Book: Intelligence by Stuart Richie

My Old Impression of Intelligence

I used to ridicule the IQ test. To me, it is nothing more than another test, and I hate tests. The IQ test also does not help its cause by sharing common segments with other standardized tests I have taken like SAT (for college) and GRE (for graduate school). Personally I have not seen much correlation between high scores in standardized test and intelligence. I have met people with impressive test-taking skill but not-so-impressive ability to do complex work. In short, I never bothered to think about the IQ test.

I even did not care much about intelligence. I like to believe most of us could achieve anything by working hard and working smart. Of course, being smart does not hurt, but intelligence should not be so important that it can make or break a career. However, my belief is dismissed by Stuart Richie in his book Intelligence: All That Matters. Stuart uses many research results spanning from the 19th to 21st century to make his point: people have different intelligence, and intelligence matters.

Intelligence Does Matter (sometimes, a lot)

Before trying to understand about intelligence, we should have a clear and succinct definition of intelligence. Here is the definition of intelligence given by Gottfredson, an expert in intelligence research:

Intelligence is a very general mental capability that, among other things, involves the ability to reason, plan, solve problems, think abstractly, comprehend complex ideas, learn quickly, and learn from experience. It is not merely book-learning, a narrow academic skill, or test-taking smarts. Rather, it reflects a broader and deeper capability for comprehending our surroundings, ‘catching on’, ‘making sense’ of things, or ‘figuring out’ what to do.

Great, the definition alone answers several of my questions about intelligence. From my experience with people, the not-so-smart ones almost always have serious troubles with abstract and complex ideas, and they seemed to be hopeless with reasoning and learning from experience. The definition also explains about the people who could easily outsmart standardized tests but could do not much else. I have also wondered why some people repeatedly interpret information, even straightforward ideas and facts, in the wrong way. It is frustrating because they could not learn much from books even if they spend considerable time and effort on reading. After all, “Making sense” of things is an important part of intelligence.

Can We Improve Our Intelligence?

Okay, intelligence varies from person to person but is there any way to improve our intelligence? Stuart answers the question using a chapter called “The easy way to raise your IQ”, only that he does not mention any way at all. (He admits that the chapter title is just a bait). At the current state, researchers around the world still do not know which is the easiest and most convenient method to raise our IQ. Should we feel depressed?

Sadly, for some people, the answer is yes. It is because the best way to raise the IQ, in my opinion, is to read good books, take good courses, learn from great people, and learn from experience. However, for a person who is not intelligent enough, how on earth can he differentiate a good book from a bad one? From my somewhat cynical point of view, the same person probably also listens and follows other stupid people. He will not learn anything from his experience and keep repeating his mistakes. That is the dilemma of intelligence. If he could do better, then he would not have needed to raise his IQ so badly.

I think if I am intelligent enough, but not successful as I might like, then my problem is likely not about my intelligence. Maybe the problem is about my perception, my vision, my friends, my character, my habits, et cetera. Heck, even if I am not smart, I will try to solve other problems anyway.

Another point Stuart makes in his book is that even among highly intelligent people, intelligence still matters. What if I am not as intelligent as my competitors? I will try to do two things: think and do.  Regardless of the problem, the more I think about it, the better chance I will solve it. Maybe my competitors are smarter and they can solve the problem faster, but they still have to spend time. They still could not do it in an instant, and there is a chance that they will not even solve the problem at all. No matter what others do, I will continue to reap the rewards by working hard. It might be more difficult for me, but it should not matter. As long as I have fun doing what I do, I will be happy. At least in my field of science and engineering, experience is as important as intelligence.

The bottom line: There will be people who are more intelligent than you, it is okay, and it is natural. Just do your best and enjoy your work. Improvement, however small you think of it, will count in the end.

Linear Algebra (LAFF) by UT Austin – Course Review

Course profile:

  • Link:                LAFF at edX
  • Professor:       Robert A. van de Geijn
  • Institution:     The University of Texas at Austin
  • Date:                Summer 2015
  • Platform:        edX

Linear Algebra was the first real mathematics course I decided to take for my current project. While the importance of linear algebra cannot be overstated, it is not exactly an accessible subject. I already took a Linear Algebra course in college, but I did not learn much (as usual, sadly). From my memory it was just another frustrating class that I stood in only to fulfill my degree requirements.

How It Went Wrong at College

My Linear Algebra professor at college focused the entire course on the techniques of linear algebra. These techniques included simple matrix-matrix multiplication, Gauss-Jordan elimination, projection, orthogonality, fundamental spaces, linear least-square, and eigen-blahblah. If you have some experience with the subject (and you really remember it), you should find those topics familiar. So in a way, my professor did teach everything he was supposed to teach. Except he did not.

The techniques, while indeed important to master, do not tell the whole story of Linear Algebra. It is not about applications either. I appreciated that my professor made some effort to give a recitation each week (most courses in my college did not even have recitation). He and the teaching assistants gave several presentations about the cool applications of linear algebra, such as image compression in JPEG file. Still this information did not help the students, including me, at all. The one thing that my professor forgot to teach, or deliberately avoided, is the same thing that should have made students fall in love with linear algebra: the insight.

