Acadia - the one and only National Park in New England

Out of the current 58 National Parks of U.S., Acadia is the only one in New England area.   A natural beauty with easy access to wooded trails, granite peaks and rocky shore lines, Acadia has been a favorite summer vacation spot of many.

This 100+ square miles (relatively) small national park is located on the Mount Desert Island of Maine, approximately 250 miles northeast of Boston.  The island itself was named in 1604 by the French explorer Samuel de Champlain, the father of New France (see my last blog), when he spotted the island and what is now called the Cadillac Mountain of the park.  Of course, with the nurturing and protection, it is no longer bare or desert-like and Cadillac Mountain has become the most popular scenic spot of the park, complete with access road and a parking lot.  

Standing at 1,528 feet or 466 meters, Cadillac Mountain is the highest point of Atlantic coast in U.S. and offers fantastic panoramic views of the surrounding islands, bays and the Atlantic Ocean.  Hiking around the summit of Cadillac Mountain, you would notice granites of all sizes cover much of the peak.  Indeed, granites make up the bulk of the Mount Desert Island which was first formed a little over 400 million years ago.  Hundreds of millions of years of gentle rubbing and nudging left long vertical and horizontal cracks on otherwise impenetrable rocks who can only be jealous of their much younger siblings like the Half Dome of the Yosemite National Park in California.

 

 

 

 

 

 

 

 

Heading back down to the foot of the mountain and continuing southeast along the coast, you will soon come to the only sand beach of the park.  For lack of imagination, the beach is called Sand Beach! The scenery though is stimulating.  With waves relentlessly beating on the adjacent wall of rocks, you would find many youngsters taking temporary refuge on the sand beach as they are teetering with the waves.  

If you have good leg power, you can hike south on the 2 miles long flat Ocean Path trail along the coast line that takes you through some of the most visited and photographed spots of the park including Thunder Hole, Monument Cove and Otter Cliff.   It is a wonderful visual treat as one wonders off the trail and rests on the orange red granite rocks enjoying the scenery, accompanied by the lonely wild flower came out of the crack between rocks and seabirds at the distance.   Hundred yards away, a small group of black water fowls left the main group moved along the waves towards to the shore as if they were ready to invade the land but then withdrew together quietly.  Occasionally some of them went into the water in obvious attempts to catch some fish.   At the Thunder Hole, the echoes from the pounding waves at high tide gave a unique musical performance to an otherwise quiet sunny afternoon. 

Looping around by car further inland counter-clockwise, one comes to the trail head for Bubble Rock north of the Jordan Pond.  Hiking a few hundred feet up, you would find a large rock (about 20 ft in diameter?) “glued” onto the edge of a slope as if it may roll off the cliff any moment.  It is tempting for the visitors to give it a hand but so far, fortunately no one has succeeded yet. 

One thing you wouldn’t want to miss when visiting Acadia is to have a feast of the delicious lobsters from their perfect habitat nearby of cold shallow water and rocky bed.   As you drive on Route 3 towards to Bar Harbor and Acadia National Park, you will see many road side Lobster Ponds.   Find on with a lot of cars parked outside with smokes on from the smoke stacks of the outdoor wood stoves, just pull over your car and order a few live lobsters sold by weight that will be ready shortly, boiled to perfection in its natural flavor.  Just make sure that you wash your hands when you are continuing on for your relaxed vacation with the renewed energy.  Talk to you soon!

The French Canada

Measured by distance from New Jersey, Quebec province of Canada is the closest region and is easily reached by car where one can experience a distinct culture and language.  In fact, Quebec and some of its neighboring areas including Nova Scotia, Newfoundland of Canada and Maine of U.S. were explored and occupied by French as a part of the New France from mid 16^th century to mid 18 century.  Till today, 250 years after the British take-over, the vast majority of Quebec people continue to speak French, the official language of Quebec, and secession remains a top political agenda which gets voted in referendum once in a while.  The last vote took place in 1995 and the referendum was defeated by a narrow margin of 49.42% "Yes" to 50.58% "No".

