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The sustainability papers of Al Bartlett

Letter to Culture Change
July 20, 2003 - Dear Friends, 
    Thanks for your letter calling attention to the new website on population.  I thought the website was excellent.  Focusing on population is the correct thing to do, but it is politically incorrect.  Of course you know this already.
    I am attaching some papers of mine dealing with these problems.  In the paper on sustainability you will find the Laws of Sustainability.  The First Law of Sustainability is: population growth and / or growth in the rates of consumption of resources is not sustainable.
    Many thanks for focusing on the heart of the problem.
Every increment of added population, and
     every added increment of affluence
     invariably destroys an increment
     of the remaining environment.
Population growth and increases in affluence
     make it impossible for reasonable increments
     of improved efficiency in the use of resources
     to enhance or even preserve the environment.
You cannot preserve the environment
     by accepting the population growth
     and the increased affluence
     that are destroying the environment.

Sincerely, AL
Professor Emeritus of Physics
            University of Colorado at Boulder
            Boulder, Colorado, 80309-0390


Two papers follow; more will be added.  Check back with us; bookmark this page! - ed.


This is a slightly revised version of an article that was published in the September 1996 issue of The Physics Teacher, Vol. 34, No. 6, Pgs. 342-343.  This journal is published by the American Association of Physics Teachers, College Park, MD.  


       There was a time, long ago, when people thought that the Earth was flat, but now for several centuries people have believed that the Earth is round . . . like a sphere.  But there are problems with a spherical earth, and a now a new paradigm is emerging which seems to be a return to the wisdom of the ancients. 

       A sphere is bounded and hence is finite, which implies that there are limits, and in particular, there are limits to growth of things that consume the Earth and that live on it.  Today, many people believe that the resources of the Earth and of the human intellect are so enormous that population growth can continue and that there is no danger that we will ever run out of anything.  For instance, after a United Nations report predicted shortages of natural resources that would follow because of continued population growth, Jack Kemp, who was then Secretary of Housing and Urban Development in the Cabinet of President George Bush,  is reported to have said, "Nonsense, people are not a drain on the resources of the planet."  (2)  

        These people believe that perpetual growth is desirable, consequently it must be possible, and so it can't possibly be a problem.  At the same time there are still a few remaining  "spherical earth"  people who go around talking about "limits" and in particular about the limits that are implied by the term "carrying capacity."  But limits are awkward, because limits conflict with the concept of perpetual growth, so there is a growing move to do away with the concept of limits.  A friend recently returned from an international conference in Germany and he reports that whenever he brought up the subject of limits, the angry rebuttal was, "We're tired of hearing of limits to growth!   We're going to grow the limits!"  Another friend sent me a clipping (3) in which an eminent national economist closes an opinion piece by saying:

  "A 3% to 3.5% growth rate is not only an achievable national objective: it is an economic and social necessity."

      A spherical earth is finite.  The pro-growth people say that perpetual growth on this earth is possible.  If the pro-growth people are correct,  what kind of an earth are we living on?


      A spherical earth is finite and hence is forever unappealing to the devotees of perpetual growth.  In contrast, a flat earth can accommodate growth forever, because a flat earth can be infinite in the two horizontal dimensions and also in the vertical downward direction.  The infinite horizontal dimensions forever remove any fear of crowding as population grows, and the infinite downward dimension assures humans of an unlimited supply of all of the mineral raw materials that will be needed by a human population that continues to grow forever.  The flat earth removes all the need for worry about limits. 

        So, let us think of the "We're going to grow the limits!" people as the  "New Flat Earth Society."


        The economist, the late Julian Simon is famous for his belief that there are no limits to growth. (4)  In a recent article  he wrote (5)

        "Technology exists now to produce in virtually inexhaustible quantities just about all the products made by nature - foodstuffs, oil, even pearls and diamonds . . .  
        We have in our hands now - actually in our libraries - the technology to feed, clothe and supply energy to an ever-growing population for the next 7 billion years . . .  
        Even if no new knowledge were ever gained . . . we would be able to go on increasing our population forever . . . "(6)

        Two friends wrote me to call my attention to this article, and one of them said in his letter that Simon had been contacted and that Simon said that the "7 billion years" was an error and it should have been "7 million years." (7)

        We should note two things.  First, there is a big difference between "million" and "billion."  In the U.S. a "billion" is a thousand million.   Second, even 7 million years is a long period of time.

