Rating: 2/10

A really unexciting and uninteresting horror movie.

The Green Hornet (Jan 2011)

Rating: 7/10

Hilarious hero comedy, with several innovations and twists. Also contains one of the most ridiculous half-car scenes I’ve ever watched.

Just Go With It (Feb 2011)

Rating: 7/10

Clever and funny. It has a semi-predictable ending, but the ride is enjoyable.

The Adjustment Bureau (Mar 2011)

Rating: 5/10

Brilliant idea, bland execution. There was so much potential in the “adjustment” idea, but unfortunately, it was not fleshed out adequately.

Battle: Los Angeles (Mar 2011)

Rating: 3/10

A mindless war action film.

Limitless (Mar 2011)

Rating: 7/10

Similar to The Adjustment Bureau, this film presents an amazing idea, but then seems to back away from it. Again, the potential was great. The end result was still okay.

The Lincoln Lawyer (Mar 2011)

Rating: 5/10

Not terrible, but I’d rather just watch an episode of Law and Order to save time.

Sucker Punch (Mar 2011)

Rating: 7/10

By far the weirdest movie in this list. It seems to be one thing at first, but when you think about it, it turns into something else. This is great on action and philosophy; however, it is kinda gimmicky on plot.

Insidious (Apr 2011)

Rating: 8/10

A genuinely scary horror movie that had a very smart development. The ending is somewhat slapstick though.

Source Code (Apr 2011)

Rating: 7/10

A film that at least required some degree of thought. It has some interesting moral consequences.

Bridesmaids (May 2011)

Bridesmaids: 7/10

Not my type of movie, but still interesting.

Pirates of the Caribbean: On Stranger Tides (May 2011)

Rating: 7/10

Funny and action-packed, but lacking in creativity compared to the other Pirates films.

The Hangover: Part II (May 2011)

Rating: 7/10

Just as funny as the first one.

X-Men: First Class (June 2011)

Rating: 10/10

A very well-done movie. Nothing tops the scene where a submarine is lifted out of the ocean.

Bad Teacher (June 2011)

Rating: 7/10

A very funny movie.

Rise of the Planet of the Apes (Aug 2011)

Rating: 8/10

Science and morality are questioned in every step of this chimp’s adventure.

Contagion (Sept 2011)

Rating: 8/10

One of the better outbreak-style films.

Mission Impossible: Ghost Protocol (Dec 2011)

Rating: 9/10

An epic action thriller.

The Girl with the Dragon Tattoo (Dec 2011)

Rating: 7/10

Still not sure what to think.

Sure, you won’t mind it most of the time. In fact, you might feel a bit good that online piracy is reduced, to a small degree. But when your most-used websites start disappearing,  and you have nowhere to turn, what will you do then?

Google on SOPA: https://www.google.com/landing/takeaction/

Onto a couple statistics. Last November it had 221k views, and it’s at around 320k right now. Thus in the past year, the blog received approximately 99,000 views.

The most popular pages in Year 2 were:

1. US Census 2010 Win (again) — 10,917 views
2. The Map of Facebook Connections — 9,274 views
3. Tumblr vs WordPress: Simplicity vs Power — 8,005 views
4. Free Will: How We Do and Do Not Have It — 6,134 views
5. List of Banned Words Constitutes a “Fail” — 5,040 views

This is a much more consistent distribution than last year, when the 1st had over 85k views, and 2nd-5th were all under 5,000. I suppose the law of large numbers is at work.

I suppose 99,000 hits isn’t bad considering I only wrote 94 posts. And these particular numbers are actually quite mathematically intriguing:

• Year 1: 221k hits in 212 posts = average of 1042 views per post
• Year 2: 99k hits in 94 posts = average of 1053 views per post

So even though I went for nearly four months without blogging, I somehow managed to achieve an almost identical views per post ratio as last year. This could very well be pure luck, but I find it interesting.

The second topic for this post is that I am doing Nanowrimo again this year, though I did not decide to start until Nov. 3, and I spent the next few days figuring out the plot and characters instead of actually writing. For those of you who don’t know, NaNoWriMo stands for “National Novel Writing Month,” and the goal is, in the month of November, to write 50,000 words in 30 days.

Last year, I kept careful track of my writing stats. By the end of Nov. 10 of last year, I was at 23,412 words. This year, I’m currently at… 5387. I guess that’s what I get for starting to write nearly 6 days late. Nonetheless, I am trying some things differently this year. I am not going to keep careful track of stats, as I feel like it was very inaccurate for smaller periods of time, where I might spend seven minutes thinking and three minutes writing. Instead, I will just look at the final word count on each day, which the NaNo website conveniently tracks.

Not sure how to describe the plot just yet. I think I need to up the word count a little before talking about it.

