Energy Policy
Arithmetic, Population and Energy, Part 9
Revision A
For the love of the human
race.
Saturday, March 29, 2014
The Source of the Question
This
study report is prompted by the labors of the late Dr. Albert Allen Bartlett (19232013),
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 challenges his listeners to check his math. This is exactly what we did. The data with which he works is a moving
target, so we will update the data, add some new data, and make suggestions, so
that concerned listeners can update and check these principles regularly.
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
Our Thesis
We believe that Dr. Bartlett’s work is unfinished: it must
be continued; newer, creative solutions, which may not have been apparent a few
years ago, when Dr. Bartlett did his primary investigations, need to be
uncovered. The single human mind is
always limited in its abilities: this work needs the contribution of every
mind. New solutions must be found.
We agree with Dr. Bartlett that any solution requires the
education and participation of every single one of the earth’s seven billion
plus residents. The problem is of such
complexity and magnitude that no one person can possibly see lasting solutions. Moreover, the problem impinges on human
freedom, so it is unreasonable to expect that lasting solutions can be achieved
by human coercion of humans.
We have investigated Dr. Bartlett’s mathematics with rigor
and found that his use of mathematics is both correct and precise. It is the task of the mathematician and the
scientist to observe reality and explain exactly how and why it works. This field is known as mapping; Dr. Bartlett’s
mapping speaks with deadly accuracy: he has been faithful in this task.
We also investigated Dr. Bartlett’s data, and observed that
his data need updating. We attempted a
partial update of the data, but this is an ongoing task that requires incessant
continued surveillance. Maintaining a
good, uptodate data set is the most difficult part of the mathematical
problem. GIGO explains why.
However, new and shifting data may require new
mappings. When situations are altered,
new maps must be used. There is nothing
wrong with the old maps, they may simply be inapplicable to the new
situation. Failing to understand this is
like trying to find a place in Denver from a map of Cleveland.
Nevertheless, opponents of truth persist in discrediting and
marginalizing legitimate practices of mathematics and science, by conveniently
ignoring the need for appropriate mapping.
This abuse is then made into the political or popular lever for claiming
that the mathematics and science are incorrect, the mathematicians and
scientists are to blame: they put forth a false theory, cried wolf, and lied to
the populace. However, it is not usually
the mathematician or scientist who lied, but rather the individuals who found
it powerful or profitable to spin the truth to their individual advantage.
That being said, Dr. Bartlett did not determine that
constant controlled growth should be the model under which we now live; society
determined this model through business, government, and individuals. Dr. Bartlett simply studied and reported
it. It is not the task of the
mathematician or the scientist to determine these objectives. On the other hand, since objectives are set by
business, government, and individuals; objectives can be changed by business,
government, and individuals. Changes
will always introduce the need for new data, mapping, and solutions.
These obstacles can defeat us: 1. Unwillingness to change in the face of the
facts. 2. Inadvertently or deliberately
ignoring the facts. 3. Failure to
collect accurate, uptodate data. 4. Inability
to find sufficient meaningful solutions.
This is not a game of blind chance. This is not a game of fear mongering. This is a zerosum game of war: if
rationality does not prevail in this war; we, our children, grandchildren, and
great grandchildren will lose. Deciding
not to play is a decision to lose. If
rationality does not prevail, the forces we call nature will make the necessary
decisions for us: we will lose and be stranded without the necessary survival
map and plan. Nobody will like the
solution.
Arithmetic, Population and Energy, Part 9
Dr. Bartlett’s talks end with part 8. The primary function of Part 9 is to review
parts 1 through 8 and make some data additions as a means of continuing Dr.
Bartlett’s life work. These data
additions are a continuing source of trouble.
Data are always out of date.
Therefore, we must form teams of committed advocates, who will work
diligently to keep them up to date, as current as is humanly possible. This lag in knowledge, and the fact that
knowledge is always growing, due to new discoveries, leads the uninitiated to
believe that the former studies were wrong, not worth the time or effort;
therefore, new studies are also a waste of time and effort.
We must persist and prevail at educating the public about
the true nature of data as a moving target.
We must show that new science is built on the foundation laid by old
science; and we throw out the old science at our own peril. We must inculcate commitment to the idea,
that new efforts are made better from what was learned in the old efforts. Even mistakes made in the old efforts are
fertile ground for fresh ideas. The
public must know that today’s predictions are not good enough for
tomorrow. Every day requires a fresh,
new map. Yesterday’s predictions are no
more valuable than last week’s lettuce. The
real science stands, and is adjusted; but, it is adjusted by rethinking it
fresh every day.
The nature of this changing data environment makes the
scientific community constantly vulnerable to adversaries who attack science to
serve their own agendas. Such agendas
are almost always motivated by the quest for power, for wealth, or out of
bitter animosity. Our cause is not
helped by the frauds and false science arising from within the scientific