While it might be hard to imagine how Quebec was like prior to the Quiet Revolution of 1960 when the dominance of Roman Catholic Church was suddenly and quickly replaced by the state, traces of the influences of Roman Catholic Church can still be seen in numerous historical sites throughout the province, not to mention so many of the roadways and streets are named after some of the 10,000+ recognized Saints.  When Mark Twain first visited Montreal in 1881, the largest city of Quebec, he was quoted to have made the observation that a person could stand on any street corner in Montreal, throw a stone and it would hit a church.

It wasn’t the case in 1534 when Jacques Cartier, the first French explorer to reach Quebec in an effort to find westward route to reach Asia, four decades after the first European explorer Christopher Columbus landed in Bahamas on behalf of the Spanish Court.  What he and his men saw were aboriginal people, vast land and resources.  He planted a cross in Gaspé Peninsula at the mouth of St. Lawrence River and claimed the land in the name of King Francis I which became the first province of New France.

When Jacques Cartier returned in his 2^nd voyage in the following year, he sailed up the St. Lawrence River and found over a thousand native people at the village of Hochelaga which is today’s Montreal (the name was derived from Mont-Royal, the highest hill of the city).  Nearly a century later, Paul Chomedey sieur de Maisonneuve, a French military officer was hired by the religious organization Société Notre-Dame de Montréal to lead colonists to set up a mission on the Montreal Island which he did in late 1642.  Montreal city was thus born which was called Ville-Marie then.

The first church, the Notre-Dame Church of Montreal was built between 1672 and 1682 and served briefly as the first cathedral of the Diocese of Montreal from 1821 to 1822.  Both the church and the bell tower can no longer be seen as they were torn down to make room for the construction of a new church, the Notre-Dame Basilica of Montreal or Basilique Notre-Dame de Montréal, beginning in 1824 to serve the needs of the congregation that was experiencing a rapid growth. 

Today, Notre-Dame Basilica of Montreal is the most visited churches in Quebec.  It was also the largest church in North America before the St. Patrick’s Cathedral was built in New York City decades later.  The basilica is a Gothic Revival architecture designed by James O'Donnell, an Irish-American Protestant from New York.  If you had been to the world famous Notre-Dame de Paris built 500 years earlier in Gothic architecture, you can clearly see their similarity in architecture.  For the interior, the brilliant choice of the color in combination of deep blue and gold gives the basilica a glorious and grand appearance yet with a surreal and peaceful feeling.  The place has served many significant events over the years, from the state funeral of Pierre Trudeau, the 15th and the most admired prime minister of Canada (from Montreal)  to the wedding of the super star singer Celine Dion. 

 

Further northeast of the Basilica in Old Montreal, you will find the Notre-Dame-de-Bon-Secours Chapel, or the “Sailor’s church”, one of the oldest churches in Montreal.  It was first built by St. Marguerite Bourgeoys, the first teacher in the colony of Ville-Marie in 1655. The current structure was built in 1771 after it was destroyed by a fire in 1754.  The church is small in size and simple in its interior decoration.  There is no pretence and one can picture sailors of those days came into the church to pray and get help from the harsh and death-ridden journey.  One can go up to the spire to get a panoramic view of the St. Lawrence river and the Old Port of Montreal. 

Southwest of the Notre-Dame Basilica in downtown Montreal lies the Cathedral-Basilica of Mary, Queen of the World (Cathédrale Marie-Reine-du-Monde) that is the seat of the Roman Catholic archdiocese of Montreal.  The Cathedral was completed in 1894 and is literally a miniature version of the Late Renaissance Saint Peter's Basilica in Vatican City.  It is a one-third model of
the St. Peter’s that is 730 ft long by 500 ft wide by 452 ft high, completed with a 137 ft high dome.   If you have visited St. Peter’s

before, the following photos will probably jog your memory although as a scaled replica, it is not nearly as sophisticated or artistic.  Nevertheless it is a far cry in terms of the luxury from the “Sailor’s Church” where we had just visited. 

From the very beginning, the catholic settlers placed the city under the protection of Virgin Mary for her compassion.  With the risk and difficulty of sea journey of those days, it is understandable that the sailors and colonists turned to her for comfort and blessing.  That reminds me of Guan Ying 觀音
in East Asia Buddhism.  For her compassion and unconditional love,  she is the most popular Goddess of Mercy (and her manifestation Mazu) for east Asia Buddhists and in particular, the fishermen and travelers alike in southeast China sea.  Here is a photo of the altar the altar of the “Sailor’s Church”.  Their figures and gestures may be very different but they both brought the relief that the believers seek.

