Sunday, December 8, 2013

Chaos Theory, Butterfly Effect, More than you want to know!

To start, I need to point to a part of chaos theory that shows the need to understand
the whole system around you, called your life!

In chaos theory, the butterfly effect is the sensitive dependency on initial conditions
in which a small change at one place in a deterministic nonlinear system can result in large
differences in a later state. The name of the effect, coined by Edward Lorenz, is derived
from the theoretical example of a hurricane's formation being contingent on whether or not
a distant butterfly had flapped its wings several weeks earlier.

Since their day, every important new advance in scientific discovery has confirmed the
Marxian outlook although scientists, because of the political implications of an association
with Marxism, seldom acknowledge dialectical materialism. Now, the advent of chaos theory
provides fresh backing for the fundamental ideas of the founders of scientific socialism.
Up to now chaos has been largely ignored by scientists, except as a nuisance or something
to be avoided. A tap drips, sometimes regularly, sometimes not; the movement of a fluid is
either turbulent or not; the heart beats regularly but sometimes goes into a fibrillation;
the weather blows hot or cold. Wherever there is motion that appears to be chaotic
and it is all around us—there is generally little attempt to come to terms with it from a
strictly scientific point of view

~~~Chaos and Dialectics
It is as yet too early to form a definitive view of chaos theory.
However, what is clear is that these scientists are groping in the direction of a dialectical
view of nature. For example, the dialectical law of the transformation of quantity into
quality (and vice versa) plays a prominent sole in chaos theory: "He (Von Neumann)
recognised that a complicated dynamical system could have points of instability critical
points where a small push can have large consequences, as with a ball balanced at
the top of a hill."

And again:

"In science as in life, it is well known that a chain of events can have a point of crisis
that could magnify small changes. But chaos meant that such points were everywhere.
They were pervasive." These and many other passages reveal a striking resemblance
between certain aspects of chaos theory and dialectics. Yet the most incredible thing is
that most of the pioneers of "chaos" seem to have not the slightest knowledge not only
of the writings of Marx and Engels, but even of Hegel! In one sense, this provides
even more striking confirmation of the correctness of dialectical materialism.
But in another, it is a frustrating thought that the absence of an adequate philosophical
framework and methodology has been denied to science needlessly and for
such a long time.

For 300 years, physics was based on linear systems. The name linear refers to the
fact that if you plot such an equation on a graph, it emerges as a straight line.
Indeed, much of nature appears to work precisely in this way.
This is why classical mechanics is able to describe it adequately.
However, much of nature is not linear, and cannot be understood through linear
systems. The brain certainly does not function in a linear manner, nor does the
economy, with its chaotic cycle of booms and slumps.
A non-linear equation is not expressed in a straight line,
but takes into account the irregular, contradictory and frequently
chaotic nature of reality.

"All this makes me feel very unhappy about cosmologists who tell us that they’ve
got the origins of the Universe pretty well wrapped up, except for the first millisecond
or so of the Big Bang. And with politicians who assure us that not only is a solid dose
of monetarism going to be good for us, but they’re so certain about it that a few million
unemployed must be just a minor hiccup.

The mathematical ecologist Robert May voiced similar sentiments in 1976.
‘Not only in research, but in the everyday world of politics and economics,
we would all be better off if more people realized that simple systems do not
necessarily possess simple dynamical properties.’"

The problems of modern science could be overcome far more easily by adopting
a conscious (as opposed to an unconscious, haphazard, empirical)
dialectical method. It is clear that the general philosophical implications of
chaos theory are disputed by its scientists.
Gleick quotes Ford, "a self-proclaimed evangelist of chaos" as saying that chaos
means "systems liberated to randomly explore their every dynamic possibility…"
Others refer to apparently random systems. Perhaps the best definition comes from
Jensen, a theoretical physicist at Yale, who defines "chaos" as "the irregular,
unpredictable behaviour of deterministic, non-linear dynamical systems."

Rather than elevate randomness to a principle of nature, as Ford seems to do,
the new science does the opposite: it shows irrefutably that processes that were
considered to be random (and may still be so considered, for everyday purposes)
are nevertheless driven by an underlying determinism—not the crude mechanical
determinism of the 18th century but dialectical determinism.

Some of the claims being made for the new science are very grand, and with the
refinement and development of methods and techniques, may well prove true.
Some of its exponents go so far as to say that the 20th century will be known for
three things: relativity, quantum mechanics and chaos.
Albert Einstein, although one of the founders of quantum theory, was never
reconciled to the idea of a non-deterministic universe. In a letter to the physicist
Neils Bohr, he insisted that "God does not play dice." Chaos theory has not
only shown Einstein to be correct on this point, but even in its infancy, it is a
brilliant confirmation of the fundamental world view put forward by
Marx and Engels over a hundred years ago.

It is really astonishing that so many of the advocates of chaos theory, who are
attempting to break with the stultifying "linear" methodology and work out a new
"non-linear" mathematics, which is more in with the turbulent reality of ever-changing
nature, appear to be completely unaware of the only genuine revolution in logic in
two millennia—the dialectical logic elaborated by Hegel, and subsequently perfected
on a scientific and materialist basis by Marx and Engels. How many errors, blind
alleys and crises in science could have been avoided if scientists had been equipped
with a methodology which genuinely reflects the dynamic reality of nature, instead
of conflicting with it at every turn!

