Discrete Thoughts

欢迎来读三段文(Three-Paragraph Blah Blah)：平时上班下班，起早贪黑，无为却碌碌；偶有空，也只能写三段，故曰三段文。

The Mind often flirts with bursts of random Thoughts, just as how a restless Monkey does with her Jumps - ooh, ooh, eeh, eeh, aah!

2024.A.Jan01: The "Homeless" Problem of the Homeless

Walking my dog home in the evening, I noticed that he was still using the sleeping bag given to him about a month ago around the past Thanksgiving. It is wind- and water-proof, bought brand new from Amazon. I have been worrying that he might have lost or dumped it due to some warm winter days. He needs it! Last week on a rainy chilly night, I also handed him my spare ski jacket and an oversized umbrella. I refer to him as "HIM" since we were never introduced. Among all the homeless in the neighborhood, he is one of the special as he rolls around a shopping cart and earns money by collecting empty bottles or cans (5 cents per one). I could never recall him begging directly on the street. The way each of us faces and reacts to the homeless is always idiosyncratic and personal.

The problem of the homeless seems to be "homeless" itself. There are maybe 15 permanent homeless fellows in this neighborhood of about ten blocks along the Broadway - not enough votes (if they have ever voted) to attract the attention of those politicians at the district or city levels. On the other hand, ordinary citizens like you and me face them almost every day - outside of the subway stations, bagel shops, or grocery stores. Most time homeless fellows are kind and even amusing. Occasionally they may raise public concerns on neighborhood sanitation or safety. 

In mega cities like New York, San Francisco, or even Vancouver (where I visited during the past summer), the homeless problem is worsening. In NYC during the Covid, in particular, there were several major incidents involving the homeless, mainly unprovoked attacks towards ordinary citizens. The death of Michelle Go was one of the most shocking tragedies involving a homeless man. This dedicated wiki page gathers more information. Even more heart-wrenching, she had volunteered for over a decade to assist low-income New Yorkers. 

In the wake, NYC Mayor Eric Adams proposed a new program to facilitate the removal and hospitalization of mentally ill  homeless people from streets (CNN). With no surprise almost immediately the policy drew harsh criticism and backlash from homeless advocates (NPR). To me as an ordinary citizen, the challenge lies in how to properly gauge the potential threat level on public safety. A mere 5- or 10-minute street scanning or snapshot does not qualify cops for making the right decision. Many homeless are indeed mentally aberrant, caused by years of malnutrition, lack of normal interaction and communication with society, and lack of minimal spectra of life activities. But most of them are harmless, indeed.

Aside from city shelters and government or non-profit programs, it seems that the homeless problem has to be dealt with at the individual level. No two homeless fellows are the same, though they may appear so. 

Back in October of 2017 or 2018, suddenly an old white couple appeared in the neighborhood. Unlike others, they possessed many boxes of belongings, stacked behind the two benches on one island in the middle of the busy Broadway. I wondered who helped them transport these boxes here. 

Even older than my parents still in China, they naturally locked in my attention. For the first few weeks, they mostly stayed under the two big umbrellas mounted on the benches. Clearly, they had some initial spendable sources. Then a few weeks later, one started to encounter the lady elder on neighborhood streets, holding a paper cup and begging. She always walked while begging, but made no familiar calls like "Please Spare Me Some Changes." She was more quiet and a bit shy. The men elder barely left that bench area. Sometimes you could hear his loud voice directing the lady elder to do something. Or that's just my fabricated imagination when I walked by.

Near the Thanksgiving of that year, the chilly rainy season kicked in. It was hard to ignore this old couple wrestling against the wind and rain with merely two wavering umbrellas. On Thanksgiving Day, just before departing for a family dinner in New Jersey, I went to a grocery store nearby and bought a full bag of quality food, including organic milk, ready-to-serve fruits, bagged meat and gourmet bread. I was preparing for unexpected scenarios so that I could still carry the food home for ourselves. 