Driving northeast along the St. Lawrence River of Montreal, one reaches Quebec City, 160 miles away at near the mouth of St. Lawrence River.  It is the capital of Quebec province and one of the oldest cities in North America.  The tiny Old Quebec where all tourists congregate is the only city north of Mexico where you can still see the city walls.  It was founded in 1608 by Samuel de Champlain, the Father of New France.

Old Quebec is a charming and pleasant place to visit.  It is small enough that you can stroll up and down the streets at ease while changing elevation in hundreds of feet between the upper and lower towns and enjoy the scenery at different angles and time of the day.  Below are two photos we took
during the trip that would give you some ideas of the views.

When in Old Quebec, you would not miss the Château Frontenac, the majestic castle hotel built in late 19^th century and the most visible landmark of Quebec City.  Situated at the end of a street in the Upper Town and bordered by the Terrasse Dufferin, the Chateau’s overwhelming presence overlooks the St. Lawrence River from top of a cliff, making it appear taller than it really is.  No wonder it is the most photographed hotel in the world according to the Guinness World Record. On the terrace, a large statue of the founder Samuel de Champlain looks to the west towards inland instead of the ocean.  Does it symbolize the French ambition for the new colony then?

A stone-throw away of the Chateau, one finds the Cathedral-minor basilica of Notre-Dame de Québec (see photo to the right).  Founded in 1647, it is the seat of the Roman Catholic Archdiocese of Quebec, the oldest in the New World north of Mexico.  Its odd asymmetric appearance is rare and intriguing.  Some say it is due to the need to balance the weight of the structure as the cathedral sits on a slope.

In the Lower town, there is the lovely Notre-Dame-des-Victoires church that was initially built between 1687 and 1723 and restored in 1816.  The church got its name of “victories” after the weather sunk the invading British fleet in 1711.  Together with previous victories, there was a strong belief that the prayers at the church were answered in the wars between French and the attacking British forces. 

Of course we know from the history books that French’s luck ran out in 1759 when British launched a surprise attack after 3 months of bombardment and siege of Old Quebec.  British and French forces of less than 10,000 men in total from both sides met and fought on the Plains of Abraham, right outside of the old city wall.  In 30 minutes, the decisive battle of the Plains of Abraham was over and French was defeated.  The battle while small in scale marks the beginning of the end of French colonization in North America and the later day unique cultural and political issue of Quebec.  When the Seven Years' War (of which the Battle of Quebec or the battle of the Plains of Abraham is a part) was concluded with the treaties of Hubertusburg and Paris in 1763, France ceded its territories in Canada (and several others) to British who in return promised the religious freedom of its new Catholic subjects.  Since then Great Britan became the most dominant colonial power for the ensuing two centuries.  One can only wonder if the outcome would be different if French won the battle of the Plains of Abraham?  What would America and Canada be like today then? 

Between the Plains of Abraham and the Château Frontenac is the impressive Citadelle, home station of the French speaking Royal 22^e Régiment of the Canadian Forces.  Built initially by French in 17^th century, the star-shaped fort we see today was built by the British between 1820 and 1831 against potential attacks by Americans!  The 40 minutes long changing of guard ceremony at 10 a.m. in the summer is a colorful tourist attraction.  What attracts most attention was not the band or the parade but the fabulous four-leg goat mascot of the regiment who went through the long ceremony in restrain and discipline.  The goat also entertains endless photo shot requests from and with the tourists!

Driving back to Maine along the scenic Quebec Route 173, aka Route-du-President-Kennedy next to the beautiful Chaudière River, one can see church spires appear frequently in the horizon and then disappeared into the tranquility at your back. Occasionally, the Quebec flag (photo to the right is published by abdallahh on flickr.com) in French Blue with white Lilies and a cross reminded people the protector Virgin Mary, the catholic church and the fact that we are in the French Canada.  Immigration and settlement, once restricted to Catholic French in early days of New France by the order of the King is now open to the world of diverse population.  The romantic notion of the colonization and missionary to convert the aborigional people to Catholicism was long gone, replaced by separation of the state and church and a democratic system.  What are left for the visitors are the legends, the history-filled stone structures and cobble-stoned streets.  For the residents, of which more than 60% of Quebec people today are catholic and more than 80% are French-speaking, some of them unquestionably find it hard to cut the umbilical cords no matter how long it is and how dry it has become.  At the same time, Quebec Sovereignty Movement, tempered with increasing economic and globalization pressure continues to adapt its formats and proposals.  The kings and physical buildings may have been gone but the struggle and negotiation between the collective memory and reality will stay for a very long time.  Talk to you soon!

