Energy Policy
Arithmetic, Population and Energy, Part 3
Revision A
For the love of the human
race.
Saturday, March 22, 2014
Our Thesis
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 oppression.
The central piece of
information to be gleaned in Part 3 is that we are running out of time.
Arithmetic, Population and Energy, Part 3
http://www.albartlett.org/presentations/arithmetic_population_energy_video1.html Better results were achieved by playing the
video clip directly from this site, rather than by linking through
YouTube. Click on the arrow in the
middle of the picture, rather than on the black bar at the top. This is Part 3.
Dr. Bartlett asks the question, “How long can growth
continue? Even with startling new
discoveries?” What kind of growth control
might be necessary? Then he quips about
controlled growth: “Arithmetic doesn’t hold in Boulder.”
This study is about growth in a finite environment; the
bacteria in the bottle. This model is
the same as the chess board model, without considering any accumulation. At 11:00 am there is one
bacterium in the bottle. Every minute
the bacteria grow steadily, doubling by division, so that the parent bacteria
divide into the children and the parents disappear. At noon the bottle is full of bacteria. What is different about this perspective of
the exponential equation is its emphasis on time, rather than size.
This must be fascinating for a biologist studying culture
growth: for over 52 minutes nothing seems to be happening, the culture appears
to be dead, unless it is observed under a microscope. Suddenly, it explodes in the last 8 minutes
filling the container.
Similarly, the baker observes rising bread. After 59 minutes, he observes that the bowl
is half full, and decides to come back in another hour or so. When he returns, the dough has run all over
the floor, the starch in the dough is completely consumed, and the dough is
ruined. After 59 minutes, the wise and
experienced baker, begins to watch the dough every minute, perhaps even
continuously, and pops it in the oven at the perfect moment.
1.
“When was the bottle half
full?
A. At 11:59, 1 minute before noon.
A. At 11:59, 1 minute before noon.
2.
“When would you first
realize that you were running out of space?
A. At 11:52 or later, when less than eight minutes remain.
A. At 11:52 or later, when less than eight minutes remain.
3.
“How long can growth
continue as a result of multiplying the available resources by 4: that is by
adding 3 times the resources ever known before?
A. At 12:02, after two additional minutes.”[1]
A. At 12:02, after two additional minutes.”[1]
Dr. Bartlett observes that this kind of thinking, “… is the
centerpiece of the national and global economies.” It should be clear by the end of this part of
Dr. Bartlett’s talk that national and global economies need to be changed. Leaders everywhere need to put the growth
mentality to death, before it puts us to death.
Here is a mathematical reproduction of Dr. Bartlett’s slide:
|
Clock Time (hr:mn)
|
Stop Watch (minutes)
|
Bacteria Count
|
Space Taken
|
Space Left
|
Time Left (minutes)
|
|
11:00
|
0
|
1
|
0.0%
|
100%
|
60
|
|
11:01
|
1
|
2
|
0.0%
|
100%
|
59
|
|
11:02
|
2