Why LAFF Works for Me (and For You)

Techniques make up only a small part of LAFF (Linear Algebra: Foundations to Frontiers). This should not be surprising. With the ubiquity of matrix libraries as good as MATLAB, we can use a computer to apply the techniques. What we should do instead is teaching the computer to solve problems for us. In addition to computation techniques, this goal requires a deep understanding of linear algebra.

Prof. Robert van der Geijn, who teaches LAFF, insists that insight can only be gained by doing mathematics. In this class, that means understanding proofs and proving theorems. In fact, Robert make all the answer keys available at the beginning of the course. A student who just wants a certificate (like the old me in college) could just enter all the answers and get a good-looking piece of paper without even knowing what Linear Algebra is. The reason for this approach is it makes absolutely no sense to use the techniques without understanding the proofs. Proofs are not created for a specific kind of creatures called mathematician. They are important for anyone who wants to learn mathematics the right way.

Admittedly I did not dare to read even one proof in the linear algebra class in college. I even did not remember the professor mentioned any proof, or whether he included proofs in the homework and exams. (He did not!) Sadly, it was and remains the standard teaching method of mathematics nowadays. I will definitely write more about the topic of mathematics teaching in near future.

Back to the course, it was the first time I tried to make proofs by myself, without any external motives like homework or exam. It may sound extremely nerdy, but math has changed me, inside out. I’m a changed man. Suddenly I find myself interested in reading and understanding proofs. My attitude towards Linear Algebra and Math in general turns a complete 360 degrees. Now I am eager to learn more. It’s crazy, but finally it seems I have found my favorite subject.

Studying math should be like this. It should be about thinking, exploring, proving, arguing and imagining. It should be a creative process, not a mechanical one like what is taught in school.

I want to thank Prof. Robert van der Geijn, his wife, and his assistants for an excellent course. Really they taught me to love math.

(Image Source: http://ulaff.net)

Book Review: Malcolm Gladwell – Outliers

I don’t think I have ever been working this hard in my life until the last few weeks. It is the first time I feel like working/studying from dawn to dusk (of course, that’s a metaphor since I can never get up at dawn). Today is Saturday, a perfect day to take a break and do something else other than write a mathematical proof. In this article, I will review a book by Malcolm Gladwell, Outliers: The Story of Success.

Below are my thoughts on several arguments made my Malcolm in the book.

The Matthew Effect or The Rich Gets Richer

When we look at a successful professional, be it a concert pianist or a renowned entrepreneur, we think he or she is special. We seem to understand how difficult it is to succeed in life. Everybody knows that we need both talent and a lot of hard work to achieve a great career. Nothing is wrong with that belief. It just does not tell the whole story.

In Outliers, Malcolm discuss a phenomenon of young ice hockey players in Canada. Somehow, the most promising players were mainly born in the first half of the year. It is absurd to believe the date of birth can affect your hockey skill. Indeed it does. Being born early in the year gives a kid a few more months of practice than another born late in the same year. A few more months may not sound a big deal for adult players, but for a five-year-old kid, that short period of time can make the difference. The better players are then selected into better teams with better coaches. These kids also have the opportunity to play with good teammates in competitive leagues. They accumulate experience fast and constantly improve as a result. Ten years later, we can guess who is better, the kid born early versus the kid born late.

Success requires good fortune, it seems. The question is: Can we create our own good fortune?

Work Hard and Watch Out for Opportunities

We cannot predict the future. However, we can prepare for it and wait for the right opportunity. How? The tentative answer is to choose a meaningful work and do it really well. But what is the definition of meaningful work? Let me try to explain it in a few sentences.

Meaningful work is something that not only compensates us well (not just money), but also contributes to society. Take Cristiano Ronaldo or David Beckham as examples, they do only one thing well – playing soccer – and that is enough to be a meaningful work. Their soccer skills entertain fans around the globe, and people readily pay big bucks to watch them playing. Meanwhile, no one ever will pay to watch me play, indicating professional soccer cannot be meaningful to me although I might be dying to play soccer day in, day out. In short, a meaningful work is a work that you enjoy doing, and it should serve people in some meaningful way, and people will reward you, usually in the form of salary and status. If you want to read more about meaningful work, Cal Newport surely has a much better explanation than I do.

In Outliers, Malcolm Gladwell lists several characters who have meaningful work: Bill Gates, The Beatles, Joe Flom among them. They shared a similar story. They worked really hard at first even though they never knew how successful they would be. They simply focused on honing their skills in their respective careers and look for opportunities to serve the society. Eventually they took the opportunities to shine and were recognized as successful.

Note that success is relative anyway. Success cannot be quantified. For me, success means that I have enough money to feed my family, and I enjoy my job. I like a simple and happy life.

Cultural Heritage and Its Influence

The last topic I want to mention is cultural heritage. Malcolm spends a significant part of the book to tell stories about different cultures. They vary from an Italian town in Pennsylvania where its residents are extremely healthy, another town in the American South where people are ridiculously violent, Robert Oppenheimer versus Chris Langan, to the alarming number of plane crashes of Korean Air. All of the stories convey the fact that many people are not aware of the power of their cultural heritage.

