Reporter: “what do you think you will miss the most? “ Sir Alex Ferguson: “Those last minute goals.” Video.

” ‘Ferguson is furious’ is the most typed phrase in premier league history. ” — Guardian.

The dilemma for someone who strives to become a global citizen while at the same time taking pride in his/her own unique cultural heritage is that one often faces choices of competing values. It is true that there are certain universal values we all share as humans, but there is no denying that values differ across the globe. Respecting different values, it seems, requires the knowledge of the root of the differences in the first place. But a lot of values are planted deep at a subconscious level that we don’t usually reflect on how they inform our decision-making: for example, patriotism or family. Being able to see the world through the lens of different value systems provides the opportunity to make those subconscious values explicit.

After spending seven years outside China and by consciously and unconsciously distancing myself from any familiar crowd of people, I have become more and more acquainted with the western ways of thinking. Every now and then, I found one or a few differences between the culture that brought me up and the culture that I live in now, but these are sporadic insights that are hardly consistent by themselves. It strikes me to the heart, therefore, to read Kissinger’s book, whose first chapter articulated the differences with enormous depth, with rich examples, and with striking clarity.

I just finished reading chapter 6, but am already overwhelmed by how much I don’t know about China. I realized that living a culture is different from understanding it. Below I sample a few paragraphs from the book on the difference between the Chinese culture and the western culture.

American exceptionalism vs Chinese exceptionalism: “It has been a complex journey, for both societies believe they represent unique values. American exceptionalism is missionary. It holds that the United States has an obligation to spread its values to every part of the world. China’s exceptionalism is cultural. China does not proselytize; it does not claim that its contemporary institutions are relevant outside China. But it is the heir of the Middle Kingdom tradition, which formally graded all other states as various levels of tributaries based on their approximation to Chinese cultural and political forms; in other words, a kind of cultural universality.”

Religious west vs secular China: “Not the least exceptional aspect of Chinese culture is that these values were essentially secular in nature. At the time when Buddhism appeared in Indian culture stressing contemplation and inner peace, and monotheism was proclaimed by the Jewish—and, later, Christian and Islamic—prophets with an evocation of a life after death, China produced no religious themes in the Western sense at all. The Chinese never generated a myth of cosmic creation. Their universe was created by the Chinese themselves, whose values, even when declared of universal applicability, were conceived of as Chinese in origin.”

Machiavelli vs Confucius:”…unlike Machiavelli, Confucius was concerned more with the cultivation of social harmony than with the machinations of power. His themes were the principles of compassionate rule, the performance of correct rituals, and the inculcation of filial piety.”

Confucius: “Confucius’s answer to the chaos of his era was the “Way” of the just and harmonious society, which, he taught, had once been realized before—in a distant Chinese golden age. Mankind’s central spiritual task was to re-create this proper order already on the verge of being lost. Spiritual fulfillment was a task not so much of revelation or liberation but patient recovery of forgotten principles of self-restraint. The goal was rectification, not progress. Learning was the key to advancement in a Confucian society. Thus Confucius taught that ‘[l]ove of kindness, without a love to learn, finds itself obscured by foolishness. Love of knowledge, without a love to learn, finds itself obscured by loose speculation. Love of honesty, without a love to learn, finds itself obscured by harmful candour. Love of straightforwardness, without a love to learn, finds itself obscured by misdirected judgment. Love of daring, without a love to learn, finds itself obscured by insubordination. And love for strength of character, without a love to learn, finds itself obscured by intractability.’ ”

War strategies: “Where Western strategists reflect on the means to assemble superior power at the decisive point, Sun Tzu addresses the means of building a dominant political and psychological position, such that the outcome of a conflict becomes a foregone conclusion. Western strategists test their maxims by victories in battles; Sun Tzu tests by victories where battles have become unnecessary.”"

Perspectives on history (progress vs. rectification): In general, Chinese statesmanship exhibits a tendency to view the entire strategic landscape as part of a single whole: good and evil, near and far, strength and weakness, past and future all interrelated. In contrast to the Western approach of treating history as a process of modernity achieving a series of absolute victories over evil and backwardness, the traditional Chinese view of history emphasized a cyclical process of decay and rectification, in which nature and the world can be understood but not completely mastered. The best that can be accomplished is to grow into harmony with it. Strategy and statecraft become means of “combative coexistence” with opponents. The goal is to maneuver them into weakness while building up one’s own shi, or strategic position.

The previous post dealt with the question of what maths to learn. This post will deal with how to learn efficiently.

In a casual discussion, Steven Gortler mentioned that books on modern mathematics are so abstract that one may not grasp clearly what the initial questions are. And these books tend to focus on proving theorems (after all that’s what mathematicians do). He specifically referred to differential geometry and topology. Some of the most helpful handouts on differential geometry he gave are actually taken from a physics book on general relativity.

