Exponential Curve 5
Arithmetic, Population and Energy, Part 5
For the love of the human
race.
Wednesday, December 03, 2014
Our Thesis
We are greatly indebted to Dr. Albert Allen Bartlett (1923-2013),
former emeritus professor of physics at the University of Colorado, Boulder.[1] These are Dr. Bartlett’s ideas, we are merely
reporting them. We have performed a
lengthy analysis of Dr. Bartlett’s “arithmetic” elsewhere.[2]
One cannot investigate either energy policy or energy theory
without a thorough understanding of the exponential curve.[3]
Arithmetic, Population and Energy, Part 5
Strength Through Exhaustion
“Energy industries agree that to achieve some
form of energy self-sufficiency the U. S. must mine all the coal that it can.”[4]
Clearly, the editors at Time Magazine are full of hot air.
David Brower (1912-2000)[5] called
this the policy of “strength through exhaustion.”
I liken this to driving at sixty miles per hour; learning
that there is an immovable concrete barrier thirty miles ahead; then deciding
to increase speed by 7% a mile.
Te
= 1 / ln (b) * ln [ ln (b) *
A / y0 + 1 ]
Te
≈ 1 / r * ln [ r * A / y0 + 1 ]
This reduces the remaining time until collision from 30
minutes to 16 minutes, increases the impact velocity to 182 miles per hour, and
triples the momentum. It also guarantees
that no one will be maimed in the accident.
The 182 mile per hour impact velocity pretty much guarantees that all
living occupants will be vaporized or reduced to dust. Any remains for burial will have to be
located with a sponge or a vacuum cleaner.
It is the instant cremation and dispersion of ashes in one swift motion.
Strength through exhaustion, simply won’t work. The sensible person slows down and puts on
the brakes. There is an end to this road
and Te is its immovable, inexorable name.
Consumption vs. Production
“1994 was the first year in our nation’s history in which we had to import
more oil than we were able to get out of our own ground.”[6]
This comment explains the major difference between energy
consumption and energy production. When
energy consumption exceeds energy production, the difference is what we must
purchase from foreign producers. We
continue to import more oil than we produce to this very day.
Energy Peaks
We have already showed that all growth plans must peak. There are only three ways to avoid a peak: 1.
Follow a zero growth model, in which case the peak is flat. 2. Follow a declining growth model, in which
case the peak is behind us historically.
3. Abstain from using the resource at all. All growth plans peak.
Momentum
We realize from the principles of momentum that it is
impossible to go from peak to zero with no elapsed time. Even a crash into an immovable object
requires a few seconds for the vehicle and its occupants to be crushed.
Gaussian Curves
Is there an “arithmetic” model that better explains such
behavior? The answer is, yes. There is a family of curves, the Gaussian
Curves, including the ordinary bell shaped curve that best explains this
behavior. All Gaussian Curves are not
bell shaped. Some have a long tail
extending to the left or to the right, which is called, appropriately, skewness. Others may be more flattened on top; this is
called kurtosis. When two or more
processes are superimposed over one another, multiple peaks occur; the name for
this is bimodalism, multimodalism, or polymodalism. Polymodalism explains why there are bumps on
the curve. Statisticians deal with these
concepts every day; so, if you find these ideas confusing, get a statistician
to explain them to you.
Peak Growth
Now Dr. Bartlett introduces the concept of peak growth. Until this point our mapping has only
considered exponential growth.
Government, business, industrial leaders, and many individuals assume the
exponential growth will continue indefinitely.
These prognosticators are evidently oblivious to the cartoon where the
exponential curve blows a hole in the ceiling.
If these movers and shakers could possibly be successful at selling their
insane schemes of indefinite growth, they would proceed with their plans until
every last ounce of any given commodity was consumed. Then the graph would come to a screeching
halt. The car would hit the
barricade. Everyone on board would be
killed and that would be that.
Discontinuity
Such an infinitely sloped decrease or increase in
mathematics is called a discontinuity.
It is easily drawn on a graph.
Fortunately, discontinuity is nearly impossible to achieve in
nature. Almost all things have some
mass, even electrons, and they cannot be made to change direction
abruptly. In the case of our car crash
model, we could observe this using high-speed, time-lapse photography, and we
could watch the car and human bodies being reshaped as energy was dissipated.
In any case there can be no question that a peak was, or
someday will be reached. It is
impossible to make exponential curves continue indefinitely: all of them
approach infinity at terrifying speed.
Finite man, simply has no capacity for infinity, which is exactly what
the word means. Infinity is usually,
perhaps always, the result of trying to divide by zero, it cannot be done. So there must be a peak. There must also be a path back downward to
zero, either catastrophic or more sloped.
In our last session we showed how to calculate the maximum peak for an
exponential curve. Simply calculate Te
using this formula.
Te
= 1 / ln (b) * ln [ ln (b) *
A / y0 + 1 ]
Then use Te to calculate the
maximum peak from this formula.
y
= a * bTe
Decision Makers
Business and political economic decision makers create and change
the shape of the curve. The shape of the
downward curve is determined largely by human decision, as is the case with the
upward curve. The mathematician and the
scientist simply create a map to explain what is happening. As human decisions change, new maps must be
created.
This does not mean that
either the math or the science was wrong.
It simply means that some decision makers changed their minds. It is the height of foolishness to abandon or
discredit the math because of a decision change made by business and political leaders.
Availability
Availability of a given resource is the one thing that business
and political economic decision makers cannot change: they can hide it; they
can lie about it; they cannot alter its reality. A peak will occur. Multiple peaks may occur. The time and size of these peaks are
determined by human decision and the availability of the remaining resource,
and not by the mathematician or scientist.
