Lesson 7 - Chaos Theory
Systems - no matter how complex they may be - rely upon an underlying order
Very simple or small systems and events can cause very complex behaviours or events
In a scientific context, the word chaos has a slightly different meaning than it does in its general usage as a state of confusion, lacking any order.
Chaos, with reference to chaos theory, refers to an apparent lack of order in a system that nevertheless obeys particular laws or rules; this understanding of chaos is synonymous with dynamical instability.
Dynamical instability is a condition discovered by the physicist Henri Poincare in the early 20th century that refers to an inherent lack of predictability in some physical systems.
The two main components of chaos theory are the ideas that systems - no matter how complex they may be - rely upon an underlying order, and that very simple or small systems and events can cause very complex behaviors or events. […]
Edited from http://whatis.techtarget.com/definition/0,,sid9_gci759332,00.html
The butterfly effect
Does the Flap of a Butterfly’s Wings in Brazil
set off a Tornado in Texas?

Satellites show faster melting of the Greenland ice than expected
BBC on line 21/1 2004
The butterfly effect, first described by [a meteorologist by the name of] Lorenz at the December 1972 meeting of the American Association for the Advancement of Science in Washington, D.C., vividly illustrates the essential idea of chaos theory. […] By the time of the 1972 meeting, he had examined and refined that idea for his talk, "Predictability: Does the Flap of a Butterfly’s Wings in Brazil set off a Tornado in Texas?" The example of such a small system as a butterfly being responsible for creating such a large and distant system as a tornado in Texas illustrates the impossibility of making predictions for complex systems; despite the fact that these are determined by underlying conditions, precisely what those conditions are can never be sufficiently articulated to allow long-range predictions. […] Last updated on: Nov 22, 2002
Edited from http://whatis.techtarget.com/definition/0,,sid9_gci759332,00.html
"Physicists like to think that all you have to do is say,
these are the conditions, now what happens next?"
Richard P. Feynman
The world of mathematics
The world of mathematics has been confined to the linear world for centuries. That is to say, mathematicians and physicists have overlooked dynamical systems as random and unpredictable. The only systems that could be understood in the past were those that were believed to be linear […]. However, the problem arises that we humans do not live in an even remotely linear world; in fact, our world should indeed be categorized as nonlinear; hence, proportion and linearity is scarce. How may one go about pursuing and understanding a nonlinear system in a world that is confined to the easy, logical linearity of everything? This is the question that scientists and mathematicians became burdened with in the 19th Century; hence, a new science and mathematics was derived: chaos theory. […] The calculations involved in studying chaos are repetitive, boring and number in the millions. No human is stupid enough to endure the boredom; however, a computer is always up to the challenge. Computers have always been known for their excellence at mindless repetition; hence, the computer is our telescope when studying chaos. For, without a doubt, one cannot really explore chaos without a computer. […]
Edited from article on the net by Author: Manus J. Donahue III
Copyright Fall 1997, all rights reserved.
http://www.duke.edu/~mjd/chaos/chaosp.html
Chaos-system studied by computer
Benoit Mandelbrot

