Energy Policy
Arithmetic, Population and Energy, Part 1
Revision A
For the love of the human
race.
Thursday, March 20, 2014
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 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.
Arithmetic, Population and Energy, Part 1
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 1.
The basic exponential equation:
y (t) = a * bt
Where, a, is the value of y0,
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.
b = 1 + r
The decimal rate of increase is r: so if r
is 5% or 0.05 per unit time, then b
would be 1.05 per unit time; if r is 100%
or 1.00 per unit time, then b would be 2.00
per unit time, in which case, y (t) would double every time a new
t milestone is passed: but that milestone could be one square,
one minute, one year, or fourteen years.
“The
greatest shortcoming of the human race is our inability to understand the
Exponential Function.”
The Exponential Function defines
patterns of ordinary constant steady growth.
In real life, growth is not a constant, but the math for variable
exponential growth is presently formidable.
We can accomplish all the necessary objectives by comparing a set of
growth rate analyses against each other {1%, 2%, 3%, … 5%, … n%},
or by limiting one growth rate to one range of values, then selecting a new
growth rate for another range of values.
In other words, by selecting a different map. Such sets of calculations will always give a
precise picture of the situation. Or we
can simply plot values on logarithmic graph paper, where steady growth will
appear as a straight line, while variable growth will graph as a curve.
The real problem is finding accurate data. Data collection and reporting are often done
fraudulently, lazily, and/or sloppily.
This data, in particular, represents gigantic amounts of money, so it
carries with it, powerful incentives and motivations on the part of all
concerned to bend the facts, distort the truth, and take shortcuts.
Doubling time, or 100% ordinary steady growth.
If we begin with an initial value of a, and a
final value of 2 * a, we find the doubling time:
y (t) = a * bt
2 * a = a * bt:
dividing both sides by a
2 = bt:
taking the ln of both sides
ln (2) = ln (bt) = t * ln (b):
dividing both sides by ln (b)
t (doubling time)
= ln (2) / ln (b):
substituting values
t (doubling time)
≈
0.693 // r/t = 69.3 // r%/t
t
(doubling time) ≈
70% // r%/t
In developing this rule of thumb 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 factor of 100 used in the lecture, simply converts a
decimal to a percent. This rule of thumb
makes it possible to calculate very accurate estimates in the head or on any
handy scrap of paper. Just divide 70
by whatever % of growth is in mind. The following table compares the accuracy of
the estimate to exact calculation.
|
|
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
|
These estimates are very good and usually err on the safe
side.
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. Dr. Bartlett starts counting at one. Here are the equations for calculating the
number of grains on any square, where b is 200% per square
and moving from square to square takes the place of time, and the
doubling time is 1 square.
y (t) = 1 * 2t
= 2t
y (n) = 2n:
numbering from zero; or,
y (n) = 2n-1:
numbering from one: for example
y (63) = 263:
numbering from zero; or,
y (64) = 264-1:
numbering from one.
The last square, whether it is called 63
or 64, contains about 9.223 x 1018 grains.
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:
Σ = a + ab + ab2 + ab3 + … +
abt: multiplying by b
b * Σ = ab + ab2 + ab3
+ … + abt + abt+1: multiplying by b
We notice that the two 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 * Σ – Σ = abt+1
– a: factoring
Σ * (b – 1) = a * (bt+1
– 1): dividing by (b – 1)
Σ = a * (bt+1 – 1)
/ (b – 1)
In this case a = 1, because we began with one
grain, and b = 2, because we’re doubling; so, at square 63 or 64, we have an accumulation of:
Σ(63) = (b63+1 – 1):
numbering from zero, or
Σ(64) = (b64–1+1 – 1):
numbering from one.
The accumulated grains amount to 18.447 x 1018 grains,
which in mathematics is called a seriously large number, it is too big to
understand, it is simply incomprehensible.
We make the observation based on an earlier square that the
number of grains on one square is always one larger than that the accumulation
of grains at the precious square.
Counting from zero the doubling at square 2 is 1
larger than the accumulation at square 1; the doubling at square 12
is 1 larger than the accumulation at square 11. We see that doubling progresses at a
formidably aggressive pace. The
following proof only applies to this case, where a = 1, and b
= 2. The general case is a
little more complicated to prove.
Σ(n) + 1 = y (n + 1): what we wish to
prove; substituting
a
* (bn+1 – 1) / (b – 1) +1 = a * bn+1: substituting values
1
* (2n+1 – 1) / (2 – 1) +1 = 1 * 2n+1: simplifying
(2n+1
– 1 +1 = 2n+1: QED
Dr. Bartlett’s use of mathematics is both correct and
precise. Dr. Bartlett’s mapping speaks
with deadly accuracy: he has been faithful in this task. This is exactly the way the exponential
growth model behaves. The exponential
growth model is, was, and continues to be the dominant social model chosen by
our leadership. Current federal budget
discussions[1] are arguing the merits of
a roughly 2.5% growth plan and a 4.5% growth plan. Neither side is willing to discuss a zero
or negative growth plan.
Moreover, the real facts are so clouded over by political obfuscation
that it is often impossible to detect the unvarnished truth. The truth lies buried under multiple layers
of varnish and wax.
We should have paid
closer attention to President Carter’s speech on energy in 1977. That was the last honest presidential
appraisal of the energy crisis: we have been living in a state of denial ever
since. Carter said “in each of these
decades (the 1950’s and 1960’s) more oil was consumed than in all of mankind’s
previous history.” That is a profound
observation.
Our Conclusion
The principal point made by this part of Dr. Bartlett’s talk
is that steady growth is in fact an aggressive, uncontrollable, vicious
monstrosity that eventually destroys the culture in which it is allowed to
exist. Growth must be restrained. If we are to take this “arithmetic”
seriously, as we must; we must convince; nay, we must compel, we must demand
that our leaders develop steady negative growth plans. If a 5% growth plan will double our
consumption in fourteen years, then a 5% reduction plan will
halve our consumption in fourteen years. The growth model must be put to death, before
it puts us to death. Nobody can live
with the 63rd/64th square.
We also ended up with a handy rule of thumb that converts
difficult to understand growth percentages into easily understood doubling
time.
t
(doubling time) ≈ 70% // r%/t
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