It was raining lightly but cold and getting dark. I walked directly towards the island between the two busy directions of the Broadway. I expressed to the lady elder that I bought this bag of food for them for Thanksgiving. She turned around, totally unexpected, and raised her voice: "No, no, we don't need food." Then the man elder, sitting always on his side of the other bench under the other big slanted umbrella, got a glimpse of me and heard our brief conversation, and also amplified his voice: "No. Tell him to leave us alone. We don't need food!" It was the most awkward. I felt obviously that I had accidentally crushed their pride (In Chinese saying: 好心干坏事 - A good heart acting harmfully). For an instant in the rain, I did not know what to do - as it was so south away from my own imagination that they would say millions of thank-you. The lady elder finally softened her voice: "Look, young man. There are several others down this street. You should give it to them." "OK, OK. So sorry. Thank you." I replied passively. Then I reached into my pocket and handed her an envelope - "Please do accept this, two hundred dollars inside." The lady elder tore open the envelope and pulled out some twenty-dollar bills. "OK, thank you..." 

Miraculously, by the Christmas time that year the couple was no longer there. With so many boxes of belongings, I assumed they had been able to return to their original home or a new one. It was a great relief and comfort to me.

Our attitudes and actions towards the homeless are certainly very diverse, driven by different personal philosophies. To me as a faithful modern disciple of Confucius, "Treat others the way you yourself want to be treated." In this life or next, in case one day I were on the street, I would also wish people could show their warm hearts - without demanding me to perform (as I might have no talents at all), without questioning my incapability of living a decent life (as even I myself might hate to review the pitfalls and failures), and without assuming that the government is capable of taking good care of me in the chilliest night of the most lonely street ...

[Disclaimer: All photos are from Google Search. Left: the "Homeless Jesus" statue outside a church; Right: from Google Search]

2023.A.Jan30:  Ancient Poems - Me, the Moon, and the Shadow

During my K-12 (in China), I was not fond of reading novels or any general thick books (other than school textbooks). I held this strange verdict that it be squandering one’s own lifetime to read about other people’s life, fiction or non-fiction. (It is very different now, of course.)

But poetry was the exception, esp. ancient Chinese poems. My young brain was good at picturesque construction of abstract concepts, including poems. Many scenes woven into ancient poems, e.g., those from the Tang (唐，AD 618-907) or Song (宋，AD 960-1279) Dynasties – the golden eras of poetry in China, are as vivid to me as Youtube or TikTok videos taken by modern birdeye's-view drones. So are the embedded subtle emotions that are deeply intertwined with the thousands of years of culture and history. 

Recently this random discrete thought has kept on firing – to translate one that I love. I have chosen Li Bai’s (李白(Last Name: Li)（701-762）) “Drinking with the Moon” (月下独酌). Much gets lost in translation. But the feeling of solitude is pristine and universal. More than a millennium later, Perry Como in his “And I Love You So” has echoed Li Bai through these lyrics: “And, yes, I know how lonely life can be. The shadows follow me, and the night won’t set me free…” (Though I myself first heard and fell in love with the song from Don Mclean. Also Elvis' version.) 

[Disclaimer: All photos are from Google Search.]

2022.A.Jan02: Give Cryptocurrency A Chance, Perhaps


These years about a century ago, relativity theories were breaking the ground of classical physics and the human society. For the first time, space and time, energy and matter, and gravity – these household concepts since the beginning of human civilization, experienced the most profound laundering and cleansing through Einstein’s washing machine of thought experiments and theoretical construction. Newton missed it, and Poincaré touched upon it, but only Einstein finally got it right.

At the time, different pathological theories or concepts were piling up to Einstein’s advantage, e.g., the totally artificial medium called “ether” or “aether” that was supposed to fill the empty universe and propagate electromagnetic waves.  Among all, one particular notion - again a household concept that seemingly any elementary school student understood so well, offered the deepest initial insight to Einstein, which is the notion of synchronized events at two different space locations. For millennia, human minds have been fooled by the illusory simplicity of space and time (including the notion of the existence of an absolute space). Einstein started to question all of them, like an innocent child.