1. Euler’s Identity

A very famous equation, Euler’s identity relates the seemingly random values of pi, e, and the square root of -1. It is considered by many to be the most beautiful equation in mathematics.

A more general formula is

When , the value of is -1, while is 0, resulting in Euler’s identity, as -1 + 1 = 0.

2. The Euler Product Formula

The symbol on the left is an infinite sum, while the one on the right is an infinite product. Theorized by Leonhard Euler once again, this equation relates the natural numbers (n = 1, 2, 3, 4, 5, etc.) on the left side to the prime numbers (p = 2, 3, 5, 7, 11, etc.) on the right side. Moreover, we can choose s to be any number greater than 1, and the equation is true.

The left side is the common representation of the Riemann zeta function.

3. The Gaussian Integral

The function in itself is a very ugly function to integrate, but when done across the entire real line, i.e. from minus infinity to infinity, it gives a bizarrely clean answer. It is certainly not obvious at first glance that the area under the curve is the square root of pi.

This formula is of extreme importance in statistics, as it represents the normal distribution.

4. The Cardinality of the Continuum

This states that the cardinality of the real numbers is equal to the cardinality of all subsets of natural numbers. This was shown by Georg Cantor, the founder of set theory. It is remarkable in that it states a continuum is not countable, as .

A related statement is the Continuum Hypothesis, which states there is no cardinality between and . Interestingly, this statement has a very strange property: it can be neither proved nor disproved.

5. The Analytic Continuation of the Factorial

The factorial function is commonly defined as n! = n(n-1)(n-2)…1, but this definition only “works” for positive integers. The integral equation makes factorial work for fractions and decimals as well. And negative numbers, and complex numbers…

The same integral for n-1 is defined as the gamma function.

6. The Pythagorean Theorem

Probably the most familiar equation on this list, the Pythagorean theorem relates the sides of a right triangle, where a and b are the lengths of the legs and c is the length of the hypotenuse. It also relates triangles to squares.

7. The Explicit Formula for the Fibonacci Sequence

where (note that this number is the Golden Ratio). While many people are familiar with the Fibonacci sequence (0, 1, 1, 2, 3, 5, 8, 13, 21, etc., where each number is the sum of the previous two numbers), few know there is a formula to figure out any given Fibonacci number: the formula that we have above, where F(n) is the nth Fibonacci number.

Remarkably, even with all the square roots and divisions, the answer will always be an exact positive integer.

8. The Basel Problem

This equation says that if you take the reciprocal of all the square numbers, and then add them all together, you get pi squared over six. This was proved by Euler. Notice that this sum is just the function on the left hand side of Equation 2 (the Euler product formula) earlier in this post, with s = 2. That formula is the Riemann zeta function, we can say that zeta of 2 is pi squared over six.

9. The Harmonic Series

This is somewhat unintuitive, because it says that if you add a bunch of numbers that keep getting smaller (and eventually become zero), they still reach infinity. Yet if you square all the numbers, it doesn’t add up to zero (it adds up to pi squared over six). The harmonic series, if you look carefully, is actually just zeta of 1.

10. The Explicit Formula for the Prime Counting Function

where is defined as

Here is the significance of this equation, in English:

Prime numbers are numbers that have no divisors other than 1 and themselves. The primes below 100 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97. From this, it is already clear that there is no apparent pattern to the primes: in some runs of numbers you will get a lot of primes, in other runs you will find no primes, and whether a run has a lot of primes or no primes seems to be totally at random.

For a very long time, mathematicians have been trying to find a pattern to the prime numbers. The equation above is an explicit function for the number of primes less than or equal to a given number.

Here are what all the letters mean:

•  — the prime counting function, which gives the number of primes less than or equal to a given number. For example, , as there are 6 prime numbers (2, 3, 5, 7, 11, 13) less than or equal to 13.
• — the Möbius function, which gives 0, -1, or 1 depending on the prime factorization of n.
• — the logarithmic integral function (not related to my last name), which is the integral of 1/(log t) up to x.
• — any of the nontrivial zeros of the Riemann zeta function.

Amazingly enough, this function will always give an exact integer! This means that, given any number, we can plug the number into this equation and obtain the number of primes less than or equal to that number. The fact that this equation exists means there is some pattern to the primes, though it may still be too early for us to understand.

1. It is NOT necessary to calculate several moves ahead.

Perhaps the most common misconception about chess is that a player needs to think 3, 4, 6, or even more moves ahead to win.

In reality, for the vast majority of moves, thinking even one move ahead is sufficient. Once you play enough games, you develop an intuition that will guide you as to which pieces to move, when to move them, and where. For example, I’ve played dozens of games that opened with the Sicilian Dragon, quite a few of them in rated tournaments. When I play a new game that opens with the Dragon, I instinctively know which strategies work and which ones don’t, and my thinking time is spent on figuring out the differences and trying to exploit them. That is, I can think about refining a strategy instead of inventing one. This saves a lot of time.