Keep in mind that most mathematicians (and hence maths textbooks) are symbolic types, and that the maths books are really geared towards those types of minds, sifting through different textbooks for the one suitable for geometric types is not an easy job. Luckily, Steven has done the worked for me.

In a larger sense, the books or the lectures presented by a particular type of mathematical minds will likely to strike the right cords of only that particular type of students. While in self-directed learning, I have the luxury of sampling differential textbooks and skipping lectures as I wish, those less fortunate (a.k.a, the students who are actually taking class for credits) are likely to experience not only intellectual hurdles but also confidence problems. I had certainly doubted my mathematical skills after physics classes by theoreticians (strangely as it sounds but true). Having Maxwell articulated the difference between symbolic and the other types proves to be helpful in understanding the difference, finding my own preference, and establishing some criteria for selecting maths textbooks.

Besides textbooks, other tools are also available. I am testing a few maths softwares including mathematica, matlab, and my own rhino scripting.

I audit three classes with heavy maths this year: one is L. Mahadevan’s ES220 Fluid Mechanics; another is Jocob Barandes’s PHY232 Advanced Classical Electromagnetism; the last one is Steven Gortler’s CS277 Geometric Modelling in Computer Graphics. I found myself cramming for necessary maths all the time. It was an interesting experience, but not the most effective one in terms of learning.

The questions I ask myself are what to learn and how to learn. The first deals with the direction, while the second deals with the speed. The post deals with direction. The next one deals with speed.

While searching for answers, I came across a few very illuminating essays by James Clerk Maxwell. The first one is an Address to the Mathematical and Physical Sections of the British Association, delivered in Liverpool, September 15, 1870. In this address, he listed three types of minds in terms of the ways they deal with maths: one symbolic, one geometric, and one vividly illustrative.

“There are, as I have said, some minds which can go on contemplating with satisfaction pure quantities presented to the eye by symbols, and to the mind in a form which none but mathematicians can conceive.

There are others who feel more enjoyment in following geometrical forms, which they draw on paper, or build up in the empty space before them.

Others, again, are not content unless they can project their whole physical energies into the scene which they conjure up. They learn at what a rate the planets rush through space, and they experience a delightful feeling of exhilaration. They calculate the forces with which the heavenly bodies pull at one another, and they feel their own muscles straining with the effort.

To such men momentum, energy, mass are not mere abstract expressions of the results of scientific inquiry. They are words of power, which stir their souls like the memories of childhood.

For the sake of persons of these different types, scientific truth should be presented in different forms, and should be regarded as equally scientific whether it appears in the robust form and the vivid colouring of a physical illustration, or in the tenuity and paleness of a symbolical expression.”

The division between the first two types and the third is not something unheard of. But what’s most illuminating to me is to divide the symbolic type and geometric type. While I can do a lot of symbolic maths, I certainly do not like to stare at any equation for any long period of time, which I believe a lot of mathematician and theoretical physicists do. My most gratifying experience is visualization in 3D. However, I do seem to share some of the prejudices with the symbolic types, such as regarding multiple examples in textbooks/lectures unnecessary, or as Maxwell put it, “The mental image of the concrete reality seems rather to disturb than to assist their contemplations“.

My need for 3D visualization and modelling put me firmly in the camp of the geometric types. Answering the question of what to learn becomes clear. The focus is geometry, from platonic solids to differential geometry. Where I would most likely to spend a lot of energy is differential geometry, not only because it underlies much of the computer modelling, but also because it provides good motivation to revisit topics such as calculus and linear algebra.

PS. Efforts to put three different types into categories of scientists and non-scientists seem troublesome. Maxwell did not have any prejudice against the third type, (which I might have made you into believing so), “For the sake of persons of these different types, scientific truth should be presented in different forms, and should be regarded as equally scientific whether it appears in the robust form and the vivid colouring of a physical illustration, or in the tenuity and paleness of a symbolical expression.“

Ignorance, the author defines, is what “describes a particular condition of knowledge: the absence of fact, understanding, insight, or clarity about something”. It is not “willful stupidity” or “individual lack of information”. In this sense, the author says that ignorance leads us to ask better questions, which is the first step to knowledge.

The book then expand this basic idea of ignorance into six chapters that elaborate on why questions are more interesting and more important in science than facts, why facts are fundamentally unreliable (based on our cognitive limits), why predictions are useless, and how to assess the quality of questions. The seven chapter give several case studies of how scientists work. It is in this chapter that I learned that Firestein, the author, had been a stage manager and director in theaters for more than 15 years before starting his bachelor in biology at the age of 30. Seemingly against all odds, he made it into grad school and the post doc before becoming a professor of neuroscience at Columbia University at NYC. The book close off with an eighth chapter that touches broader issues on public awareness of science and science education.

