**Next message:**ACampnona@aol.com: "Preach as you go and teach as you go LO24559"**Previous message:**AM de Lange: "Values and feelings LO24557"**In reply to:**Heidi and Dan Chay: "Energy quality of oil, etc.. LO24532"**Next in thread:**AM de Lange: "Energy quality of oil, etc.. LO24571"**Reply:**AM de Lange: "Energy quality of oil, etc.. LO24571"**Reply:**Folke Günther: "Energy quality of oil, etc.. LO24600"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Mail actions:**[ respond to this message ] [ mail a new topic ]

Replying to LO24532 --

Last week in a link-dense post I wrote:

*> Is anyone out there thinking about learning organizations in terms of 7
*

*> generations -- or 2?
*

*>
*

*> What are the implications of exponential growth -- where things double,
*

*> then
*

*> double again, and again...? Here's an interesting link:
*

*> http://www.npg.org/reports/bartlett_index.htm .
*

This link will take you to a paper by Dr. Bartlett who in the 1970's gave

as lucid a presentation as I've seen on the dynamics of exponential

growth. Here is an excerpt:

...Excerpt begins...

II. BACKGROUND

When a quantity such as the rate of consumption of a resource (measured in

tons per year or in barrels per year) is growing at a fixed percent per

year, the growth is said to be exponential. The important property of the

growth is that the time required for the growing quantity to increase its

size by a fixed fraction is constant. For example, a growth of 5 % (a

fixed fraction) per year (a constant time interval) is exponential. It

follows that a constant time will be required for the growing quantity to

double its size (increase by 100 %). This time is called the doubling

time T2 , and it is related to P, the percent growth per unit time by a

very simple relation that should be a central part of the educational

repertoire of every American.

T2 = 70 / P

As an example, a growth rate of 5 % / yr will result in the doubling of

the size of the growing quantity in a time T2 = 70 / 5 = 14 yr. In two

doubling times (28 yr) the growing quantity will double twice (quadruple)

in size. In three doubling times its size will increase eightfold (23 =

8); in four doubling times it will increase sixteenfold (24 = 16); etc.

It is natural then to talk of growth in terms of powers of 2.

III. THE POWER OF POWERS OF TWO

Legend has it that the game of chess was invented by a mathematician who

worked for an ancient king. As a reward for the invention the

mathematician asked for the amount of wheat that would be determined by

the following process: He asked the king to place 1 grain of wheat on the

first square of the chess board, double this and put 2 grains on the

second square, and continue this way, putting on each square twice the

number of grains that were on the preceding square. The filling of the

chessboard is shown in Table I. We see that on the last square one will

place 263 grains and the total number of grains on the board will then be

one grain less than 264.

How much wheat is 264 grains? Simple arithmetic shows that it is

approximately 500 times the 1976 annual worldwide harvest of wheat? This

amount is probably larger than all the wheat that has been harvested by

humans in the history of the earth! How did we get to this enormous

number? It is simple; we started with 1 grain of wheat and we doubled it

a mere 63 times!

Exponential growth is characterized by doubling, and a few doublings can

lead quickly to enormous numbers.

The example of the chessboard (Table I) shows us another important aspect

of exponential growth; the increase in any doubling is approximately equal

to the sum of all the preceding growth! Note that when 8 grains are

placed on the 4th square, the 8 is greater than the total of 7 grains that

were already on the board. The 32 grains placed on the 6th square are

more than the total of 31 grains that were already on the board. Covering

any square requires one grain more than the total number of grains that

are already on the board.

...End excerpt...

This line catches my eye, "...the increase in any doubling is

approximately equal to the sum of all the preceding growth!"

Thinking systemically, I'm interested in the relation of the doublings

I've more or less experienced in the last thirty to fifty years,

continuing growth trends, ramifications of delay in feedback, and

Zeitgeist assumptions of growth. For example, I understand vehicle growth

globally went from roughly 50 million cars in 1950 to more than 500

million cars now. The greenhouse gas curve similarly curves sharply up .

So, too, as I understand, with regard to our reliance on petroleum to fuel

intensive agricultural methods. So, too, RE the transport of goods.

Etc..

Do At's essentialities apply here? How about spareness, quantity-limit?

Oil, because of its quality, has been a rich source of free energy, i.e.,

as At observes, energy not needed simply to maintain current level of

organization, available, I assume, to emergent reorganization.

Today I read in the news about the US congress "a bill with bipartisan

support from two key senators was introduced Thursday to triple the use of

ethanol over the coming decade."

Yet here is what I have read from one of those other links I sent you

earlier: "Energy companies are in business to make money - not energy.

For example, economic subsidies allow ethanol companies to waste energy

while making a profit. Specifically, about 71% more energy is used to

produce a gallon of ethanol than the energy contained in a gallon of

ethanol. [24] Obviously, alternative energy technologies that require

energy subsidies are only viable as long as we don't need them!"

Enough for now.

Best wishes,

Dan Chay

--"Heidi and Dan Chay" <chay@alaska.com>

Learning-org -- Hosted by Rick Karash <Richard@Karash.com> Public Dialog on Learning Organizations -- <http://www.learning-org.com>

**Next message:**ACampnona@aol.com: "Preach as you go and teach as you go LO24559"**Previous message:**AM de Lange: "Values and feelings LO24557"**In reply to:**Heidi and Dan Chay: "Energy quality of oil, etc.. LO24532"**Next in thread:**AM de Lange: "Energy quality of oil, etc.. LO24571"**Reply:**AM de Lange: "Energy quality of oil, etc.. LO24571"**Reply:**Folke Günther: "Energy quality of oil, etc.. LO24600"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Mail actions:**[ respond to this message ] [ mail a new topic ]

* "Learning-org"
and the format of our message identifiers (LO1234, etc.) are
trademarks of Richard Karash.
*