Energy Policy
Arithmetic, Population and Energy, Part 10
Revision A
For the love of the human
race.
Tuesday, December 09, 2014
The Source of the Question
This
study report is prompted by the labors of the late Dr. Albert Allen Bartlett
(1923-2013), who labored as a Professor of Physics at the University of
Colorado, Boulder. Even though he was
fully qualified as a subject matter expert in physics, it is evident that his
favorite topic was what might be termed the arithmetic of energy and
population, an intense application of the exponential curve. So we are indebted to Dr. Bartlett, and write
this in his honor, with a view to continuing his mission.
In
his lectures Dr. Bartlett introduced the subject of sustainability. It turns out that Dr. Bartlett is one of the
world’s leading authorities on sustainability.
http://www.resilience.org/stories/2009-11-06/dr-albert-bartletts-laws-sustainability
http://www.albartlett.org/articles/art_meaning_of_sustainability_2012mar20.pdf
http://en.wikipedia.org/wiki/The_Limits_to_Growth
http://www.resilience.org/stories/2009-11-06/dr-albert-bartletts-laws-sustainability
If we need to review the crises that prompt the discussion
of sustainability, here are the major sources we used.
http://www.albartlett.org/
http://www.albartlett.org/presentations/arithmetic_population_energy.html
http://en.wikipedia.org/wiki/Albert_Allen_Bartlett
http://www.youtube.com/watch?v=umFnrvcS6AQ
These were thoroughly reviewed in our corresponding reports
Arithmetic, Population and Energy, Parts 1 through 9, which are located at:
http://swantec.blogspot.com/
Sustainability, Part 1
http://www.albartlett.org/articles/art_meaning_of_sustainability_2012mar20.pdf
Sustained
Availability
Very early in his paper, The
Meaning of Sustainability, Dr. Bartlett introduces the concept of
Sustained Availability as a means of dealing with the energy crisis. He begins with the basic equation:
y(t) = y0 * e-kt
We have seen this equation before, or something very much
like it in Arithmetic, Population and Energy, Part 1, where Dr.
Bartlett introduced the basic exponential equation:
y(t) = a * bt = y0 * bt
In this case Dr. Bartlett is using the equation to examine estimates
of production, P. The
differences in the two equations are minor.
We observe, as we did before, that these families of curves cross the
ordinate axis, the y axis at a fixed point, a or y0,
which turns out to be, very conveniently the quantity of a thing when we
begin. Whereas b can be
any number we replace it with the mathematically convenient fixed constant e,
which is approximately 2.718, and turns out to be a very handy number
throughout engineering, mathematics, and physics. Placing a constant, k, before the
t, introduces concepts related to time constants. The minus sign indicates that we are in a
state of decay, rather than growth. In
general, the two equations are handled quite similarly. The idea,
b = 1 + r
is lost.
“The greatest shortcoming of the human race
is our inability to understand the Exponential [Equations].”[1]
Using logarithmic differentiation we arrive at the
following:
ln(y) = ln(y0 * e-kt) = ln(y0)
–kt * ln(e)
d/dt [ln(y)] = d/dt [ln(y0) –kt * ln(e)]
since y0 and e are
both constants, their derivatives are zero; also ln(e) is
conveniently 1; so we find this:
d/dt [ln(y)] = dy/y // dt = 0 –k * 1 = –k
k = –dy/y // dt = –dy/dt * 1/y
Dr. Bartlett uses the notation P instead of y
in these equations. We found it
convenient to draw a comparison with the previous talks. Otherwise, the equations are the same. As Dr. Bartlett points out dy
or dP turns out to be negative.
This is the same curve found in nuclear chemistry, engineering, and
physics for radioactive decay. It is
also used in electricity and electronics to describe the buildup or decay found
in capacitor voltage and inductor current changes.
As before, the area under the curve represents the total
quantity of a resource that will ever remain: the sum of all actual reserves
and all the undiscovered quantities that will ever be found. However, since the undiscovered quantities
are as yet undiscovered, we will apply these equations as though they will
never be discovered. This will give us
some hope that we can conserve whatever we presently have until we actually
find the undiscovered quantities, or until help arises from another
source. In other words, this arithmetic
will provide a means of conserving our precious resources for as long as
possible. We approach the problem using
logarithmic integration. The area under
the curve is:
A(t) = ∫ e-kt dt (from 0 to ∞)
We use 0 to represent time where we are now,
and ∞
to represent where we would like to be; because, if at all possible we would
like to make this resource, whatever it is, last forever.
Let z = e-kt
ln(z) = ln(e-kt) = -kt * ln e = -kt
dz = -k * z dt = -k * e-kt dt
Since k is a constant, we can arrive at an
integral form by dividing outside of the integral and multiply inside of the
integral.
A(t) = 1/-k ∫ -k *e-kt dt (from 0 to ∞)
A(t) = 1/-k *e-kt (from 0 to ∞)
By evaluating e-kt at 0
and ∞
we arrive at:
A(t) = 1/-k *(0 – 1) = 1/k
If A(t) = 50 years-worth of something we
conclude that a declining rate of 2% will in theory make that resource last
forever.
This is like the joke about the famished engineer and
mathematician who are only forty feet away from an elaborately set banquet
table, laden with a festal cornucopia of delicious things to eat, all in
quantities that stagger the imagination.