The mathematician and scientist are simply trying to provide a
reasonable means of prediction based on contemporary decision policy, and
predicted reserves.
Decline
Even if the peak is reached abruptly, the crash will take
some time as local storage is used up.
The resource producer will be the first to realize that he is out of
business. The end user will have his
last tank to budget as he tries to plan his survival. How long can you conserve a tank of gas? A downward slope is inevitable. It may be skewed, it may have bumps, it may
be bimodal, it may be slow, but it probably won’t be abrupt. Why?
Undiscovered Resources
We have a good idea where the remaining reserves are
located, and what their size is. Most of
these reserves are not yet in production.
Starting production costs money and takes time. Decision makers are the ones who determine
when and where it is a good financial decision to open a new mine, buy new
equipment, invest in a new process, or build a new refinery. Several of these reserves are shale oil. Shale oil is not processed the same way as
crude bubbling up out of the ground. Deep
mines are operated differently than strip mines.
Limits of Technology
Technological obstacles also exist. This is why we can only get 50% of the coal
out of the ground. Even if we know how,
costs may be prohibitive. The value of
coal will have to increase dramatically to motivate going after it. Not many years ago the depth of wells was
limited by pressure to roughly 3,000 psi.
Hydraulic equipment was designed for those pressures. When deeper drilling was desired, new
technology was developed, pushing pressures beyond 3,000 toward 6,000 and even
10,000 psi. Oil is a very dangerous
substance at 3,000 psi: the presence of any air guarantees a fire. At 6,000 or 10,000 psi explosions can be
guaranteed, and the limits of material strength are being reached. Common steel can only withstand around 36,000
psi: so things wear out more rapidly, it takes more force to pump at such
pressures. The costs go up, and progress
goes down. It takes time and money to
solve such technological problems.
Public Attitude
Popular obstacles also exist. The neighbors will probably object to an
operation destroying the view from their picture window, cutting down their
favorite forest, muddying their water supply, or locating a nuclear reactor in
their back yard. Public outrage can
slow, modify, or even stop a project.
Undeniable Reality
All of these factors
militate that the downward slope will become progressively slower as it becomes
harder and harder to locate and develop new reserves. The obvious mathematical map is some kind of a
negative growth curve for much of its path.
An even better, more realistic map is that of a Gaussian curve, a bell
curve, which accounts for the necessary negative growth rate changes on the
bottom path.
So it is impossible to deny the reality of peak theory. Granted, this is a bit like trying to map a bumpy
emergency crash landing, but it would still be nice to have something to aim
at: like a nice soft pasture, or a convenient highway with no traffic.
Problems
Dr. Bartlett notes that possibly 3.2 G-bbl of crude oil
exist in the Arctic Wildlife Refuge: about a 15 month supply at current
consumption. The peak in the extraction
rate of U. S. crude oil was predicted to occur between 1966 and 1971. This prediction was made by Dr. Hubbert in
1956 when world oil consumption was still growing steadily at 7.04% per
year. The U. S. Department of Energy
fixed the actual U. S. peak at about 3.5 G-bbl per year in 1970. The Alaska reserves were discovered around
1982.
The curve development
was dramatically shifted by the Alaskan discovery and OPEC increases in world
oil prices, which prompted the U. S. energy crisis.
Coping
Dr. Bartlett continues.
“The estimated U. S. supply [of crude oil] from undiscovered resources
and demonstrated reserves is 36 years at present rates of production or 19 years
in the absence of imports.”[7] “Please note that this is tracking faithfully
down the back slope of the Peak Oil curve.”3
This will certainly continue to be a major problem for us, our children,
grandchildren and great-grandchildren.
By refusing to deal with this emergency crisis we are mortgaging the
future to the detriment of world society.
The obvious solution is
to reduce consumption drastically.
No one will (like this solution, but it is necessary to
preserve life.
We, the consumers of
oil, can change the occurrence of peak oil by changing our use habits. A 50% reduction in gasoline consumption would
move the graph considerably.
Our Conclusion
Dr. Bartlett’s defense of Peak Oil theory is correct. The attempts to discredit this theory will
finally prove to be vain. The final
shape of the curve may not be known: the size and time of the peak, bimodal
behavior, and a degree of skewness or kurtosis are all possible within the
practical application of this math. That
being said, the peak or peaks have or will take place, and the downhill
progression is inevitable. The final
shape of such bell shaped curves is ultimately determined by decision makers,
not by scientists; but, once the downhill slide is begun it cannot be halted by
decisions. Instead of a crash, this is
more like that sickening feeling you get when you run out of gas in the middle
of nowhere. You are hopelessly out of
control as your engine sputters, and you coast to a stop.
Our leaders are not taking the sensible steps to put on the
brakes and manage this crisis. We should
be operating on reduced growth conservation plans, negative percentages. Our federal budget should be considering a
-5% budget, instead of a +5% budget. Our
president should be pushing for cuts, rather than performing draconian
theatrics to get the increases he wants.
The falsification of news reports continues, unabated.
Where are the real
leaders who will stand up and face this crisis honestly and head on?
[1] http://en.wikipedia.org/wiki/Albert_Allen_Bartlett
[2] http://swantec-ep.blogspot.com/2014/11/energy-policy-analysis-5-ra.html
[3] http://www.albartlett.org/presentations/arithmetic_population_energy_video2.html
[4] Time
Magazine, May 19, 1975, page 55
[5] http://en.wikipedia.org/wiki/David_Brower
[6]
Dr. Bartlett
[7] Science,
January 27, 1984, page 382
[8] If you have been blessed or helped by any of these meditations,
please repost, share, or use any of them as you wish. No rights are reserved. They are designed and intended for your free
participation. They were freely
received, and are freely given. No other
permission is required for their use.
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