A century later, we are now being pumped into this Internet Age under Universal Connectivity, and even on the verge of the Metaverse, or “The Matrix”. The “gravity” holding together the sophisticated modern human society, whether physical, digital or meta, is the notion of currency, or “money,” without which universal exchanges in services or goods wound become paralyzed. If different societal entities are represented as nodes in a graph, the flows connecting these nodes are more or less all related to currencies or money’s: (a) how the US government sent out Covid Relief money to individual households, (b) how Harvard University paid their staffs and professors, (c) how students paid their tuitions or applied for student loans, (d) how a newly wedded couple were approved for a car loan, (e) how a young cashier got her first hourly paycheck from a neighborhood grocery store, …

Yes, currencies or fiat money’s, define the very “space,” “time,” or “gravity” of the modern society. For millennia, from actual commodities to seashells, and from gold to paper tenders ($USD for example), we have only observed different implementations of currencies in different societies and different historical environments. But have we, as a finally integrated human race, ever fundamentally figured out the true meaning and true fair implementation of a universal currency on this planet? The answer does not seem to be optimistic.  What we do know or observe, just as a century ago in physics, numerous pathological behaviors of the current notion or implementation of currencies, e.g., printing, printing, printing, and the cancerous global inflation that is at this very moment devouring all the hardworking middle classes!  Hence, perhaps pause, ponder, and give the new or curiosity a chance.

2021.A.Jan29: A Winter Day in NYC


      It is eight degrees below zero Celsius.

                Freezing air and frozen days, feel timeless.

      Around corner is the Blue Bottle Coffee.

                The tables outside are all empty,

                          - no hot steams I can see.

      They say the drip coffee is tasty.

                I only see a falling leaf, rolling under the seats!


      It is eight degrees below zero Celsius.

                Walking Sammie finds no opposite excuse.

      With no mask, the boy wags his tail so free.

                With a mask, my glasses just turn foggy,

                          - not far ahead I can see!

      They say masks keep us secure and healthy.

                I only see a laughing virus, showing no mercy!


      It is eight degrees below zero Celsius.

                The Riverside Park has self-declared a recess.

      Wind from the Hudson, whistles over the bald trees.

                Noises from soccer games, fade deep into memories,

                          - how long yet to wait I cannot see!

      They say this is the new normal to stay,

                 I only see the old good sun, shining the Milky Way!


2020.B.May: China

The US-China relationship is free falling. I have never been more concerned during my 26 years’ stay in US. Covid-19 certainly activated the trigger, but it is not the main gravity that is pulling hysterically. It is the extreme nationalism of both the Trump Administration and China’s Xi Administration, commonly dressed up as patriotism or national security. Both have been fanning the nationalism flame to their political advantages, which endangers a fragile but vital bridge that was built wisely and courageously by our former leaders in 1972 despite the ongoing cold war then. (Without this bridge, China could have become a gigantic version of today's North Korea.)  

More concerning is that China seems to be retrogressing to the Cultural Revolution era of the 1960's and 1970's. By striping off the 2-term capping restriction on presidency from the Constitution in 2018, the central government is virtually forging a new Emperor, whose wisdom is claimed superior to all the rest, and whose governing policies do not allow any grassroots party members to analyze or criticize sharply (under The “妄“ Rule). Furthermore, the policies and approaches to regions with historical intricacies (e.g., Hong Kong) have largely proven failed.

The practice of the current Administration not only disappointingly lags behind the progressive trend of modern civilization, but also goes against two monumental Chinese figures and their embraced principles – Dr. Sun Yat-Sen (孙中山), the Father of Modern China whose revolution overthrew the last feudalism dynasty of China in 1911, and Confucius (孔夫子). 

