Friday, June 20, 2014

Miracles No More?!

When we see or hear about an event that we did not expect it to happen, we react with surprise.  We describe them as rare, unusual, improbable, coincidence, unbelievable, and sometimes outright miracles.  Have you ever felt that these supposedly rare events seem to happen much more often than you expected?  I submit that many of us feel the same.  Further, throughout the human history, people have been seeking explanations why these improbably events happen.

One possible explanation is that many of such events indeed shouldn’t have happened.  Therefore, since they did, they must be caused by the power of some unknown non-human entities or forces.   Another possibility is that our expectation was too low.  We probably have failed to account for some factors and thus significantly underestimated the possibility for those events to occur.  That is, they are not rare events to begin with.  Or it is simply that we haven’t acquired sufficient knowledge and tools to provide adequate explanations.

To address this issue is by no means easy.  Fortunately, with the advances in philosophy, sciences and mathematics, we have already come a long way in clarifying and quantifying the issue rationally and logically.  In fact, there are decent tools now for us to tackle the question if the occurrence of certain events is likely to be truly unusual.

But the harder problem is actually in convincing those who thought an event is a miracle when it is not in the first place.  Part of the challenge is to show the reasoning to laymen who are not familiar with the language and tools of mathematics and statistics.  The landscape has changed earlier this year when David Hand, professor emeritus of Imperial College London and a former President of the (British) Royal Statistics Society, published his beautiful little book The Improbability Principle – why coincidences, miracles, and rare events happen every day

As the title indicates, Professor Hand showed us eloquently with many real-life examples and stories how easy and often we get impressed with events/news that we thought should not have happened but did.  He identifies the main culprit what he called Improbability Principle – a collection of strands/laws, each of which is sufficient to produce outcomes that appear to be highly improbable to the uninitiated.  What makes the matter much worse and so difficult to discern is that these strands of Improbability Principle can “intertwine, braiding together and amplifying each other, to form a rope connecting events, incidents and outcomes.”

To give you a sneak preview, in Chapter 4 of the book, Professor Hand brings forward the Law of Inevitability which says “even if each of the possible outcomes has a tiny probability of occurring, it’s certain that one of them will.”  One example he gives is the stock tipster scam whereby the perpetrator sends letters to say, 1024 individuals and claims falsely to have the ability to predict the daily ups and downs of stock market.  Most of us would dismiss such a claim instinctively.  But the scammers are pretty smart people too and have their ways to combat the skepticism, making use of the law of inevitability!   The perpetrator would send 1024 distinct predictions of market movements of 10 future business days, one for each of these 1024 individuals.   If you and I are making a random guess, we would have less than 1 in 1,000 chances to get it right.  But guess what?  Since there are only 1024 possibly distinct outcomes of up-down movement over any 10 business days, one of these 1024 individuals is guaranteed to have received from the scammer the correct 10-day long pattern.  Such an incredibly impressive achievement (to the one who received the correct prediction) could be sufficient for the perpetrator to profit from the scam follows.   

In Chapter 5 of the book, Professor Hand recalls a number of interesting real stories, ranging from someone had won multiple lotteries over a short period of time to a woman saw a book in a used-book store that she used to own many years earlier.  You and I would probably react to such stories with “Wow, what an amazing coincidence!” and soon forgot about it.  Then we find ourselves react similarly soon enough with yet another such a story.  To show us why such stories seem to take place so frequently, Professor Hand introduces the Law of Truly Large Numbers that says “with a large enough number of opportunities, any outrageous thing is likely to happen.

