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Thursday, January 8, 2004
More on IBS - Chaos and the Butterfly Effect
I hope you had a great new year
celebration. Last week, January 1, there was no newsletter, other than
best wishes for the coming year and for you to have a wonderful relaxing
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And now to the main subject of this
week's newsletter: Chaos and the Butterfly Effect. There were 2
articles published on this subject, one in Washington post, where I was
mentioned for my work in fractals and one in my
forum that I
And here they are:
"Chaos" describes the apparently random
behavior of systems which are actually exhibiting very mechanical behavior.
Most people think of physical behaviors as being either deterministic or
random. If you know the starting conditions in a deterministic system, you
know exactly what the future behavior will be. In contrast, random systems
are unpredictable. Much to the frustration of scientists, numerous systems
seem to be random. In particular, weather, vibrating structures, and
subatomic particle I dynamics are considered random, and most scientists
have simply settled for statistical descriptions which are poor for drawing
any concrete conclusions.
An emerging field of science has revealed that many systems previously
believed to be random are actually described by systems of deterministic
mathematical equations. Prior to the availability of computer graphics, such
chaotic systems were difficult to visualize. However, it is now possible to
visualize chaotic systems from which emerge elegant patterns such as in
Izak Matatya’s computer graphics, fractals and
"strange attractors", thus giving rise to the phrase "order out of chaos."
Izak Matatya also happens to implement betting strategies for hazard games
with random outcomes. His superior knowledge of statistics, mathematics,
computers and sublime taste of graphic art is a wonderful contribution to
solutions in chaos theory. His betting systems have a solid background and
his analysis of random pattern correlations are above any level seen so far.
An essential characteristic of a chaotic system is its sensitivity to tiny
differences in initial conditions. Any difference in a chaotic system's
initial conditions grows exponentially as the system evolves over time.
Eventually, the magnified difference results in apparently unique and random
behavior despite the similarity of the initial conditions. Even though full
knowledge of such conditions would in theory permit long term predictions of
a chaotic system's behavior, it is impossible to know them all to the
infinite precision necessary. Thus, we may possibly never make reliable long
term weather predictions.
The "Butterfly Effect" is a popular example of the importance of seemingly
negligible initial conditions. As recounted by Edward Lorenz in "The Essence
of Chaos", the phrase has a curious history. It appears to have arisen after
he presented his paper entitled "Does the Flap of a Butterfly's Wings in
Brazil Set Off a Tornado in Texas?" A computer graphic of a chaotic system
studied by the author resembled a butterfly and many people assumed the
coincidence was intentional. Others point to Ray Bradbury's classic story "A
Sound of Thunder" in which a time-traveling hunter steps on a butterfly
while stalking a dinosaur and finds his world changed upon his return.
Edward Lorenz points out that “perhaps the butterfly, with its seeming
frailty and lack of power, is a natural choice for a symbol of the small
that can produce the great.”
Where it is possible to reasonably manage most of the details, chaos theory
has solved scientific problems, such as why the asteroid belt has empty
bands. The reason is that each time an asteroid passes Jupiter, it feels a
gravitational tug. If the distance of the asteroid from Mars and Jupiter is
correct, i.e. the asteroid is in a suitable band of the asteroid belt, it
will feel periodic tugs which result in chaotic motion and cause it to drift
out of orbit. The chaos-inducing resonance only occurs when the frequencies
of the tugs are related by low-order rational numbers, hence the appearance
of specific gaps in the asteroid belt.
When a butterfly flaps its wings in Maui,
does it cause a hurricane in the Caribbean? Or, a tornado in Kansas? Or, a
rainstorm in Shanghai? "The Butterfly Effect' is a familiar parable that
illustrates how outcomes are dependent upon initiatory conditions. Even
grand events -- like hurricanes, tornadoes, and rainstorms -- are
ultra-sensitive to the smallest influences.
The notion goes something like this: (1) A butterfly on a small tropical
island flaps its wings. (2) The minor disturbance creates an air current
that carries out over the ocean. (3) The deviation adds to the accumulative
effect on global wind systems which are constantly in motion. (3) The result
is an apparition of weather in different parts of the world.