community itself. The specific
vulnerability caused by ever changing data and predictions, is the accusation
of “crying wolf” when there appears to be no wolf. Science must report its unbiased findings to
the best of its ability at the time. The
wolf, however, is a cleverly disguised moving target: he has the annoying
capability of making us seem incompetent.
We must firmly refute our adversaries, especially by our unrelenting
quest for truth. Equally, we must screen
out and eliminate frauds arising from within the scientific community itself.
Science is not the pristine objective environment it appears
and even claims to be. Most science is
funded by the powerful and wealthy, who are often science’s worst
adversaries. When someone is holding
your next meal, or your wife and children hostage, by controlling and limiting
food, clothing, and shelter: it is difficult to deny their requests. Consequently, the underlying science may be
perfectly correct and legitimate. On the
other hand, the spokesperson chosen to report the science may have cleverly
spun the report to mean something entirely different, something false. Meanwhile, the working scientists are
“educated” so that they do not publicly disclose the fraud. Scientists who refuse “education” are quickly
eliminated or marginalized so that they have no credibility left, with which to
expose the fraud. The scientific
community is not a place for the exercise of free speech.
This adds up to the necessity for commitment to incessant
vigilance among us.
Part
1
Part 1 of Dr. Bartlett’s talk emphasizes the fact that
steady growth is in fact an aggressive, uncontrollable, vicious monstrosity
that eventually destroys the culture in which it is allowed to exist. The exponential curve inevitably blows a hole
in the ceiling/roof and keeps on going.
Dr. Bartlett introduces the concept of doubling time, and produces, a
very useful ruleofthumb, the rule of seventy: for its handy and accurate
approximation, DT = 70 / % rate of growth, is reasonably accurate
to 10%, and can be calculated in the head. We verified this rule by deriving it from the
basic exponential equation. Dr. Bartlett
introduces the energy crisis of the 1970’s from the viewpoint of doubling.
Part
2
Part 2 of Dr. Bartlett’s talk applies the conclusions of the
exponential curve and doubling to problems of inflation and population. We expanded on these ideas, and introduced
one objection coming from the Christian community. We also added a few observations about
population from our own study of the subject.
Then we included the problem of consumption, which Dr. Bartlett hinted
at in the energy crisis. Finally, we
compared the three problems in an attempt to evaluate their relative
merits. We voiced the hope for the
development of a mathematics of sustainability.
Part
3
Part 3 of Dr. Bartlett’s talk examines the exponential curve
from the perspective of time, rather than size.
This emphasizes the fact that time is running out in which we may make a
rational decision about whatever problems may be increasing exponentially. Not only is time running out, but the problem
is not even identifiable or recognizable until the last half of the fourth
quarter, when the ballgame is almost over, and most of the fans have gone home
in defeat. Dr. Bartlett observes that
this kind of thinking, “… is the centerpiece of the national and global
economies.” Now Dr. Bartlett moves from
a population model (cell division) to a crude oil model. We reconstructed Dr. Bartlett’s hardtoread
slide in a spreadsheet, and provided detailed directions for recreating
it. Then we introduced new data from a
2012 report, which was contrasted with Dr. Bartlett’s data. This revealed the 1980, break in the curve
from around 7% to nearly 0% due to the 1970’s energy crisis. Using other new data and regression analysis
we were able to calculate the new growth rate at 1.030%. We also were able to establish that the 1980
break saved a lot of oil and most likely averted a national disaster. Finally, we emphasized that much, much more
needs to be done.
Part
4
Part 4 of Dr. Bartlett’s talk resumes with a brief review of
the remaining time for the disastrous culmination of the oil crisis; then he
turns the discussion to coal. This
produces the need to calculate the remaining time on the exponential curve from
knowledge of existing or anticipated reserves.
As suggested, we developed Dr. Bartlett’s equation using calculus,
finding again the exact equation, and its ruleofthumb approximation, TE
= 1/r * ln(r * R / y_{0} + 1).
We evaluated Dr. Bartlett’s coal data and compared it to a 2008 report we
found on the internet. We discovered in
agreement with Dr. Bartlett that our coal reserve is in alarming jeopardy, in
some instances as brief as 30 to 50 years or less. The problem with predicting coal consumption
is that it is a less desirable fuel than either natural gas or oil and will not
likely be hard pressed for maximum production until natural gas and oil are
gone.
A variety of authorities in the 1980’s said, “There is no
reason to be concerned.”
“Don’t believe any
prediction of the life expectancy of a nonrenewable resource until you have
confirmed the prediction by repeating the calculation.”[1]
“The more optimistic
the prediction the greater is the probability that it is based on faulty
arithmetic or on no arithmetic at all.”^{1}
Part
5
Part 5 of Dr. Bartlett’s talk investigates the theory of
“strength through exhaustion,” which we compare to a highspeed automobile
collision. Then Dr. Bartlett introduces
Dr. Hubbert’s theory of Peak Growth, or Peak Theory, possibly better known as
Peak Oil. We explored this theory at
some length and do not see how it could possibly be wrong. The very logical physical application of the
exponential curve requires that it cannot continue indefinitely: indefinite continuation
requires an infinite power source, which does not humanly exist. The only discussion can be over the size and
timing of the peak and the nature of the descending curve: these three things