Unfortunately, our pair of heroes is only allowed to advance by half of
the remaining distance every minute. The
mathematician does the math and concludes that he will never get there;
consequently, he leaves in a huff to search for another place to eat. As he is rushing off, the engineer exclaims,
“I’ll be close enough.”
Let’s see how that works out. At one minute, he is at 20 feet; at two
minutes, 10; at three, 5; at four, 2.5; at five, a little bit more than a foot
away. The table itself is more than a
foot wide, and he can easily reach a foot without being ill mannered. For all intents and purposes, he may as well be
seated at the banquet table or standing in the middle of it.
Even if the table were one hundred feet away, the numbers
would be 100, 50, 25, 12.5, 6.25, 3.125.
In five minutes he’s a little more than 3 feet from his goal. Considering the width of the table, he may be
already touching it.
As a practical rule-of thumb it is usually considered
impractical to continue this calculation beyond five time constants. Engineers consider this to be a practical limit. The mathematician is a little too picky for his
own good. Even in a one thousand foot
room, the distance will be diminished in minutes. It is of the nature of exponential functions
to devour time. In the growth model that
property worked against us. Here we are
employing that nature to help us: but, it has practical limits; we cannot keep
cutting forever. How long can we
continue?
From our original equation:
y(t) = y0 / 2 = y0 * e-kt
1 / 2 = e-kt
ekt = 2
ln(ekt) = kt * ln(e) = ln(2) ≈ 0.693
t = ln(2) / k ≈ 0.693 / k
This is our old friend, the rule of seventy, and if we
multiply both denominator and numerator by 100 we get the formula in
percentages, just as the rule of seventy expresses it. Instead of doubling time, we have halving
time, or as the nuclear folks express it, half-life.
In our original example of 50 years, which represented a
necessary decline of 2% (-2% growth): we may now calculate a half-life of 35
years. The mathematician concludes that
we can make that resource last forever.
The engineer says that this is practically good for about 175 years.
On the other hand, 2% is not a draconian cut, so maybe we
can do better in this case. It should be
obvious that a 5% annual cut will make the resource last even longer. The goal of 2% reduction is merely the minimum
amount that will allow a limited resource approach the behavior of an infinite
or renewable resource. To make a finite
or limited resource into a truly sustainable resource, we would have to abstain
from using it at all. This defeats the
purpose of a resource: the decision not to use a resource at all is
philosophically no different than not having the resource to begin with.
Practically there are many other considerations. If we chose to use a resource, are we
damaging or destroying something else in the bargain? In the case of coal, the carbon may supply
vital nutrients for forest growth and sustainability, such as is the case with
terra preta.[2] Burning coal also produces carbon monoxide,
toxic byproducts from contaminants such as sulfur, and waste heat, which may
threaten global warming. Every decision
necessitates tradeoffs, some of which may be exceedingly destructive. We remember Dr. Bartlett’s illustration of
the Aswan Dam.
The major point being made here is that we can and we must
change the way we think. We must
disabuse ourselves of utopian dreams of growth, and replace them with practical
ideas of conservation. Growth is an ugly
word. Conservation is a life preserving and
saving word. We are already in a state
of decline; we had better learn how to manage it.
k = 1/A, and
t = ln(2) / k ≈ 0.693 / k,
These two equations furnish guidelines for accomplishing
such management. This is nothing
new. Long ago, our forefathers knew,
“Waste not; want not.”
Here are the current figures for the United States.
|
Sustained Availability
|
|
Resource
|
Reserve (years)
|
Report Year
|
Remaining Reserve (years)
|
Sustainability Reduction Rate (%)
|
Half-life (years)
|
Realistic Expectation (years)
|
|
Current Year
|
|
2014
|
|
|
|
|
|
Coal
|
223.23
|
2008
|
217.23
|
0.5%
|
150.57
|
753
|
|
Oil
|
10.48
|
2012
|
8.48
|
12%
|
5.88
|
29
|
|
Natural Gas
|
14.52
|
2012
|
12.52
|
8%
|
8.68
|
43
|
Calculating world figures is not currently beneficial. First of all, the world’s problem is the
United States with its massive consumption.
If we bring United States resources into a state of sustained
availability, most of the world will fall in line. Second, we can only teach by example. With United States resources in a state of
sustained availability, places not already under control can follow our
example. Third, these calculations are
not difficult, so any nation can easily establish its own sustained
availability policy.
