When Principles Collide

One of the things about growing up with a sheltered life is that you rarely ever have to stand up for your principles. This could be due to several reasons: maybe they’re not really your principles, but your parents’; maybe you’re just not placed into situations where conflicts occur; maybe your principles themselves seek to avoid confrontation. I recall so many times when I was younger that I had some well thought-out idea for something but then instead went along with someone else’s idea without question, in the interest of avoiding conflict. I’m not saying that you should always insist what you’re doing is correct, but I think on the spectrum I was too far on the side of passivity.

Throughout college (and perhaps starting senior year of high school), I found myself more often at points where I needed to disagree. It wasn’t really conflict for the sake of conflict, but rather to get to the truth or to make a situation better, by challenging faulty ideas or plans. I think this change is evident on my blog: in the past, most of the topics I wrote about were very non-controversial, but recently, they have been more questioning of commonly held ideas. Granted, my online persona (including on Facebook) and my real life character are still quite different—in real life I don’t go around seeking to criticize peoples’ religious beliefs, an activity that is reserved for the internet. That’s another topic.

Contradictory Principles

For a really simple example, consider the principles “be honest” and “don’t be a jerk.” Everyone follows these principles, and most of the time they support each other. You’d be quite a jerk if you lied to your friends about so many things to the point where nothing you say has any credibility. However, when you find minor fault in something someone did, you could be honest and tell them, but most of the time it’s better to be silent about it. Of course, the best choice depends all on the situation.

contradiction-signs
I respect both ownership rights and aesthetic cleanliness—do I pollute whitespace by citing the image source, especially if the image isn’t all that special?

Perhaps a more pertinent contradiction is that between tolerance of others and… tolerance of others. For example, most of my audience probably tolerates the LGBT community. Yet, there are many people in America who do not. This leads to a tolerance paradox (that I think many of us don’t think about): Is is possible to simultaneously be tolerant of LGBT individuals and tolerant of people who are intolerant of them? Is a hypothetical all-tolerant person also tolerant of intolerance?

This depends somewhat on how you define tolerance, but it points to a deeper issue, that simply using the principle “tolerate others” is insufficient in these fringe cases. There must be some overriding principle that tells you what to be tolerant of and what not to be tolerant of. I think that being intolerant of intolerance is still tolerant.

In chess, one of the most important principles, among the first to be taught to new players, is to never lose their queen unless they can get the opponent’s queen as well. While this is a great principle 99.9% of the time, there are cases where losing your queen (for no pieces or just a pawn in return) is the best move, and there are even cases where it is the only non-losing move. It’s because the principle of “win the game” overrides the principle of “don’t lose your queen.”

Interestingly enough, even meta-principles can contradict one another. For me, “stand up for your principles” is a good principle, and so is “be open-minded about your principles.” Often blindly standing up for principles is a very bad idea (in the typical novel/movie, the antagonist may have good intentions but focuses on one idea or principle to the exclusion of all others, thus causing more overall harm than good; on the other hand, this principle seems required to become a politician).

Throughout my first two years of college, I wanted to go into academia, and I naively shunned finance because I thought people went into it just for money. Of course, once you start thinking about what to do after college and the need for money comes closer, you realize that you need money to live(!) and that despite the negative outside perception, the industry is not all evil people trying to figure out how to suck away all your money. Of course, on the “stand up for your principles” front, this change fails pretty hard, but it follows “being open-minded about your principles,” which I consider to override the first in this case. After all (to add one more layer of contradiction), it is standing up for the principle of being open-minded.

Standing Up in a Crowded Theater, Studying for Tests, and Other Game-Theoretic Dilemmas

Everyone is sitting down in a crowded theater, comfortably seated and with a good view. All is well until one person decides his view is not good enough, so he stands up to get a clearer view. This ruins other peoples’ views, so they stand up as well. A while later, everyone is standing up but has the same view as before, resulting in each being in a position strictly worse than when everyone was sitting.

This particular example is typically avoided since the social norm in a theater is to sit. In fact, in numerous examples of this game, there are either direct (laws) or indirect (social norms) methods of control to prevent such disasters from happening. Here are two for illustration:

  • Crime. If one person stole a little, this person would be in a better position and society would not be harmed by much. However, if everyone did this, society would collapse. The criminalization of theft prevents this problem (for the most part). This concept applies to many types of crimes.
  • Environmentalism. If one person polluted more, there would be virtually no change to the environment. However, if everyone did so, the environment would feel the full effects. (This still isn’t quite resolved, but in most developed countries it is well on its way.)