are somewhat subject to human manipulation, but they cannot be prevented. There is no good reason to doubt that with
considerations for kurtosis and skewness, the bell curve will prove to be the
best fit. Human manipulation can also
produce bimodal distributions. We also
discuss some of the factors that necessitate some slope on the downward
curve. Leaders may attempt to live in
defiance of Peak Growth, but they will ultimately fail, simply because they do
not possess infinite power.
“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.”[2]
Part
6
Part 6 of Dr. Bartlett’s talk reinforces the idea that every
new energy discovery must be carefully examined against its related
consumption: even enormous finds prove to be minuscule in the face of our
increased consumption. Ethanol fuels
appear to be counterproductive for a variety of reasons. America’s consumption of oil is out of touch
with the rest of the world. Within the
greater scheme of things, the era of fossil fuels is but a pimple within the
eons of human history. Someday we will
be out of fossil fuels. It is in our
best interests to attempt to evaluate and manage this ultimate reality.
“We cannot let other people do our thinking for us.”
Unfortunately, “We worship growth.”
Dr. Bartlett outlines some his essential points for
successful national and worldwide programs.
1.
“we ought to have a big increase in the funding for research in the
development and dispersion of renewable energy.”
2.
“We must educate all of our
people to an understanding of the arithmetic and consequences of growth,
especially in terms of the earth’s finite resources.”
3.
“We must educate people to
recognize the fact that growth of populations and growth of rates of
consumption of resources cannot be sustained.”
Finally, Dr. Bartlett introduces his First Law of
Sustainability. We responded by
proposing The Law of Carrying Capacity:
0
≤ CC ≡ P * C_{pc} ≤ 1
Part
7
Part 7 of Dr. Bartlett’s talk exposes the fallacy of
technical optimism.
“We must educate people
to see the need to examine carefully the allegations of the technological
optimists who assure us that science and technology will always solve all of
our problems of population growth, food, energy and resources.”^{1}
Chief among these optimists was Dr. Julian Simon (19321998)
who held powerful influence in the “beltway.”
We took pains to refute his ideas about biomass.
We also examined Dr. Asimov’s bathroom parable, but replaced
it with an empty plate parable of our own.
We rejected Dr. Bartlett’s analysis of decreasing government. We also rejected the idea that Global Warming
is a significant problem; because, Global Warming will most likely stop with
the depletion of fossil fuels. Dr.
Bartlett maintains that he is merely reporting facts; he denies that he is
predicting the future. In spite of the
denial, predicting the future is exactly what this arithmetic is about. The question is not whether the future will
be predicted; but rather, how can it be predicted more accurately, in an
uptodate, and timely manner. Dr.
Bartlett’s arithmetic will remain the arithmetic of choice for exponential
growth predictions. Dr. Hubbert’s
modified bell curves will most likely remain the map of choice for Peak Growth
predictions.
Part
8
Part 8 of Dr. Bartlett’s talk concludes the series with
several terse quotes and some observations about the Aswan Dam, as an
illustration of man’s fixing things, only to make matters worse. However, his main point is this:
“So here’s a challenge. Can
you think of any problem, on any scale, from microscopic to global, whose long
term solution is in any demonstratable way, aided, assisted, or advanced by
having larger populations in our local levels, state levels, national level, or
global level? Can you think of anything that can get better if we crowd more
people into our cities, our towns, into our state, our nation, or on this
earth?”^{1}
Our answer is, “Yes, we can think of at least one problem
that might be resolved by an increase of population.”^{ }^{2} The
depletion of fossil fuels will result, temporarily in steam power, but
ultimately in horse, man, and other animal power to replace the work done by
internal combustion engines: it takes hundreds of horses, and possibly
thousands of men to do the work of one internal combustion engine. This introduces the possibility that survival
without fossil fuels may require more, not less men: but these will necessarily
be more widely distributed, and not crowded together. In essence, we have been left with a
modernized version of the Malthusian
Catastrophe.[3]
The thinking of Kenneth Arrow,[4] Paul Ehrlich,[5] and the like needs to be
brought into consideration. The
questions raised, need to be answered now, not ten years from now.
Part 9, Additions
Oil
Updates
The following
chart adds a column for USGS publicly reported undiscovered oil
statistics. This addition completes the
total volume of oil in the opinion of top experts. Since all countries are not included in this
evaluation, the world total will be at least this big, but not by much. The total calculated directly in the USGS
spreadsheet is only 1,666 Gbbl. Every
country contributing 5 Gbbl or more was included. Anyone wishing to complete a more thorough
study should consult: http://pubs.usgs.gov/dds/dds069/dds069ff/downloads/Excel%20tables/
or other sources. Open the Country Summary.xlsx file.
The mathematics
used in these tables is absolutely correct.
The only disputable factor is the data, which requires incessant
scrutiny.
There is no
excuse for the United States not to have a firm Federal Energy Policy, which
provides for reporting this information to the public every year, while
updating and reporting this information with special reports immediately after
any significant verified discovery.
The public should
not be forced to drill down in endless complicated and highly technical data
sources to find out the truth. This
should make front page headlines.
Rank

