Tuesday, November 18, 2014

Exponential Curve 3


Exponential Curve 3

Arithmetic, Population and Energy, Part 3


For the love of the human race.

Tuesday, November 18, 2014

Our Thesis


We are greatly indebted to Dr. Albert Allen Bartlett (1923-2013), former emeritus professor of physics at the University of Colorado, Boulder.[1]  These are Dr. Bartlett’s ideas, we are merely reporting them.  We have performed a lengthy analysis of Dr. Bartlett’s “arithmetic” elsewhere.[2]

One cannot investigate either energy policy or energy theory without a thorough understanding of the exponential curve.[3]

Arithmetic, Population and Energy, Part 3


The central piece of information to be gleaned in Part 3 is that we are running out of time.

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.”

Speed Matters

Dr. Bartlett illustrates such questions with a model of growth in a finite environment: bacteria in a 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.[4]

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.  We could multiply practical examples from cooking and explosives.[5]

1.     “When was the bottle half full? 
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.
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.”
[6]

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.

Momentum

What is also important to observe is that growth, as we approach high noon, 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.[7]

Oil

In the energy crisis, “we have a classic case of exponential growth against a finite source.”[8]

The average growth rate of world crude oil consumption, between the years 1880 and 1970 is approximately 7.04% per year.[9]  Continuing at this growth rate, without the discovery of massive new reserves, the world’s supply of crude oil would have been half consumed by 1991 and totally consumed by 2001.  Even with the discovery of massive new reserves, the rate of consumption is now so large that the available time remaining until total practical depletion, amounts to a few mere decades.

Dr. Bartlett notes, “Fortunately, the growth rate slowed because OPEC raised their oil prices.”  We calculated the new growth rate for the world from historical production data (1980-2012) and found it to be 1.030% per year.[10]  The doubling time has been extended from ten years, one decade to nearly seventy years.

Doubling Area Plot

This speed of exponential growth is demonstrated very forcefully by a doubling area plot.[11]

Coober Pedy

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,[12] 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.

Limited Progress

We have slowed growth to 1.030% per year.  Good for us.  Oil still doesn’t grow on trees.  We need to do more.  The sad facts are that both our nation and the world are nearly bankrupt in terms of oil reserves.  At the outside the world now has a nearly 95 year supply of oil.[13]  The wildly optimistic USDI report suggests that the United States might have an almost 58 year supply of oil.  Against this rising tide of destruction, we continue to discuss growth plans, rather than conservation plans.

China

China is becoming a major consumer of automobiles, and internal combustion fuels.

Disaster

Growth is a disaster waiting to happen.  We need a solid plan to contain and manage this disaster.  Sadly, 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.[14]  Instead of growth plans we need conservation plans.

Our Conclusion


Dr. Bartlett has correctly alerted us to the fact that we are out of time.  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.  The growth problem is not recognizable until 87% of the available time is gone.  Even at 87%, few would be observant enough to realize that there is a problem.  Shrewd observers might detect a problem when 97% of the time is gone; but most will be unaware, even at the last minute.  On the real life clock, it would appear that, realistically, we have only a few decades to wake up and change.  We have made significant changes since 1970, but these are scarcely sufficient.  We may have delayed our own death sentence by thirty years or so.




[1] http://en.wikipedia.org/wiki/Albert_Allen_Bartlett
[2] http://swantec-ep.blogspot.com/2014/11/energy-policy-analysis-3-ra.html
[3] http://www.albartlett.org/presentations/arithmetic_population_energy_video1.html
[4] If y = a * bt is growing to astronomical size in a very brief period, its velocity is growing much faster: v(y) = a * bt * ln(b) or ln(b) times as large as y: it increases from the third minute onward, and by noon it passes 4 times the size of y.  Acceleration is more alarming: a(y) = a * bt * ln(b) * ln(b) or (ln(b))2 times as large as y: it increases from the third minute onward, and by noon it is nearly 17 times the size of y.  This is the same as the unlimited ability to increase acceleration.
[5] Of course the time scales change with each example.  The actual doubling time must be measured in each case.
[6] Dr. Bartlett’s critical questions: if these three questions are understood, all of Part 3 is understood.
[7] As long as there is sufficient raw material present, food for the bacteria, the bacteria will continue to double.  The bacteria will only cease doubling when food is depleted or when conditions such as humidity and temperature alter their doubling pace.
[8] James R. Schlesinger, U. S. Secretary of Energy, in Time Magazine, April 25, 1977, p. 27  http://en.wikipedia.org/wiki/James_R._Schlesinger
[9] 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/
[10] http://www.indexmundi.com/energy.aspx?product=oil&graph=production
[11] Courtesy of Prof. Mario Iona (1917-2004), University of Denver, Physics Department: http://www.rbs0.com/Iona.htm
[12] http://en.wikipedia.org/wiki/Shale_oil_extraction
[13] This figure was revised upward from 85 years by using a more optimistic report for the United States.  It includes the maximum estimate for Coober Pedy.  Based on 2012 data this estimate is now 93 years.  These figures are already obsolete and need to be updated.
[14] http://www.eia.gov/pub/oil_gas/petroleum/feature_articles/2004/worldoilsupply/oilsupply04.html
[15] If you have been blessed or helped by any of these meditations, please repost, share, or use any of them as you wish.  No rights are reserved.  They are designed and intended for your free participation.  They were freely received, and are freely given.  No other permission is required for their use.

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