~~~Butterfly Effect and Edge of Chaos
It is clear that the disturbance to the natural environment caused by the oil gusher
is more than the flapping of the butterfly's wing, which represents but a small change
in the initial condition of the system. Given the change that the unprecedented oil
gusher is bringing about in the global ecosystem, this is likely to cause a chain of events
leading to substantial large-scale phenomena.

Had this butterfly not flapped its wings, the trajectory of the system might have been
vastly different. It leads to the possibility of "Chaos", that whatever is the most
unexpected thing at the time happens, ie, a true "Black Swan".
As a result, nothing is predictable and even the slightest action can
have the most complex reaction. According to the Upanishads, some of which date
back nearly 3,000 years, "As is the human body, so is the cosmic body.
As is the human mind, so is the cosmic mind. As is the microcosm, so is the macrocosm.
As is the atom, so is the universe!"

The views of the "Father of Chaos Theory" -- Edward Lorenz (1917-2008), who was a
Meteorologist and Professor at MIT -- are worth noting. Among some of Lorenz's famous

1. The discovery of "Deterministic Chaos" brought about "one of the most dramatic changes
in humankind's view of nature since Sir Isaac Newton," concluded the committee that awarded
Lorenz the 1991 Kyoto Prize for basic sciences. The "Lorenz Attractor" is a relatively simple
attractor with complex behaviour. This becomes the typical characteristic of chaos: the
step by step manifestation of complexity out of simplicity.

2. The Butterfly Effect, the scientific concept that small effects lead to big changes, is 
illustrated by the Lorenz attractor. The butterfly was originally a seagull in Lorenz's paper
written in 1963 for the New York Academy of Sciences. One meteorologist remarked that
if the theory were correct, one flap of a seagull's wings would be enough to alter the course
of the weather forever! Once the weather changes, so does the history of humankind. 
By the time of his talk at the December 1972 meeting of the American Association for
the Advancement of Science in Washington, DC, the sea gull had evolved into the
more poetic butterfly -- the title of his talk was, "Predictability: Does the Flap of a
Butterfly's Wings in Brazil set off a Tornado in Texas?"