|
4
|
0.0%
|
100%
|
58
|
|
11:03
|
3
|
8
|
0.0%
|
100%
|
57
|
|
11:04
|
4
|
16
|
0.0%
|
100%
|
56
|
|
11:05
|
5
|
32
|
0.0%
|
100%
|
55
|
|
11:06
|
6
|
64
|
0.0%
|
100%
|
54
|
|
11:07
|
7
|
128
|
0.0%
|
100%
|
53
|
|
11:08
|
8
|
256
|
0.0%
|
100%
|
52
|
|
11:09
|
9
|
512
|
0.0%
|
100%
|
51
|
|
11:10
|
10
|
1,024
|
0.0%
|
100%
|
50
|
|
11:11
|
11
|
2,048
|
0.0%
|
100%
|
49
|
|
11:12
|
12
|
4,096
|
0.0%
|
100%
|
48
|
|
11:13
|
13
|
8,192
|
0.0%
|
100%
|
47
|
|
11:14
|
14
|
16,384
|
0.0%
|
100%
|
46
|
|
11:15
|
15
|
32,768
|
0.0%
|
100%
|
45
|
|
11:16
|
16
|
65,536
|
0.0%
|
100%
|
44
|
|
11:17
|
17
|
131,072
|
0.0%
|
100%
|
43
|
|
11:18
|
18
|
262,144
|
0.0%
|
100%
|
42
|
|
11:19
|
19
|
524,288
|
0.0%
|
100%
|
41
|
|
11:20
|
20
|
1,048,576
|
0.0%
|
100%
|
40
|
|
11:21
|
21
|
2,097,152
|
0.0%
|
100%
|
39
|
|
11:22
|
22
|
4,194,304
|
0.0%
|
100%
|
38
|
|
11:23
|
23
|
8,388,608
|
0.0%
|
100%
|
37
|
|
11:24
|
24
|
16,777,216
|
0.0%
|
100%
|
36
|
|
11:25
|
25
|
33,554,432
|
0.0%
|
100%
|
35
|
|
11:26
|
26
|
67,108,864
|
0.0%
|
100%
|
34
|
|
11:27
|
27
|
134,217,728
|
0.0%
|
100%
|
33
|
|
11:28
|
28
|
268,435,456
|
0.0%
|
100%
|
32
|
|
11:29
|
29
|
536,870,912
|
0.0%
|
100%
|
31
|
|
11:30
|
30
|
1.074E+09
|
0.0%
|
100%
|
30
|
|
11:31
|
31
|
2.147E+09
|
0.0%
|
100%
|
29
|
|
11:32
|
32
|
4.295E+09
|
0.0%
|
100%
|
28
|
|
11:33
|
33
|
8.590E+09
|
0.0%
|
100%
|
27
|
|
11:34
|
34
|
1.718E+10
|
0.0%
|
100%
|
26
|
|
11:35
|
35
|
3.436E+10
|
0.0%
|
100%
|
25
|
|
11:36
|
36
|
6.872E+10
|
0.0%
|
100%
|
24
|
|
11:37
|
37
|
1.374E+11
|
0.0%
|
100%
|
23
|
|
11:38
|
38
|
2.749E+11
|
0.0%
|
100%
|
22
|
|
11:39
|
39
|
5.498E+11
|
0.0%
|
100%
|
21
|
|
11:40
|
40
|
1.100E+12
|
0.000%
|
100%
|
20
|
|
11:41
|
41
|
2.199E+12
|
0.000%
|
100%
|
19
|
|
11:42
|
42
|
4.398E+12
|
0.000%
|
100%
|
18
|
|
11:43
|
43
|
8.796E+12
|
0.001%
|
100%
|
17
|
|
11:44
|
44
|
1.759E+13
|
0.002%
|
100%
|
16
|
|
11:45
|
45
|
3.518E+13
|
0.003%
|
100%
|
15
|
|
11:46
|
46
|
7.037E+13
|
0.006%
|
100%
|
14
|
|
11:47
|
47
|
1.407E+14
|
0.012%
|
100%
|
13
|
|
11:48
|
48
|
2.815E+14
|
0.024%
|
100%
|
12
|
|
11:49
|
49
|
5.629E+14
|
0.049%
|
100%
|
11
|
|
11:50
|
50
|
1.126E+15
|
0.098%
|
100%
|
10
|
|
11:51
|
51
|
2.252E+15
|
0.195%
|
100%
|
9
|
|
11:52
|
52
|
4.504E+15
|
0.391%
|
100%
|
8
|
|
11:53
|
53
|
9.007E+15
|
0.781%
|
99%
|
7
|
|
11:54
|
54
|
1.801E+16
|
1.563%
|
98%
|
6
|
|
11:55
|
55
|
3.603E+16
|
3.125%
|
97%
|
5
|
|
11:56
|
56
|
7.206E+16
|
6.25%
|
94%
|
4
|
|
11:57
|
57
|
1.441E+17
|
12.5%
|
88%
|
3
|
|
11:58
|
58
|
2.882E+17
|
25%
|
75%
|
2
|
|
11:59
|
59
|
5.765E+17
|
50%
|
50%
|
1
|
|
Noon
|
60
|
1.153E+18
|
100%
|
0%
|
0
|
|
12:01
|
61
|
2.306E+18
|
200%
|
-100%
|
-1
|
|
12:02
|
62
|
4.612E+18
|
400%
|
-300%
|
-2
|
What is important to observe from this table is that growth is
now moving at express train speed. The
problem is undetectable until there are less than 8 minutes left
on the clock. It may now be impossible
to stop the train in time to avoid a catastrophe. The momentum is very great. By 1:00 pm the bacteria will have spilled out
of all 4 bottles, consumed the laboratory, and taken over the entire building. This is the same mathematical model as that
used for explosions.