Take the lottery story as an example.  Most of us understand that the chance for a randomly chosen player to win a huge jackpot can be astronomically small (by design).  Further, most of us also understand that the chance of an individual would win two large jackpots of independent lotteries is exponentially smaller – the odds to win both would be a trillion to 1 if winning one is a million to 1.   But then, should we be surprised upon hearing the news that someone had won two lotteries somewhere?  It turns out that we really shouldn’t be surprised.  Part of our problem is that we were looking at the wrong measures.  While the chance of winning a large jackpot of a lottery is indeed tiny, what the news and we were actually talking about was the (expected) number of occurrence of such an event over an unspecified period of time – or how many winners would you expect to have such an unbelievable luck of winning two jackpots.   Were you ever surprised when someone did win the jackpot of a lottery?  Once you realize how many lotteries there are and how many people are playing multiple lotteries and bought many tickets regularly, why should we be surprised if once in a while, one of them won two lotteries somewhere over a long period?  The lesson is that although the probability for an event to occur is tiny, we tend to forget the number of attempts is can be much larger than we expected and consequently, the event is almost certain to happen in due time.

These two are just tips of the icebergs.   Human beings do have at least a few more blind spots that can mislead us as well.  In chapter 6, Professor Hand notes the Law of Selection that says “you can make probabilities as high as you like if you choose after the event”.  While I trust none of us would cheat by drawing the target after shooting the arrows, we do commit, from time to time, unconsciously the act of fitting questions to answers and identifying causes to result after the event has taken place.  When was the last time you heard someone attributes a good thing happened to him/her (after it happened) due to his/her prayer made earlier?  What he/she might have neglected was the other nine hundred ninety nine times when nothing memorable happened!  No one was harmed in these type of stories of course.  But what if it is a scrupulous investment advisor who is telling you examples of selected clients who had made insane profit?  Would you be so impressed and invest your life time savings to his scheme?  By the way, this is closely related to the so-called Confirmation bias that we tend to count and remember only those events that you want to include for whatever the reason.

If all these were not enough, we definitely are not helping ourselves by getting little too relaxed or sloppy.  Complementing the Look-elsewhere Effect, Professor Hand’s law of near enough says that events which are sufficiently similar are regarded as identical.  With this powerful law, you will see that we can ensure the “connection” we want to draw can be true.  

Let me show you with the following example.  Let us say you try to initiate a conversation and “connect” with a girl in a bar.  First, the Look-elsewhere effect expands the space of search – if she did not come from your town, ask if she is coming from the same county or state.   If that is not the case, the law of near enough will likely do the job – you can ask if she knows someone from the state you come from.  You will be impressed how effective this trick works.   I used to brag about I can find some connection quickly with any stranger from Taiwan – a place of 26 million people.   That was before I learned that someone has already formalized a theory of Six Degrees of Separation that everyone and everything in the world can be connected within six “connections”!   Interestingly, most of us accept matching 5 numbers is not worth much in a lottery where the jackpot requires the matching of all 6 numbers.  The trap is, while 5 deceptively close to 6, the cases of five matches is so incredibly larger than that of matching 6!

There are a couple more laws the book discusses.  You can read them at your own leisure and reach your own conclusion.  Even if you don’t agree with some of points made in the book, you should at least be aware that many legit as well as scrupulous people/organizations do use these laws to their advantage to try to get your money.  If you do find the analysis interesting and helpful.  Here is an exercise for you.  When you open a fortune cookie the next time, tell us if it is relevant and applicable to you and if any of these laws are at work.  

Sorry, the world is more boring than you and I thought.  Believe it or not, there simply aren’t as many improbable events and miracles.   Talk to you soon!

Tuesday, June 10, 2014

Till Seas Run Dry and Rocks Turn Soft 海枯石爛

The most commonly used prayer in American wedding ceremony ends with “Till Death Do Us Apart”. Chinese on the other hand has gone much further to“the end of time” and express with an idiom for the permanency of one’s love that literally says “till seas run dry and rocks turn soft 海枯石爛 .  If you want to see what that state on earth might look like, you can just visit the Arches and its adjacent Canyonlands National Parks on the Colorado Plateau in Southwestern United States.

Rising above sea level at an average of 5000+ feet, the Colorado Plateau covers a significant portion of the Four Corner states – Utah, Colorado, New Mexico, and Arizona.  With a size of almost 10 times of that of Taiwan, the plateau proudly claims 9 out of the 59 National Parks and 16 out of the 109 National Monuments of U.S.   Many of them including Arches and Canyonlands National Parks are on the honor rolls of 1,000 Places to See Before You Die.

