  years.  The discovery ...
has an estimated ultimate recovery in excess of 700 million barrels of oil
and gas."  The  700 million barrels of oil sounds like a lot -- until you
note that at that time the U.S. consumption was  16.6  million barrels /
day, so that this "largest oil discovery in the Gulf of Mexico in the past
20  years" would supply the needs of the U.S. for only  42  days!

2)  The headline in the Wall Street Journal for July 18, 1986 proclaimed
that "U.S. Oil Output Tumbled in First Half as Alaska's Production Fell
Nearly 8%."   In the body of the story we read that the chief economist for
Chevron Corporation observes that, "The question we can't answer yet is
whether this is a new trend or a quirk."   The answer to his question is
that it is neither; it is an old trend!  It is exactly what one expects as
one goes down the right side of the Hubbert Curve.

3)  Another headline on the front page of the Wall Street Journal (April 1,
1997) said: "Four Decades Later, Oil Field Off Canada is Ready to Produce.
Politics, Money and Nature Put Vast Deposit on Ice; Now It Will Last  50
Years:  Shot in the Arm for U.S."  In the body of the story we read that:

The Hibernia field, one of the largest oil discoveries in North American in
decades, should deliver its first oil by year end.  At least  20  more
fields may follow, offering well over one billion barrels of high-quality
crude and promising that a steady flow of oil will be just a quick
tanker-run away from the energy-thirsty East Coast.
Total U.S. oil consumption in  1996  was about 18 million barrels a day.  Do
the long division and one sees that the estimated "one billion barrels of
high-quality crude" will supply the needs of the U.S. for just 56 days!
This should be compared with the "50 Years" in the headline.
4)  In the Prime Time Monthly Magazine (San Francisco, September 1995) we
find an article, "Horses Need Corn" by the famous radio news broadcaster
Paul Harvey.  He emphasizes the opportunity we have to make ethanol from
corn grown in the U.S. and then to use the ethanol as a fuel for our cars
and trucks: "Today, ethanol production displaces over 43.5 million barrels
of imported oil annually, reducing the U.S. trade balance by $645 million. .
.  For as far ahead as we can see, the only inexhaustible feed for our high
horsepower vehicles is corn."

There are two problems with this:

A)  The 43.5 million barrels must be compared with the annual consumption of
motor gasoline in the U.S.  In 1994 we consumed 4.17 billion barrels of
motor vehicle gasoline. (Annual Energy Review, 1994, DOE / EIA 0384(94), p.
159)   The ethanol production is seen to be approximately  1 %  of the
annual consumption of gasoline by vehicles in the U.S.  So one would have to
multiply corn production by a factor of about  100  just to make the numbers
match.  An increase of this magnitude in the farm acreage devoted to the
production of corn for ethanol would have profound negative dietary

B)  It takes energy (generally diesel fuel) to plow the ground, to fertilize
the ground, to plant the corn, to take care of the corn, to harvest the
corn, and then more energy is needed to distill the corn to get ethanol.  So
it turns out that in the conventional production of ethanol, the finished
gallon of ethanol contains less energy than was used to produce it !  It's
an energy loser!  The net energy of this "energy source" is negative!

5)   The Clinton administration, in a "Draft Comprehensive National Energy
Strategy" (February 1998)  talks about America's oil as being "abundant,"
(pg. 4) and it advocates  "promoting increased domestic oil ... production"
(pg. 2) to reverse this downward trend in U.S. oil production.  The peak of
the Hubbert Curve of oil production in the U.S. was reached in 1970 and we
are now well down the right side of the Curve.  The Draft Strategy calls for
"stabilization of domestic oil production" (pg. 12) which is explained in
"Strategy 1" (pg. 12) "By 2005, first stop and then reverse the decline in
domestic oil production."   The Hubbert Curve rises and falls in a manner
like that of a Gaussian Error Curve, and once one is over the peak, one can
put bumps on the downhill side, but except for such "noise," the trend
after the peak is always downhill.  A large national effort might reverse
the decline in U.S. oil production for a year or two, but it hardly
plausible to propose to "stabilize" domestic oil production for any extended
period of time.  It almost seems as though the U.S. Department of Energy has
not studied the works of Hubbert, Campbell & Laherrere, Ivanhoe, Edwards,
Masters and other prominent petroleum geologists.

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