Tidbits of Chinese Language

I just came across a draft flyer by the Asia Club students of my wife’s for their upcoming screening of an award winning documentary film I Love You Mommy  In it, there is the Chinese translation of the title 我愛你媽  (Wo Ai Ni Mommy) that got me thinking. 

For those whose mother tongue is mandarin Chinese, there is something funny about this translation since it could be and often is taken to mean I love your Mommy.  The issue is that in Chinese language, the possessive pronoun in western grammar is accomplished formally by appending the determiner particle 的 (de) to the pronoun.  Thus your school for example will be expressed as 你 you 的 de 學校 school.  However the determiner particle 的 de is often omitted when the relationship with the object is a personal one.  Thus one would say my mom as 我媽媽, my house as 我家 and f#@! your mom as …

Of course, another way to rid of the ambiguity is to use punctuation marks.  One could say I love you, Mommy 我愛你,媽 (Wo Ai Ni, Mommy) or better yet, by shuffling the words and just say Mommy, I love you 媽,我愛你 (Mommy, Wo Ai Ni).  Unfortunately this solution does compromise slightly the aesthetics of the flyer. 

By the way, the omission of punctuation marks in ancient Chinese literature is one of the reasons why they are so difficult to read.  As a result, there have been some never-ending debates about the proper interpretation and intents of the writings by scholars including Confucius since different placements of punctuation marks could alter the meaning completely.  Here is one of my favorite stories that most Chinese speaking people would probably have heard of since childhood.  It is about a host who tried to get rid of a guest who overextended his welcome.  The host left a note without punctuation marks for the guest that says “It is a rainy day; a weather for one more day of stay.  The heaven may want to keep you here, but I do not!”下雨天留客天天留我不留.  Our witty guest upon reading the note, took a pen and added few punctuation marks at key places.  The note then became “It is raining, The heaven wants me to stay.  Do you want me to stay here every day? Yes!” 下雨﹐天留客。天天留我不﹖留﹗

Generally speaking, Chinese language is highly context dependent and is not as rigid in terms of sentence structure.  For example, while Chinese language is usually classified as belonging to the SVO (Subject-Verb-Object) family, it also allows for SOV and OSV constructs as well.  Further, Chinese words have only one single grammatical form with few exceptions; for example, tenses of verbs are expressed through the particles and orders. All these make it easy to have fun with the ordering of words.  Here is an example.   If you want to hint to your boyfriend that it is time to buy you new dresses, you might say 我沒衣服穿 that means “I don’t have dresses to wear” which is in SOV form.  But if you make the unfortunate mistake of sticking with the SVO, you could have reversed the order of words and say instead 我沒穿衣服“I don’t have my cloth on”!

You might think while it could be embarrassing sometimes, it is no big deal to make a mistake in the ordering of words in Chinese sentences/phrases.  It is not so simple.  The long standing “One China” declaration has been a huge issue for People’s Republic of (aka Communist) China and Republic of China (aka Taiwan) as well as international powers including U.S.  For almost twenty years since 1992 Consensus, the disagreement has been boiled down to mere four characters: the latter stick to the position of 一中各表 (or  一個中國，各自表述 One China, separate interpretations.). The former insisted on however 各表一中. Is it clear to you now the disagreement?

By now, you are probably close to getting idea that one can be very creative given the flexibility in ordering of Chinese words.  Yes, that is indeed the case.  For instance, one can come up with sentences that read the same backward or forward, such as 別離還怕還離別.

More impressively, for more than a thousand years, writers have written many reversible poems 回文詩 – effectively two poems in one when read forward and backward.  Here is a famous example:

《兩相思》Missing Each Other (李禺 Yu Li of Song Dynasty) 

About husband missing his wife, when read forward.