"The Butterfly Effect" has become synonymous with chaos theory. Chaos theory
postulates that small changes at the micro level can lead to much more
significant consequences at the macro level. A more scientific explanation
is that making small changes in initial input values impacts the final
outcome of the progression. Using a mathematical example -- if I were to add
.0001 to any simple equation, no matter how large the number, the final
answer would be altered because my disruption. No matter if I add .001 to
the number 3, or 3 million -- the impact is the same. Hence, a butterfly
flapping its wings can and does change the weather half way around the
If The Butterfly Effect can account for weather changes, might it also apply
to other worldly events? If you are a believer in chaos theory, the answer
should be obvious:
History -- In 1914, an obscure political leader was assassinated in Bosnia.
It all started with a tiny newspaper clipping that was mailed from a secret
band of terrorists in Croatia to their comrades in Serbia. The article
declared that Austrian Archduke Franz Ferdinand was to pay a visit to nearby
Sarajevo. The clipping was the torch which illuminated the idea of an
assassination attempt. Archduke Ferdinand's death a few days later sparked a
cataclysmic chain of events that instigated World War I. Four years later,
25 million people were dead and new national boundaries were drawn. What
might have happened if that tiny newspaper clipping had been lost in
transit, or the assassination attempt had somehow been foiled? How might
history have changed? How different would the world be today? Without World
War I, would World War II have occurred? Or the Cold War? Or atomic weapons?
Finance -- Slight fluctuations in one economic market can effect many
others. In June 1997, Thailand ordered 16 finance companies with high levels
of bad debt to merge with healthier ones. Thailand's currency (the baht)
quickly plunged more than 20 percent in currency exchange markets. Next,
Thailand asked for a bailout from the International Monetary Fund. This
triggered economic instability in other Asian markets -- including the
Philippines, Malaysia, Hong Kong, Indonesia, South Korea, and eventually
Japan. In November, a drop in the Tokyo stock market made it abundantly
clear that Asia was in the midst of a severe economic crisis. Declining
markets in Asia soon impacted all foreign markets, including the United
States. Some economists later suggested the Asian crisis created a global
recession. Might today's economy be different if a few financial
institutions in Thailand not made so many questionable loans?
Biology -- Many scientists believe that a small, once seemingly
insignificant virus in African monkeys mutated into a deadly disease that
now effects human populations all around the world. It's been hypothesized
that the HIV-virus originated in chimpanzees found in the rainforests of
Gabon, Cameroon and parts of Nigeria. Later, humans contracted the deadly
virus. What horrific mutation triggered this global epidemic? Biological
mutations are only a tiny fraction of the size if butterfly wings. But the
aftermath of these microscopic changes can be catastrophic for millions of
people. Think about it.
Psychology -- Thought patterns and consciousness altered by small changes in
brain chemistry can produce extraordinary human behavior. Seemingly trivial
impulses inside the cerebellum may inspire the creation of great works of
art by some individuals -- and terrible acts of crime by others. Mental
delusion motivated one man to paint several masterpieces (Van Gogh) and
another to commit murder (Son of Sam). In fact, the human brain may be the
most volatile laboratory of chaos theory set in constant motion.
Religion -- A little over 2000 years ago, a man was born in the Middle East.
Despite never attending school, or writing a book, or holding a position of
authority -- he would go on to change history and alter billions of lives in
successive centuries. But what if the man had never lived? Or, what if he
had not lived beyond infancy? Keep in mind that infant mortality rates were
30-40 percent in his time. What if Jesus had died before he reached
adulthood? The same question goes for Moses and Muhammad. How would our
belief systems -- including our morals and ethics -- be different in modern
society if these great men of history had never lived?
If the pitter-patter of butterfly wings causes hurricanes and heat waves, if
molecular agents can either kill or cure millions from infectious diseases,
just imagine what you or I can do -- much larger human forces with a more
profound physical impact on the people and objects around us. Just as chaos
theory is manifested in our worldly experiences, it is so in gambling, as
Examples of chaos theory abound in casinos and are revealed in all games of
chance -- from roulette wheels to card games. Inside card rooms, there's a
seemingly chaotic ritual that recycles vast amounts of wealth and time, chip
by chip and hour by hour, slowly but surely transforming its cast of
characters into a primordial pecking order of winners and losers. Every
batted eyelash and hand gesture inconspicuously alters the course of events
which follows. A cough or sneeze may go unnoticed but can make a poker
dealer shuffle the cards in a slightly different manner than he would
otherwise, thus changing "poker history" by altering the outcome of the next
hand, and the next, and the next -- ad infinitum.