The
Sustainability Question
“Can we transform our
society to a solar-based society which will probably have to be mainly an
agrarian society, while keeping and sharing throughout the world the benefits
of modern medicine and technology?”[3]
Sustainability
Politics
“We've arranged a
global civilization in which most crucial elements – transportation,
communications, and all other industries; agriculture, medicine, education,
entertainment, protecting the environment; and even the key democratic
institution of voting – profoundly depend on science and technology. We have also arranged things so that almost no
one understands science and technology. This
is a prescription for disaster. We might
get away with it for a while, but sooner or later this combustible mixture of
ignorance and power is going to blow up in our faces.”[4]
Sustainability
War
“Modern warfare is
extremely dependent on fossil fuels and minerals; hence, war can’t be a part of
a sustainable society. The world in 2012
seems to have a deep commitment to perpetual war. In today’s wasteful and destructive
environment of unceasing hostility we can have little or no hope of achieving
global sustainability.”[5]
“In [the Day of the Lord] … Proclaim this among the Gentiles; “Prepare war, wake
up the mighty men, let all the men of war draw near; let them come up: beat
your plowshares into swords, and your pruning hooks into spears: let the weak
say, I am strong.”[6]
“In the last days … He shall judge among the
nations, and shall rebuke many people: they shall beat their swords into
plowshares, and their spears into pruning hooks; nation shall not lift up sword
against nation; neither shall they learn war anymore.”[7]
“The Day of the Lord”
and “the last days” appear to refer to the same epoch. The exact nature of this epoch remains a
Mystery. “It is not for you to know the
times and the seasons.”[8] In this epoch Yahweh calls all the nations of
earth to final judgment. They may, if
they wish, strap on their armor, and continue to wage war against God, which is
futile, and can only result in their destruction. On the other hand, they may freely submit
themselves to God in faith and repentance, put an end to war, strap on their
agricultural tools, and commence to farm the good earth in peace and security. Perhaps the best arbitrating passage indicating
this sort of idea is found in Isaiah 1:18-20.
“ ‘Come now, let us reason together,’ says
the Lord, ‘though your sins be as scarlet, they shall be as white as snow;
though they be red like crimson, they shall be as wool. If you are willing and obedient, you shall
eat the good of the land: but if you refuse and rebel, you shall be devoured
with the sword:’ for the mouth of the Lord hath spoken it.”[9]
These passages affirm what Dr. Bartlett claims: there is no
such thing as a sustainable war. War and
sustainability are utterly incompatible.
War, war efforts, maintenance, and support very likely consume 50% of
the monetary expenditures of the United States.
Roughly 25% may be spent directly by the military; while another 25%
goes to research and education where war planning and preparation are the major
beneficiaries of that research and education.
That explains what these expenditures do; but it does not
explain who profits by them. Who does
profit? Certainly not the bulk of the
military: most military employees barely make a livelihood. Who then?
The very powerful 1% of the population that really run our country, its governments,
and its industries. If we are to be
successful in building a sustainable culture, we must convince this 1% to stop
waging war
If we fail at this task we will still succeed at building a
sustainable culture, but the process may be considerably more painful.
Our
Choices
One. We
may refuse to become sustainable, continue war and oppression, with the
inevitable result that when fossil fuels are abruptly consumed, many people
will die of exposure and starvation.
With the final consumption of natural gas and oil we will no longer be
able to provide heat, air conditioning, food, medicine, transportation,
electricity, police, fire, and many other services to vast segments of the
population. Other segments of the
population will limp along on the remaining coal for a few more years: then
they too will face exposure and starvation.
Two. We
may come together as a committed and unified nation and have a chance to solve
this crisis in a meaningful way. Yet,
when the fossil fuels are gone, sustainability will the only life choice
left. Other choices will only result in
death.
Who Really Decides? The 1% live, for the most part, trapped in
prisons, we call cities. These places
are the most dependent on fossil fuels, and they will be the first to
fail. The safest places are among those
who are already least dependent on fossil fuels. If the 1% want to live, they are going to have
to turn to the 99% for help. When the
fossil fuels are gone, our paper money will lose all of its remaining value,
and the 1% will be bankrupt. The 1% have
more reason than anybody else to commit to sustainability if they wish to live,
or if they hope to save any semblance of our culture. The 1% have the power to end war.
The Law of Carrying Capacity
“Where: P is the
population at any time and place, and Cpc is the per
capita consumption due to that same population.
One (1) is 100% of Carrying Capacity which
cannot be exceeded. Once conditions of 100%
sustainability equilibrium are reached for any fixed location, further growth
in CC cannot take place.
If P increases by a factor of u, Cpc
must decrease by a factor of 1/u.
If Cpc increases by a factor of v,
P must decrease by a factor of 1/v.
“If individuals attempt to violate these
equilibrium conditions, nature will restore them by force: people will die or
they will experience uncontrollable shortages of resources.
“If greedy individuals decide that it is
necessary to consume more than their fair share, they are in effect committing
murder. Fair share is not a worldwide
constant. People living in the tropics
have different needs than people in the polar regions. Arid climates create different needs than
humid climates.
“Therefore, CC must be
maintained in balance both globally and regionally: but CC must
be tuned, region by region. Moreover,
sharing mechanisms must be in place to maintain CC under changing
conditions. For this reason it would be
wise to incorporate a safety factor to accommodate unusual conditions.”[10]
The Law of Carrying Capacity expresses the worldview of
hunter gatherers. Its fundamental
assumption is that man contributes nothing more or less to the environment than
his bodily waste, and takes nothing more or less from the environment than his
bodily needs, as is the case with any other living animal or plant. Under this constraint, man is incapable of
making either a positive or negative contribution to the equation: man is
merely another unintelligent and irresponsible creature. Since, we commonly believe that this is
untrue, man is both intelligent and responsible; we will be looking for another
broader model that expresses the effect of human contribution on The Law of
Carrying Capacity very soon.