From a game-theoretic perspective, however, each individual taking the selfish path is making a rational decision. The problem is that the system may not discourage the selfish activity sufficiently.

Someone who doesn’t recycle may (justifiably) argue that they do in fact care about the environment, but that the impact of their not recycling is negligible to the environment. While this is true, if everyone thought like this, then we would all be standing up in the theater. The main point of this post to go over some less commonly cited situations.

Studying for Tests

I would argue that studying for a test falls into the category of standing up in a theater. From both high school and college, I have observed or have heard of people studying hours upon hours for tests and often barely remembering any of the material after a semester. A test should measure how well you understand something, not how well you can memorize and cram facts into your brain for the next day.

People who know me from high school and college know I don’t study much (if at all, depending on the class) for tests. Perhaps some see this as a sign of not caring, but I would argue that I care about the knowledge just as much, if not more, than people who study far greater hours. In the cases where I do study, I go for the “why” rather than the “what,” and I study to load the concepts into long-term memory, rather than the details into short-term memory. If you do need the details at a later time, cram it in then when it is relevant and when you have the big-picture understanding.

Let’s pretend that studying for tests were not allowed. Then what would a test measure? Would it measure how much attention someone paid in lecture? How well they comprehended the main points? What part of the homework they didn’t copy from someone else?

In fact, everyone’s grades would still be similar. In classes where grades are curved, if everyone does “worse” on a test the same way, then the grades will be unaffected (though there may be some shifting around). The tests would just become more genuine.

So it may seem like I have something against studying for tests. But what part specifically of studying for tests do I have an issue with? Well, as mentioned before, I think if everyone studied for tests, it makes the test scores more a measure of who studied the most and who could cram in material the most efficiently, instead of who actually understood the content. But even if this problem were somehow irrelevant—letsay an irrefutable study comes out tomorrow saying that cramming ability is just as relevant for the real world as understanding—I would still have an issue with studying, namely the time spent. Suppose someone is taking 4 classes and studies 4 hours for each midterm and 8 hours for each final. That’s 48 hours spent studying in a semester. Multiply that by 8 semesters to get 16 days spent on studying. These 16 days are the difference between sitting down and standing up.

Preparing for Colleges/Job Interviews

Sure, the informative power of some of the tests I’ve mentioned above may be arguably above zero. For example, maybe it’s feasible that a dedicated premed student university should cram before a bio test because the details do matter, though the question remains of whether such a student will remember anything years later. But there’s still one very important test taken all around the country that really has no arguable intellectual merit: the SAT.

This test is probably the biggest insult to intelligence when taken seriously. I try my hardest to resist cringing whenever I hear smart people talking about their SAT scores. From the CollegeBoard site:

The SAT and SAT Subject Tests are a suite of tools designed to assess your academic readiness for college. These exams provide a path to opportunities, financial support and scholarships, in a way that’s fair to all students. The SAT and SAT Subject Tests keep pace with what colleges are looking for today, measuring the skills required for success in the 21st century.

Yes, I’m sure it’s very “fair to all students.”

sat-scores-by-wealthAnd I’m sure that by “keep[ing] pace with what colleges are looking for today, measuring the skills required for success in the 21st century,” what CollegeBoard means is that the skills required for success in today’s world are… wealth, certain racial backgrounds, and access to prep courses.

Anyways, I guess my point is that if nobody studied for the SAT, nobody took prep courses, and no one cared so much, then:

  • Students wouldn’t be wasting their time studying for it.
  • Many families would save time and money on SAT prep by not having to do it.
  • As a result, less privileged students would stand a better chance, and thus the test would be more fair.

Of course, while this may sound good, it is easier said than done. To not study would be shooting yourself in the foot, or in this case, to sit down in the theater in which everyone is standing. It would be like one country’s reducing its greenhouse emissions while other countries are not decreasing theirs.

(Personally, I refused to study for the SAT, though at the time I had to give off the impression that I was studying for it to appease my Asian parents. If you really want the story, it’s in the latter part of this post.)

I would go further to say that preparing for job interviews in some ways fits this type of game. On this subject, however, I have very little experience as my only important interviews were of the type where it would be very difficult to prepare for, i.e., math puzzles. Answering such questions did not hinge on knowing certain advanced equations, but instead on using simple tools that almost everyone knows, in unusual ways.