Known for their spectacular valleys, canyons, and rock formations such as fins, hoodoos, arches, etc., these two National Parks are considered Photographer’s Heaven.  Scientists have estimated that they have been sculptured by the nature for over 300 million years.   To understand the sculpturing process, you can watch online a short 3.5 minutes animated film Geology of Arches on the official Arches National Park website. Discovery Channel has also co-produced with National Park Services a 15 minutes video Secret of Red Rocks that introduce these two wonderful National Parks.

If you are a first time visitor but find the scenery of the area look familiar, it is probably because the setting has appeared in many popular Hollywood movies since 1940’s.  They include movies such as Rio Grande, Indiana Jones and the Last Crusade, Thelma and Louise, Hulk, Mission Impossible II, and 127 Hours. If you are not obsessed with cost efficiency, i.e., seeing most places in the shortest amount of time possible, you should take your time to hike/bike, in addition to riding in a car/bus, to appreciate properly these two incredible parks and their surrounding areas. 

To reach these two national parks by air, a good regional airport to use is Grand Junction on the Colorado River at the southwestern Colorado which has been a major transportation hub of the region for more than a century.  At the airport, you can rent a car and drive across the Colorado-Utah state border to the town Moab at the gate of the Arches National Park. 

Grand Junction is an interesting small town in its own right.   With a population of fewer than 60,000, the town supports a public Art on the Corner program for over 30 years that has by now over 100 sculptures on every block and corner on its main street.   One of most eye-catching pieces is Lou Willie’s Chrome on the Range II - a steel framed bison made with numerous pieces of hand cut, polished chrome car bumpers!  (see photo at right).  Along with several western towns and Moab where we stayed for the whole trip, Grand Junction has recently been named by a Travel+Leisure Magazine article as one of the “America’s Coolest Desert Towns”.  

Traveling by car from Grand Junction to Moab, you have a chance to see one of the most beautiful scenic drives if you take the Utah Scenic Byway Route 128 instead of staying on the Interstate Highway 70.  Shortly after exiting I-70 at exit 214 and passing through the ghost town Cisco, one picks up Rte 128 and soon begins to follow the course of Colorado River.  You will get a nice sneak preview of this amazing red rock country.  

In this section, the 1,450 miles long Colorado River is still narrow, gentle and not as hurried.  In another few hundred miles, with a larger flow resulting from infusion of more tributaries and steep gradient, cutting through the Colorado Plateau, it becomes the principle river for water supply, irrigation, and hydropower generation that 10s of millions people’s livelihood depends on directly.   Indeed, Colorado River is the most engineered and managed river in the world with every drop of its water allocated and controlled.  How good a job have we done?  The river now doesn’t even reach the sea as the last 100 miles of the river has dried up for sometimes with many serious and controversial issues being debated.

100 miles from Grand Junction, one reaches the southern end of Utah Rte 128 and arrives at the small desert town of Moab which is the most convenient base for those who want to visit Arches and Canyonlands National Parks and/or other outdoor activities in the area.  

Moab has had its ups and downs since the early Euro-American settlers’ days in early and mid 19th century.   It began to lose its economic power as a trade center in late 19th century when a railroad was built north of it that bypassed Moab.  Hollywood got interested in Moab when John Ford, the legendary western movies director, came to the area to shoot some of his most popular movies.  Then, significant uranium deposit was discovered in the area in the 1950’s when nuclear weapon and power generation is drawing world’s attention.  However when the cold war thawed and new nuclear power plant stopped being built, demand for uranium dwindled and local economy tanked again.   Today, Moab thrives as a tourist and outdoor adventure center.   But as one drives north from Moab to the Arches National Park, Department of Energy’s UMTRA (Uranium Mill Tailings Remedial Action) project site is very much visible and active in an effort to clean up and relocate the tailings that poses huge threat to the environment.  (See photo at the right.)