Proof
of The Law of Carrying Capacity
The Law of Carrying Capacity is a simple and straightforward
application of the fundamental laws of thermodynamics. Since these laws are commonly taught in high
school general science and physics classes as the laws of conservation of mass,
conservation of energy, or conservation of mass-energy, we do not believe that
there is any further need for proof. QED
Relationship
with Dr. Bartlett’s Laws
The First Law.
The only independent variables named in the First Law are population and
rates of consumption. These two
variables are all of the necessary and sufficient conditions in a hunter
gatherer society. Since the Law of
Carrying Capacity incorporates both of these variables in a thermodynamically
consistent mathematical model, we may consider Dr. Bartlett’s First Law to be a
corollary of the Law of Carrying Capacity.
All of Dr. Bartlett’s comments are sub-corollaries. However, some of these comments may be
overstated. Even so, we are in hearty
agreement with most of them.[11]
The Second Law. The Law of Carrying Capacity encompasses the
Second Law for the same reasons that it encompasses the First Law. It simply adds the caveat that an unsustained
society carries with it an increasing momentum (M = P * Cpc)
which becomes more and more difficult to overcome as it increases in size. In other words, the ability to achieve a
sustainable society is detrimentally and directly opposed by its momentum of
unsustainability.[12]
The Third Law.
The Third Law relates exclusively to the Population factor, and draws
attention to the “response time” or “population momentum” as it is applied to
human fertility. This law misleads in
part as it is not liked to factors like disaster, exposure, famine, pestilence,
plague, or war. It relates only to
family planning, or the practice of celibacy.
Otherwise, the sub-corollaries are for the most part true. However, this Law provides a 70-year solution
in a matrix that demands 8.5 to 30 year solutions. So this Law results in senselessly “spinning
the wheels”.[13]
The Fourth Law. The Fourth Law relates carrying capacity
directly to population sustainability.
This is an error. Carrying
capacity must be related to the product of population and consumption. Population by itself is a raw number without
capacity meaning. Per capita consumption
in terms of volume, mass, energy, money, etc. adds the necessary capacity
meaning. One person times zero
consumption requires zero carrying capacity.
Zero population times any amount of consumption, is impossible to
attain. Dr. Bartlett introduces the
concept of standard of living, but this is just another term, which is
identical in meaning to per capita consumption.
The Fourth Law does draw attention to the fact that P and Cpc
are inversely related, with which we agree.[14]
The Fifth Law.
The Fifth Law draws attention to the fact that differences in Cpc
will create pressures that will tend to cause a flow from higher pressures to
lower pressures. However, it should be
obvious that such pressures may be contained, and their related flows stopped
by a wide variety of cultural, natural, and psychological obstacles. Therefore, this is mostly an opinion about
morality, having little to do with the scientific facts; else, how can we
explain the fact that 40% of American wealth is in the hands of 1% of the
population. If this disparity exists
locally, how are we to explain the greater worldwide disparity? It is absurd to argue, because pressures and
obstacles work against each other, that they are necessarily wrong. Almost all of science depends on this
interaction between pressures and obstacles.
That such pressures and obstacles are evil is a moral argument, not a
scientific one.[15]
The Sixth Law.
The Sixth Law introduces the idea that carrying capacity must be
evaluated as a closed system. If
carrying capacity is imported it is no longer the carrying capacity of the
region under evaluation. All regions
cannot import or export net carrying capacity at the same time. Net trade must be zero to obtain a
sustainable equilibrium. This law as
stated by Dr. Bartlett has more to do with per capita consumption than it has
to do with carrying capacity. It is
none-the-less true. Dr. Bartlett deals
with the population factor in Law Seven.[16]
The Seventh Law. The Seventh Law like the Sixth Law deals with
this fact that Law of Carrying Capacity only applies to closed systems. The earth in its total relationship to the
Sun and to our solar system is effectively a closed system. Radiation crosses this boundary in both
directions, but this does not appear to be significant in the present
discussion. The Sun must be included
because, it is the final thermodynamic heat source available, and for purposes
of this discussion, must be considered a mathematically infinite source. We have not yet introduced the idea of people
doing meaningful work, but it should be clear that people crossing the solar
boundaries is an unsustainable idea. Few
people are able to do it. The time spans
involved ensure certain death for those who do.
The same law which must apply to the whole system, must also be applied
to its sub-systems. Importation of
people or labor is a violation of the basic concept, and if it is done the
sub-systems must incorporate it in order to remain thermodynamically closed.[17]
The Eighth Law. The Eighth Law is true as stated, but is
moot. After the depletion of fossil
fuels “the desired standard of living” cannot be maintained. It is dubious that “the desired standard of
living” can be maintained under present conditions. When fossil fuels are gone, no one will be
happy with the resultant standard of living, which will consist of whatever we
must do to survive. Moreover, “the
desired standard of living” is a concept that is nebulous to define: if it
means anything other than per capita consumption it becomes nonsensical. Everyone wants a better standard of living. From the standpoint of sustainability wanting
a standard of living is irrelevant; what matters is the real cost (not the
monetary cost) in terms of per capita consumption. We have no special dispute with the sub-corollaries.[18]
The Ninth Law.
The Ninth Law makes another moral political argument. The idea that unsustainable growth is good
for the powerful and wealthy 1% is false.