The average growth rate of world crude oil consumption, between
the years 1880 and 1980 is approximately 7.04% per year.[3] Without the discovery of massive new reserves
the world’s supply of crude oil would have been half consumed by 1991. Even with the discovery of massive new
reserves, the rate of consumption is now so large that the available time left
for total practical depletion, amounts to a few mere decades. At a continuing depletion rate of 7.04%
we are able to reproduce the following table of estimated values.[4] The computer produces slightly more precise
numbers than the slide rule or logarithmic paper: this explains the minor
differences between the talk slide and the table below.
Dr. Bartlett’s slide is hard to read, so we reconstructed it. In any case, we need our own spreadsheet with
which to examine various growth rates and fresh data. Here is how we did it.
|
Year
|
Crude Oil
Production (G-bbls) |
Accumulated
Consumption (G-bbls) |
Reserves
Left (G-bbls) |
Fraction Left
|
Time
|
|
1971
|
7/8
|
11:57
|
|||
|
1972
|
|||||
|
1973
|
20.4
|
334
|
1,765
|
||
|
1974
|
21.8
|
356
|
1,743
|
In the first row we entered whatever titles suited us. In keeping with modern international notation
we used the letter G instead of billions.
In the 1971 row we reasoned backward that this was the 7/8
reserves left point or 11:57 on our bacteria bottle clock model, so we started
there. From that point on we reserved
one row for each year.
In the 1973 row we entered that data exactly as we found it
on Dr. Bartlett’s slide.
In the 1974 row we made the following calculations using
7.04% as our Depletion Growth Rate. This
number was stored in its own block on the spreadsheet.
·
In the second column: y
(t) = a * bt; a = 20.4,
b = 1.0704, t = the current year – 1973. It looks like this:
=$C$88*(1+$D$84)^(B89-$B$88). Notice
that the blocks for a, b, and the starting year are
all frozen: the F4 key creates the $ that freeze the location.
·
In the third column: we
simply added the number above to the number on the left: =D88+C89.
·
In the fourth column: we
subtracted the number from column two on the left from the number above: =E88-C89. Then we refined it with a conditional
statement that prevented the calculation from going below zero: =IF(E88-C89<0,0,E88-C89).
·
Finally, we added notations
for the fractions remaining and the time on the bacteria bottle clock
model. These latter are not essential,
but they help dramatize the acceleration present in this chart.
Now we simply copy these calculations down for as many years
into the future as we care to study.
Scientists may want a 100 year or longer plan. Business planners may be happy with a 30
year plan. Nearly everyone needs
to have access to some kind of a plan or other.
As each year passes, the predictive calculations can be replaced with
hard data. In this case the second
column calculation will need to be corrected: for 1973 will no longer be the
starting year. If many depletion growth
rate changes are anticipated we can easily add a column for depletion growth
rate, to account for shifts in growth.
Hopefully, we would be able to stem this tide, and see zero growth, or
even negative growth rates, as we learn to better conserve our natural resources.