Country

Reserves (Gbbl)

Undiscovered F95, F50, & F5 (Gbbl)

Production (Mbbl/y)

Years at Zero Growth

Years at 1.03% Growth

1

Venezuela

296.5

5.984

767.0

394

157.9

2

Saudi Arabia

265.4

20.241

3,250.7

88

62.7

2.5

Australia (3.5223
Gbbl) 
223

1.389


3

Canada

175

11.208

986.2

189

105.1

4

Iran

151.2

35.707

1,497.5

125

80.4

5

Iraq

150.0

68.197

876.6

249

123.7

6

UAE

136.7

2.105

876.6

158

94.1

7

Kuwait

101.5

2.458

840.1

124

79.9

8

Russia

80

68.272

3,652.5

41

33.9

9

Kazakhstan

49

8.542

547.9

105

71.3

10

Libya

47

4.944

620.9

84

60.4

11

Nigeria

37

8.225

913.1

50

40.1

12

Qatar

25.41

0.030

401.8

63

48.8

13

China

20.35

28.339

1,497.5

33

28.1

14

United States

29.0

27.723

2,070.0

27

24.2

15

Angola

13.5

3.174

694.0

24

21.5

16

Algeria

13.42

11.773

620.9

41

33.9

17

Brazil

13.2

21.061

767.0

45

36.8

Offshore

1,181.225


Calculated World Total without Australia

1,604

1,613

21,367

151

91.1


Reported World Total

1,324

1,666

20,710

144

88.6


Calculated World Total with Australia

1,827

1,614

21,367

161

95.1

Dr. Bartlett and Dr. Hubbert have come under considerable
controversy over the Peak Oil theory.
The gainsayers generally follow along some line of declaration over how
much undiscovered oil remains in the ground.
These charts report the data taken from the United States Geological
Survey as of its 2011 study.[6] Other information was drawn from a United
States Department of Interior report.[7]
One must be very careful when handling this data. The units can be very confusing. When production is reported in units per day,
we must insist that someone is deliberately distorting the data to make
production seem smaller than it really is.
The USGS report gives several figures, the most representative of which
appears to be around 1,614 to 1,666 billion barrels worldwide. We will show more data in the United States
specific chart, for you to get the idea.
This number is actually smaller than Dr. Bartlett’s estimate of 2,000
billion barrels. There is no significant
reason to doubt Dr. Bartlett’s estimate that the world oil peak came at 2004,
and the world will run out of oil around the year 2100. Dr. Bartlett’s 3,000 billion barrel and 4,000
billion barrel curves are wildly generous in the light of the current data.
Gainsayers should be pushed hard to putup or shutup. If they have new information about other
sources of undiscovered oil, let them deliver their data to USDI and USGS for
verification and detailed reporting. Our
predictions are no better than our data.
Let them speak now, or forever after hold their peace. Gainsayers need to be forced to improve the
data if they are able.
Rank

Source

Country

Reserves
(Gbbl) 
Undiscovered F95, F50, & F5 (Gbbl)

Production (Mbbl/y)

Years at Zero Growth

Years at 1.03% Growth

United States Oil Reserves (Wiki)[8]


14

2011

United States

29.0

0

2,070.0

14

13.1

USGS

F95

29.0

5.4

17

15.3


USGS

F95, & F50

29.0

10.7

19

17.5


USGS

F95, F50, & F5

29.0

11.7

20

17.9


USGS

average

29.0

27.7

27

24.2


USGS

maximum

29.0

36.1

31

27.3


USDI[9]