According to the author, the book is for non-scientists. but I think it is equally relevant for scientists, maybe even more relevant. It provides a perspective that we normally do not get from day-to-day lab work and serves as a reminder why and how we do science. There are a number of reasons why I like this book so much, the least of which is Firestein’s passion for pithy quotes. I share that passion. Here is a partial list:

• “I would have been briefer if I’d had more time.” – Pascal
• “All models are wrong, but some are useful.” - George Box
• “Thoroughly conscious ignorance is the prelude to every real advance in science.” Maxwell
• “Of what use is a newborn baby?” - Faraday
• Enrico Fermi told his students that an experiment that successfully proves a hypothesis is a measurement; one that doesn’t is a discovery.
• Some of Firestein’s own: ‘It is not so easy to create the condition where you can have perspective and involvement simultaneously”; “Being a scientist requires having faith in uncertainty, finding pleasure in mystery, and learning to cultivate doubt. There is no surer way to screw up an experiment than to be certain of its outcome.”

Aside from a passion for pithy quotes, a more serious reason is that it came at a time when I feel the need to think strategically what  I want to do in my scientific career. It provides a distinct perspective from which I can start to answer some of my more urgent and pertinent questions such as how to discipline curiosity, how to deal with maths, how to judge the maturity of a field, where to look for research questions, and how to prepare myself for taking on these questions.

I also resonate with the author’s opinions on the some of the failings on scientific education. A specific symptom, as the author describes, is below:

“Perhaps the most important application of ignorance is in the sphere of education, particularly of scientists. Indeed I first saw the essential value of ignorance through teaching a course that failed to acknowledge it. The glazed-over eyes of students dutifully taking notes and highlighting line after line in a text of nearly 1,500 pages, the desperation to memorize facts for a test, the hand raised in the middle of a lecture to ask only, “Will that be on the exam?” These are all the symptoms of a failing educational strategy.”

Lastly, a piece of advice from Firestein. For my non-science friends, here is what you need to do if you want to get your science friends talk: “So if you meet a scientist, don’t ask her what she knows, ask her what she wants to know. It’s a much better conversation—for both of you.”

Alas, skewed proportions. Wiley people…

Read the paper here.

They never get all the smooth color transition right in the final published cover.

Read the paper here.

人之初，性本善，性相近，习相远。
Men at their birth are naturally good. Their natures are much the same; their habits become widely different. Translation shamelessly copied from here.

子曰：学而时习之，不亦说乎？有朋自远方来，不亦乐乎？人不知而不愠，不亦君子乎？

Confucius said, “To learn and to practice what is learned time and again is pleasure, is it not? To have friends come from afar is happiness, is it not? To be unperturbed when not appreciated by others is gentlemanly, is it not? Translation from here.

子曰，学而不思则罔，思而不学则殆。

Confucius said, “To learn without thinking is labour in vain. To think without learning is desolation.” Translation from here.

知之为知之，不知为不知，是知也。

When you know a thing, to hold that you know it; and when you do not know a thing, to allow that you do not know it – this is knowledge. Translation from here.

The flight to DC was late. Even worse, I got to the airport an hour earlier than usual, so I ended up reading the first two chapters of the Hobbit in the airport lounge, thinking I would definitely be late for dinner.

I started my first day in DC randomly walking around. There isn’t much to be seen in White House, with its layered securities and fences. I was even fortunate enough to get a decent photo of its front view. Memorials, on the other hand, are accessible, and they are all massive. With their classical orders and spacious gardens, architectures of this sort would be dedicated to gods or heavens in other cultures, but here they commemorate humans. Lincoln Memorial is the most impressive of all.

Museums are plenty, and most of them are free. They are where I spent most of my time. The National Portrait museum is full of good quotes (in addition to good pictures of course). One particular line has sticks to my mind since: “Art is a birth, and you can’t go to a teacher and find out how to be born… you have to struggle until that image, the one that comes out of your need to create, emerges. — Malcah Zeldis”

Georgetown has much more lively streets with more vibrant colors. I guess because it is during the school break, the most crowded place is a cupcake shop!

It’s winter, and it’s school break. With the congress still in session for the budget talks, the general mood of DC was sober and tense. They all made visiting a cemetery more bearable than usual. A good place for reflection isn’t it?

Day 1: White House, WWII, Lincoln Memorial, FDR Memorial, Jefferson Memorial

Day 2: National Gallery of Art, and Sculptures.

Day 3: Spy Museum, National Portrait Gallery and Sculptures.

Day 4: Capitol and Georgetown

Day 5: Arlington Cemetery