They will be the first to die in the collapse of society. Those who survive will most likely be
attacked and killed by angry mobs, as in the French Revolution. It is in the best interests of this 1% to
help find a solution while they are still alive. This is irrelevant to the science of
sustainability, which simply seeks to explain the necessary and sufficient
conditions for sustainability. What any
individual or group decides to do with this science is not a scientific
decision. What is good for General
Motors, is obviously not good for the country.
Charles Wilson (1890-1961), “Engine Charlie” of GM was never faced with
declining economy or energy, and did not speak to such issues. Nor did Charles Wilson (1886-1972), “Motor or
Electric Charlie” of GE ever confront these issues. Everybody profits in a growth economy. The problem is that we all remember growth
economy, and we all want it, but we cannot have what we cannot obtain. This explains why I have not attained the
earning capacity of my father, and why my son will not and cannot attain my
earning capacity. This downward slide in
standard of living will continue until sustainable equilibrium is restored.[19]
The Tenth Law.
The Tenth Law relates to fixed resources that cannot be renewed and are
hence, not sustainable. This topic was
thoroughly covered in parts 1-8, and a temporary repair was suggested under the
topic, Sustained Availability, above. We
agree with the law and its sub-corollaries, but it is not relevant to the
present discussion. The only way to make
a fixed resource sustainable is not to use it at all.[20]
The Eleventh Law. The Eleventh Law also relates to fixed
resources and offers appropriate conservation suggestions. Efficiency improvements only conserve a few
percentage points, and are not sufficient in and of themselves to be a major
conservation contributor. This is not to
say that they are unimportant: their contribution does add up. Sustained Availability is theoretically
infinite, but is practically limited to a few years (Coal: 150 years; Oil: 5-6
years; Natural Gas: 8-9 years). Fixed
energy resources cannot be recycled: this would apply to things like aluminum,
glass, and steel. The best recycling
method is simply to reuse the item with no other recycling process than washing.[21]
The Twelfth Law. The Twelfth Law simply points out that
efficiency gains are modest, easily wiped out, and no match for a growth
mentality. This is also irrelevant to
the current discussion. We are pursuing
the Laws of Sustainability which assumes that a growth mentality is no longer
in play, and that is has been replaced with a conservation mentality. This change from a growth mentality to a
conservation mentality will inevitably take place: either by human choice, or
by natural force. There is nothing wrong
with the Twelfth Law, it just does not apply to our current quest.[22]
The Thirteenth Law. The Thirteenth Law as with the Twelfth Law
contributes wisdom that does not enhance our present quest. Since Carrying Capacity is, by definition,
the product of population and consumption, changes in population or consumption
(conservation/preservation) are automatically accounted for.[23]
The Fourteenth Law. The Fourteenth Law is less than an explicit
statement of the Second Law of Thermodynamics.
While the rest of the statement is true, such pollution is part of
consumption, and it must be counted as such in the Law of Carrying Capacity,
whether it is cleaned up or not.[24]
The Fifteenth Law. The Fifteenth Law is again wise council, with
which we agree, but it does nothing to advance our search for sustainability
arithmetic.[25]
The Sixteenth Law. The Sixteenth Law adds the factor of human
contribution. The Law of Carrying
Capacity needs to be modified to accommodate human behavior above and beyond
that of a hunter-gatherer society. We
are indeed being pushed toward the Malthusian Crisis. We agree that agriculture must be made a
sustainable pursuit, and the defects mentioned by Dr. Bartlett must be
overcome.[26]
The Seventeenth Law. The Seventeenth Law is a natural corollary of
the Law of Carrying Capacity.[27]
The Eighteenth Law. The Eighteenth Law is a non sequitur as
stated.[28]
The Nineteenth Law. The Nineteenth Law is true but moot. Sustainability commitment must be inculcated
before widespread panic sets in, else widespread death will follow. The Laws of sustainability have no control
over when and how they will be applied. These are political and leadership decisions.[29]
The Twentieth Law. The Twentieth Law simply notes that
sustainability must become more than a buzz word. This is well and good, but we cannot force
anyone to become earnest or sincere about any social issue.[30]
The Twenty-first Law. The Twenty-first Law is also moot. With human extinction the earth will quickly
return to its own equilibrium. The point
is well taken, man may not survive. If
we are that foolish and careless with God’s property, we don’t deserve to
survive.[31]
Summary.
Laws One through Seven and Seventeen are natural corollaries of the Law
of Carrying Capacity. Laws Eight through
Twenty-one provide interesting comment, are sometimes corollary, but add
nothing to our effort to devise a functioning math model, with the following
two exceptions. The Eleventh Law applies
to Sustained Availability and not to sustainability proper. The Sixteenth Law (and to some extent the
Seventh Law) adds a new category of human participation which must now be added
to our consideration. But how?
The Law of Caretaking
0 ≤ CC+ HCpc *
P ≡ P * Cpc ≤ 1
Where: HCpc is the
per capita human contribution to carrying capacity. It may contribute to the carrying capacity or
detract from it. It should be clear that
most of man’s contemporary behavior is detrimental to the carrying capacity and
we need to rethink how we behave. As
before, P is the population at any time and place, and Cpc
is the per capita consumption due to that same population. One (1) is 100%
of Carrying Capacity which cannot be exceeded.