29.0

134.0

79

57.7


World Oil Reserves (Wiki)^{7}


14

2012

United States

26.8

0

2,556.8

10

10.0

USGS

F95

26.8

5.4

13

11.8


USGS

F95, & F50

26.8

10.7

15

13.7


USGS

F95, F50, & F5

26.8

11.7

15

14.0


USGS

average

26.8

27.7

21

19.3


USGS

maximum

26.8

48.5

29

25.7


USDI^{9}

min

26.8

134.0

63

48.5

The 2011 “updated” information is slightly larger in its
reported reserves, because the original report has another year of
production. There may be other
inconsistencies. We wanted to show how
the USGS report details its reporting.
The F95 USGS number reports a volume with a 95% probability of success:
5.4 Gbbl is the USGS F95 number times 95%.
10.7 Gbbl is the USGS F50 number times 50% added to 5.4. 11.7 Gbbl is the USGS F5 number times 5%
added to 10.7. 27.7 Gbbl is the USGS
weighted (average) total which was reported with the worldwide figures: because
F95, F50, and F5 define three points on a curve, this USGS weighted (average)
total evaluates the entire curve, and thus is the best statistical value
available. 48.5 Gbbl is the raw total
of the F95, F50, and F5 USGS figures.
134 Gbbl is the figure reported in the Wiki, United States Oil Reserves
report which drew upon the USDI source.
These USGS and USDI figures clearly show that in 2012 we had
about 10 yearsworth of oil left in the United States. If undiscovered oil is actually discovered
and produced we might have another 3 to 53 years of oil left for our wildest
dreams. As anyone can plainly see,
undiscovered oil is exactly that: undiscovered.
And it is a probabilistic dice throw, whether we will find that oil or
not find it. At a span of less than 63
years, we are once again spending our children’s and grandchildren’s future.
There is absolutely no reason whatsoever not to conclude
that we remain in a serious energy crisis, in which we have very little time to
find remedies. There is more than
adequate cause for us to demand a simple accurate Federal Energy Policy that
explains the problem clearly, and in no uncertain terms. It is time for us to act together as a
unified nation. At the very least we
need to reduce our annual consumption to match the pace of undiscovered oil as
it is actually discovered, and brought into production. Moreover, we have no business selling oil to
anybody else. Out of respect for the
rest of mankind, our Federal Energy Policy needs to provide relief for the
world’s dwindling 95 year supply of oil, as well. We have an obligation to deal with this
crisis so as to minimize the risk of death from famine and exposure.
Natural
Gas
There is a massive public advertising campaign to draw
attention away from oil and gasoline shortages, and direct that attention to
natural gas and natural gas liquids.
Natural gas liquids are the heavier compounds removed from a natural gas
cut: these compounds include propane and butane. Liquid natural gas (LNG) is a different
beast: LNG is ordinary natural gas made liquid by compression; natural gas and
LNG are chemically identical. The topic
of natural gas liquids is too complex to report here, but we can look at
natural gas. Dr. Bartlett did not investigate
natural gas or natural gas liquids: so, this represents a considerable hole in
our understanding of energy.
Rank

Country

Reserves
(Tm^{3}) 
Undiscovered F95, F50, & F5
(Tm^{3}) 
Production (Tm^{3}/yr)

Years

Years at 5% Growth

1

Iran

33.60

3.21

0.1461

252

53

2

Russia

32.90

6.74

0.6696

59

28

3

Qatar

21.00

0.00

0.1167

180

47

4

Turkmenistan

17.50

1.55

0.05950

320

58

5

United States

9.460

2.38

0.6513

18

13

6

Saudi Arabia

8.200

1.19

0.09923

95

35

7

Venezuela

5.525

0.47

0.03120

192

48

8

Nigeria

5.246

0.50

0.09200

62

29

9

Algeria

4.502

1.17

0.08461

67

30

Offshore

117.60


Other

2.915


Calculated World Total

187.3

156.6

3.605

95

36

Worldwide natural gas reserves and undiscovered deposits are
in worse shape than for oil. Oil is
reporting 161 years of reserves, compared to natural gas at 95 years of
reserves. These numbers look enormous
until we consider two vital facts:
One. This is all the oil and
natural gas that there is and ever will be.
Two. Man’s destructive and
gluttonous penchant for growth militates that these numbers will drop like
rocks to 95 and 36 years respectively, or even less.
World Gas Reserves (Wiki)
Rank

Source

Country

Reserves
(Tm^{3}) 
Undiscovered F95, F50, & F5
(Tm^{3}) 
Production (Tm^{3}/yr)