      One of these friends asked me: if the world population in 1995 is  5.7 billion people  (5.7 x 109), what would its size be (P7) if it grew steadily at  1%  per year for 7 million years ? (8) 

        Although arithmetic is falling out of fashion, let's do some calculations so that we can understand how the old fashioned "spherical earth" scientists would treat the problem. 
       We will do this calculation assuming the length of time is  exactly  7 million years and the growth rate is  exactly  1%  per year.  For the case of an annual growth rate of  1% ,  the value of  k  is 0.010 . . . per year.   It is easy enough to set up the equation for  P7 , which is the world population after 7 million years of  1%  annual growth:

  1)          P7 = (5.7 x 109) exp(0.01 x 7 x l06)                       = (5.7 x l09) exp(7 x 104)

  Here is where we separate out those who understand algebra from those who only know how to do key strokes on a calculator.  When you do the keystrokes to evaluate      exp(7 x 104)     many calculators will flash the message "ERROR" because these calculators are not able to handle numbers larger than 9.99... x 1099. (9)  One must have some understanding of algebra to work around this limitation.   
What we want to find is the value of  B  in Eq.2.

2)                exp(7 x 104) = 10B

  If we take the natural logarithm of both sides we have   7 x 104 = B ln(10) 
B = 7 x 104 / 2.303 . . .

3)          B = 30400.6137 . . .

  (Remember that we assumed the input numbers were exact.)  Equation 1 now becomes

              P7 = 5.7 x 109 x 1030400.6137 . . .

  4)             = 5.7 x 1030409.6137 . . .

  If one wants to express this as an integer power of ten, we can note that  100.6137 = 4.11, so that

              P7 = 5.7 x 4.11 x 1030409

  5)          P7 = 2.3 x 1030410

      This is a fairly large number!

        If we had used Simon's original number of  7  billion years, we would have had  B = 3.04 x 107.

        It is hard to imagine the meaning of a number as large as the one given in Eq.5.  To try to understand the meaning of this large number, let us compare it with an estimate the number of atoms in the known universe.  If we assume the known universe is a sphere whose radius is  20  billion light years, the volume of the sphere is about 3 x 1085 cubic centimeters.  If the average density of the universe is one atom per cubic centimeter, then the number of atoms estimated to be in the known universe is about 3 x 1085.  The number given in Eq.5 is something like 30 kilo-orders of magnitude larger than the number of atoms estimated to be in the known universe!

        Note that in making this calculation we are assuming that the universe, like the Earth, is spherical, which could hardly be correct if the Earth is flat and is of infinite lateral extent.  

      A related question comes to mind: if world population growth continues at a rate of  1%  per year,  (k = 0.01 per year)  how long would it take for the population to grow until the number of people was equal to this estimate of the number of atoms in the known universe?   This calls for us to find  t  in the following equation.

  6)          3 x 1085 = 5.7 x 109 exp(0.01 t)

              5.26 x 1075 = exp(0.01 t)

              174 = .01 t

              t = 17 thousand years

  This indicates that the population of the Earth, growing at  1%  per year, would grow to a number equal to the number of atoms estimated to be in the known universe, in a period of time something like the period since a recent ice age. 

      We could also ask, what growth rate would be required for the world population to grow from  5.7 x 109  to  3 x 1085  in  7  million years?  We must find the value of  k  in this equation

  7)          3 x 1085 = 5.7 x 109 exp(7 x 106 k)

  Solving this, we find  k = 2.5 x 10-5  per year.  This is  2.5 x 10-3  percent per year.  In the first year this growth rate would produce an increase of world population of about 1.42 x 105 people.  Contrast this with the present increase of about 9 x 107 per year.  

      These numbers make it clear to us old fashioned "spherical earth people" that the world population cannot continue to grow for long at anything like its present rate.  There are signs that the population growth rate is already slowing in some parts of Europe and Asia.