The Law of Caretaking expresses the worldview of agrarian
society. Its point is to express
mathematically, ideas expressed in Dr. Bartlett’s Seventh and Sixteenth
Laws. Caretaking, nurturing, or the
older husbanding, all suggest that man has a custodial responsibility to
creation, especially on earth. The Bible
commands such caretaking, and from earliest times, specialties developed in
this endeavor.
This statement leaves out another factor: that which
describes industrial society. Since, our
discussion is motivated by the potential collapse of fossil fuel dependent
industrial society, there is no real point in developing its theorem. This would simply involve adding another
factor for per capita industrial contribution (ICpc).
0 ≤ CC+ (HCpc
+ ICpc) * P ≡ P * Cpc ≤ 1
Once again ICpc
may contribute or detract. What this
model of an industrial worldview makes clear is that the loss of fossil fuels,
if abrupt, will send a shock wave through the system as ICpc
suddenly becomes zero. We return to our
point.
0 ≤ CC+ HCpc *
P ≡ P * Cpc ≤ 1
We are still dealing with a thermodynamically closed system,
except for the issue of radiation. We
cannot devise a thermodynamic boundary that radiation cannot cross. We will consider this difficulty overcome if
we can devise a system that does not alter our present radiation gains and
losses. Nevertheless, this is not a
minor concern. Scientists are well aware
that a single magnetic pulse from the Sun with the wrong polarity could wipe
out the earth with a single flash.
Scientists are equally aware that earth’s heat absorption and radiation
is related to a wide variety of factors: atmospheric oxygen density, global
warming, ozone layer, and other factors well outside of our present ability to
control. We neglect all of these in the
hope of finding any solution, preferably a solution which will stabilize some
of these uncontrollable factors. Neither
population nor resources can cross the thermodynamic boundaries under
consideration. If either population or
resources must cross the thermodynamic boundaries to arrive at a functional
system, then the boundaries must be redefined to include this population and
resources so that no crossing takes place.
Corollary One.
A first corollary immediately comes to mind. In an agrarian model all real wealth is
created by farming, fishing, and forestry.
The industrial model had another category: factories, which are now
considered to be mostly defunct.
Corollary Two.
A second corollary is that money is excluded from consideration. We may find it convenient, in rare
circumstances, to express the factors of the equation in monetary values, but
this would usually mislead, because money has no real value. The Law of Caretaking and the Law of Carrying
Capacity are about real tangible values; among which, money is not a
consideration.
A definition of sustainability. Sustainability is the maintenance of a closed
thermodynamic system in a steady state, so that at any time of observation it
will be exactly as it is at any other time of observation, no matter how close
or distant these observations may be in relationship to each other.
Corollary Three. A sustainable process must result in the
returning of a resource to the place where it was found. Coal mining and combustion can never be made
into a sustainable process because it is absolutely impossible to restore coal
to the same place from where it is mined.
Tomorrow’s observer will see that there is significantly less coal than
there is today. Moreover, any systems that
are dependent on that coal are now irrecoverably destroyed. There is not much that man can do that is
truly sustainable.
Corollary Four. A nearly sustainable process must result in
the returning of a resource to the place near where it was found in a timely
manner. Since fire already destroys
forests and they regrow, we can consider the process of clear cutting and
immediately replanting as a nearly sustainable process in which we also manage
forest fires. We must also beware of
other dangers so that we do not cause flooding and other disasters, which
already occur. If we succeed in managing
both fires and floods we have made a significant contribution under the Law of
Caretaking. We still need to be
concerned that waste heat from wood combustion does not contribute to global
warming. Another nearly sustainable
process is that of agriculture conducted without the aid of fertilizers,
herbicides, and insecticides manufactured from fossil fuels. Here we have the additional concerns of
erosion and soil depletions which need to be resolved immediately, because much
of our soil is already severely depleted and eroded. Fishing, however, is not presently a nearly
sustainable process for the same reasons that farming is not presently a nearly
sustainable process: our oceans and lakes are severely depleted, so we need a
plan to restore oceanic health before we begin.
Corollary Five. A nearly sustainable process may be evaluated
at nearly any scale. For example, it
could be the carrying capacity of x acres of land devoted to carrot production,
human skill at enhancing carrot production, and human consumption of
carrots. If it is possible to maintain
relatively local markets, without fossil fuels, the set of P involved in carrot
production, and the set of P involved in carrot consumption do not have to be
the same set. Sharing, division of
labor, and specialization may develop in the same thermodynamic community,
provided that parity can be maintained between specialists.
0 ≤ CC+ HCpc *
P1 ≡ P2 * Cpc ≤ 1
Corollary Six.
Quantifying the Law of Caretaking necessitates that the laws of supply
and demand reach their natural balance.
We most likely know what the current demand for carrots is in the United
States. We can probably break that
number down into smaller market units.
We would probably have more difficulty in determining the local carrot
demand. As a first rough estimate we can
calculate the national average carrot production and multiply that by the local
population. Then we would need to learn
if suitable land for carrot production was available in the local community,
and if anyone was interested in carrot farming.
If those conditions were met, production could commence, and at the end
of the year we would know if production was short or long in terms of
production. Eventually we would find an
acceptable, if not perfect balance.