枯眼望遙山隔水，
往來曾見幾心知？
壺空怕酌一杯酒，
筆下難成和韻詩。
途路陽人離別久，
訊音無雁寄回遲。
孤燈夜守長寥寂，
夫憶妻兮父憶兒。

When read backward, it becomes a poem that the wife misses her husband:

兒憶父兮妻憶夫，
寂寥長守夜燈孤。
遲回寄雁無音訊，
久別離人陽路途。
詩韻和成難下筆，
酒杯一酌怕空壺。
知心幾見曾往來，
水隔山遙望眼枯。

There are even more complex geometric arrangements in circular form (that you could start at multiple points) or squares that you can read horizontally, vertically and diagonally.   I will stop here though.  If you are interested in this topic, just google any search engine with 回文詩.  Have fun! Talk to you soon.

The Butterfly Effect – When Science meets the Pop Culture

No, I haven’t seen the 2004 Hollywood movie The Butterfly Effect that “Change one thing, Change everything”.  I am talking about the serious mathematics and science of Chaos Theory and Fractals that have caught so much public attention and imagination for the last quarter century.  Have you ever seen or owned posters or T-shirts with graphics like these “fractal arts” below?

Did you know that these beautiful pictures represent what is known in science and math world the Mandelbrot Set which was introduced in 1975 by Benoir Mandelbrot, a highly regarded mathematician using an innocent looking quadratic polynomial z_n+1 = z_n² + c in complex plane?

Fractal, as Mandelbrot called it in his 1975 book Les objets fractals, forme, hasard et dimension (an English translation Fractals: Form, Chance and Dimension was published in 1977) [Wikipedia] is often referred to as the geometry of chaos theory.   It aptly provides, among other contributions, incredible visualization of some intricate structures found in nature that contain tiers of miniature sub-structures that look exactly the same as the whole.  But what is chaos theory anyway?
 

It all began when Edward Norton Lorenz (1917-2008), a MIT professor in mathematics and meteorology, published in 1963 a very important paper Deterministic Nonperiodic Flow in the Journal of the Atmospheric Sciences.  It is not clear however if the paper had attracted much attention outside his research area at the time.   Almost a decade later in 1972, Lorenz gave a presentation before the American Academy for the Advancement of Science.  The title of the talk was "Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?”  Being a grounded scientist and mathematician, according to the legend, the choice of the butterfly metaphor was made by the session convenor Philip Merilees and Lorenz originally was using sea gull.   

The vivid contrasting image of a beautiful but fragile butterfly penetrated and stuck to people’s mind and the reference of “butterfly effect” began to be widely used and abused ever since.  Can you imagine what would happen if it was called “sea gull effect”?  Although one had never ruled out the possibility of what Lorenz had discovered accidentally, it was Lorenz’s who demonstrated clearly and called people’s attention to the fact that realizations or trajectories of some nonlinear systems could be dramatically different given ever so slight a difference in the system’s earlier state - such as if an unknown butterfly in thousands of miles away flapped its wing, or not. 

It is not clear how it happened but the literary reference of the butterfly effect often suggests a “scientific theory” that a slight different action or choice can cause a huge impact down the road all by itself. This cannot be further from the truth and is in fact the opposite of what Lorenz’s discovery says.  Ignoring the technical reasons of such a erroneous statement, the significance and the implication of Lorenz’s work is that there is an inherent limitation (like the famous Heisenberg’s Uncertainty Princicplein Quantum Mechanics) in predicting accurately the future behavior of a complex (nonlinear) system, in this case, the weather system – arguably the most complex yet observable natural system to each of us, given the possible high sensitivity to some of the variables.  This is a perfect demonstration of the traps and hypes that sciencentific and mathematical discovery can run into when people got carried away with wild imaginations and misinterpretations.>/p>

The story did not stop there. Few years later, two Mathematics professors, James Yorke  and Tien-Yien Li (李天岩) published a paper in 1975 on the American Mathematical Monthly a paper entitled Period Three Implies Chaos that marked the first time the term chaos was used to refer to the behavior of this type of systems.  The name Chaos Theory became a household vocabulary when James Gleick published his bestselling book Chaos: Making a New Science in 1987.  The book made it possible that a reader can feel and see the discovery without knowing anything about science and mathematics.
 Merriam-Webster dictionary tells us the familiar word chaos came from Greek and means:

1 obsolete : chasm, abyss
2 a) often capitalized : a state of things in which chance is supreme; especially : the confused unorganized state of primordial matter before the creation of distinct forms — compare cosmos b) : the inherent unpredictability in the behavior of a complex natural system (as the atmosphere, boiling water, or the beating heart)
3 a) : a state of utter confusion  b) : a confused mass or mixture.