In addition, I understand that an interview not only judges the answers to the questions, but also the interviewee’s character. If it is evident that someone prepared a lot for an interview, that fact in itself would be considered in the interviewer’s assessment. However, I think that in a world in which no one prepared for interviews, both sides would benefit as the interviewee would save time and stress while the interviewer gets a more genuine view of the interviewee, not a carefully constructed outer shell.

And for a preemptive defense, to the claim that studying or preparing is simply a result of competition, I have nothing against capitalism or competition. If anything, freeing up students’ time from studying for tests would make them be able to compete in other areas, and be able to take additional classes or learn new skills (I picked up programming while pretending to study for the SAT). I see the time wasted as an inefficiency. The point of not studying is to have more time, and hence be more productive.

Sitting down in a standing theater is a difficult decision. But if everyone sat down, we might all live in a better place.

Why Are College Students Not Choosing Math/Science?

microscope

From the Wall Street Journal in 2011:

Although the number of college graduates increased about 29% between 2001 and 2009, the number graduating with engineering degrees only increased 19%, according to the most recent statistics from the U.S. Dept. of Education. The number with computer and information-sciences degrees decreased 14%

After coming up with the topic for the post, I found this article from 2011 with a similar title and citing the same WSJ story. It argued that the high school teaching environment was not adequate in preparing students for rigorous classes in college. 

In addition, the article includes the argument that in the math and sciences, answers are plain right or wrong, unlike in the humanities and social sciences.

I can agree with these two points, but I want to add a few more, with the perspective of year 2013. Also, I am going to narrow down the STEM group a bit more, to just include math and science. The main reason is that in the past years, the number of CS majors has actually increased rapidly. At Cornell, engineering classes can be massive and there does not seem to be a shortage of engineers. Walk into a non-introductory or non-engineering-oriented math class, however, and you can often count the number of students with your fingers. So even though STEM as a whole is in a non-optimal situation, engineering and technology (especially computer science) seem to be doing fine. So then the question remains.

Why Is America Leaving Math and Science Behind?

I mean this especially with regards to theoretical aspects of math and science, including academia and research.

In this situation, money is probably a big factor. The salary of a post-grad scientist (from one article at $37,000 to $45,000) is pitiful compared to that in industry (which can a median early-career salary of up to $95,000, depending on the subject, according to the same article). Essentially there is a lack of a tangible goal.

There are other factors besides money. Modern math and science can be quite intimidating. All major results that could be “easily” discovered have already been discovered. In modern theoretical physics, for instance, the only questions that remain are in the very large or the very small—there is little left to discover of “tabletop” physics, the physics that operates at our scale. Most remaining tasks are not problems in physics, but puzzles in engineering.

Modern mathematics is very similar. While there are many open questions in many fields, the important ones are highly abstract. Even stating a problem takes a tremendous amount of explanation. That is, it takes a long time to convey to someone what exactly it is you are trying to figure out. The math and science taught in high school is tremendously unhelpful in preparing someone to actually figure out new math and science, and it is thus difficult for an entering college student to adjust their views of what math/science are.

Even the reasons for going to college have changed. More than ever, students list their top reason for going to college as getting better job prospects rather than for personal or intellectual growth.

In addition, society seems more than before focused on immediate gain rather than long term investment. Academia’s contribution to society, especially in math and science, is often not felt until decades or even centuries after something was invented. Einstein’s theories of relativity had no practical application when he made them, but our gadgets now use relativity all the time. Classical Greece knew about prime numbers, but prime numbers were not useful until modern-age data encryption was required. Even a prolific academic could receive very little recognition in one’s own life.

However, with the rise of online social networks in the last several years, you can now see what your friends are up to and what they are accomplishing in real-time. This should at least have some psychological effect on pushing people towards a career where real, meaningful progress can be tracked in real-time. Doing something that will only possibly have an impact decades later seems to be the same as doing nothing.

Considering the sentiment of the last few paragraphs, it might sound like I am talking about the decline in humanities and liberal arts majors. Indeed, while the number of math and science majors is increasing (though not as much as in engineering/technology), it almost seems like the theoretical sides of math and science are closer in spirit to the humanities and liberal arts than they are to STEM. The point is not for immediate application of knowledge, but to make contributions to the overall human pool of knowledge, to make this knowledge available to future generations.

Is this just a consequence the decline of education or the fall of academia in general? STEM is not really education in the traditional sense. It is more like technical training.

In all, the decline of interest in theoretical math/science is closely correlated with the decline of interest in the humanities/liberal arts. Our culture is fundamentally changing to one that values practicality far more than discovery. (For instance, when is NASA going to land a human on Mars? 2037. JFK might have had a different opinion.) Overall this is a good change, mainly in the sense of re-adjusting the educational demographics of the workforce to keep America relevant in the global economy. But, we should still hold some value to theory and discovery.