        Calculations similar to these remind us that the major effect of steady growth in the rates of consumption of non-renewable resources is to shorten dramatically the life-expectancy of the resources. (10)

        Julian Simon has claimed that the human mind is "the ultimate resource."  As was noted in the review of his 1981 book, this is true "only if it [the human mind] is used." (11)


        If the "we can grow forever" people are right, then they will expect us, as scientists, to modify our science in ways that will permit perpetual growth.  We will be called on to abandon the "spherical earth" concept and figure out the science of the flat earth.  We can see some of the problems we will have to solve.  We will be called on to explain the balance of forces that make it possible for astronauts to circle endlessly in orbit above a flat earth,  and to explain why astronauts appear to be weightless.  We will have to figure out why we have time zones;  where do the sun, moon and stars go when they set in the west of an infinite flat earth, and during the night, how do they get back to their starting point in the east.  We will have to figure out the nature of the gravitational lensing that makes an infinite flat earth appear from space to be a small circular flat disk.  These and a host of other problems will face us as the "infinite earth" people gain more and more acceptance, power and authority.  We need to identify these people as members of  "The New Flat Earth Society" because a flat earth is the only earth that has the potential to allow the human population to grow forever.


(1)       Earlier pieces in the series, "The Exponential Function," were published in The Physics Teacher as follows:

      I.        Vol.14, October 1976, Pgs. 393-401       II.       Vol.14, November 1976, Pg. 485            III.      Vol.15, January 1977, Pgs. 37-40             IV.      Vol.15, March 1977, Pg. 98 
V.      Vol.15, April 1977, Pgs. 225-226            VI.        Vol.16, January 1978, Pgs. 23-24           VII.      Vol.16, February 1978, Pgs. 92-93          VIII.      Vol.16, March 1978, Pgs. 158-159            IX.      Vol.17, January 1979, Pgs. 23-24             X.      Vol.28, November 1990, Pgs. 540-541

(2)   High Country News, (Paonia, Colorado), January 27, 1992, P. 4

  (3)  Felix G. Rohatyn, TIME, May 20, 1996, P. 46

  (4)   J.L. Simon, The Ultimate Resource, Princeton University Press, Princeton, NJ, 1981

  (5)   Cato Policy Report, "The State of Humanity: Steadily Improving", Vol. 17, No. 5, September / October 1995, P. 131, Cato Institute, Washington, D.C. 

  (6)   The Cato Institute report identifies the author:  "Julian L. Simon is a professor of business and management at the University of Maryland and an adjunct scholar at the Cato Institute.  This essay [from which these quotations are   taken] is based on the introduction to his latest book, The State of Humanity, just published by the Cato Institute and Blackwell Publishers."  
        The Cato Institute is a think tank in Washington, D.C. that advises government leaders on policy questions.  
At the annual meeting in February of 1995, Julian Simon was elected a  Fellow of the American Association for the Advancement of Science. 

  (7)   I am indebted to Mark Nowak of Population-Environment Balance, in Washington, D.C. and Dr. John Tanton, Petosky, MI, for calling this article to my attention.

  (8)   The growth rate of world population in the early 1990s was around 1.7%  per  year.

  (9)   In doing these calculations, I was surprised to find that my new Hewlett-      Packard Model 20S hand-held calculator will handle powers of ten up to  500.

  (10) A.A. Bartlett, American Journal of Physics,          Vol. 46, September 1978, Pgs. 876-888.

  (11) A.A. Bartlett, American Journal of Physics,          Vol. 53, March 1985, Pgs. 282-285


September 9, 1998.  This is an article that was published in Wild Earth (A journal for creatures who care about their habitat. P.O. Box 455, Richmond, Vermont, 05477) Vol. 7, No. 3, Fall 1997, Pgs. 88-90.  It has been slightly revised.


by Albert A. Bartlett

        My answer to the question is "YES" there is a problem.  The scale of human activities is now so large that we are appreciably affecting the climate and ecosystems in the U.S. and the world.

        The total impact of people on the environment is proportional to each of two factors:

        A)  The number of people, and 
B)  The average impact of each person.

        If we are to reduce the total impact of people on the global environment, we must address the first, or preferably both, of these factors.

        There are many strong forces that will cause continued growth of the average impact of each person on the global environment.  To the extent that people in underdeveloped countries seek to increase their material standard of living to levels more like ours, material consumption per capita will grow.  So we are left with the imperative of halting population growth, and then of studying the question, "Can this stable population be sustained?" 

        To gain a better appreciation of the seriousness of the problem, let us review some very elementary arithmetic. Let us consider a quantity that is experiencing steady growth at a rate such as  5%  per year.  