Years

Years at 5% Growth

5

2012

United States

9.460

0

0.6513

15

11.0

USGS

F95

9.460

0.776

16

11.7


USGS

F95, & F50

9.460

1.651

17

12.4


USGS

F95, F50, & F5

9.460

1.837

17

12.6


USGS

average

9.460

2.382

18

13.0


USGS

maximum

9.460

6.290

24

16.0


USDI

no report

0

In our natural gas analysis we used 5% as a realistic growth
factor, because that is a number being bandied about in Federal Budget
debates. God knows what a more realistic
number might be. The way natural gas
power interests are pushing for expansion, it should be obvious that the sky is
the limit. It should be equally obvious
that fracking[10]
is with us, whether we like it or not.
As long as the money and the demand is on the table our leaders will
continue to ride roughshod over public interests: common man has no real voice
in this matter, other than to stop using the products.
The United States supply of natural gas is not eternal as
the ubiquitous advertisements boldly claim: far from it; at best, we have a 10
to 30 year supply. This compares to oil which
has a 10 to 63 year supply. This is
about money, and is directly opposed to the public interest. This is a plan to crash the country. The movers and shakers don’t give a damn that
millions of people will freeze or starve to death, while many others undergo
extreme hardship.
Coal
Updates
Natural gas will most likely be depleted first: it is
commonly advertised as the more desirable, clean fuel. It is also more easily produced: water removal,
scrubbing to remove dirt, and extraction of propane, butane, etc. may be all
that is required. Oil must be pumped,
distillation is more complex, and cat cracking may be involved. After natural gas and oil are depleted the
energy load will fall upon coal. There
is very little hope that the world will awake in time to deal seriously with
nuclear, wind, solar or other, more sustainable, energy technologies: man is
more like a lemming, than like a wizard.
When the coal is gone we will commence to burn our forests to the
ground.
Interestingly, we could find no data for undiscovered
coal. Such deposits must exist: but,
they are most likely under our forests, which will be destroyed when we mine
the coal. We did find a crude area plot from
USGS, Bulletin 1450B that paints a rough picture of undiscovered coal
deposits.[11]
Rank

Country

Reserves
(Mtons) 
Undiscovered (Mtons)

2008 Production (Mtons/yr)

Years at Zero Growth

Years at 2.69% Growth

1

United States

237,295

1,063

223

73


2

Russia

157,010

328.6

478

99


3

China

114,500

2,802

41

28


4

Australia

76,400

399.2

191

68


5

India

60,600

515.9

117

53


6

Germany

40,699

192.4

212

71


7

Ukraine

33,873


8

Kazakhstan

33,600

111.1

302

83


9

South Africa

30,156

252.6

119

54


10

Serbia

13,770


11

Columbia

6,746

74.0


12

Canada

6,528


13

Poland

5,709

144.0

40

27


14

Indonesia

5,529

240.2

23

18


15

Brazil

4,559


16

Greece

3,020


17

Boznia Herzegovina

2,853


36

All Others

5,613

182


Calculated World Total

860,884

6,869

125

55


2011 Report

860,884

7,695

112

52

The USGS area plot suggests that there is another 1,721,000
Mtons of undiscovered coal that is recoverable; and 2,583,000 Mtons of
undiscovered coal that is not recoverable without significant technological
advancements, and financial inducements.
Here are the worldwide approximations:
Status

Reserves
(Mtons) 
Undiscovered
(Mtons) 
2011 Production (Mtons/yr)[12]

Years at Zero Growth

Years at 2.69% Growth

Reserve

860,884


7,695

112

52

+ Recoverable

860,884

1,721,768

7,695

336

86

+ NotRecoverable

860,884

4,304,420

7,695

671

111

Here are the United States approximations:
Status

Reserves
(Mtons)

Undiscovered (Mtons)

2008 Production (Mtons/yr)

Years at Zero Growth

Years at 2.69% Growth

Reserve

237,295


1,063

223

73

+ Recoverable

237,295

474,590

1,063

670

110

+ NotRecoverable

237,295

1,186,475

1,063

1,786

146

Before we start crowing about a 1,786 year supply of coal,
and coal running out of our ears, we should consider a few sobering facts: One. More than 1,000 yearsworth of that coal is
presently notrecoverable. Two. At a minuscule 2.69% growth, even these gigantic
time spans are whittled down to less than 146 years of coal left. More realistically, we might have between 73
and 110 years of coal left. Once natural
gas, natural gas liquids, and oil are gone, no one will be able to restrain massive
and sudden coal production increases.
Here is the same chart based on modest 8% growth.
Status

Reserves (Mtons)

Undiscovered (Mtons)