Once one turns the corner of this eye sore and continue driving further north on Rte 191 along the Moab Fault, entrance to the Arches National Park appears in sight in no time.  With more than 2,000 arches and peculiar red rock formations, the park is an amazing world by itself waiting for you to discover and explore. 
At a little less than 80 thousand acres, Arches National Park is one of the smaller national parks.  The 1500 feet elevation difference between the lowest (at the park entrance) and the highest point suggests easier hikes with limited elevation changes of the trails.   Better yet, many of the most impressive formations and overlook are easily accessible as they are within a short walk from a 18 mile long nicely laid scenic drive of the park. 

A picture is worth a thousand words.  To give you a feel for what you can expect, below are some selected pictorial highlights with brief descriptions. 

Park Avenue
Park Avenue: The name doesn’t do justice to these gigantic fins.   Sorry, there are no elevators, no doormen, and no butler services.

A little north of Park Avenue, one can see Three Gossips, Sheep Rock, and Tower of Babel. Driving a little further before reaching the Balanced Rock, you can see what I consider the loneliest formation in the park (photo at right) with the La Sal Mountains at the distance peaked at almost 13,000 feet.

Balanced Rock
Balanced Rock (pictured to the right).  It reminds me of the iconic “Queen’s head” in Yeliu, Taiwan which is shown in the photo below which is sourced from a Taiwan government website.
Queen's Head in Yeliu, Taiwan

Double Arch
Turning right after Balanced Rock, one comes to a small parking lot from where you can walk a short distance to North and South Windows, Turret Arch, and Double Arch.  The latter’s name suggests “buy one get one for free”.  How often can you get such a good deal in nature?  Climbing through them, and crawling through the north window and under the Turret Arch will definitely get you some fantastic photographs.  

Turret Arch

North Window

A must-see of the park is the iconic, unofficial symbol of Utah – the 65 feet tall free standing Delicate Arch on top of a huge rock shaped like an amphitheater.  It does require more leg work.  Following the 1.5 mile trail with almost 500 feet elevation change, one would walk up and over a huge slickrock standing in the way between the arch and the parking area.  By the way, the torch relay of the 2002 Winter Olympics at the Salt Lake City passed through the arch.  To experience the extremely fine and thick sand like those in the best beaches, one can take a short walk to visit the Sand Dune Arch.

Many visitors rush through the Arches National Park daily without visiting the adjacent Canyonlands National Park which is a big mistake.   Colorado River and its main tributary Green River confluence near the center of Canyonlands National Park like the letter “Y” and thus divide the park into three disjoint regions. The top of the “Y” has an intriguing name -  Island in the Sky.  The photo to the right which is from the promotional material by the Moab Area Travel Council alludes to where the name might have originated from.   At a mere 30 miles drive from the entrance of the Arches National Park, Island in the Sky is the most accessible of the three regions of the Canyonlands since there is no means to across the rivers in between the regions.

Mesa Arch
If you use a PC and have used the desktop background library that comes with it, you probably have seen one of the iconic landscape photos of America - Sunrise at Mesa Arch.  I wasn’t dedicated enough to get up and leave hotel by 5 a.m.  Instead, we went to it later in the morning and once more in late afternoon as the arch is only  5-10 minutes walk from the parking lot.  The photo to the right was taken a little after 5 p.m.  that is still more than 3 hours away from sunset.

Island in the Sky can be explored using a 20 miles long paved scenic drive.  There are plenty of incredible views you can enjoy even if you don’t want to walk much or take a 4-wheel drive vehicle to the white rim of Green River.  Below of some photos we took that would give you some idea of the differences and similarity in scenery with the Arches National Park.

Green River Overlook - note the horse shoe shape bend
Shaffer Trail Overlook

Buck Canyon Overlook - Colorado River is visible

Upheaval Dome: it is not resolved why the dome is so different from the surrounds.  One theory is that the dome is the result of a meteoroid collision 60 million years ago.  

If you drive south from Moab on Rte 191 and turn west on Rte 211, you can reach the Needles - the bottom right region of Canyonlands.  Before reaching the park gate, you will be rewarded with views like the photo to the right shows.  