Additional resources:

  • National Science Foundation statistics – [link]
  • National Center for Education Statistics – [link]
  • Pew social trends – [link]

Stress and GPA-centrism in College

studying

Every time papers, projects, and prelims come around, the campus stress level rises dramatically. Sleep is lost (or outright skipped), meals are avoided, and all activities other than studying are brushed off. This happens not once a semester but throughout, corresponding to large assignments for every class.

And every time this happens, it seems that many students are focused not on actually learning the content, but on scoring higher grades than others. Of course, this phenomenon occurs in certain majors (engineering) much more than others. And I would guess that it happens at Cornell at an above average rate compared to that of the typical university. But it raises some questions that I want to explore.

Just a couple of notes. First, this article will mainly focus on the math/science/engineering side. And second, I do not think I need to mention why Cornell should be concerned about student stress.

Should Competition Be GPA-Focused?

Competition to a certain degree is beneficial, and I think no one would argue with that. As a math major I know very well that competition leads to efficiency. But there is a line where the marginal benefit in efficiency is not worth the huge increase in stress levels, and in this respect I think Cornell has crossed the line for good.

In addition to the GPA competition, there is the additional factor that students are competing for jobs, internships, and research positions. I think the competition here is mostly fine (except regarding salaries vs societal contribution; this topic deserves its own post). Combined with academic competition, however, this induces a vast amount of anxiety and stress in the students.

Without mentioning names, I will list some of the extreme behaviors I have observed of people I know:

  • A student pulled multiple all-nighters in a row to finish a project. While this might be plausible in real life for a rare occasion such as a doctoral thesis or a billion dollar merger, the student did this regularly for his classes.
  • A student has problem sets due on four out of five of the weekdays, and spends literally all his time outside of class eating, sleeping, or doing problem sets. In one particular class, the problem sets he hands in are 10-20 pages per week.
  • A student took 50+ credits in one semester, though he claims to know of someone who took 61.
  • A student brought a sleeping bag, refrigerator, and energy drinks to one of the school computer labs, and pretty much lives there, returning to his living place once every few days to shower.

Interestingly enough, I think these particular students will do fine, as they seem to know their own abilities and limits, and more importantly, they are all aware of what they are doing. They are also all very smart people who can actually learn the material. This “top tier” of students is not really adversely affected by competition, since they are smart enough to excel regardless of whether competition exists. Moreover, these students don’t seem to be grade-focused: they learn the material, and the grade comes as a byproduct of learning.

The group I am actually concerned about is the second tier. (Note: I just realized after typing this how judgmental that statement sounds, but hey, from statistics, unless you define the first tier to include everyone, there must be a second tier.) This group I would define to be the smart people who don’t seem to understand how the first tier operates. They see the students in the first tier getting high grades and know those students are smart, so they think that if they prepare the tests well and get high grades, they will become as smart.

What they don’t realize is the difference in cause and effect. The first tier prioritizes understanding first and the grades come as a byproduct, whereas the second tier prioritizes grades first and hope to gain some understanding as a byproduct.

Again, just as a disclaimer, these are just arbitrary definitions for first and second tier I made up for this particular observation. I am not saying that this criterion is the final say, and of course, there are numerous other factors regarding how well one does in college.

But from my experience, it is precisely the students in this second tier who are stressed. They are the ones trying so desperately to beat the test instead of to learn the material. And they are the ones who make college seem so competitive, as you can always hear them talking about tests and what their friends got on the tests and how they are being graded and what the format of the test will be.

On the other hand, the student I mentioned above who lives de facto in one of Cornell’s computer labs—I have not once heard him talk about anything specifically regarding a test.  The closest was talking about the material that was to be covered, but he was talking about stuff that was beyond what the class taught for the topic, stuff that he knew was not going to be on the test.

Some of you might be thinking, “That’s great, but what kind of job is he going to get if he is not grade-focused?” Good question. After working there for a summer internship, this same friend rejected a return offer from Goldman Sachs.

How to Break from GPA-centrism

I am not worried about this person’s career at all. I am worried about the second tier, the smart people doing mundane tasks, wasting a lot of potential creative brainpower that the world needs more than ever. Renewable energy, bioengineering, artificial intelligence, space exploration and colonization, nanotechnology—there are so many people here who would be excellent for these fields, yet many of them seem too bogged down by current competition-induced stress to even think into the future.