2008 Production (Mtons/yr)

Years at Zero Growth

Years at 8% Growth

Reserve

237,295

1,063

223

38


+ Recoverable

237,295

474,590

1,063

670

51

+ NotRecoverable

237,295

1,186,475

1,063

1,786

64

Now we are able to project a 38 to 51 year supply of coal
remaining: up to 64 years if our technology improves greatly.
The human ability to destroy and devour is without bounds.
Population
Our population data showed a current world population of 7
billion, 162 million people, and a United States population of 317 million
people. Of course these numbers change
every day, so we arbitrarily froze the numbers at what we hope are reasonable
values: but in a year or so, they will be hopelessly out of date.
The world has over 4 billion acres under cultivation, and another
10 billion acres in fixed crops, such as forests, fruit trees, bushes, etc.: an
aggregate in excess of 14 billion acres of useable land worldwide. The United States has over 1 billion acres of
useable land.
Dividing the usable acres by the population yields the
number of acres per person: the world average is 2.01 acres per person; the
United States, 3.67; India, 0.45; China, 0.66; Russia, 16.04; Brazil,
7.49. We collected data for nearly every
country imaginable.
With the total depletion of fossil fuels, the ability to do
work will be greatly diminished.
Replacement of internal combustion engines with animal and human power
sources will be accomplished at magnitudes of hundreds and thousands. We do not know what the population saturation
point for earth is. It may well be that
the population will need to increase, but be better distributed.
Electricity[13]
According to the Wiki report world electricity production
looks like this:
·
Coal 41%
·
Oil 5%
·
Gas 21%
·
Sum of Fossil Fuels 67%
·
Nuclear 13%
·
Hydroelectric 16%
·
Wind 1%
·
Sum of Renewable 18%
·
Bio other 1%
United States (the world’s
largest user) production looks like this:
·
Coal 49%
·
Oil 1%
·
Gas 21%
·
Sum of Fossil Fuels 71%
·
Nuclear 19%
·
Hydroelectric 6%
·
Wind 1%
·
Sum of Renewable 8%
·
Bio other 2%
Top Users
1.
United States 22%
2.
China 17%
3.
Japan 5%
4.
Russia 5%
5.
India 4%
6.
Canada 3%
7.
Germany 3%
8.
France 3%
9.
Brazil 2%
10.
South Korea 2%
11.
UK 2%
12.
Italy 2%
Other
We have put no real effort into forest, oxygen, soil, or
other vital necessity depletions. We
desperately need the contributions of more and better minds to deal with these
weighty and complex issues.
We are also caught in a dilemma over Global Warming. If fossil fuels are depleted, even if only
gas and oil are gone in a few years, man’s ability to produce waste heat will
be greatly diminished, and Global Warming will probably stop all by
itself. We will be more concerned with
freezing and starvation. On the other
hand, if massive new discoveries of gas and oil become a reality, Global
Warming could prove to be a considerable danger; because man, given the
opportunity, will only increase consumption, with its attendant escalation of
waste heat.
Equations
The basic exponential equation:
y
(t) = a * b^{t}
Where a, is the value of y_{0},
the intercept where y (t) crosses the y axis, the
initial value when the horizontal, or x value is zero;
b is the exponential constant; and t is the time,
distance, or other factor plotted on the horizontal, or x axis. If r is the rate of growth:
b
= 1 + r
Doubling time, or 100% ordinary steady growth:
If we begin with an initial value of a, and a final value of
2a, we find the doubling time:
y
(t) = a * b^{t}
2a
= a * b^{t}: dividing both sides by a
2
= b^{t}
ln
(2) = ln (b^{t}) = t * ln (b)
t
(doubling time) = ln (2) / ln (b)
≅ 0.693
/ (r / t) or (69.3%) / (r% / t) or (70%) / (r% / t)
In developing the ruleofthumb approximation, we make note
of the fact that for r values of 10% or less, the ln
(1 + r) ≈
r, and 69.3% ≈ 70%.
The following chart compares exact and ruleofthumb calculations. These estimates are very good and usually err
on the safe side.