Therefore, I hope the Chinese Government can at least return to the track of several progressive core principles at the state level, such as “Reforming and Opening to the Outside World” (“改革开放”) ，“Releasing Power to the People and the Business Enterprises” (“简政放权，政企分开，党政分开”等), and “Practice and Its Outcomes are the Only Touchstone for Evaluating a Policy (Instead of Merely Someone's Words)” (“实践是检验真理的唯一标准”)， that were established around 1980 right after the disastrous Cultural Revolution was put to an end. My overall complex feelings can be roughly expressed by these two poemlets composed in ancient Chinese style:

2020.A.April: Home

Outside the window, snowflakes are falling like damp feathers. By noon they shall all be gone in the sun. What will keep snowballing is Covid-19, and its haunting fear. About a month ago when the NYC number was fast approaching 500, I packed up my Honda SUV till 3am and virtually fled to an upstate NY town with my family. Rumors and fears were sweeping across the entire Manhattan island then. Now by late April, the number is ruthlessly breaching 150K, though it seems to stabilize in recent days. It reminded me what Steve Smale once shared – driving the family to the border of Mexico during the Cuban Missile Crisis in 1962. All these years I have come to believe that our generation will be spared. But Covid-19 upends all traditional beliefs. Even crude oil futures are trading with negative prices.

It is a small cottage near the upper Delaware River that overlooks a moderate hill. Our host is a kind and caring artist, whom we found through AirBnB. Individual houses scatter along major roads winding through the hills or valleys, with almost the perfect social distance – about one every 100 yards or so. The locals always greet us friendly as we walk our Sammie or hike along the rustic roadsides. A grocery store about 10 minutes away really secures the normal life quality. They even have toilet papers, the extinguished species in NYC now.

I even managed to squeeze into my overloaded SUV the HP laser printer, the Apple TV box, rice cooker, etc. With WiFi, Netflix and the Zoom, the normalcy of life seems indistinguishable from NYC. It is a dream coming true for me, once a boy growing up in a farmer’s house and more used to big and open spaces, as well as the bright stars overlooking the treetops, birds chirping in the early mornings, and streams and springs that sing Nature’s songs. Through Zoom, my wife teaches normally, as well as collaborates with doctors to help analyze the incoming waves of new Covid-19 data. She is also volunteering in response to the call of the medical school. I thought it is the same normal new Home to her. But after three weeks I can see she is missing Home - hard, that rented apartment in NYC that we call Home. I guess Home is not only about where one watches TV, cooks or dines, or gets WiFi and online. These activities can be easily transferred, such as to this pretty cottage. It is more about a package, that encapsulates both physical activities and mental comfort. The little but lethal virus is destroying this comfort of millions of Americans and people around the globe. It is the World War III, so to speak. Many of us are so moved by Lady Gaga’s “One World – Stay at Home” online concert. United we can win this war, and most importantly, restore the comfort and normalcy of our Homes and Hometowns…

2018.A.Jan: A Squirrel 

Sitting alone on a ski lift in a chilly and windy evening, watching the sunset in the distance and a squirrel crawling on the snowy ground between ski tracks, I was instantly visited by a discrete thought -

Top of the mountain, freezing windy.

Wonder who out there, missing me.

My young kid, playing in the city,

Or my elder mom, other side of the sea?



Quiet sunset, embraced by the mountain giant.

Golden rays, from the Eye of the divine kind.

Wonder if I've been brought here,

with the most important mission to pair!



Or just the squirrel down in the woods.

Combing through the snow, for food.

Entirely lost track of her hidden nut.

Hide, forget, collect; collect, hide, forget.

2017.D: Democracy and Confucius

Extreme social conservatism hardens an evolving cocoon to a cold stone and ends the life cycle of a potentially beautiful butterfly. Similarly, extreme social liberalism dismantles the critical columns supporting the grand mansion of our intricately complex societies. A rational modern society, if such a concept does make sense, must achieve the delicate balance between social conservatism and liberalism. The human civilization as a whole has come to the general conclusion that democracy provides such a fundamental balancing force.