Needles viewed from the gate
Needles viewed from Elephant Hill access road
As one approaches the gate from east, the skyline of the Needles – sandstone spires - emerges at the horizon.  If we were aliens, we might be mistaken it as a lost city of some civilization.    While we did get a few more good photos of the Needles from afar in the park, we weren’t prepared for the amount of time and efforts it would take to actually reach those formations.  Next time, we would use a combination of a 4-wheel drive vehicle and hikes to the Chesler Park and Elephant Canyon that appear to be the best way to see the Needles.

One curious site in this part of the Canyonlands is the Pothole Point which is less than half of a mile from the road.  Two depressions of a Cedar Mesa Sandstone rock were able to trap and hold enough sand and rainwater to support a life system, completed with fairy shrimps, tadpoles, grass, and more!

You may wonder about the bottom left region of Canyonlands – the Maze.   We didn’t make to it; there isn’t any road for 2-wheel drive vehicles.  How remote is it?  Well, remember the1969  movie Butch Cassidy and Sundance Kid played by Paul Newman and Robert Redford?  The legend says Butch Cassidy had used the area as a hideout after some of his robberies.

What are you waiting for?  Go visit the Arches and Canyonlands National Parks and pledge your love!  Talk to you soon!

Wednesday, January 22, 2014

Puerto Rico – the Spanish U.S.

¡Hola!  In addition to the familiar 50 states and the (Federal) District of Columbia, U.S. has a number of territories.  These are land masses that the country has acquired over the centuries in Caribbean and Pacific Ocean.  With a size of over 9,000 square kilometers (1/4 of the size of Taiwan) and 3.7 million population, Puerto Rico at the (means “Rich Port”) tropical Caribbean, east of Haiti/Dominican Republic, is technically an organized (i.e. self-ruled) but unincorporated (i.e. U.S. Constitution does not fully apply) territory.  It is also the largest and most populated of all territories.  Although both English and Spanish as its official languages, Spanish remains the dominant language.  Incidentally Luis Muñoz Marín International Airport at the Metropolitan San Juan, Puerto Rico, is the busiest passenger hub for the entire Caribbean.

Going back 520 years to November 19th of 1493, Christopher Columbus reached Puerto Rico and claimed it for Spain in his second voyage to Americas with the purpose of establishing settlements and permanent colonies.  What happened in the ensuing centuries to the indigenous Taíno people of the region was the familiar sad stories of the colonial world – forced tributes, forced labor, slavery, oppression, epidemic diseases, completed with cultural genocide inclusive of religious practice and belief.

During the subsequent 400+ years of occupation and rule of Puerto Rico, Spanish Empire had successfully suppressed the initial Taino insurrections, fended off the attacks by other colonial powers such as French, British, and Dutch.  However, after decades of decline of the Spanish Empire in 19th century, the final blow was delivered by U.S. with the 10 week long Spanish-American War of 1898 when U.S. intervened in the Cuban Independence under the name of protecting its citizens and business interests in Cuba.  Spain was defeated in both theaters - Philippine and Guam in Pacific, and Cuba and Puerto Rico in Caribbean.  The result was the Treaty of Paris by which Spain ceded all its colonies to U.S. outside Africa including Puerto Rico and Philippine.  For U.S., the victory changed the American public sentiment and boosted significantly the American imperialism and international involvement.  It also sent the war hero Theodore Roosevelt into White House a few years later as the popular 26th president of U.S.

Unlike Cuba of which U.S. promised the support for the independence from the very beginning of the war, Puerto Rico’s political status has remained unclear with the population divided in preferences ranging from independence to statehood.  While ballots are now the places to express choices, tension between U.S. Federal government and pro-independence movement had sometimes reached boiling point during the last half of the 20th century.   Extreme groups such as Fuerzas Armadas de Liberación Nacional (FALN) had resorted to “armed struggles” and violent “terror attacks”.  However the latest Puerto Rico status referendum in 2012 reports about 54% of voters do not want to continue with status quo and among voters who answered the multiple choice question of statehood, independence or a sovereign nation in free association with the United States, 61% chose statehood and 5.5% chose independence.