Cultural heritage defines who we are, influences what we do and how we think. I know this too well after coming to the US from Vietnam. The two cultures cannot be more different. I suffer from this difference even in simple, everyday conversations with Americans. I still don’t know how to handle a conversation in a large group. I used to blame my own personality for my failure to communicate. But truth be told, I just do not fully understand their culture as well as my own.

Adaptation is a crucial part of any success story. As an instance, the Jewish immigrants of New York in the early 20th century, as told by Malcolm, worked hard in negotiation skills. Despite the language barrier, many Jewish immigrants could expand their markets by negotiating with American capitalists. Right now, negotiation is only something I wish I could do.

This lesson, and not the popular “10,000 hours rule”, is what I appreciate most in Outliers. I will definitely try to work on my public speaking and negotiation skills. The time has come to grow up.

September Plan

This post is the first report of my current project. It will not exactly be a fun post but I want to write something anyway, simply because it’s better to jot down my thoughts once in a while. I plan to write more interesting articles in near future. I will write book reviews to summarize things I learned while reading. Maybe I will also write about the cool things about the courses I’m taking.

The beginning
Since initiated the project last month, I have finished two courses on Coursera, MATLAB Programming by Vanderbilt University and Algorithms, Part I by Princeton University and one mini-course on Codecademy, Introduction to Python.

Algorithms, Part I was a challenging yet enjoyable course. It taught me about the beauty as well as the importance of algorithms that I never realized before. I did take one data structures and algorithms course during college but I insisted on solving every assignment by brute force. I guess because my professor did not have a sophisticated grader like the one used by Dr. Sedgewick from Princeton, I managed to escape with perfect scores despite never applying the algorithms I was supposed to learn. At least it’s a different story now. Thanks to the machine grader on Coursera, I was forced to write clean, maintainable, efficient and sometimes even elegant Java code.

Still one thing Algorithms, Part 1 did not do is teaching the theory behind the algorithms since it only focuses on implementation. I have never been interested in theory, and math in particular. I used to avoid rigorous proofs like a plague. This is a good time to change. Fortunately, Dr. Sedgewick will offer the Analysis of Algorithms course next week. Let the math journey begin.

My goal is to be (surprise, surprise,) a math whiz

Speaking of math, I would like to discuss why I decide to change my attitude towards math. In the last few weeks, I have been thinking about all the gaps in my background, and why I have struggled immensely although I have spent a lot of time studying. It turns out my lack of mathematical maturity is the culprit.

I have two big issues relating to math. First, I do not have good strategies of attacking a problem methodically. In other words, I have always found it difficult to think clearly and make progress while working on a problem. I think this ability comes from working on the proofs in all the math courses: discrete math, calculus, linear algebra to name a few. It’s a shame that I never, ever cared about proofs.

Secondly, I simply do not have the math background to understand intermediate to advanced engineering materials. Stuffs like linear algebra, Fourier series, Laplace transform are the basic tools for any professional scientist or engineer. Because I never acknowledged the applications of these math subjects, I avoided learning them. My professors in college also did not help the cause by giving easy As. Now I have to re-learn all over again. Is it painful? Hell yes. But it must be a hell lot of fun too.

September Plan
Here is my plan for September. I will discuss some of them in more details in later posts.

Coursework:
Linear Algebra: Foundations to Frontiers, UT Austin.
Effective Thinking Through Mathematics, UT Austin
Algorithimic Thinking (Part 1) and Principles of Computing (Part 1), Rice University.
Game Theory, Stanford.
Analysis of Algorithms, Princeton.
Calculus I, Ohio State University

Reading:
Brendon Burchard – The Motivation Manifesto.
Geoff Colvin – Humans are Underrrated.

Codename: Before Sunrise

It has been just over three months since the last time I wrote in my blog. Many things have happened during a great summer here in upstate New York. My girlfriend will start her PhD in two weeks. We are already settled in a nice, comfortable apartment in a small, quiet town.

Unfortunately, my career as a graduate student is totally in chaos. I really do not know whether I could or should continue with fundamental research.  Research is a too big ask for my current ability. Fundamental research requires a solid foundations in math, physics, statistics to name a few. Certainly I have not mastered the fundamentals well enough. I know I must rethink my career.

In the next 9 months, I will try to regroup by doing three things. First, I will study mathematics and physics from scratch, starting with Calculus, Classical Mechanics, Linear Algbera up to Electromagnetics, Integrated Circuits, and Stochastic Processes. Second, I will study Computer Science from ground up. I will learn C++, algorithms, data structures, web developement, etc. And lastly, I will try to read as many books as possible. After this period, I will try doing research once more and regardless of the result, move on with my life.

As usual, I will give this huge project a name. I will call it Before Sunrise, as “it is always darkest just before the dawn.”

Let me believe that it will be beautiful when the sun finally rises next year.

(photo source)