Here is the full completed chart at 7.04% growth:
|
Year
|
Crude Oil
Production (G-bbls) |
Accumulated
Consumption (G-bbls) |
Reserves
Left (G-bbls) |
Fraction Left
|
Time
|
|
1971
|
7/8
|
11:57
|
|||
|
1972
|
|||||
|
1973
|
20.4
|
334
|
1,765
|
||
|
1974
|
21.8
|
356
|
1,743
|
||
|
1975
|
23.4
|
379
|
1,720
|
||
|
1976
|
25.0
|
404
|
1,695
|
||
|
1977
|
26.8
|
431
|
1,668
|
||
|
1978
|
28.7
|
460
|
1,639
|
||
|
1979
|
30.7
|
490
|
1,609
|
||
|
1980
|
32.8
|
523
|
1,576
|
||
|
1981
|
35.2
|
558
|
1,541
|
3/4
|
11:58
|
|
1982
|
37.6
|
596
|
1,503
|
||
|
1983
|
40.3
|
636
|
1,463
|
||
|
1984
|
43.1
|
679
|
1,420
|
||
|
1985
|
46.2
|
726
|
1,373
|
||
|
1986
|
49.4
|
775
|
1,324
|
||
|
1987
|
52.9
|
828
|
1,271
|
||
|
1988
|
56.6
|
884
|
1,215
|
||
|
1989
|
60.6
|
945
|
1,154
|
||
|
1990
|
64.9
|
1,010
|
1,089
|
||
|
1991
|
69.4
|
1,079
|
1,020
|
1/2
|
11:59
|
|
1992
|
74.3
|
1,154
|
945
|
||
|
1993
|
79.5
|
1,233
|
866
|
||
|
1994
|
85.1
|
1,318
|
781
|
||
|
1995
|
91.1
|
1,409
|
690
|
||
|
1996
|
97.5
|
1,507
|
592
|
||
|
1997
|
104.4
|
1,611
|
488
|
||
|
1998
|
111.8
|
1,723
|
376
|
||
|
1999
|
119.6
|
1,843
|
256
|
||
|
2000
|
128.0
|
1,971
|
128
|
||
|
2001
|
137.1
|
2,108
|
0
|
Noon
|
|
|
2002
|
146.7
|
12:01
|
|||
|
2003
|
157.0
|
||||
|
2004
|
168.1
|
12:02
|
As Dr. Bartlett notes, “Fortunately, the growth rate slowed
because OPEC raised their oil prices.”
But the terrible wars we’ve fought since 1990 have been, to a great
extent, over this oil and who owns it.
In the process of waging these extravagant wars, we have succeeded in
squandering huge quantities of these precious oil reserves
A 2012 report[6] rates the world oil
reserves at 1,324 G-bbl.
My calculations from the same report show 1,602 G-bbl, so
the report seems to contain errors.
Adding in the latest shale oil find at Coober Pedy, Australia, yields a
maximum of 1,825 G-bbl. At
the present estimated rate of world production of 58.5 M-bbl per day,
or 21.367 G-bbl per year, we have roughly an 85 year
supply of oil at zero growth.
The problem is that oil production is not a zero growth industry. At a modest 1.030% growth per year,
the world has less than 62 years before it runs out of oil. In the same report, the United States claims 26.8
G-bbl, being produced at 7 M-bbl per day, or 2.557 G-bbl
per year. At this pace we have a
10 year supply, at which point we will be totally dependent on
foreign oil. If we increase our
production, we have even less than 10 years.
Russia, on the other hand, reports reserves for 22 years at zero growth
and less than 19.8 years at 1.030% growth.
Here is our complete set of data as collected:
|
Rank
|
Country
|
Reserves
(G-bbl) |
Production
(M-bbl/d) |
Production
(M-bbl/y) |
Years at
Zero Growth |
Years at
1.030% Growth |
|
1
|
Venezuela
|
296.5
|
2.1
|
767.0
|
387
|
156.3
|
|
2
|
Saudi Arabia
|
265.4
|
8.9
|
3,250.7
|
82
|
59.3
|
|
2.5
|
Australia (3.5-223 G-bbl)
|
223
|
0
|
0.0
|
0.0
|
|
|
3
|
Canada
|
175
|
2.7
|
986.2
|
177
|
101.1
|
|
4
|
Iran
|
151.2
|
4.1
|
1,497.5
|
101
|
69.3
|
|
5
|
Iraq
|
150.0
|
2.4
|
876.6
|
171
|
98.8
|
|
6
|
UAE
|
136.7
|
2.4
|
876.6
|
156
|
93.2
|
|
7
|
Kuwait
|
101.5
|
2.3
|
840.1
|
121
|
78.6
|
|
8
|
Russia
|
80
|
10
|
3,652.5
|
22
|
19.8
|
|
9
|
Kazakhstan
|
49
|
1.5
|
547.9
|
89
|
63.5
|
|
10
|
Libya
|
47
|
1.7
|
620.9
|
76
|
56.0
|
|
11
|
Nigeria
|
37
|
2.5
|
913.1
|
41
|
33.9
|
|
12
|
Qatar
|
25.41
|
1.1
|
401.8
|
63
|
48.8
|
|
13
|
China
|
20.35
|
4.1
|
1,497.5
|
14
|
12.7
|
|
14
|
United States
|
26.8
|
7
|
2,556.8
|
10
|
10.0
|
|
15
|
Angola
|
13.5
|
1.9
|
694.0
|
19
|
17.7
|
|
16
|
Algeria
|
13.42
|
1.7
|
620.9
|
22
|
19.5
|
|
17
|
Brazil
|
13.2
|
2.1
|
767.0
|
17
|
15.8
|
|
Calculated Sum
without Australia |
1,602
|
58.5
|
21,367
|
75
|
55.6
|
|
|
Reported Sum
|
1,324
|
56.7
|
20,710
|
64
|
49.2
|
|
|
Calculated Sum
with Australia |
1,825
|
58.5
|
21,367
|
85
|
61.4
|
Just look at Australia.
