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Boletín CF+S > 37: Fe en el progreso > http://habitat.aq.upm.es/boletin/n37/aabar.en.html |

Boulder (Colorado), September 1996.

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 desireable,
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 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»
(**Rohatyn**, 1996).

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 accomodate 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 **Julian Simon** (1981) is famous for his belief
that there are no limits to growth. In a recent article he
wrote:

Technology exists now to produce in virtually inexhaustable 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...

Simon, 1995:131[3]

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».[4]

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 ×10^{9}), what would its size, namely
P_{7}, be if it grew steadily at 1% per year for 7
million years? [5]

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 P_{7}, which is the world population after 7
million years of 1% annual growth:

1) P_{7}= (5.7 ×10^{9}) ×exp(0.01×7 ×10^{6}) = (5.7 ×10^{9}) exp(7 ×10^{4})

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 ×10^{4}) many
calculators will flash the message

because these
calculators are not able to handle numbers larger than
9.99... ×10`ERROR`^{99}.[6] 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.

If we take the natural logarithm of both sides we have2) exp(7 ×10^{4}) = 10^{B}

7 ×10so we have:^{4}= B ln(10); B = 7 ×10^{4}/ 2.303...

(Remember that we assumed the input numbers were exact.) Equation 1 now becomes:3) B = 30400.6137...

If one wants to express this as an integer power of ten, we can note that 104) P_{7}= 5.7 ×10^{9}×10^{30400.6137...}= 5.7 ×10^{30409.6137...}

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 ×105) P_{7}= 5.7 ×4.11 ×10^{30409}= 2.3 ×10^{30410}

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 ×10^{85} 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 ×10^{85}. 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.

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.6) 3 ×10^{85}= 5.7 ×10^{9}exp(0.01 t)5.26 ×10^{75}= exp(0.01 t)174 = 0.01 t

t = 17.400 years

We could also ask, what growth rate would be required for the world
population to grow from 5.7 ×10^{9} to 3 ×10^{85} in 7
million years? We must find the value of k in this equation:

Solving this, we find k = 2.5 ×107) 3 ×10^{85}= 5.7 ×10^{9}exp(7 ×10^{6}k)

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.

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.»

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.

Bartlett, Albert Allen(1978-1996) «The Exponential Function»,The Physics Teacher, Serie de artículos; Maryland: American Association of Physics Teachers.

Bartlett, Albert Allen(1978) «Arithmetic, Population, and Energy»,American Journal of Physics, Vol. 46, septiembre de 1978, pp. 876-888. (Existe una version castellana (adaptada) de Gabriel TobarAritmética, Población y Energía. Los fundamentos olvidados de la crisis energética, http://www.jlbarba.com/energia/arpoen, 2006.)

Bartlett, Albert Allen(1985) «The Ultimate Resource»,American Journal of Physics, Vol. 53, marzo 1985, pp. 282-285

Bartlett, Albert Allen(1994) «Reflections on Sustainability, Population Growth, and the Environment»,Population &Environment, Vol 10, número 1, pp. 5-35. (Existe una versión castellana de Gabriel Tobar:Reflexiones sobre Sostenibilidad, Población y Medio Ambiente, http://jlbarba.com/energia/sostenibilidad.htm.)

Bartlett, Albert Allen(2006) «La parábola de las pizarras»,The Physics Teacher, Vol 44 pp. 588-589. (Hay una versión castellana de Gabriel Tobar, http://ninuclearniotras.blogspot.com/2007/05/la-parbola-de-las-pizarras.html.)

Rohatyn, Felix G.(1996) «Fear of inflation is stifling the Nation»,TIME, 20 de mayo de 1996, p. 46, http://www.time.com/time/magazine/article/0,9171,984560,00.html

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

Simon, J.L.(1995) «The State of Humanity: Steadily Improving»,Cato Policy Report, Vol. 17, número 5, septiembre/octubre

[1]: N. de E.: 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. 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.

[3]: 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.

[4]: 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.

[5]: The growth rate of world population in
the early 1990s is around 1.7% per year.

[6]: 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.

Edición del 30-9-2008

Revisión:

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Ciudades para un Futuro más Sostenible

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Escuela Técnica Superior de Arquitectura de Madrid — Universidad Politécnica de Madrid

Grupo de Investigación en Arquitectura, Urbanismo y Sostenibilidad

Departamento de Estructuras y Física de la Edificación — Departamento de Urbanística y Ordenación del Territorio