When iterative equations are applied to points in a certain region of the complex plane, a fractal from the Mandelbrot set results
Benoit Mandelbrot was born in Poland in 1924. […] [Some time after 1977, and] with the aid of computer graphics, Mandelbrot was able to show how [an almost forgotten mathematician] Julia’s work was a source of some of the most beautiful fractals known today. The Mandelbrot set is made up of connected points in the complex plane. The simple equation that is the basis of the Mandelbrot set is included below.
Changing number + fixed number = Result
In order to calculate points for a Mandelbrot fractal, start with one of the numbers on the complex plane and put its value in the "Fixed Number" slot of the equation. In the "Changing number" slot, start with zero. Next, calculate the equation. Take the number obtained as the result and plug it into the "Changing number" slot. Now, repeat (iterate) this operation an infinite number or times. When iterative equations are applied to points in a certain region of the complex plane, a fractal from the Mandelbrot set results.
Edited from article on the net by Author: Manus J. Donahue http://www.duke.edu/~mjd/chaos/chaosp.html
Coex systems
Stanislav Grof’s Coex system indicates that the Mind also organize itself in fractals
A COEX system is a dynamic constellation of memories (and associated fantasy material) from different periods of the individual’s life, with the common denominator of a strong emotional charge of the same quality, intense physical sensation of the same kind, or the fact that they share some other important elements.
Grof, Beyond the Brain p.97
The COEX systems
The COEX systems represent a general organizing principle operating on all levels of the psyche.
Now (leading to) Earlier similar event (leading to) Earlier similar event (leading to)
Earlier similar event (leading to) ( etc.) (leading to) Birth (leading to) Myth (leading to) Past life
Grof: Beyond the Brain p.97
If you like fractals, it is because you are made of them
[…] It is now established that fractals are quite real and incredible; however, what do these newly discovered objects have to do with real life? Is there a purpose behind these fascinating images?
The answer is a somewhat surprising yes. Homer Smith, a computer engineer of Art Matrix, once said, "If you like fractals, it is because you are made of them. If you can’t stand fractals, it’s because you can’t stand yourself." Fractals make up a large part of the biological world. Clouds, arteries, veins, nerves, parotid gland [A salivary gland situated in front of and below the ear] ducts, and the bronchial tree all show some type of fractal organization. […] Understanding and mastering the concepts that govern fractals will undoubtedly lead to breakthroughs in the area of biological understanding. Fractals are one of the most interesting branches of chaos theory, and they are beginning to become ever more key in the world of biology and medicine. […]
Edited from article on the net by Author: Manus J. Donahue http://www.duke.edu/~mjd/chaos/chaosp.html
The butterfly effect
Chaos theory and Crisis counseling
Time bombs
The core is that part of the trauma which is most important for the individual. "What is it that is too much?"
The "core" is the most important for the client to be able to contact, describe, and possible to work with.
This, what is too much may immediately manifest itself as a breakdown or reactive psychosis, or it may remain hidden for shorter or longer time, until something else happens. It is important to be aware, that what may trigger these time bomb can be seemingly innocent events!
Edited from Certificate in Counselling,
Trauma and Crisis counselling
Chaos theory and Earth Changes
The twinkling of an eye - the butterfly effect
When Edgar Cayce, the sleeping prophet, was asked exactly when the Earth Changes would begin, and on what day the lord will reveal his presence to the world at large, he quoted Christ, who, when asked a similar question by his disciples 2000 years ago, give the following answer:
But of that day and hour no one knows, not even the angels of heaven, but the Father only. Edgar Cayce also explained that the fulfillment of prophecy, including its manner and timing was dependent on a number of factors - one of those factor being the thought and intent of Enlightened Beings -both human and angelic or celestial - whose influence could help to forestall and or modify the prophecy’s fulfillment.
Famous examples of Edgar Cayce’s predictions:
What great change or the beginning of what change,
If any, is to take place in the earth in the year
2000 - 2001 AD?
When there is a shifting of the poles. Or a new cycle begins
As to the changes physical again: The earth will be broken up in the western part of America.
The greater portion of Japan must go into the sea. The upper portion of Europe will be changed as in the twinkling of an eye. Land will appear off the east coast of America.
There will be the upheavals in the Arctic and in the Antarctic that will make for the eruption of volcanoes in the Torrid areas, and there will be the shifting of the poles - so that where there have been those of a frigid or semi - tropical will become more the tropical, and moss and fern will grow.
Edgar Cayce, 1934
Earth ‘entering uncharted waters’
BBC News 21/1 2004

The Earth has entered a new era, one in which human beings may be the dominant force, say four environmental leaders.
In the International Herald Tribune, they say the uncertainty, magnitude and speed of change in many of the Earth’s systems is without precedent.
The four, who include Margot Wallstrom, the European environment commissioner, say uncertainty cannot excuse inaction.
They believe humanity may cross some critical thresholds unawares, setting off changes which cannot be reversed.
Change at a gallop
The other authors are Professor Bert Bolin, founding chair of the Intergovernmental Panel on Climate Change; Professor Paul Crutzen, winner of the 1995 Nobel prize for chemistry; and Dr Will Steffen, director of the International Geosphere-Biosphere Programme (IGBP).
Their article, The Earth’s Threatened Life-Support System: A Global Wake-Up Call, marks the publication of an IGBP book, Global Change And The Earth System: A Planet Under Pressure.
They write: "Our planet is changing fast. Change is a fact of life, but in recent decades many environmental indicators have moved outside the range of variation of the last half million years…
"It is the magnitude and rate of human-driven change that are most alarming.
"The human-driven increase in atmospheric carbon dioxide is nearly 100 parts per million and still growing - already equal to the entire range experienced between an ice age and a warm period such as the present.
"And this human-driven increase has occurred at least 10 times faster than any natural increase in the last half million years."
They envisage the possibility, beyond 2050, of "rapid regional climate change, as would be caused by changes in ocean circulation in the North Atlantic, and irreversible changes, such as the melting of the Greenland ice sheet and the concomitant sea-level rise of six metres".
No compass
The authors write: "The Earth has entered the so-called Anthropocene - the geologic epoch in which humans are a significant and sometimes dominating environmental force.
"Records from the geological past indicate that never before has the Earth experienced the current suite of simultaneous changes: we are sailing into planetary terra incognita."
They argue for a precautionary approach, partly because natural systems can flip very rapidly from one stable state to another.
The writers say: "We are unsure of just how serious our interference with Earth system dynamics will prove to be, but… there are significant risks of rapid and irreversible changes to which it would be very difficult to adapt."
Dr Steffen told BBC News Online: "It would take about a millennium for the Greenland ice sheet to melt. But we could reach the trigger point that makes the process unstoppable within the next century.
"The book makes the point that this is global change - it looks at the range of effects, at how they’re happening simultaneously, and at how they’re reinforcing each other.
"It’s a synthesis of the science, the best consensus - and it honestly acknowledges the unknowns."
http://news.bbc.co.uk/2/hi/science/nature/default.stm