With the find at Coober Pedy, Australia has the potential of being the
third largest reserve in the world.
Potential. Let’s face some
realities: it is shale oil,[7] not liquid pumped crude;
it’s not in production; its exact volume is unknown and could be as low as 3.5 G-bbl,
which would make it the world’s smallest reserve; not the overly optimistic 223
G-bbl that everyone grasps after. This
is like claiming victory in war before the first shot of the first battle is
fired.
Let’s compare this with Dr. Bartlett’s data.
|
Year
|
Crude Oil
Production (G-bbls) |
Accumulated
Consumption (G-bbls) |
Reserves
Left (G-bbls) |
Fraction Left
|
Time
|
|
1973
|
20.4
|
334
|
1,765
|
||
|
2012
|
21.4
|
1,825
|
y (t) = a * bt:
dividing by a
bt =
y / a: taking the root 1/t
b = (y / a)(1/t):
substituting values
b = (21.4 / 20.4)(1/(2012-1973)
= 100.1%: solving for r
r = b – 1 =
0.119%
Now we have some reasonably hard data to show that between
1880 and 1980 the growth rate of fuel production is approximately 7.04%
per year. Somewhere around the
end of that era the growth rate was broken, largely due to the efforts of the
Carter administration. From 1973/1980 to
the present, based on predictions the growth rate of fuel production was
reduced to around 0.119%. Even
though this calculation is a crude estimate, which we shall improve with new
data, it is corroborated by the fact that very little money was invested in new
refineries since this period.
We recently located annual world production data for the
period between 1980 and 2012.[8] By analyzing this data with a regression
analysis of its ln plot we get the best possible data. The end point analysis by the formula we just
used yields 0.715%. Regression
analysis shows an actual growth rate from 1980 to 2012 of 1.030%. This is actual data analysis, not a predictive
approximation.
We can also calculate the peak production maximum value and
latest date from these numbers. Factors
that we have not yet considered will also influence this date: principal among
them are changes in growth rate and new discoveries, which may be evaluated by including
undiscovered oil. Based on 1.030% growth
without including undiscovered oil world oil production cannot peak at greater
than 40 G-bbl per year or later than 2073.
United States oil production cannot peak at greater than 2.8 G-bbl per
year or later than 2022. These peaks are
based on the catastrophic failure assumption.
Based on other considerations we have good reason to believe that these
peaks have already occurred.
If we multiple the production rate of 21.4 by the 39
intervening years, we discover that 833 G-bbl of oil was produced in this
period. Since we began with 1,765 G-bbl
of oil, we saved about 932 G-bbl of oil worldwide. This is very good news, because at 7.04% we
were destined to consume every drop of this by 2001. This is truly a notable conservation effort:
but it is not enough. Since that time we
have found about 886 G-bbl of new reserves, a truly impressive find: but it is
not enough. The figures are deceptive;
it looks like a lot of oil; it looks like we are better off than in 1973; it
looks like somebody “cried, Wolf!” The
bad news is that all of this oil, our remaining reserve of 1,825 G-bbl of oil will
last a mere 85 years if we don’t increase world oil production at all, not even
1% per year. The chances that we will
not double world oil production in a few years are very small. As China comes on line with a pent-up demand
for motor vehicles, they will soon eclipse the United States as the world’s
largest oil consumer. We will do well if
this reserve lasts 43 to 62 years worldwide.