Indeed, this GPA competition is a force to be reckoned with, as it really is self perpetuating. Those students in other groups or who are apathetic to grades will tend to become more grade focused just from sitting in lecture, as there are always people who ask for as much details of the test as possible. I feel that this defeats the purpose of a test, which is to measure how well you know the material or how well you can apply a certain skill, not how much of the test structure you can memorize or how much content can you cram the night before.

Overall though, there are some measures that can be taken to reduce this kind of stress.

  • Reduce the importance of the GPA. I do not know if I would go so far as to remove it, though. For example, at Brown University, the GPA is not calculated. Somewhere in the middle ground should be best.
  • Stop showing score distributions, or show them only for major tests like a midterm/final. In many engineering classes at Cornell, the first thing that is requested after a test is graded is to see the score distribution (often in graph form), along with the mean, median, standard deviation, etc. In fact, this has become so common that it is now the first thing the professors put on their lecture slides. Moreover, the computer science department uses an online course management system which automatically tells students the mean, median, standard deviation, etc. for every single assignment, not just tests. Being a math major who would normally love extra statistics, I thought this was cool at first. But now I despise it—it is just too much information that I don’t need in order to learn the material, and it only detracts from my learning experience. And the way the page is setup, it is not something you can just ignore.
    • A side note: One of my classes in the CS department actually does not list grades, and I definitely feel more pressured to actually learn in that class, not more pressured to beat other people at grades like in other CS classes. Props to Professor John Hopcroft.
  • Teach better math/science/engineering/CS much earlier in the education system. A friend showed me this article today, a comparison between the CS education systems of the US and Vietnam, a comparison that is horrific for the US. If students already knew the foundations, then college would be what it was supposed to be: going really deep into a topic in a learning atmosphere, not treating us like elementary school children because, well, frankly that’s the level of engineering/CS of many college entrants. For instance, I think it’s great that students are trying to take Calculus 1 freshman year and then do engineering. Hard work is certainly a virtue. But wouldn’t it be much better for both the student and the college if they mastered calculus in high school? Imagine how much better our engineers would be.

What I envision is a class where students are trying to learn, not to beat each other on a test. I hope this vision is not too far-fetched.

Survival of the Selfish Gene

After reading The God Delusion, I decided to study some of Richard Dawkins’ earlier works. For this post, I read The Selfish Gene (and among the books on my queue are The Blind Watchmaker and The Greatest Show on Earth).

the-selfish-gene

Published in 1976, The Selfish Gene explores the phenomena at play regarding the behavior of replicators, namely genes and memes. I was expecting to see lots of biological arguments, and while there are many, I was shocked at what I found was the main tool used in the book: game theory.

Of course, once you think about it, it makes perfect sense that game theory is extremely important when talking about genes and how they spread from one generation to the next. And by game theory, I do not mean board games or video games, but economic game theory, applied to biology in what is now known as evolutionary game theory. In fact, this book would be an excellent read for people interested in mathematics or economics, in addition to the obvious group of those interested in biology. Dawkins uses concepts like Nash equilibria, though the term is not explicitly stated (consider the date of the book), and the Prisoner’s Dilemma, just for a couple examples, to explain many biological behaviors found in various animals, including humans. This kind of game-theoretic analysis followed largely from the work of John Maynard Smith.

In addition to having studied a bit of game theory, I have also studied dynamical systems, though from the perspective of pure math and not biology. Even so, the concepts in the book were very familiar. I do not think The Selfish Gene is controversial from an academic standpoint. The now 40-year old ideas are still relevant today, and the ideas are really not that difficult to understand, given a sufficient mathematical and scientific background.

Instead, the controversy around the book seems to come solely from the title itself, and perhaps the attached stigma to writing anything about evolution, which seems to be more of an issue today than it was in 1976. Dawkins notes this years later in the preface to the second edition:

This is paradoxical, but not in the obvious way. It is not one of those books that was reviled as revolutionary when published, then steadily won converts until it ended up so orthodox that we now wonder what the fuss was about. Quite the contrary. From the outset the reviews were gratifyingly favourable and it was not seen, initially, as a controversial book. Its reputation for contentiousness took years to grow until, by now, it is widely regarded as a work of radical extremism.

I do find this amusing. It seems to have not to do specifically with the theory of evolution itself, but with the unfortunate anti-intellectual sector of the US. (Of course, Dawkins is from the UK, but I am talking about American opinion of these kinds of books.)

In current society it seems like a fad to wear one’s ignorance on one’s sleeve, as if boastfully declaring, “My ignorance is just as good as your knowledge.” Of course I am not advocating that we should go the opposite direction and be ashamed for not learning, but we should be able to come together and agree that ignorance is not a virtue, especially not in the most scientifically advanced country in the world. I am not really sure how the United States is supposed to recover from this, other than that we become more reasonable over time. And that will take education, not ignorance.

The title of the book is somewhat misleading, only if one does not understand what the word “selfish” is describing. The “selfish gene” is not so much talking about a gene that causes selfishness in individuals (this is an ambiguous notion in itself), but rather, it describes the word “gene” directly, that genes themselves propagate themselves in a manner that appears selfish. The individual is merely a “survival machine” for the gene. There is a critical difference here between the two notions.

The selfish gene is merely a gene that, for practical reasons, has a higher chance of being passed on. It does not really contradict any current notion of evolution, and in fact, at the time of publication, it became the new and improved theory of evolution that is now the textbook standard. In any case, the message is that evolution works not by the survival of the fittest individuals, but by the survival of the fittest, or most selfish, genes.

When we look at the selfish gene, there are situations (as demonstrated in the book) where the intrinsically selfish thought appears on the outside as altruistic. Mutual back-scratching benefits both individuals, and moreover, benefits the gene for it, thus making the gene more likely to spread. So while the behavior of back-scratching seems altruistic, it may be nothing more than concealed selfishness. This idea can be extrapolated to many phenomena. Often people put on acts and fake displays of kindness only for the selfish benefit of “seeming” nice. Or they are so “humble” that they announce their humbleness everywhere they please and make you feel bad for not being as humble as they are. The list goes on. However, I will not comment too much on this as this goes under cultural behavior and not strictly genetic behavior, although they are related.

The controversy around this book also seems to stem from perceived personal offense. Included in The Selfish Gene is an interesting quote from Simpson regarding historical developments in explaining how the current species on Earth came to be:

Is there a meaning to life? What are we for? What is man? After posing the last of these questions, the eminent zoologist G. G. Simpson put it thus: ‘The point I want to make now is that all attempts to answer that question before 1859 are worthless and that we will be better off if we ignore them completely.’

While this statement is perfectly true in trying to understanding biology, I can see how religious people might take offense. To declare that all mythological ideas in this area before Darwin’s The Origin of Species are worthless is a bold claim, even when it is correct.

Regarding the actual content of the book, I have already mentioned that Dawkins makes extensive use of game theory. There are many numbers in some of the more technical chapters, making the book possibly difficult to read in real-time unless the reader is versed in mental mathematics. Though, with some deliberate thought on these chapters, any reader should be able to get through them.

The Selfish Gene is a remarkable book, giving clear explanations of basic biology and evolutionary game theory for the layman. It is a shame that such educational material is viewed as controversial. I wish I could succinctly summarize the fascinating interplay of evolutionary game theory in a single post, but it would be better to leave it to you to pick up this book and think about it for yourself. If you do not like evolution, however, you have been warned.

Thoughts on Classes, Spring 2013

In a previous article, I posted my schedule and about my decision to double major in mathematics and computer science. The computer science department seems to be quite backed up at the moment, so I have not received any official response yet.

I can see why the CS department is really backed up. In most of my experience at Cornell, I had class sizes of 10-30, with larger class sizes (150-250) only at introductory level courses such as Sociology 1101 or Astronomy 1102. It would be quite rare to have an advanced level course with that many people in them.

goldwin smith 132

But, CS easily has 150-250 people in each class. In the first few days of class, even in large lecture halls, there were no seats left and the late-arrivers had to sit in the aisles. I think students here see CS as too lucrative of a skill to pass up. Some difficult or otherwise time-consuming homework assignments have caused class sizes to drop significantly, but there are around 150-250 people in the CS classes. On the other hand, my math classes have 14 and 6 people respectively.

Math 4340 – Abstract Algebra

Professor: Shankar Sen

Cayley-Graph

This is a fairly trivial class so far. We are covering basic group theory and it is quite a relief compared to some of the more intense math I did last semester (*cough* topology). The course is supposed to move on to rings and modules later; however, in linear algebra we actually covered much of the foundations of ring theory and modules.

However, given the lack of difficulty of the topic so far, the homework grading has been quite harsh. I usually skip writing down every rigorous step if I think some part is obvious. Learning the material is more important than writing down every detail of the proof, in my opinion.

Math 7370 – Algebraic Number Theory

Professor: Shankar Sen

Relatively-Prime-Grid-Points

There are no exams, no prelims, and no homework. However, it is a graduate level seminar-type class and it is pretty insane. I have put up my lecture notes on Scribd, and even if you know nothing about college math, if you click that link, you can probably see how much more difficult 7370 is than 4340.

It is a really good thing I had a basic introduction to ring theory and modules before taking this course. Knowing what PID (principal ideal domain) and UFD (unique factorization domain) mean, knowing the difference between prime and irreducible, etc., was extremely helpful.

This class is even more difficult than the graduate Complex Analysis course that I took last year. Before I took complex analysis, I actually knew quite a bit about complex variables, complex functions, and contour integrals. I had even studied the Riemann zeta function in high school. And on top of that, I was not the only undergraduate in that class—there were at least 3 others.

But for algebraic number theory, this is really new material, most of which I haven’t seen or even heard of, and moreover, I am the only undergrad in the class. However, I talk with the professor outside of class and I am confident that I can learn the material if I really try.

Math 4900 – Independent Research/Reading – Elliptic Curves

Elliptic-Curve

Since I felt that I was doing too much CS and not enough math, I decided to add on an independent reading class. The book is The Arithmetic of Elliptic Curves by Joseph Silverman.

I have seen elliptic curves in complex analysis in the form of the Weierstrass P-function and equating points in the complex plane by a lattice. To see the algebraic side of it will be interesting though, especially because I am interested in number theory for possible research.

In addition to this official reading, I am also reading and doing problems from Tom Apostol’s Introduction to Analytic Number Theory, so that I can get both the algebraic and analytic sides to it.

CS 4820 – Introduction to Algorithms

Professor: Dexter Kozen

Minimum-Spanning-Tree

This is a really fun theoretical and mathematically oriented class. After all, Kozen is practically a mathematician.

Given my mathematical background, especially the combinatorics class I took last semester, this algorithms course is not too difficult and in fact fairly trivial so far. But, I expect it to get more sophisticated once we get over the introductory stuff. For instance, on our discussion board on Piazza, one student asked how to use a contradiction proof. In just topology alone, I probably used about a hundred.

In addition, Kozen shares some very interesting stories during lecture. Just last Friday, he was talking about dynamic programming and discussed a project using body scan data to analyze the number of dimensions it took to store the size information of a human body. “Are women 2-dimensional? I don’t think so,” said Kozen. In fact, he recalled from the study that women were around 5-dimensional and men were fewer.

Also, when he was explaining the growth of the Ackermann function A(n), he noted that even A(4) was an extraordinarily large number, and in fact that it was “even higher than Hopcroft’s IQ.”

CS 4850 – Mathematical Foundations for the Information Age

Professor: John Hopcroft

Large-Graph

From the title of this course, one might think it is really easy, but even as a math major, I find it nontrivial (that means hard, in math terms). In fact, I’d say at least 30-40% of the class has dropped since the first day. The fact that Hopcroft won a Turing award makes the class no easier.

It is essentially a mathematical and statistics course with applications. We proved the Central Limit Theorem on the first day of the class and then looked at spheres in high dimensions, with the intent of generating random directional vectors in high dimensions. As it turns out, most of the volume of a high-dimensional sphere is on a narrow annulus or shell, and when a given point is taken to be the north or south pole, the rest of the volume is located at the equator.

Currently we are studying properties of large random graphs, in particular, properties that appear suddenly when the edge saturation of the graph passes a certain threshold. For instance, below a certain number the components of the graph are all small, but above that number, a giant component arises. For an assignment I showed how this giant component phenomenon arises in connections of the Reddit community.

CS 3410 – Computer System Organization and Programming

Professor: Hakim Weatherspoon

32-bit-ALU

In contrast to the high-level programming I have done in the past, this course is about low-level programming and the hardware-software boundary. The programming language for this course is C.

We are building up a processor from the ground up, one could say, with basic logic gates to begin with. The first project was to design a 32-bit arithmetic logic unit (ALU) using Logisim, a circuit simulation program. For instance, for a subcircuit we needed to create a 32-bit adder with overflow detection.

The above picture is actually a screenshot of the overall ALU that I designed for the class. The subcircuits are not shown (this project is not due yet, so it would break academic integrity to show a more coherent solution).

On the Naming of Terms in Several Disciplines

Astronomy

Recently I watched an entertaining talk by Neil deGrasse Tyson in which he poked fun at the confounding complexity of biological and chemical terms, in contrast to the elegant simplicity of terms in astrophysics. The segment starts at 14:34 of the talk and goes till about 17:00.

[15:01] What do you call spots on the Sun? [Pause] Sunspots!

sunspots

Indeed, terms like sunspot, red giant, supergiant, nova, supernova, ring, moon, black hole, pulsar, dark matter, dwarf planet, spiral galaxy, singularity, solar flare—it is immediately obvious what these things describe. Even terms like neutron star or Trans-Neptunian object are clear if one is familiar with neutrons or Neptune. Let us see what term sound like in other disciplines.

Biochemistry

What do you call the most important molecule in your body that contains all your genetic information? Deoxyribonucleic acid. What do you call the energy molecule that your body runs on? Adenosine triphosphate. What do you call the most common liquid you drink (if you aren’t a college student)? Dihydrogen monoxide.

Water

Things like these are what Tyson was getting at, where, without even going into the ideas or concepts, a student may be already confounded by the sheer terminology.

Granted, at the core all these names make sense and are very systematically denominated. For instance, “dihydrogen monoxide” describes exactly what the constituents of the molecule are: 2 hydrogen atoms and 1 oxygen atom. And “deoxyribonucleic acid” is really just a nucleic acid (a nucleotide chain) with deoxyribose as the sugar component. Even the term “deoxyribose” is well named, as it is the sugar obtained by removal (de-) of an oxygen atom (oxy) from a ribose sugar.

In this respect, I don’t think biochemical terms are really as confounding to a scientifically literate population as Dr. Tyson makes them out to be; however, I do see his point in that they would confuse the hell out of someone who is not scientifically literate. Even then, these terms would not cause an illiterate person to gain a wrong understanding.

I claim that while biochemical terms are quite abstract, at least they are not misleading.

Economics

“This allocation of resources is Pareto efficient.”

This term might have a positive connotation, as efficiency is associated with good, and so the masses may support a policy having anything having to do with it. However, it is possible that an allocation where the top 1% controls 99% of the resources is Pareto efficient. Indeed, an allocation where one person controls 100% of the resources is Pareto efficient, as the term only concerns whether the allocation could be changed such that one could benefit without harming any one else. Given the misleading connotation, it would be disastrous if this term were ever uttered by an economist—or worse yet, a politician—in public discourse.

Economic-surpluses

It is especially misleading as economics generally has very simple, intuitive terms: supply, demand, goods, depression, inflation, market, labor force, bubble, money, wage, etc. These are all good terms. But sometimes, a term is just plain misleading: for instance, the fiscal cliff.

Medicine and Psychology

The terms disease and disorder are pretty misleading. A disease does not have to be infectious, and someone with a disorder could behave just as normally, whatever that means, as a “normal” person. Even sane and insane are notoriously difficult to tell apart.

one flew over the cuckoos nest scene

And what does it mean to cure someone?

A-Clockwork-Orange-lodovico-technique

That said, most psychology terms are pretty self-explantory, albeit sometimes difficult to test accurately.

Sociology

A field like astrophysics in which the terms are extremely clear. The only term I find troubling is postmodern, which seems to imply something that it is not.

Physics

This is a very technical field, where speed and velocity mean different things, and if you are describing a scenario, you must use words like force, momentum, and energy very carefully. Technicality aside though, it is very obvious what the terms are about.

Linguistics

Given that linguistics should have something to do with this point, you might expect linguistics to have very intuitive terms. Depending on the subfield, however, there are some very non-obvious terms. What is a morpheme?

Computer Science

Like math, it is very unintuitive at times. For instance, computer scientists have no idea what a tree is supposed to look like.

Mathematics

Singularity

Math terms are both super-technical and very non-obvious, given that half the terms are named after a person. Even for the half that are words in English, there are some issues. In topology, for instance, you might think that open is the opposite of closed, but in reality a set can be open, closed, neither open or closed, or both open and closed (in which case it is called clopen). What about injectionsurjection, and bijection—what is a “jection”?

The term rational numbers for fractions makes sense as fractions are ratios, but who came up with real, imaginary, or complex? It becomes worse in abstract algebra, where you have things like groups, rings, and fields. At least the word object is what you think it means: just anything. And measure theory makes a lot of sense. A measure is pretty much what you think it means, and almost means almost what you think it means.

I think math is the only subject where two renowned experts can have a discussion, each not having a clue what the other is talking about. In this respect, I think mathematics beats biochemistry in confusion of terminology.