One of the most interesting examples of The Butterfly Effect was once told
by Phil Hellmuth, who recounted a story several years ago involving Dan
Harrington, winner of the 1995 World Series of Poker. Hellmuth was in a
unique position to observe what happened that day, because he sat at
Harrington's table when a monumental hand took place which may very well
have changed poker history.
The key hand occurred in the $2500 buy-in no-limit holdem event, which
preceded the $10,000 main event that same year. Harrington decided to enter
the event merely as an afterthought. He hadn't done much in poker
tournaments up until that time, and was primarily known for his tight play
in no-limit side games. Down to seven tables in the tournament, Harrington
was dealt A-J. One opponent from early position made a $600 raise with
pocket jacks. Another player in late position called the raise with pocket
eights. Harrington (a player with a very tight reputation at the time)
decided to re-raise $2000 more with A-J. Knowing Harrington's style, the
first player mucked his J-J. The other player called the raise with 8-8. The
flop came all rags (helping neither player). After it was checked,
Harrington moved all-in with his last $6500 hoping to take the pot right
there. The opponent called and Harrington knew he was in big trouble. The
turn was a blank as Harrington stood up ready to walk away. The river card
was dealt. It was a jack -- giving Harrington the pot.
Hellmuth, who was watching the hand, later noted that several things had to
go just right for Harrington to pick up that key pot. First, Harrington had
to get out of line with a relatively weak hand (highly unusual for
Harrington). Then, the player with J-J had to respect Harrington's game
enough to fold pre-flop. Then, the player with 8-8 had to call the raise.
Next, Harrington had to move his stack in after the flop and get called.
Finally, he had to hit either an ace or the case jack to win the pot.
Harrington succeeded in doing so, and went on to win his first major poker
tournament. A week later, he was the World Champion. Then, a month later
Harrington won the European poker championship. What an amazing run!
That incredible sequence of events started with a single card coming at just
the right moment. Meaning no disrespect to Harrington, it's quite possible
that poker history took a jolting detour because of what happened on that
one hand. Scooping that pot gave Harrington a sizable stack, as he became
more aggressive in the tournament. He went on to win this first gold
bracelet. Loaded with self-confidence, he proceed to win the next two
no-limit events he played entered -- and the lives of countless other poker
players on the tournament trail were affected by his wins (since the order
of finish in every event thereafter was altered). In fact, one could make a
rather persuasive argument that every motion, every action, and every hand
has an impact on the ultimate course of events which follow.
Every poker player has memorable moments, recollections of key hands that
might have altered their state of affairs. Had Scotty Nguyen not won a seat
in a super satellite in 1998 would he have gone on to win the World Series
that year? What about Stu Ungar? Had it not been for a last minute phone
call from a backer, Ungar would not have had $10,000 to buy into the 1997
championship and won his third title. How about Chris Ferguson? His fateful
moment all came down to a three-outer on the last card of the 2000 World
Series. How might his life (and TJ Cloutier's) be different today had that
A-Q held up versus the A-9?
The biggest poker events aren't the only places where lives are in a
constant state of transition. Even small stakes games have ramifications
that can reverberate throughout the poker world. A pebble thrown in a pond
today might create a sonic boom tomorrow. How many future world champions
are now toiling away in $4-8 holdem games trying to learn the game as you
are reading this right now? How many players around the world are catching a
key hand right this moment which gives them the confidence to go out and buy
a book and want to learn more about poker? A year later, that player wins a
tournament. Then another. The next year, the player wins a gold bracelet.
It's happened. Many times.
Poker and history are connected. How many great poker players like Erik
Seidel once lost their jobs and took up poker playing as a profession? How
many professional players dropped out of college because they were making
more money at the card table than any entry-level job? How many great poker
players were expelled from foreign countries, and how might poker be
different today if the Vietnam War had ended differently? How many fortunes
have been won and lost, how many marriages and divorces have occurred, and
how many lives have been changed for better and worse by what happened in a
poker game? Fate is as fragile as the wings of a butterfly.
Wishing you all the best,
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