3. Every day things are chaotic, chaos leads to creativity and life. 
The "Edge of Chaos" is where creativity happens!
Lorenz's discovery continues to influence the scientific world, which has yet to grasp its
implications fully. Chaotic systems have been recognised in all branches of science.
As mathematicians started to unravel its mysteries, science reeled before the implications
of an uncertain world intricately bound up with chance. The human heartbeat is chaotic,
as indeed are the stock market, the solar system and of course the weather.
In fact the more we learn about chaos the more closely it seems to be bound up with nature.
Fractal structures seem to be everywhere we look: in ferns, cauliflowers, the coral reef,
kidneys... Rather than turn its back on chaos, nature appears to use it and science is
beginning to do the same. When will large scale corporate capitalism and government
structures metamorphose to embrace the butterfly effect and make us live sustainably 
at the edge of chaos? When each one of us changes! Mahatma Gandhi said,
"As human beings, our greatness lies not so much in being able to remake the world
that is the myth of the atomic age -- as in being able to remake ourselves!"

 ~~~The Butterfly Effect of Recognition
The Butterfly Effect, it turns out, is an interesting notion from Chaos Theory that has
some eye-opening implications for organizational development and change management.
(And not, as you might be thinking, anything to do with Ashton Kutcher.)
In 1979, a meteorological researcher named Edward Lorenz suggested that the flap
of a butterfly’s tiny wings somewhere in South America could set off a tornado in Texas a
month from now. He was using the example to illustrate the idea that one tiny change
can result in a huge impact on a large complex system—like weather patterns.

Or like organizations.
That’s because it is in the “chaos” of the small day-to-day activities of employees and
managers that we often see the most far-reaching and unpredictable effects
(positive or negative) on organizations. Here are a few things about complex,
nonlinear systems that we can take from Chaos Theory:

Systems are very sensitive to initial conditions, which set the stage for the ultimate behavior.

Systems tend to cluster their activity around and iterate on a typical behavior, called an attractor.

Systems tend to be dissipative, meaning without a continued driving force they cease to move.

These three ideas are really important as we look at how organizations behave and as we
seek to create a productive, engaged workforce.
The Butterfly Effect itself is not predictable in its outcome, because it is such a tiny,
singular event. But what if you multiplied those events exponentially, as you can do
with organizations? Then you would begin to see many little events that have a strong,
iterative and ongoing effect on your outcomes, consistently driving a controlled
change for the better. I probably don’t even need to say that employee recognition
can be this kind of Butterfly Effect, but I will.

Recognition is an ideal initial event to create change in a complex system, because it is
organic and inspired, and because it is self-propagating.

The iterative (repeating and growing) nature of public recognition means recognition
worthy behavior is constantly being reinforced and replicating itself, but because it is
guided by your stated values, it stays close to the attractor you have designated.

Recognition begets recognition. A healthy, well-designed recognition program becomes
a constant driving force to keep the organization moving forward.

Recognition is a terrific change management tool because it flourishes within parameters
you set for your company: the values and goals that form the award criteria.
This essentially harnesses the chaos of day-to-day activity and directs it into the
advancement of your organizational objectives.

~~~The butterfly effect gets entangled
A hidden partnership between two of the hottest topics in physics — quantum entanglement
and chaos theory — may have been uncovered by a series of ingenious experiments with
caesium atoms. The relationship could provide clues about where the quantum realm ends
and the classical world begins.

Chaos theory describes how the slightest change in the starting conditions of a system can
have dramatic effects on how it develops. It's usually explained using the 'butterfly effect',
in which the atmospheric changes caused by the beating of a butterfly's wings in one location
could eventually lead to the production of a tornado in another.

Chaos is usually thought to be a large-scale phenomenon, associated with classical physics
and absent from the microscopic quantum realm.
But now Poul Jessen, at the University of Arizona in Tucson, and his colleagues have found
the fingerprints of chaos in a quantum system. Their discovery links chaos to entanglement
the purely quantum property in which multiple particles can become inextricably intertwined,
so that making changes to one instantly affects its partners.

"They've brought together two sexy concepts in physics that are usually thought to operate in
completely different regimes," says optical physicist Nir Davidson at the Weizmann Institute
of Science in Rehovot, Israel. "That is surprising and interesting."