Bananas, on the other hand, could never be quantified, because the
available production sites exclude bananas from any reasonable thermodynamic
boundary. Bananas are a luxury, they
could not possibly be made into a nearly sustainable process in the United
States. This presents two additional
quantification problems. One, the glut
of bananas in banana producing countries must be resolved: their local
communities cannot possibly consume all the bananas they produce. Two, a suitable fruit substitute for bananas
must be found, or the local community could suffer serious health problems: the
obvious substitute is pumpkin. This
quest to quantify and balance carrying capacity with consumption must be
completed for every conceivable necessary product: water, sanitation, clothing,
energy (wood, wind, sun, etc.), and shelter.
Every one of these necessities must be brought into local balance or
considerable hardship will result.
Creating this local balance should be the immediate concern of the town
leaders, schools, and universities. Our
equation, allowing for divisions of labor, now looks like this:
0 ≤ CC+ HCpc *
P1 ≡ P2 * Cpc ≤ Q
Where Q is the quantity of any conceivable product by mass,
volume, weight or other quantitative measure.
Corollary Seven. In the process of quantifying our formula
into tons of carrots we are met with an additional problem. Carrots don’t grow at a constant rate year
round, they grow by annual seasonal production.
So, a method of carrot storage must be developed, or the local community
must adapt to the inconvenience of only having carrots seasonally. This could actually turn into a considerable
hardship. The cold root cellar must be
revived. A locally supported or home
canning industry would be very beneficial, and possibly life-saving. Perhaps, the old ice plants will come back
into production, but there is very little hope that we will have
refrigeration. We can hope that wind
produced, nearly renewable electricity, will develop sufficiently to save our
bacon.
Corollary Eight. So far we have proposed some sort of survival
community. Even so, new ways need to be
found to maintain law and order, firefighting; reduced dental, medical, and
pharmacy services; schools, libraries, road maintenance, transportation, etc. Everything in an existing community needs to
have either a salvage plan, or an elimination plan with an accompanying coping
plan.
Corollary Nine. Crowding is an immediate problem. Even with the best plan in operation; and the
greatest possible human contribution per capita; gross production may not be
sufficient to meet the demands of
P2 * Cpc.
In this case some of the population must disburse. If there is no space for the population to
disburse, population will be a problem.
This is the Malthusian Catastrophe.[32] We hope that the use of fossil fuels in
agricultural production has not catapulted us into the Malthusian
Catastrophe. At our present state of
knowledge population may or may not be an immediate problem. It should be obvious from our fundamental equation
that infinite population cannot be supported or sustained.
0 ≤ CC+ HCpc *
P1 ≡ P2 * Cpc ≤ Q
P2 = ∞ overloads the system, but so does Cpc
= ∞. We need to find out where we are within the
constraints of this one equation.
Other Considerations. We did not develop a corollary for this, but
it should be obvious that back yard gardening and stock raising could make a
considerable contribution toward solution.
Existing city ordinances limiting back yard gardening and stock raising
need to be reconsidered. Educational
support is also necessary. Currently,
back yard gardening and stock raising is unlikely to be a winning effort. Feed, fertilizer, herbicide, insecticide, and
irrigation costs make it prohibitive.
Such problems need to be fixed.
We did not discuss the effects of pollution. These are quantifiable within HCpc
* P1 as a negative quantity.
No process is truly sustainable until all its elements are returned to
whence they came.
We have discovered in the Law of Caretaking all the
arithmetic we need to develop a sustainable culture. Separating the community through division of
labor, it now looks like this.
0 ≤ CC+ HCpc *
P1 ≡ P2 * Cpc ≤ Q
This arithmetic needs to be applied and reapplied until a
local community realizes that it can stand on its own two feet without
importing or exporting any goods services.
The maximum functional size of this local community depends completely
on which transportation modes survive the termination of fossil fuels. Buckboards and Pony Express, anyone?
Conclusions.
We have found all the arithmetic we need to develop a
sustainable community, and culture, the development of this arithmetic on a
larger scale and a broad change in public attitudes will result in a
sustainable society. The growth
mentality must be destroyed and replaced with a conservation mentality. What we have not found is if we have the
means and determination, the grit to actually do this.
k = 1/A, and
t = ln(2) / k ≈ 0.693 / k,
These two equations express all the arithmetic we need to
conserve our fixed resources for a maximum length of time.
0 ≤ CC+ HCpc *
P1 ≡ P2 * Cpc ≤ Q
This is the only arithmetic we need to figure out where we
are and where we need to go to become sustainable. HCpc and P1
can be developed by education, planning, and hard work. P2 and Cpc
can be managed by education, planning, and immediate judicious belt tightening.
[1]
Dr. Bartlett, oft repeated sayings
[2] http://en.wikipedia.org/wiki/Terra_preta,
http://phys.org/news/2014-01-combine-terra-preta-statistics-early.html, and http://www.ehow.com/info_8440821_homemade-terra-preta.html
[3] http://www.albartlett.org/articles/art_meaning_of_sustainability_2012mar20.pdf
[4] Sagan,
Carl, The Demon-Haunted World: Science as a Candle in the Dark,
(Ballentine Books, 1997). Quoted in http://www.albartlett.org/articles/art_meaning_of_sustainability_2012mar20.pdf
[5] We
removed the following from Dr. Bartlett’s quotation, because we believe it to
be untrue. “In seeking to abolish war we
must remember that overpopulation is a major factor that drives people to make
war.” People have loved war since the
first Sumerians populated Mesopotamia around or before 3000 BC. The quest for domination has always been
among us, since the fall of Adam. There
is every reason to believe that war stems exclusively from the perversion of
the human heart, and has nothing to do with overpopulation. Overpopulation simply makes engaging in war
more easily accomplished; and attempts to solve the problem by moving away from
it, impossible.
[6]
Joel 3:1, 9-10 (ca. 740)
[7]
Isaiah 2:2, 4 (745-680)
[10] http://swantec.blogspot.com/2014/02/arithmetic-population-and-energy-part-6.html
[11]
We have not quoted from these laws, because we do not know which of them, if
any, are protected by copyright. In lieu
of quotation we suggest that the reader is best served by reading all of Dr.
Bartlett’s Sustainability Laws in their entirety and in their context. Here is the best link to these Laws that we
have found. http://www.resilience.org/stories/2009-11-06/dr-albert-bartletts-laws-sustainability,
First Law
[12] http://www.resilience.org/stories/2009-11-06/dr-albert-bartletts-laws-sustainability,
Second Law
[13] http://www.resilience.org/stories/2009-11-06/dr-albert-bartletts-laws-sustainability,
Third Law
[14] http://www.resilience.org/stories/2009-11-06/dr-albert-bartletts-laws-sustainability,
Fourth Law
[15] http://www.resilience.org/stories/2009-11-06/dr-albert-bartletts-laws-sustainability,
Fifth Law
[16] http://www.resilience.org/stories/2009-11-06/dr-albert-bartletts-laws-sustainability,
Sixth Law
[17] http://www.resilience.org/stories/2009-11-06/dr-albert-bartletts-laws-sustainability,
Seventh Law
[18] http://www.resilience.org/stories/2009-11-06/dr-albert-bartletts-laws-sustainability,
Eighth Law
[19]
This is the obvious and inescapable result if Peak Energy Theory. Energy peaked in the United States around
1971. Studies of Dr. M. King Hubbert: http://en.wikipedia.org/wiki/M._King_Hubbert,
http://en.wikipedia.org/wiki/Hubbert_peak_theory, http://en.wikipedia.org/wiki/Peak_oil,
http://www.princeton.edu/hubbert/the-peak.html, http://conspiracywiki.com/articles/peak-oil/hubbert-peak-oil-theory/,
http://swantec.blogspot.com/2014/02/arithmetic-population-and-energy-part-5.html,
http://www.resilience.org/stories/2009-11-06/dr-albert-bartletts-laws-sustainability,
Ninth Law
[20] http://www.resilience.org/stories/2009-11-06/dr-albert-bartletts-laws-sustainability,
Tenth Law
[21] http://www.resilience.org/stories/2009-11-06/dr-albert-bartletts-laws-sustainability,
Eleventh Law
[22] http://www.resilience.org/stories/2009-11-06/dr-albert-bartletts-laws-sustainability,
Twelfth Law
[23] http://www.resilience.org/stories/2009-11-06/dr-albert-bartletts-laws-sustainability,
Thirteenth Law
[24] http://www.resilience.org/stories/2009-11-06/dr-albert-bartletts-laws-sustainability,
Fourteenth Law
[25] http://www.resilience.org/stories/2009-11-06/dr-albert-bartletts-laws-sustainability,
Fifteenth Law
[26] http://www.resilience.org/stories/2009-11-06/dr-albert-bartletts-laws-sustainability,
Sixteenth Law
[27] http://www.resilience.org/stories/2009-11-06/dr-albert-bartletts-laws-sustainability,
Seventeenth Law
[28] http://www.resilience.org/stories/2009-11-06/dr-albert-bartletts-laws-sustainability,
Eighteenth Law
[29] http://www.resilience.org/stories/2009-11-06/dr-albert-bartletts-laws-sustainability,
Nineteenth Law
[30] http://www.resilience.org/stories/2009-11-06/dr-albert-bartletts-laws-sustainability,
Twentieth Law
[31] http://www.resilience.org/stories/2009-11-06/dr-albert-bartletts-laws-sustainability,
Twenty-first Law
[32] If
and when population overcomes the food supply, Malthus’ conditions are
met. Although Malthus did not believe
that this could or would happen, the application of fossil fuels to agriculture
has inflated crop production far beyond the normal carrying capacity of the
land. We are now left in a state of
ignorance over what might happen when fossil fuels are gone. The necessary and sufficient conditions that
will produce the Malthusian Catastrophe may well be present, and we would not
have an inkling that such conditions exist.
We are not arguing for yet another apocalyptic hoax. We are arguing that now is the time to find
out where we are, and what we intend to do about it. Plunging ahead as though the problem doesn’t
exist is foolhardy indeed. The utopian
optimism espoused by contributors like Julian Simon is not
constructive. The need for new solutions
is upon us and it is time for the creative technological elements among us to
produce: it would be constructive if we notified them that immediate action is
called for. If necessity is the mother
of invention, and it is, it is time to start inventing. http://en.wikipedia.org/wiki/Malthusian_catastrophe,
and http://en.wikipedia.org/wiki/Thomas_Robert_Malthus