Growth % per year /
Growth time (years)


% / t

1

2

3

4

5

Exact

69.66

35.00

23.45

17.67

14.21

Estimate

70

35

23.3

17.5

14

% put

6

7

8

9

10

Exact

11.90

10.24

9.01

8.04

7.27

Estimate

11.7

10

8.8

7.8

7

In the chess board problem: we may number the squares from 1
to 64, or from 0 to 63. Since the Exponential Function always starts at t = 0, we prefer
including the idea of zero. Here are the
equations for calculating the number of grains on any square, where b =
200% per square and moving from square to square takes the place of
time, and the doubling time is 1 square:
y
(t) = 1 * 2^{t} = 2^{t}
y
(n) = 2^{n}: numbering from zero; or 2^{(n1)}:
numbering from one
Geometric accumulation:
The chess board problem also considers
accumulating the numbers as we go along.
This sum is known as a geometric series and solving it involves a
mathematical trick. Here it is:
∑_{1} =
a + ab + ab^{2} + ab^{3} + … + ab^{t}: multiplying by b
b
* ∑_{1} = ab + ab^{2} + ab^{3} + … + ab^{t} + ab
^{(t+1)}
We notice that both equations are identical
except for the first and the last terms: so, subtracting the first equation from
the second equation we arrive at something we can always calculate quite
easily.
b
* ∑_{1} – ∑_{1} =
a * b ^{(t+1)} – a: factoring
∑_{1}
* (b – 1) = a * (b ^{(t+1)} – 1):
dividing
∑_{1}
= a * (b ^{(t+1)} – 1) / (b – 1)
Dr. Bartlett’s remaining time equation:
T_{E}
≅
1 / k * ln (k * R / r_{0} + 1)
We begin by observing that: if
exponential growth is in actual practice, that the reserve is equal to the area
under the exponential curve.
y
(t) = a * b^{t}: the exponential curve
A (t) ≡ ∫ y (t) dt = ∫ a * b^{t} dt + C
The initial value, a, or y_{0},
is a constant. Let z = b^{t}. We employ logarithmic differentiation:
z
= b^{t}: taking the natural logarithm and
applying its properties
ln
(z) = ln (b^{t}) = t * ln (b)
dz
/ z = ln (b) dt
dz
= ln (b) * z dt = ln (b) * b^{t} dt:
integrating
∫ a*b^{t} dt =a / ln (b) ∫ ln (b) * b^{t} dt = a / ln (b) *
b^{t} + C
At t = 0, A = 0, and always a
= y_{0}
A
= 0 = y_{0} / ln (b) * b^{0} + C:
solving for C
C
= – y_{0} / ln (b): substituting and
factoring
R
= A = y_{0} / ln (b) * b^{t} – y_{0} / ln (b) = y_{0}
/ ln (b) * (b^{t} – 1): multiplying
(b^{t}
– 1) = R * ln (b) / y_{0} = ln (b) * R / y_{0}:
adding
b^{t}
= ln (b) * R / y_{0} + 1: taking the natural
logarithm
t
* ln (b) = ln [ln (b) * R / y_{0} + 1]:
dividing
T
= 1 / ln (b) * ln [ln (b) * R / y_{0} + 1]
We remember from before that b = 1 + r, and
that for small r (less than 0.10), ln (1 + r)
≈ r:
substituting….
T
≈ 1 / r * ln[r * R / y_{0} + 1]:
QED
So, now we have both an exact formula that even applies to
enormous values of r, and an approximation similar to the Rule of 70, which can
be worked with a slide rule and a pencil.
The natural logarithm is no longer a problem, since modern spreadsheets and
scientific calculators tackle it quite easily.
Our Conclusion
In the not far distant future, the world will return to an
agriculturally based economy. There will
be no job shortage: for, farm and forest hands will be in great demand. If there are automobiles, they will be steam,
muscle, solar, or battery powered.
Automobile manufacturing, sales, or maintenance will probably not
survive. Media businesses will diminish
or disappear. Boats will be wind
powered. Much of our present social
structure will be gone. Central national
governments, if they survive at all, will be replaced in power by smaller, more
efficient local governments. Public
services will vanish. Medicine and most
education will be taken away. Human beings
will be forced to find a different way, just to live. This is not all bad: life will be simpler.
[1]
Dr. Bartlett
[2]
Swanson
[3]
See http://en.wikipedia.org/wiki/The_Population_Bomb and http://en.wikipedia.org/wiki/Malthusian_catastrophe.
[4] http://en.wikipedia.org/wiki/Kenneth_Arrow
[5] http://en.wikipedia.org/wiki/Paul_R._Ehrlich
[6] http://pubs.usgs.gov/dds/dds069/dds069ff/downloads/Excel%20tables/
[7] http://en.wikipedia.org/wiki/Oil_reserves
[8] http://en.wikipedia.org/wiki/Oil_reserves_in_the_United_States
[9] http://pubs.usgs.gov/dds/dds069/dds069ff/
[10] http://en.wikipedia.org/wiki/Hydraulic_fracturing
[11] http://pubs.usgs.gov/bul/b1450b/b1450.htm
[12]
Updated production figures were applied to the 2008 data.
[13] http://en.wikipedia.org/wiki/Electricity_generation