Arithmetic, Population and Energy, Part 1

Energy Policy

Arithmetic, Population and Energy, Part 1

For the love of the human race.

Saturday, February 15, 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 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, up-to-date 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, up-to-date 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 zero-sum 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.

Our report, which will soon be published, will examine Dr. Bartlett’s mathematics, science, mapping, data, and proposed solutions in detail.

http://www.youtube.com/watch?v=umFnrvcS6AQ

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 * b^t

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.

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 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 (time) = ln(2)/ln(b) ≅ .693/(r / t) or (69.3%)/(r% / t) or
(70%)/(r% / t)

In developing the 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.

	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.  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 * 2^t = 2^t

y(n) = 2^n: numbering from zero; or 2^(n-1): numbering from one

y(63) = 2^63: numbering from zero

y(64) = 2^(64-1): 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:

∑ = a + ab + ab^2 + ab^3 + … + ab^t: multiplying by b

b * ∑ =  ab + ab^2 + ab^3 + … + ab^t + ab^(t+1)

We notice that the two equations are identical except for the first and the last terms: so, subtracting Σ from b * Σ we arrive at something we can always calculate quite easily.

b * ∑ - ∑ = ab^(t+1) - a: factoring

∑ * (b - 1) = a * (b^(t+1) - 1): dividing

∑ = a * (b^(t+1) - 1)/(b - 1)

In this case b is 2; so, at square 63 or 64, we have an accumulation of:

Σ(63) = 2^(63+1) - 1: numbering from zero

Σ(64) = 2^(64-1+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)

a * (b^(n+1) - 1)/(b-1) + 1 = a * b^(n+1): substituting

1 * (2^(n+1) - 1) + 1 = 1 * (2^(n+1))

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 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.

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.