How much attention would it have drawn if Gleick chose a book title like Order and Properties of Nonlinear Dynamic Systems – a new development in science?  Although it is a much more accurate description of what Chaos Theory really is, how many copies do you think it would sell?  To give you an idea of how visible chaos theory is to the society, some people apparently felt it is necessary to look into its implication on religion, see e.g. the 1997 article Theological Reflections on Chaos Theory by John Jefferson Davis.  Indeed the irony is that the real driving force of all these explorations by the mortal scientists and mathematicians is to discover orders and to make sense of the seemingly chaotic world. 

I have not studied Chaos Theory previously other than few brief encounters with others’ research work on self-similar traffic and “long tail” studies and analysis in data networks in early 90’s.  I do know enough about nonlinear dynamic systems to be dangerous though.  Recently, I got a chance to view the 24 thirty-minutes lectures series on Chaos recorded in 2008 by Steven Strogatz, a Professor of Applied Mathematics and of Theoretical and Applied Mechanics at Cornell University.  The November 6, 2008 Chronicle Online, the daily newspaper of Cornell, had the following to say: “… Strogatz designed a course targeted to a generally well-educated audience -- light on the math, but including a wide variety of angles he hadn't explored before. That meant brushing up on the chaotic paintings of Jackson Pollock, learning about ancient Babylonian culture, and pondering the text of the Declaration of Independence.”  Wow! Isn’t that exciting? A theory that cut across physical and life sciences, engineering, arts and culture!  Let me tell you what I have learned and what I thought after watching these 12 hours of videos on my laptop with great interest.

The good: I did learn a great deal about Chaos Theory from the lectures and began to get a sense of what it really is.  I also learned a few rather interesting scientific discoveries and speculations through the applications and examples Strogatz uses in the lectures.  One such an example is the Kleiber’s Law in lecture 17 “Fractals inside us”.  Biologist Max Kleiber claimed in 1932 that for the vast majority, an animal's metabolic rate is proportional to the ¾ power of the animal's mass which suggests some efficiency of scale (i.e. more “energy” per pound is needed to sustain the life of a lighter animal).  Or, algebraically, the law can be written as (presumably in some averages) metabolic rate ~ (body mass)^3/4 , an example of the power law.  Waht is amazing is that this ¾ power law appears to hold true over 27 orders of magnitude of body mass from enzymes in respiratory complex to mammals!   The open question is why do most animals “obey” such a law despite their distinctly different mass and metabolic rate? 

Chaos theory and fractals may offer an answer to it, according to Srogatz.  Noting the networks of the pulmonary arteries and airways of the lung are branching networks architecturally, Strogatz argues why evolution or Natural selection might favor “fractal networks” which 1)is an extremely efficient way to distribute and communicate in a 3-D space using a branching network in 1-D tubes, 2)has enormous surface areas, 3)is easy to “program” as it involves a recursion of branching or splitting.  He cited the 1997 work by the theoretical physicist and biologists Geoffrey West, Brian Enquist, and James Brown in which they proposed a mathematical model and showed under certain simplifying assumptions that fractal network is the optimum branching network solution.  Further they showed since the terminating capillaries are the same in size for all mammals, the ¾ power law rises out of their mathematical models! Chaos theorists are excited about such a result as it suggests that chaos theory may hold the key to explain some mysterious properties in nature.  Is such a belief correct? Are we getting close to be able to understand something fundamental and common about life forms?  Many scientists remain (legitimately) unconvinced about the validity and applicability of those claims and models.   For one, wouldn’t it contradict the observations that Darwin’s natural selection that does not suggest or require optimality as mentioned in my last blog?