Let L=0, 0.1, 0.2, ..., 0.9, 1.0 quantify the levels of this "X-ism", say, with L=0 reflecting extreme liberalism, and L=1.0 extreme conservatism. Let PL denote the portion of people whose "X-ism" is at level L. Thus for example, for the United States, as many as 300 MM * P0.5 people are roughly in the middle ground - not too far right nor too far left. Most likely this distribution in a normal democratic society is bell-shaped (like the one illustrated on the left panel). The entropy of such an "X-ism" society is in general positive: E = - ΣL PL Log(PL) > 0, implying an inherent degree of "X-ism" noisy dispersion in a democratic society.

About 2,500 years ago in China, Confucius had the ambitious vision of crushing this entropy to zero, i.e., constructing a homogeneous society with P0.5 =100%. Thus the old man traveled all over ancient China, trying to persuade every warlord that this goal could actually be achieved by (1) a persistent Confucius Teaching (儒家学说), (2) advocating the general principle of "Staying in the Middle" or "Avoiding being Radical" (中庸), and (3) constructing a strict social order (i.e., a son must treat his father like a father,  or a Minister must be loyal to his Emperor (父父子子，君君臣臣) ). From China to Japan, much of this spirit has eventually evolved into a single Mandarin character - 和，or the Great Harmony. Modern democracy and feminism certainly hate such a doctrine (esp. when in later dynasties some scholars generalized the principle to rules like "a Wife must obey her Husband"). Nevertheless, in this era of almost blind or over-optimistic "internationalization" (mainly fueled by market-driven capitalism), it is possibly beneficial to review where the West and the East have come from.  

2017.C: Cichlids 

Earlier this year, I adopted several baby sibling cichlids from a good friend, and raised them in a same aquarium. Several months later, their sizes differ so much - the biggest is almost three times as big as the smallest. I have been feeling so sorry (and unfair) for the smaller ones, as the bigger ones eat fast and swallow big pellets smoothly at feeding times, and then grow even bigger! 

Play with a little bit of mathematics. Let S and F denote the body size and food consumption for a given cichlid. Set time interval dt to be one day, say. Then we have two basic equations (with two parameters a and b):

The combination of the two equations results in: dS =( ab)*S*dt,  an exponential growth law! The solution is well known:  S(t) = S(0)*exp((ab)*t). Given any two cichlids, let ΔS denote their size difference. Then we have: ΔS(t) = ΔS(0) * exp((ab)*t).

A small size difference can amplify at an exponential rate! No wonder what I see in my aquarium! Or in the news - how Warren Buffet is getting even richer! Or in our society - how certain social inequalities or gaps are further widening!

2017.B.April: Steve Smale

Steve came to the CUNY mathematics department to deliver three talks - one general and two on the mathematics of the genomes. In the general one, Steve shared his personal inspirational figures - Newton, von Neumann, Turing, and Watson, as well as the reflection on his own mathematics, i.e., the power of mathematical "abstraction", and the pursuit of "foundations" of dynamics, complexities, computing, economics, languages, emergence (flocking), learning theory, genomes, and beyond. 

It has been a decade since last time I visited Steve for a semester in Chicago. The time arrow has never slowed down Steve's pursuit of the mathematical foundations of our innate curiosities. 

The arrow should not be allowed to slow us down either.          

                                                  (Left: Fall, 2006@Chicago;  Right: April, 2017@NYC) 

2017.A: Offer Letter

Cloudy outside of my office on the 17th floor. The Statue of Liberty stands tall and quiet at the spacious opening of the Hudson River (and the Wall-Street zone). Beyond and afar, are the vast Atlantic Ocean, and a constant whisper of freedom. 

In generations, both in the East and the West, we have all been looking for "liberty" and "freedom," because they are so precious. Su Shi (苏轼), one of the greatest Chinese writers, poets, and statesmen (1037-1101, AD) once wrote in a poem:

长恨此身非我有                  （This deep sorrow that I have never owned myself !）

何时忘却营营                      （When can I be set free from making a living?!）

夜阑风静縠纹平                    ( In this quiet night with no trace of wind or waves,)

小舟从此逝，江海寄馀生     ( How I wish a boat can take me to the ocean, and afar!)

With my signature on the new offer letter, instead, the boat will soon take me to the next company - the next harbor.