Sustainability 105

Sustainability 105

Thursday, May 29, 2014

Sustainability Quiz 2 Answers

Now that finals are over and you finally graduated.  It’s about time!  Here it was.  Time for another quiz.  You are beginning to slack off.  You need to be reenergized with a quiz that you can’t possibly flunk.

1. How much verified reserve oil is currently in the Unites States?

Answer 1.  Just about any number will do, provided that you’re happy with it.  Only you can decide whether it’s important to strive for hard data or accept what the hype from advertisers and politicians say is true.  Here is a hint.  What advertisers and politicians say is frequently true, but their words are often cloaked in such a way as to hide their real impact.

ü If you get your number from an internet report, what is the date of the report.

ü If you invent a silly guess number just to see where this might be going, invent a date.

ü Watch out for lookup number scales: M means thousands on a Latin scale; MM means millions on a Latin scale; I use SI units where M (Mega) means millions, G (Giga) means billions, and T (Terra) means trillions.  Most reports use Latin scales: tricky devils aren’t they?  If you get confused as an engineering, math, or science major.  Shoot for a number in barrels (bbl), and Oh, btw, barrel size isn’t standardized worldwide.  Aren’t you glad this isn’t a real test?

ü Here is a hint.  I found 26.8 G-bbl of oil in a 2012 report.  What did you find?  Did you get a better date or number?  What might have caused that?

2. How much undiscovered oil is currently in the Unites States?

Answer 2.  Same as Answer 1.

ü No, I’m not a fruit cake, there really is such a thing.  It was discovered by seismic echos, compared to know production formations, and given a probability of success from the comparrison.  Slick, huh?  These oil men are sneaky.

ü The same rules apply.  Invent a number if you want too.  Watch out for scale sizes.  Get help if you need it.

ü Here is a hint.  The biggest number I could find was 134.0 G-bbl of oil in a 2012 report.  That is a serious lot of oil folks.

3. How much oil is currently in production in the Unites States?

Answer 3.  Same as Answers 1 and 2.

ü I found 7 M-bbl per day.  Here is where it gets really tricky.  The lookup number was 7 MMbbl (millions, remember, Latin?).  My M means Mega, that’s millions too (SI).  But it’s per day, so we have to multiply by 365.25 days in the average year.  Who wants to do this stuff in days?  What did you come up with?  I came up with 2,557 M-bbl per day, give or take.  That’s the same as 2.557 G-bbl per day, close enough.

ü If you got a seriously bigger number, what might cause that?  Take a stab at it.

4. Now divide the answer for question 1 by the answer for question 3.  What did you get?

Answer 4.  Check your calculator or computer.

ü I got 10 years.  Make sure your units are the same size when you divide.

ü This is the minimum number of years for oil to last.  Scary ain’t it?

ü But wait!  My report was made in 2012, this is 2014.  I’ve got to subtract the two years that are already gone.  That’s 8 years left.  What did you get?

5. Look at question 2 again.  What do you think the odds are for finding all that undiscovered oil?  Multiply that number by the answer for question 2.

Answer 5.  Same as Answer 4.

ü I’m an optimist.  I used 100%.  Gee, I wish that were really true.  Don’t you wish that every well drilled came in like the Mary Sudik, that blew oil all the way from OKC’s south side to Norman.  Oh well, back to reality.

ü Still 134.0 G-bbl of oil at 100%.

6. Now divide the answer for question 5 by the answer for question 3.  What did you get?

Answer 6.  Same as Answers 4 and 5.

ü I got 53 years.

ü Add that to the final answer in question 4.  Hmm…  8 + 53 = 61 years.

ü This is the maximum number of years for oil to last.  As Porky Pig used to say at the end of the kids cartoons, “Yuk.  Yuk.  That’s all there is folks.”

ü I don’t care if you got 80 and 5,300.  This is science folks, not advertising or politics.  It would be nice if one of us got the right answer though.  Then we could come up with a plan.

7. Here is a hardball question.  How long will that oil last if we speed up production and become the world’s largest producer of oil?

Answer 7.  Here is the equation you need to make the calculation.

T = 1 / ln(b) * ln[ln(b) * R / y₀ + 1]

The number b is a business or political descision.  If you decide to grow any industry at 5% per year, b = 1.05 and ln(b) ≈ .05.  For 2% growth, b = 1.02 and ln (b) ≈ .02.  R/y0 are the results we calculated in Questions 4 and 6: namely 8 and 61 years, respectively.  Eight years is so short it doesn’t change much: 2% growth reduces to 7.4 years, while 5% growth reduces to 6.7 years.  The undiscovered oil allows more working room, provided that we find it.  Sixty-one years is cut to 40 years at 2% and 28 years at 5%.  When our government plans a 5% annual growth in the economy, they are planning to destroy our nation.  You do the math.

8. Want another one?  What would we have to do to make that oil last forever?

Answer 8.  This is the theory of Sustained Availability, which is the use of exponential equations to make a substance last forever (theoretically).

k = 1/A, and

t = ln(2) / k ≈ 0.693 / k,

So using the results for Questions 4 or 6: 1/8 = .125 or 12.5% and 1/61 = .016 or 1.6%.  These numbers mean that if we have 8 years worth of oil left, we can make it last forever by reducing consumption/production by 12.5% per year, every year for eternity; or if we have 61 years worth of oil left, we can make it last forever by reducing consumption/production by 1.6% per year.  As a practicality this cannot be made to work forever.

The second equation suggests that a half life for 8 years worth of oil with consumption reduced at 12.5% per year will be over 5.5 years and with continued careful conservation of this precious resource we can make it last almost 28 years.  Careful conservation can stretch a 61 year supply of oil to over 211 years.

A 12.5% reduction for at least 5 years is pretty hard to achieve.  Reducing consumption by 1.6% per year for 5 years should be a piece of cake.  It should be obvious that greater reductions for longer periods will extend the life of the resource even more.

9. Last question.  It’s your move.  What is your move?

Additional bonus questions

10. Repeat questions 1-9 for natural gas.

11. Repeat questions 1-9 for natural gas liquids (NGL).

12. Repeat questions 1-9 for coal.

13. Repeat questions 1-9 for forests.

14. Repeat questions 1-9 for any other resource of interest to you.

Final Grade

As far as this quiz is concerned you got an A++, 105%, better than Ivory soap.  Your real grade will be determined by your performance in life and by history.

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.