A good place to start with in retracing the old Spanish colonial history in U.S. is the Old San Juan, the oldest Spanish settlement in Puerto Rico.  Connected to the main island via three bridges, Old San Juan is a narrow and tiny island near north shore of Puerto Rico.  At a mere ½ mile long and 2.5 mile wide with plenty of facilities from lodging, restaurants to stores and galleries concentrated in western half of this small island, it is a perfect place for tours on foot.  

Much of the old San Juan is still surrounded by centuries old 40+feet tall thick stone walls.  Thanks to the efforts by a few local activists, scholars and political leaders in late 1940s, the neighborhood escaped the bulldozer and modern redevelopment elsewhere and was revived while retaining its original Spanish architecture (photos above).   Today, one can stroll down the narrow cobble stone streets at ease, admire the bright and colorful two story houses with windows and balconies often decorated with flowers.  When tired, one can rest at the benches of public squares, sit with the late salsa composer Tite Curet Alonso (center photo above), have a cup of coffee/espresso with Mallorca.  When hungry, go into one of many eateries and have some pernil (roasted pork shoulder) and mofongo.

Located at the mouth of the San Juan Bay and as a gateway to the main island, Old San Juan’s military importance 500 years ago was obvious.  Fort San Cristóbal at the northeastern shore of Old San Juan was the largest fort Spanish ever built in Americas to protect the city from land attack.  Today, only 1/3 of the fort remains but still impressive.  On the top level of the fort, one can see the skyline of the (new) San Juan in its east.  See photos to the left.
Less than a mile west of Fort San Cristobal, there lies an even more impressive Fort San Felipe del Morro at the tip of the northwest corner of Old San Juan.  It is now a part of the National Park system and one of the UN World Heritage Sites.   Designed, constructed and continuously enhanced and updated since 16th century, El Morro is a 6-story structure with 18 ft thick walls and interconnecting tunnels, rising from the sea at 145 ft tall.  It performed its duty quite well to defend the threat from the sea and protect the port of San Juan.    Right next to it on the shore is the Santa María Magdalena de Pazzis Cemetery where many famous Puerto Ricans were buried, see photo at right.

As a popular tourist destination, Puerto Rico has plenty of natural beauties to offer from tropical rain forests to pristine beaches.  A less known but magical place to visit is Vieques, a small island east of the main island accessible by ferry or frequent 8-seater propeller planes.  Measured at 4 mile long and 21 mile wide (comparable in size to the Kinmen island, see my blog Kinmen Highlights), Vieques has a sparse population of fewer than 10,000 with increasing number of tourists as its popularity grows.

During the first three hundred years of Spanish rule, Vieques was not getting much attention by the Spaniards and was frequented by pirates and outlaws.  It wasn’t till the 19th century when Spanish began to make more earnest efforts to establish order on the island and to set up large sugar cane plantations.  However the growing economic development took a nose dive when sugar market tanked in 1920s and the Great Depression commenced.  Vieques’ course took another dramatic churns when World War II broke out and U.S. Navy acquired and expropriated 2/3 of the land of the island.

One of the most visible reminders of the Vieques modern history is El Rompeolas (The Mosquito Pier), a one mile long pier to nowhere at the northwestern shore of the island; see photo to the right.  You can’t miss it from the air when you fly in and out of the tiny airport on the north shore of the island.   In 1941, when U.S. saw the development of World War II at Europe became worrisome with the distinct possibility that Great Brittan might fall and the war could spread to the Americas, it decided to build a giant navy facility in Caribbean for the U.S. Atlantic fleet and the surviving British fleet.   Initial constructions include a sea wall that would connect Vieques and the main island of Puerto Rico 8 miles west. 