        First we note that this growing quantity will double in size in a fixed time.  This doubling time is found by dividing  70  by the percent growth per year.  For example, the doubling time for a steady growth rate of  5%  per year is  70 / 5  =  14 years.

        Second, we note that a few doublings can give enormous numbers.  It is convenient to remember that ten doublings causes the growing quantity to increase in size by a factor of approximately 1000:  twenty doublings will cause an increase by a factor of 1,000,000, etc.

        Let us look at some current approximate, data (1997).  
United States   World Population       
270 million       5700 million

   Annual increase              
3 million            90 million

   Annual growth rate      
1 %   per year     1.6 %  per year

   Doubling Time             
70 years              44 years

  The smallness of the annual growth rates is both deceiving and disarming.  We might initially think that surely nothing bad could happen at growth rates as small as 1 % or 1.6 %  per year.  A study of the doubling times brings us back to reality.  If the world population continues to grow at its present rate, it will double before today's (1997) college students are my age (74)!  Think what this means in terms of food and resource consumption.  

      Population growth rates do not remain constant; they change in response to physical and social factors.  The world population growth rate was close to zero through most of human history, and it started to increase significantly a few centuries ago.  Around 1970 it reached a high of about  2 %  per year, from which it has recently declined to the estimated  1.6 %  per year.  Detailed social studies and more elegant mathematical models can give us insight into the mechanisms that affect these rates of growth.   

        Why, then, do we need to look at the simple models of constant growth rates?

        First, they are a useful, though approximate, representation of the facts.

        Second, we in the United States are in a culture that worships growth.  Steady growth of populations of our towns and cities is the goal toward which the powerful promotional groups in our communities continuously aspire.  If a town's population is growing, the town is said to be "healthy," or "vibrant," and if the population is not growing the town is said to be "stagnant."  Something that is not growing should properly be called "stable."  Yet, the promoters of growth universally use the word "stagnant" to describe the condition of stability, because "stagnant" suggests something unpleasant while "stable" would suggest something worthwhile, pleasant and desirable. 

        Since continued growth is the goal of the promoters in our communities, we should understand the arithmetic of steady growth.

        Now let's look at some global aspects of our population problem.

        1)  Global Warming. 
        There is a growing scientific consensus that the early phases of global warming may be upon us now.  With each passing year, our knowledge of the situation will increase so that we will know better if the earth is warming, and if so, how rapidly change may occur.  Whether or not the earth is warming, it is clear that by pouring increasing quantities of greenhouse gases into the earth's atmosphere each year,  we are embarked on a global experiment whose outcome we don't know.  We don't know if the effects of increasing the greenhouse gases in the earth's atmosphere are reversible.  We don't know if the atmosphere go back to its pre-industrial condition if we stopped all emissions of greenhouse gases, and if it would go back, we don't know how long it would take.   

      On the scale of a human lifetime, these changes happen very slowly.  So the burden of dealing with the unknown outcome of the present global experiment, will not fall on today's political decision makers: it will fall on our children and grandchildren.   Present population growth, so ardently advocated by the many in the older generations, is putting our children and grandchildren at risk.  For centuries, parents have worked so their children could have better lives and opportunities than they had.  We may now be doing just the reverse.  We may be guaranteeing that our children will not have the resources, opportunities and environment that we have enjoyed. 

        2)  The Ozone Hole 
       The destruction of ozone in the high atmosphere allows more ultra-violet light to reach the surface of the earth where it can have serious biological effects on plants and animals, including humans.

      3)  Food Grain 
The Worldwatch Institute reports that global annual per capita production of grain dropped from 346 kilograms per person in 1984 to 313 kilograms per person in 1996. ii  This is a drop of  9.5 %  in just 8 years.   

      We've all heard it said that per capita food production has been growing ever since the time of Thomas Malthus, and that this growth has proven him wrong.  Since the late 1980s grain production has leveled off, so the continuing growth of populations means that the per capita production of food is declining.  Perhaps Malthus was right after all.

        4)  World Oceanic Fisheries 
        Growth in the annual oceanic fish catch stopped in 1989, and since then the available fish per capita has been declining.  For many of the world's people, fish is a major source of protein.  Most of the world's major fishing areas are seriously depleted.  The Grand Banks off of Newfoundland was one of the world's major fisheries, with stocks of fish once thought to be unlimited.  Now, these fish stocks are apparently almost gone.   