Another interesting example is the Feigenbaum Numbers mentioned in Lecture 23.  Anytime, if you find a rare universal constant that pops up in many seemingly unrelated systems, you know you are onto something.  Mitchell Feigenbaum did just that.  He was awarded the prestigious Wolf Prize in Physics in 1986 for his discovery of the Feigenbaum Constants, that have been observed in many natural systems and phenomena possessing a period-doubling bifurcating process - a fancy way of saying “splitting into two”.   The first constant is 4.6692…, the limiting ratio of each bifurcation interval to the next.  The second one is 2.5029…, the ratio between the width of a branch and the width of one of its next sub-branches.  Next time, if you run into these two numbers but not sure why, you might be staring at one such a mysteries form!

The bad:
The part of lecture that I found most distrubing and does not help the credibility of the story is the second half of the Lecture 18, the Fractal Art, albeit the discussion is very enjoyable and entertaining.  Professor Strogatz, apparently prodded by the Teaching Company who produces and sells the DVD, used

Jackson Pollock’s abstract painting as an example of an application of chaos theory.  In case you did not know who Jackson Pollockis, he is one of the most influential and revered American painters of the 20^th century, having left deep marks on Abstract Expressionism.  Just because the appearance of Jackson’s drip and splatter paintings appears “chaotic” to the naïve eyes of viewers, you might wonder, like I did, how is that having anything to do with the Chaos Theory?  How could Strogatz possibly pose the silly and ridiculous question on an art that Are these drip paintings random or fractals?!  Strogatz’s story is based on the controversial fractal analysis by the physicist and fractal enthusiast Richard Taylor who claimed to have found “pattern” or consistent fractal dimension (think of it as an embedded signature of a figure if you don’t know what that is) of Pollock’s paintings in progression by year.  The purported applications of fractal analysis thus include authentication and identification of “chaotic” paintings of Pollock’s.  Even if the claim turns out to be valid, I hope Chaos Theorists have higher goals and would not waste their time like this!  Of course, it could be about money.  Jackson Pollock’s drip painting entitled “No. 5, 1948” (see the photos to the right) was rumored to have been sold in 2006 for $140 million dollars that would make it the most expensive painting on record in history so far.  By the way, Jackson Pollock’s work preceded the Chaos Theory.  He created his original drip painting techniques in 1940s.

In addition to the above What!? There are some “so what’s” here and there such as the story of the unexpected horizontal oscillations and repair of the newly built London Millenium Bridge in 2000.  All in all, to be fair, Strogatz is an excellent speaker and hard to imagine one can deliver the stories much better, no wonder he had won so many teaching awards in top universities.  Further, chaos theory and fractals has made exciting new advance in the study of nonlinear dynamic systems and I should not be overly critical just because it is popular or misrepresented by some.  The research did and will continue to offer a new way to examine the behaviors of some complex systems and help identifying common characteristics of things found across many disciplines from physics, chemistry to biology and ecology.  The fact that validated governing models are based on same type of equations do tell us a lot about the systems; it clearly suggests that the similarity more likely are derived from some common features rather than the chance or coincidence.  After all, mathematical model is an invaluable and indispensible tool in science and engineering and good models do reflects our understanding of the subject it models after.  But based on what I have learned from the lectures, I do not think Strogatz’s claim is valid that Chaos Theory is the third revolution in science in 20^th century, after Relativity Theory and Quantum Mechanics.  The claim is at best premature and at worst, a hyperbole. 

In sum, it is a fact that we often found ourselves limited by our own experiences and language and that we have to borrow existing words, notions and analogies to describe something new.  We often forgot models are limited and necessarily simplistic.  Validated theory such as Newtonian mechanics may fail when operated outside the regions they were designed for.  The misconception and misuse of the words and notion of chaos theory is a perfect example to remind us what can happen when a difficult and intricate subject could be overwhelmed in sensations and excitement. Strogatz did insert carefully words like seemingly or appearance of in front of the word Chaos at places.  Unfortunately, these critical qualifying words tend to get dropped and forgotten and messages got severely distorted as they propagate in time and space.

By making it so easy to understand, haven’t we introduced and suffered from the very butterfly effect: that ever so little simplification of the complex truth could be amplified exponentially in time till we are lost in the intricate world of fractals?  It is critical to be intellectually curious but it is equally important that we stay truthful somehow in every step along the way. How can we guard against the danger of amplifying the little butterfly’s flutter when science meets the pop culture just because something sounds better and cool?