It turns out the real threat came from Pacific rather than from the Atlantic when Japanese made the surprise attack of Pearl Harbor 6,000 miles away on December 7th, 1941.  The navy base and sea wall construction was stopped and later abandoned.  Vieques island itself however has become a convenient place for military exercises and used as a bombing target by U.S. Navy ever since.  After many decades’ numerous but fruitless protests by the locals, the 1999 incident of the death of a civilian in a Navy bombing exercise finally drew the national and international attention.  Many celebrities and activists in U.S. and world joined the protests and civil disobedience.  Eventually U.S. Navy relented and withdrew from the Vieques and turned its land to the U.S. Fish and Wildlife Service in May 2003.  Till this day, parts of the eastern and western ends of the island remain restricted because of the danger posed by unexploded bombs.   Some local residents are still angry and bitter about their or their parents’ forced relocation that occurred more than 70 years ago. 

Today the tranquil farms, ranches and former fishing villages on the island no longer hear the bombs and missiles fly over their heads and explode nearby.  Instead they are increasingly invaded by tourists and entrepreneurs.  Beautiful white-sand beaches with azure water are not crowded and easy to reach by (rental) car, bike, taxi, "carros publicos" (shared van bus) or for some, simply walking.
When you are tired of tanning and water, try horseback riding.  Like most of stables in U.S. that cater to tourists, you can do a horseback riding without any prior lessons or experience in Vieques as well.  It is a wonderful outing at sunrise or sunset to ride horses on the beach, through the trails into valleys and over the hills with panoramic views of the island and ocean.  

Viequest horses are quite special.  They are Paso Fino (meaning the horse with fine gait), descendents of Spanish horses the conquistadors brought at the beginning of 16th century.   These horse are born with the ability to make evenly spaced four-beat lateral moves at varying speed called paso gaits.  It is so pleasing to hear and see a horse walking down the street in this fast distinct paso gaits – hooves moving close to the ground in order of right rear, right fore, left rear, left fore.   For a video demonstration and explanation of gaits of Paso Fino, you can click on the following Youtube video  By the way, horse gaits simply describe the ways horse moves that include the well-known (in an increasing speed) – walk (4-beat), trot (2-beat), canter (3-beat), and gallop (4-beat).   I suppose in a similar way, some of us are born with the ability to perform certain rhythmic dances and some can’t!

To top your list off, you must take an evening kayaking tour during new moons of the rarely seen natural phenomenon - bioluminescence.  There are many living organisms found from land to sea that emit light.  Fireflies are perhaps the most familiar and popular insect that can be seen flashing light at night.  Marine bioluminescence is more mysterious due to the limited accessibility but there are plenty of organisms in water from bacteria and protists to fish and squid that are luminous.  (Sorry, there are no luminous mammals, flowering plants, birds, reptile, or amphibians.)

If you have never experience the phenomenon before, you may have seen the computer animated whale scene ( in the 2013 Oscar winning film Life of Pi which is a dramatized and exaggerated version of it.   Indeed, according to the winning cinematographer Claudio Miranda of the film, the inspiration and idea occurred to him and Director Ang Lee when they saw bioluminescence in a bay in central Taiwan. 

In nature, one major actor is a single-celled micro-organism (a type of algae) called dinoflagellateUnlike adult fireflies who use flash patterns of bioluminescence to communicate with each other for courtship, dinoflagellates flash blue or green lights as a defense mechanism when its cell are pressed.  For a scientific explanation of how dinoflagllates generate light, you can start with the following UCSB link  It suffices to say that dinoflagellates garner their energy from photosynthesis and other food/nutrients during the day that allows them to produce sparks when the water they live in are agitated.

The Bio Bay of Vieques is one of few places one can see easily such an amazing phenomenon in significant scale.  As you paddle and move your kayak, a blue trail is left behind in otherwise a total darkness.  While not doing the justice, the photos sourced from the net do give you some idea of what is like.  What is more amazing is when you see a fast moving fish or a school of fish pass by.  You see long flashes move around rapidly in the water.  When you scoop up some water, your hands light up like a small X’mas tree with blue sparks for a short brief moment.   There is no words to describe those moments other than being purely magical.

Puerto Rico, I will be back.  Adios, voy a hablar con usted pronto!