      5)  Fresh Water 
A report in January of 1997 from Stockholm indicated that by the year 2025, two-thirds of the world's people will suffer from water shortages, and the report noted that the rate of use of fresh water was growing at twice the rate of world population.

        All of these problems are caused by population growth, and none of these problems can be "solved" if population growth continues.  

        Today we hear many people talking about "Sustainability," as though we can accommodate continued population growth with something vague and ill-defined that is called "sustainable development."  The thought seems to be that there is no need to worry about population:  all we need to do is to make minor modifications of our way of life, (conserve, recycle, etc.) and this will suffice to make our society "sustainable."  Please remember the First Law of Sustainability: iii  

            It is not possible to sustain population growth or growth in the rates of consumption of   resources.  We now must address two questions:

        1)  Where on Earth is the population problem the worst?  

      It is my opinion that  the world's worst population problem is right here in the United States.  This is because of our high per capita resource consumption.  It has been estimated that a person added to the population of the United States will have  30  or more times the impact on world resources as will a person added to the population of an underdeveloped nation.  Indeed, resource consumption in North America is roughly the same as resource consumption in the entire rest of the world.

        2)  Where should we apply our efforts to have the most beneficial effect in helping to solve the population problem?

        The answer is, right here in the U.S.

        For many people, the population problem is a problem of "those people," in distant undeveloped countries.  In early 1997, many people successfully lobbied Congress to restore family planning assistance in the U.S. foreign aid programs.  This was a great victory, but it treats "those people" as though they were the big problem.   As one member of Congress said,

        "Unchecked population growth in the Third World means depletion of water resources.  It means famine.  It means suffering.  It pushes populations to clear rainforests.  It pushes populations to go out and graze on land that cannot sustain cattle, and that leads to expansion of deserts worldwide.  We all have a stake in the global environment." iv

      It is so easy to blame the problem on others and to identify what other people should do to solve the problem, while we ignore our own responsibilities and avoid doing anything to reduce the population problem in the U.S.  We need to work to stop population growth in the U.S.

        There are two sources that contribute approximately equally to population growth in the U.S.: the excess of births over deaths, and immigration.  Both of these must be addressed.

        Let's compare three aspects of efforts to stop population growth in other countries with efforts to stop population growth in the United States.

        1)  When we give family planning assistance to other countries, we are dealing with countries over which we have no legal jurisdiction and where we have little or no immediate political responsibility.

        When we confront population growth in the United States, we are dealing with a country where we as citizens have full and complete jurisdiction, and where we have political and family responsibilities.  It should be much easier to solve our problem than it is to solve other peoples' problems.

        2)  The negative effects of runaway population growth in an underdeveloped country are generally felt only in that country and in its immediate neighbors.

        The negative effects of population growth in the U.S. are felt throughout the entire world, because of our enormous per capita consumption of resources.  Indeed, one of the aims of the many free-trade agreements about which we currently hear so much, is to open up the world's resources for consumption by consumers in the U.S.

        3)  In countries receiving family planning assistance from the U.S. there will always be individuals who will claim that this assistance is a form of "genocide."  They will be strengthened in this belief if we in the U.S. fail to take steps to halt our own population growth.  As Tim Wirth of the U.S. Department of State has said, the best thing that we in the U.S. can do to help other countries stop their population growth, is to set an example and stop our own population growth.

        As you think about addressing the problem of population growth in the U.S., please ponder this 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 continued population growth  
- At the local level, the state level, the national level, or globally?

      So we can see that Pogo was right:  "We've met the enemy, and they's us!"

     Ed. note:  This article is adapted from a talk Prof. Bartlett gave on a panel on population at the  49th annual World Affairs Conference at the University of Colorado, Boulder, April 9, 1997

      The other speaker on the panel was the distinguished Russian physicist Sergey Kapitza from Moscow.  Presiding was Dr. Judith Jacobsen of Boulder.

back to main Overpopulation webpage


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Renewable and alternative energy information.

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Culture Change/Sustainable Energy Institute mailing address: P.O. Box 3387 , Santa Cruz , California 95063 USA
  Telephone 1-215-243-3144 (and fax)

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