In the meantime, the United States economy will tank,
because our piddling, minuscule oil reserve of 10 years will be gone, and we
will be at the total mercy of those few nations who are still willing to sell
oil to us. At this point we will learn
how many real friends we have: and I fear we will discover that we, like Smaug,[9] have made a lot of
enemies.
We have slowed growth, we have nearly stopped it. Good for us.
Oil still doesn’t grow on trees.
We need to do more. The sad facts
are that our nation is nearly bankrupt in terms of oil reserves. The world is nearly bankrupt in terms of oil
reserves. At the outside we have an 85
year supply, without more, much needed, discoveries we could have as little as
a 43 year supply left worldwide. Against
this rising tide of destruction, we continue to discuss growth plans, rather
than conservation plans. China is
becoming a major consumer of automobiles, and internal combustion fuels. This is a disaster waiting to happen. We need a solid plan to contain and manage
this disaster. Sadly the industrialized
nations will suffer most: for they are the ones who have built their vast
empires on fossil fuel dependency. When
fossil fuels die, these nations will also die, because they haven’t got the
sense and foresight to develop alternative energy sources in a timely manner.[10]
Our Conclusion
Dr. Bartlett has correctly alerted us to the fact that we
are out of time. There is nothing wrong
with his understanding of the exponential curve with respect to its
implications for time. The focus of Dr.
Bartlett’s analysis is moving away from overpopulation to overconsumption as
his argument develops. As promised, we
updated his data with the best data we could find at the moment. However, this is an ongoing quest, and we are
very dependent on energy data experts for accurate data. We promise to provide similar updates for
coal, natural gas, and any other resource of importance to us. This part of the study emphasizes the fact
that on the scaled down bottle clock model, we have only minutes left to make a
rational decision, before the raging forces of nature make all the decisions
for us. On the real life clock, it would
appear that, realistically, we have only a few decades to wake up and change. We have made changes since 1970, but these
are scarcely sufficient. We may have
delayed our own death sentence by thirty years or so.
1.
“When was the bottle half
full?
A. At 11:59, 1 minute before noon.
A. At 11:59, 1 minute before noon.
2.
“When would you first
realize that you were running out of space?
A. At 11:52 or later, when less than eight minutes remain.
A. At 11:52 or later, when less than eight minutes remain.
3.
“How long can growth
continue as a result of multiplying the available resources by 4: that is by
adding 3 times the resources ever known before?
A. At 12:02, after two additional minutes.”1
A. At 12:02, after two additional minutes.”1
In the energy crisis,
“we have a classic case of exponential growth against a finite source.”2
[1]
Dr. Bartlett’s critical questions: if these three questions are understood, all
of Part 3 is understood.
[2]
James R. Schlesinger, U. S. Secretary of Energy, in Time Magazine,
April 25, 1977, p. 27 http://en.wikipedia.org/wiki/James_R._Schlesinger
[3]
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/
[4]
Watt, Kenneth E. F., The Titanic Effect (e. P. Dutton, 1974: 268
pages): http://books.google.com/books/about/The_Titanic_Effect.html?id=5lw0AAAAMAAJ
[5]
Courtesy of Prof. Mario Iona (1917-2004), University of Denver, Physics
Department: http://www.rbs0.com/Iona.htm
[6] http://en.wikipedia.org/wiki/Oil_reserves
[7] http://en.wikipedia.org/wiki/Shale_oil_extraction
[8] http://www.indexmundi.com/energy.aspx?product=oil&graph=production
[9]
Smaug is the fictional dragon in J. R. R. Tolkien's, The Hobbit. He is an apt picture of American gluttony and
greed. If Nazi Germany were the Smaug of
Tolkien's lifetime, the United States is the Smaug of our world today. The curse of the ring still plagues us.
[10] http://www.eia.gov/pub/oil_gas/petroleum/feature_articles/2004/worldoilsupply/oilsupply04.html
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