Quantum kick
Jessen's team searched for signs of chaos within a set of cooled caesium atoms, using
them as the quantum equivalent of an everyday object that displays chaotic a child's
spinning top. Just as the axis of the spinning top changes direction and can wobble
wildly if it is nudged, each caesium atom can be characterized by an internal quantum
property known as spin — the direction of which will change if it is 'kicked' by
applying pulses of a magnetic field. The goal was to see if kicking this 'quantum top'
caused the spin to change direction chaotically.

According to the team's calculations, if the quantum top behaved like a classical top,
then kicking it should produce two possible outcomes depending on the initial
direction of its spin. If the top's initial spin direction lay in one of three subsets
of possible directions dubbed islands of stability — each successive kick would
knock the spin in a regular way, sending it around a stable orbit within that island.
If, however, the initial spin direction lay outside these islands, in the 'chaotic sea',
the spin should jump around rapidly and unpredictably.

When they did the experiment, they found almost exactly that behaviour — if the
quantum top started out in an island of stability, its spin changed in a regular way,
but if not, chaos ruled and its spin direction changed quickly and erratically.
"It looks like the quantum system knows about classical boundaries and respects
them," says Jessen. Physicist Fritz Haake of Duisburg-Essen University, Germany,
was one of the first to propose that chaotic signatures might show up in a quantum
top, and admires the experimental achievement. "It has taken both ingenuity and
advances in technology to demonstrate quantum chaos this way," he says.

Tangled up
Having seen chaotic behaviour, Jessen's team then explored its possible ties to
entanglement. Caesium atoms contain electrons that orbit a nucleus, and it is possible
for the direction of an electron's spin to become entangled with that of the nucleus's
spin. The team began their experiment with a set of atoms that did not display this
kind of entanglement and then checked whether kicking the atoms would provoke
the electron and nuclear spins to entangle.
"We found that atoms starting out in one of the islands of stability remained
unentangled, but for those that started out in the chaotic sea, the electron and nuclear
spins rapidly became entangled," says Jessen. "This suggests that chaos may have some
fundamental connection to entanglement."

The finding has implications for building quantum computers that, in principle, work by
closely controlling the entanglement of atomic spins. "This underscores how hypersensitive
quantum systems are to slight perturbations," says Jessen. "You really have to worry about
how easily errors can be generated — which, of course, those trying to build
[such systems] have already seen."

The result also touches on a fundamental question in physics: where does the exotic
quantum realm end and the familiar classical world begin? The study supports long
standing ideas that there is no single sharp boundary between the quantum and
classical worlds, says quantum physicist Wojciech Zurek of the
Los Alamos National Laboratory in New Mexico.
"The obvious thing to do now is to look at which classical features emerge first
and which quantum features last longest," he says. Jessen and his team hope
to investigate how larger quantum systems blend into the classical regime.
"It's a challenge," says Jessen. "But we're taking our first baby steps in that direction."

 ***There are many ways to put all of this.
Life is entanglement and it is everywhere!
 "Quantum entanglement isn't only spooky, you can't avoid it."

Or like the quote I like to say.
"No man is an island. No one is self-sufficient; everyone relies on others."
From the seventeenth-century English author John Donne.

Or even is beliefs, legends when you kind of look at them!
"The red string of fate, also referred to as the red thread of destiny, red thread of fate,
and other variants, is an East Asian belief originating from Chinese legend and is also used
in Japanese legend. According to this myth, the gods tie a red cord around the ankles
of those that are to meet one another in a certain situation or help each other in a certain
way. Often, in Japanese culture, it is thought to be tied around the little finger.
According to Chinese legend, the deity in charge of "the red thread" is believed to be
Yuè Xià Lǎ"

Looking in to all of this relating to your life is kind of like a Fractal Zoom but it's
a start of your journey!
(Note I went to a vocational school in the 80's with one of Mandelbrot kids,
they are a Strange crew!)

No comments: