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.

Math or Computer Science?

Well this is an interesting situation. Just a month ago I announced that I was adding a computer science degree, so that I am now double majoring in math and computer science. The title of the post, after all, is “Computer Science AND Math.” Given the circumstances at that time, I think it was a good decision. My work experience had been mostly in software, and a CS degree from Cornell should look pretty good. In addition, I was wanting a more practical skillset.

decisions-2

In the past week, however, things have changed. I received and accepted an internship offer from my dream workplace, based on my background in mathematics and not in CS (though my prior CS experience was a plus). Based on this new situation, I have considered dropping the CS major (next semester) and taking more advanced math:

  • The CS degree has some strict course requirements, and I am afraid that if I go for the degree, I may be forced to skip certain math classes that I really want to take. For instance, I may have to take a required CS class next semester that has a time conflict with graduate Dynamical Systems, or with Combinatorics II. And given that I am currently a second-semester junior, I don’t have that much time left at college.
  • Even this semester, I am taking Algorithms, which meets at the same time as graduate Algebraic Topology. While Algorithms is pretty interesting and the professor is excellent, I am already very familiar with many if not most of the algorithms, extremely familiar with the methods of proof, and I feel that the experience is not as rewarding as possibly taking Algebraic Topology with Allen Hatcher, who wrote the textbook on the subject. I feel that I could learn algorithms at virtually any time I want. But learning algebraic topology with Allen Hatcher is a once-in-a-lifetime opportunity that I am afraid I am missing just because I want to get a CS degree to look good.
  • Even not being a CS major, I will still be taking some CS classes out of curiosity. However, these classes will no longer feel forced, and will not restrict me from taking the higher level math courses that I want to take.
  • My risk strategy for grad school is different now because of the internship. In the past, I would have been willing to take a decent grad school in math or really good job. (I would prefer grad school over getting a job, but of course, a good job is better than a mediocre grad school.) However, now that I have my dream internship, I am willing to play the grad school game with more risk.
  • But whether for grad school, trading, or just for curiosity, I would prefer taking advanced (graduate) math classes over undergraduate CS classes. In a sense, my taking of the CS degree was a hedge bet, as I wanted to reduce the possible cost of the worst case scenario. I knew that it would directly inhibit my ability to take advanced math classes via class time conflicts, but the thought was that if I couldn’t get into a good math grad school or get a good job using math, at least I would have a CS degree from Cornell. But, in this new situation, I think the risk is significantly reduced and the hedge is no longer necessary.

Interestingly enough, the primary motivation for dropping CS wouldn’t be to slack off, but to be able to explore more advanced math. (At least, that’s what I tell myself.)

I think this might be the second time in my life where I have had to make an important decision. (The first time was deciding where to go to college, and I certainly think I made the right choice there.) Unfortunately, I really can’t be both taking as many interesting math courses as I can, and at the same time be pursuing a CS degree. As much overlap as there is, I can’t do both. In an ideal world this might be possible, but not currently at Cornell.

So instead of the idea of having math and computer science, I am now having to think in terms of math or computer science. I am currently in favor of going with math, but I am not completely sure.

Edit: Thanks for the discussion on Facebook.

Making Mistakes—And Quickly Correcting Them

A couple days ago on my math blog, I talked about my interview experiences with a certain trading firm. I would normally write about job or life experiences on this current blog, but given the amount of mathematics in those interviews, I wrote it over there instead.

walking-off-cliff

An Interview Mistake

One of the things I did not mention in that post was a particular chip betting situation during one of the on-site interviews. I do not want to give away their on-site questions on the web, but I can say enough of it to make a point here.

The situation was a game where I had positive expected value. That is, if I played it again and again with my strategy, then over the long run I would gain chips.

My interviewer added a new rule to the game which did not affect the expected payoff of the game given that I kept the same strategy. However, the new rule was psychologically intimidating enough that I changed my strategy, and after a couple of plays, I realized I was now losing chips on average, instead of gaining.

My old strategy would have kept gaining chips, but the new strategy that I switched to was losing chips. I only realized this after 3 rounds, and just before the interviewer started the 4th round, I interjected, saying I realized my new strategy was a bad strategy, and I stated what the new (negative) expected value was for this strategy.

At this moment I felt that I had made a fatal error that would be reflected on in the decision. But instead of giving me a stern look for my mistake, my interviewer suddenly became really happy that I had corrected it! In fact, he said that almost everyone they interviewed had done the same thing, by switching their good strategy to a bad strategy when that new rule was added.

Acknowledging Mistakes

The first and most important part of correcting a mistake—and eventually benefiting from one—is to acknowledge the mistake. This most likely sounds trite, but acknowledging a mistake really is the most significant step of this process.

In matters involving numbers, it can usually be very easy to acknowledge a mistake. In my interview, all I had to do was to sense something fishy about the bet, and then recalculate the expected value to see that I had made a mistake. Since numbers don’t lie (and since I had chips on the table), I acknowledged the mistake as quickly as possible.

It can be much tougher, however, when the mistake is on some emotionally vested or less clear-cut issue. We’ve all had arguments with someone where we were totally sure we were correct, and only much later, we realized we were flat-out wrong.

And then sometimes we still maintain our original position even though we know we are completely wrong. This can lead to strange effects, but often, a person in such a state of mind is difficult to convince otherwise. Anyone who has tried arguing on the internet can give testament to this phenomenon.

Looking at the Evidence

Someone in such a state undergoes several cognitive biases:

  • Refusal to look at opposing evidence.
  • Cherry-picking evidence to only consider supporting evidence.
  • Blaming something else for opposing evidence, and waving it off.
  • Etc.

Let’s say that during my interview, I was adamant that my new strategy was good. After I start losing chips for a while, I might explain away losing streaks as bad luck, while at the same time explaining winning streaks by superior choice of strategy. I might complain that the coin was unevenly weighted, that the die was rigged, or that the deck had been stacked.

While these are somewhat reasonable conclusions to make, the problem would be if I were confronted with the fact that my strategy was bad. For instance, if I knew I was losing chips (say I lost 20% of them), but I believed in my mind that my strategy was still winning chips, then suppose the interviewer informed me that my strategy was losing chips. My first reaction, in this state, would be to reject this information and maintain that my loss of chips was due to bad luck or to unfair conditions. Of course, this behavior would be disastrous in an interview, and I would probably be rightfully rejected right there.

In the real scenario, I had some intuition about the probabilities involved, so I realized after 3 rounds that my strategy was flawed. But even if I had no intuition about what the probabilities were, after I played say 10 rounds, I would have seen the evidence and realized I was losing chips, and would have begun to start questioning my strategy.

Catching Mistakes and Learning From Them

Sometimes you are not afforded enough time to completely think something through. In this case, you need to give a most likely answer, but the important part is to keep thinking about the answer even after you have stated it. Sometimes, you might be given additional time to reanalyze it, other times what you state is final. This can be the worse feeling, when you catch a mistake only after making a final decision.

chess-sketch

I used to play chess competitively, and while at the high levels winning often requires outsmarting your opponent, at the lower levels a win is typically achieved simply by making fewer mistakes than your opponent. If I were ever to get back into chess, my #1 area of improvement would be to reduce the number of blatant mistakes. I have turned many equal or favored positions into hopelessly lost positions by accidentally dropping a piece.

It is often psychologically damaging in chess because sometimes you know you’ve made a mistake after you made your move but before your opponent makes a decision. At this point you could hope your opponent doesn’t see your mistake. Or, you could think about how to avoid that mistake in the future. I think in the latter part of my chess playing, I dwelt too long on the first option and didn’t spend enough time on the second, and as a result, my chess rating hit a plateau.

Lies, Damned Lies, and Statistics

In addition, in 9th/10th grade I went through a phase where I thought global warming was not a well-founded theory. I subscribed to the solar cycle explanation for the “recent” warming, and thought that was more significant than the greenhouse effect contribution. I do have to add one caveat though for the record: even with that position on global warming, I still considered myself an environmentalist—I thought there were many issues with the environment, some which were far more urgent than global warming, and that global warming shouldn’t have eaten up all the priority and public interest. However, as debates go, my opposition always were able to label me as a “denier” of a sort, even though I never really denied it.

Anyways, I think the evidence since then has put a nail in the coffin. I knew the burden of proof was on the solar cycle model, and I waited to see if the temperature would drop back down. But it kept going up (in fact, even it had just stayed constant, it would have contradicted the solar cycle model). Moreover, one of the leading advocates of the solar cycle model abandoned it a couple years later. As a result, sometime during 12th grade, I went back to the scientific consensus view on this.

The Portals of Discovery

Realizing a mistake can be a rewarding experience. There is a quote by Donald Foster:

No one who cannot rejoice in the discovery of his own mistakes deserves to be called a scholar.

And a good one by James Joyce:

Mistakes are the portals of discovery.

Wile E Coyote(Well, not if you keep making the same mistakes.)

For Science: Neil deGrasse Tyson’s “Death by Black Hole”

Death By Black Hole

Death by Black Hole is an epic read. What makes this stand out from the average science essay collection is Neil deGrasse Tyson’s unwavering expertise in combination with his remarkably down-to-Earth explanations of not only how things happen, but also of how we discovered how things happen.

For instance, everyone today knows there is a constant speed of light, and we actually encounter it, sometimes in latency in the Internet. But as far as our intuition goes, light moves infinitely fast, i.e. it is instantaneous. In fact, I still remember Bill Nye the Science Guy trying to outrun a beam of light in his show. After many tries, he was never able to succeed.

Tyson reveals to us that even Galileo, in 1638, thought that light was instantaneous, when his lantern experiment failed to yield a measurable delay. It was not until Ole Rømer who first saw and interpreted correctly the evidence that light is not instant. In “Speed Limits”:

Years of observations had shown that, for Io, the average duration of one orbit—an easily timed interval from the moon’s disappearance behind Jupiter, through its re-emergence, to the beginning of its next disappearance—was just about forty-two and a half hours. What Rømer discovered was that when Earth was closest to Jupiter, Io disappeared about eleven minutes earlier than expected, and when Earth was farthest from Jupiter, Io disappeared about eleven minutes later.

Rømer reasoned that Io’s orbital behavior was not likely to be influenced by the position of Earth relative to Jupiter, and so surely the speed of light was to blame for any unexpected variations. The twenty-two-minute range must correspond to the time needed for light to travel across the diameter of Earth’s orbit. From that assumption, Rømer derived a speed of light of about 130,000 miles a second. That’s within 30 percent of the correct answer—not bad for a first-ever estimate…. (p. 120)

That someone deduced the speed of light with 1600’s technology is remarkable.

In addition, Tyson enlightens us with the exciting information we all want to know. Antimatter, for instance, annihilates on contact with normal matter, releasing tremendous amount s of energy. In Dan Brown’s Angels and Demons, a tiny vial of antimatter explodes with the violence of a nuclear bomb. But what if a Sun made out of antimatter collided with our own Sun? How big would the blast be? According to Tyson in “Antimatter Matters,” the explosion would be frighteningly large:

If a single antistar annihilated with a single ordinary star, then the conversion of matter to gamma-ray energy would be swift and total. Two stars with masses similar to that of the Sun (each with about 1057 particles) would be so luminous that the colliding system would temporarily outproduce all the energy of all the stars of a hundred million galaxies. (p. 106)

While this anthology is comprised of essays which are all distinct and divided into categories, it is still possible enough to read it like a normal book from start to finish if you are a science enthusiast.

However, given the sheer variety of different topics, there are wide jumps of topics and some overlap of subject material between essays that might alienate a some readers. This was not too much of an issue for me, but I did find the lack of an overall thesis sort of strange, and this this forced me to read it in a different manner than for most books. For someone interested in a popular book on astrophysics that was originally intended as a book, I would highly recommend Michio Kaku’s Physics of the Impossible, which is more coherent and packs more punch than Death by Black Hole.

This is not to say that Death by Black Hole is without merit. It is one of the few books to explain not just the contents of scientific discoveries, but also the discovery process itself, which can oftentimes be more fascinating to learn about than the results. Neil deGrasse Tyson is one of the finest communicators of science in our time, and I always find his talks on YouTube fascinating. As an essay collection on science, Death by Black Hole is unmatched.

Why I Approve of Richard Dawkins’s “The God Delusion”

I have heard a variety of reports on this book, ranging from brilliant to demonic. As one who realizes the social and political importance of the secular movement in the years to come, I had to pick up The God Delusion by Richard Dawkins, to examine the book myself.

The-God-Delusion

This may be one of the most influential books to contemporary society. Contrary to my expectation, Dawkins’ overarching thesis is not a single argument or even a set of arguments against the existence of God (or gods). Though he does make many strongly supported biological arguments and includes many other types of arguments that have been echoed over the centuries, the main point, I could tell, was not to provide other atheists with arguments against the existence of God. A plethora of such arguments can be found on the Internet, at your local library, in your classroom, or even in the thoughts of your brain.

The Special Treatment of Religion

The real point, which makes this book stand out from others on atheism and religion, is the argument that, whether religion is right or wrong, we as a society need to change our special treatment of religion.

There is an undeserved respect of religion in our culture. In daily life it is considered perfectly okay to argue about our favorite sports teams, our differences of taste in food and music, and even our political beliefs. But the moment religion is brought up, it suddenly becomes “rude” or “offensive” to disagree with a believer or to even slightly question his or her beliefs. This, of course, is prime hypocrisy as many religions downright treat agnostics and atheists as subhuman or fools: “The fool hath said in his heart, ‘There is no God.'” (Psalm 14:1). Imagine the public outcry that would occur if, in some atheist meeting, the members called all religious believers “fools.” Yet when religious people call all atheists “fools,” it’s perfectly okay, because you got to respect their religious beliefs. I suppose when religious people call blacks or women inferior, you’re supposed to respect that too? Does the religiosity of a belief make it immune to criticism?

Dawkins argues that the discussion of religion, like any other topic, should not be taboo, and that when a religious person makes an absurd proclamation (all 3 examples in the last half-year), you have every right in the world to criticize it, and moreover you should be able to criticize it without ever having to worry about “offending” them or their religion or anyone else’s religion.

Christianity and Islam

While Dawkins primarily targets Christianity, since it is the dominant religion in Western culture, he also mentions the even more undeserved respect for Islam that arises simply because it is is a minority in places like the US and the UK. In response to a Danish newspaper in 2006 which satirized the Islamic prophet Muhammad, demonstrators burned Danish flags, trashed embassies and consulates, boycotted Danish products, physically threatened Westerners, burned Christian churches (with no Danish or European connections at all), and killed 9 at the Italian consulate in Benghazi. This series of events would be tragically repeated in 2012. From Dawkins, on the 2006 incident:

A bounty of $1 million was placed on the head of ‘the Danish cartoonist’ by a Pakistani imam – who was apparently unaware that there were twelve different Danish cartoonists, and almost certainly unaware that the three most offensive pictures had never appeared in Denmark at all (and, by the way, where was that million going to come from?). In Nigeria, Muslim protesters against the Danish cartoons burned down several Christian churches, and used machetes to attack and kill (black Nigerian) Christians in the streets. One Christian was put inside a rubber tyre, doused with petrol and set alight. Demonstrators were photographed in Britain bearing banners saying ‘Slay those who insult Islam’, ‘Butcher those who mock Islam’, ‘Europe you will pay: Demolition is on its way’ and, apparently without irony, ‘Behead those who say Islam is a violent religion’. Fortunately, our political leaders were on hand to remind us that Islam is a religion of peace and mercy. (p. 47-48)

Dawkins doesn’t explicitly say it, but I think the message is pretty clear. He sympathized with the Christians in the larger religious conflict. Similar sentiments are echoed by Sam Harris, who has stated, quite explicitly, that of these two Abrahamic religions, Christianity is the lesser of the two evils.

Again, the political refrain from criticizing the response of Islamic extremists demonstrates undeserving respect of religion in our society. Politicians, always fearful of losing their constituency, feel to afraid denounce such violence. As a result, we let it go on. Until we as a society allow ourselves to discuss religion openly, we will always be at the hands of its extremists who thrive on the inability of our leaders to take meaningful action.

Faith is Not a Virtue

Another undeserved respect we give to religion is accepting its dogma that faith is a virtue. Faith, by definition, is believing in something with insufficient evidence, and oftentimes in practice, it means believing in something without a shred of evidence. Dawkins argues that faith is in fact the opposite of virtuous:

…what is really pernicious is the practice of teaching children that faith itself is a virtue. Faith is an evil precisely because it requires no justification and brooks no argument. Teaching children that unquestioned faith is a virtue primes them—given certain other ingredients that are not too hard to come by—to grow up into potentially lethal weapons for future jihads or crusades. Immunized against fear by the promise of a martyr’s paradise, the authentic faith-head deserves a high place in the history of armaments, alongside the longbow, the warhorse, the tank and the cluster bomb. If children were taught to question and think through their beliefs, instead of being taught the superior virtue of faith without question, it is a good bet that there would be no suicide bombers. Suicide bombers do what they do because they really believe what they were taught in their religious schools: that duty to God exceeds all other priorities, and that martyrdom in his service will be rewarded in the gardens of Paradise. And they were taught that lesson not necessarily by extremist fanatics but by decent, gentile, mainstream religious instructors, who lined them up in their madrasas, sitting in rows, rhythmically nodding their innocent little heads up and down while they learned every word of the holy book like demented parrots. Faith can be very very dangerous, and deliberately to implant it into the vulnerable mind of an innocent child is a grievous wrong. (p. 347-348)

This is an important point to make. What can be more dangerous than people who have the capacity to do great harm, who have been taught that doing so is justified, but without the capacity to question their thoughts? What is more dangerous than one who destroys the lives of others while believing without question that they are doing the right thing? Intriguingly, Dawkins also brings up the fact that many extremists were not raised by extremists, but by well-meaning parents or perhaps even a well-meaning community, but whose individual determination went too far. This is an important point for “liberal” and “moderate” religious people to consider. It is the majority of otherwise non-fundamentalists that enable the extremists.

Group Selection

In addition to the social commentary, which to me is the most important point of this book, Dawkins uses his expertise as an evolutionary biologist to explain the origin and early persistence of religion in some of the middle chapters. The main thesis here is that evolution early on favored brains who would unquestioningly accept what their parents or their elders spoke. For instance, the child who obeyed “Don’t punch a sleeping bear” probably had a higher chance of survival than the one who didn’t obey. Hence, the unquestioning acceptance of dogmatic belief and passing on that dogmatic belief could actually be hardwired in our brains.

But, as Dawkins points out, it is not that simple. If an elder said “Don’t punch a sleeping bear, and every month we must sacrifice a goat,” a child is not able to process that one statement is sensible and the other is absurd, and hence accepts both of them. Since it works (or at least seems to work), the child later passes on the knowledge to his or her own children, and the cycle repeats. The useless monthly sacrificing of a goat is a freeloader that is passed on into the next society without helping it at all. This is not unlike how many useless DNA mutations arise in genetic drift.

Some religious ideas survive because they are compatible with other memes that are already numerous in the meme pool—as part of a memeplex. (p. 231)

After all, Richard Dawkins is the originator of the term “meme.”

Overall

Indeed, religion has been unjustly immune to criticism for far too long. Even by claiming that we should be allowed to openly discuss religion, Dawkins has been denounced as offensive to religious belief, when the unquestioning belief itself is what should offend a modern society. Many say that it is the extremists who are harmful and that most moderates don’t do any harm—and while this is true in that they don’t cause any damage directly, the religious moderates and even liberals comprise the enormous base of support who enable the extremists. When 46% of the United States, the most technologically and scientifically advanced country in the world, believes in creationism and 73% of our population is Christian, it is difficult to criticize the democratically elected Rep. Paul Broun’s statement that “All that stuff I was taught about evolution and embryology and the Big Bang Theory, all that is lies straight from the pit of Hell.” (This guy is a part of the congressional science advisory board.) Instead, many religious “moderates” and “liberals” don’t denounce Broun’s ideology at all, and merely state that he is too literally interpreting the Bible or something, as if they know how to interpret the Bible better than he does. They play this interpretation game instead of dealing with the actual problem, the religion itself, because in the end they are on the same side as Rep. Broun. Until we address this root cause, we cannot move forward as a society.

The God Delusion, published in 2006, is likely to be the most important book of its decade. This timing is especially crucial because the 2000’s is the same decade in which the Internet engulfed everything and people became closer together through social networks. With the increasing interconnections and intercultural frictions that have arisen, it more important than ever that we stand by reason and not by superstition, that we stand by tolerance and not by dogma, and that we stand by progress towards the future and not by ancient myths of the past.

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).

What I Learned from 2012, and My Topics for 2013

calendar

I’ve had a pretty busy start-of-the-year so far, and I plan to get into a regular posting schedule on this blog for 2013. Currently, the plan is one post every Sunday for the remainder of the year.

This decision was largely based on some past problems. Here are some issues I have identified with my blogging in the past, especially in the years 2011 and 2012.

Problems

  1. Lack of Schedule. I pretty much posted whenever, sometimes three times in a day, and other times not a single post for months. This is ultimately not a good way to attract regular readers.
  2. Incoherency. As I wrote in my reflection The Future of this Blog (2012), there is an issue with the sheer number of different topics. I have already partially solved this problem by making a dedicated math blog, so that on this current one, I do not have to worry about alienating those without an advanced math degree. However, my topics are still quite varied, and because of this, I feel that there is too much breadth and not enough depth.

Solutions

The one-post-every-Sunday rule gets rid of the first problem. The second problem is a bit more difficult, given that I had already tried to solve it, without much success.

board-meeting

So here is my new solution. I will write about the topics that I am most passionate about and those that I am strongest at writing about. After reviewing my blog history as well as my current interests, I have formulated a new list of topics.

1. Atheism and Religion

I have previously been quite passive about the subject of religion. But the more I read about and watch what happens in the world, the more I realize it is one of the biggest problems right now. The amount of intolerance and violence that is justified in the name of religion is astounding. And even when it is not explicitly invoked, it has caused, is causing, and will cause great detriment to scientific understanding and societal progress unless the discussion of religion is taken more seriously. Towards the end of last year, I started writing a few articles about atheism and religion. I hope to continue this discussion in 2013.

2. Writing

In the past, I used to write plenty about the writing process. Somewhere in 2011 I ended up just dropping the topic. I plan to pick it back up and perhaps make some writing advice posts.

3d blue Diagram with arrow

3. Productivity

Ever since I read Geoffrey Colvin’s excellent book Talent is Overrated, I have spent a lot of time thinking about productivity, as well as what I want to achieve with my life. Plus, I have written about productivity several times in the past.

4. College Life

Who is more qualified to talk about college life than an upperclassman college student? Just kidding about the qualification part. But I do think writing about college experiences can make college less of a mystery to the general community. And it might help convince you that I am an actual human and not some distant automaton on the internet.

5. Multi-Disciplinary Topics

I think one of my stronger skills right now is applying knowledge in one field to another. At least, I can do this on the internet. I played Diablo 3 last year, and was involved on the forums for some time. Using standard research skills, I wrote forum posts on how relevant ideas in probability, statistics, discrete mathematics, psychology, economics, history, and even sociology were responsible for many of the issues or situations in the game or player perception and responses to the game. These posts were all highly upvoted, linked many times and even reposted by other members of the community.

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6. Space: the Final Frontier

My interest in space goes back to first grade, when I first looked out at the skies through a telescope. Recently, some incredible discoveries were made, especially the statistical result that 17 BILLION stars in just the Milky Way have an Earth-sized planet! Moreover, the announcement of Mars colonization from MarsOne turned heads. I will be writing more space posts once MarsOne releases more details, for a human landing on Mars will be sure to provoke scientific curiosity around the world for years to come.

7. Mathematics

Fortunately, you are spared of math topics on this blog. Of course, I will be have them on my new math blog.

Final Remarks

If you have any reactions or topic suggestions, please leave a comment below.