Sometimes, however, you will need to calculate an exorbitant number of moves ahead. I recall a game in the 2006 National Open that ended up in a rook and pawn endgame.  On the last move of the game, I thought for perhaps 40 minutes, calculating no fewer than 10 moves ahead. When I played that move, my opponent thought for an entire hour and then resigned. What made the position so complicated? Here’s what was going through my mind: pawns dangerously close to queening, rook and pawn checks, queen checks after 2 pawns queening, mating nets, as well as king positioning. This is an extreme exception though, and most of the time I don’t calculate over two moves ahead.

2. A balance between intuition and calculation is important.

As I mentioned above, intuition plays an enormous role in chess. With it, you feel like you “know” what to do. Should I attack the queenside or the kingside? Or should I try to break open the center? Should I trade a bishop for a knight? Should I push the g-pawn or the h-pawn to start the attack? Instead of calculating such things from scratch, you can often use intuition to develop a preliminary answer, and then use calculation to confirm or deny your hunch. This is incredibly useful in a tournament setting, where your clock is ticking.

One can go the other extreme and rely too much on intuition, or rather, too much on generalizations. At some point in a game, I was winning by a knight for a pawn, a pretty huge material advantage, but had slightly less board space than my opponent did. A third-party was watching the game, and told us that he thought my opponent was winning because he had more space.

I disagreed with the third-party because, based on the current board position, the space advantage did not make up for the material deficiency. In fact, I thought it did not even compensate a loss of one pawn, let alone two pawns (the equivalent of a knight for a pawn).

3. You don’t have to calculate every possible move.

This is why humans were able to beat even the best of computers for so long. We lasted until 1996. Even though computers could calculate orders of magnitude faster than the human brain at that time, and even before, they did not do the calculations in as smart a manner. For instance, say we are in some position in the middle-game, and that I have 20 legal moves, to each of which my opponent has 20 replies. Then to calculate just one move ahead, I would have to look at 400 positions to fully cover every scenario. (In chess lingo, a “move” consists of one move by white and one move by black.) To calculate two moves ahead, it would be 400², or 160,000 positions. For a human to do this, even analyzing one position per second, it would take several hours to compute. Now suppose you want to calculate 10 moves ahead: 400^10. This is roughly 10^26 positions to analyze. Even a computer analyzing these at a billion (10^9) positions per second would require 10^19 seconds, or 300,000,000 years. It would be impossible for a human.

So how is it possible that a human can calculate 10 or more moves ahead? Well, we (unconsciously) use a technique called pruning, or ignoring certain moves. For instance, out of the original 20 moves, only 3 of them look interesting at all, and the other 17 seem either accomplish nothing or are silly moves that lose material immediately. For a full “move,” this would be 9 positions, and calculating 10 moves ahead would give 9^10 = 3.5 billion positions. This is much more reasonable, but is still an extravagant amount. What happens in real calculation is that many moves are forced, in which there is only one response. Other times, one or two of the three interesting moves degenerates into a clear position at which you can stop calculating. Thus in calculating 10 moves ahead, it is possible that you may only need to look at 15 final positions, which is much less than 3.5 billion or 10^26.

The reason computers are beating humans now isn’t because the computers think faster—it’s because they think smarter. If it can prune 20 moves into 3, then it might only need to calculate 3.5 billion positions to think 10 moves ahead. And at a billion positions per second, this would only take 3.5 seconds.

Conclusion

There were also some occasions where I played blitz chess (speed chess) and blind chess, though not concurrently. Speed chess is normal chess with strict time restrictions. This effectively limits the number of moves ahead you can calculate. It emphasizes speed over accuracy of calculation. This is also where experienced players perform really well, as intuition reduces the time spent dramatically. This is why in speed chess it can appear that the players are playing instantly and not thinking. They actually are thinking, but just in a different way.

Blind chess is also the same as normal chess, only you are not allowed to look at the board. You have to call out what move you want to make, and your opponent calls out the response, etc. The trick is about making sure you know where all your pieces are. The easiest way to do this is to keep a mental image of the board in your head, and memorize all the moves that occurred in the game. That way, if you are ever unsure of where a piece is supposed to be, you can play through the previous moves to track that piece’s location.

Overall, I treat normal chess, blitz chess, and blind chess as the same game; only a few changes in the thinking process are needed. So in response to the question “How many moves ahead do you calculate?”, my answer is one or two moves usually, more if necessary. How many moves ahead do YOU calculate?

Today (or rather, yesterday, since I am passing the midnight mark as I am typing this) was one of those days: it was the day of the Cornell homecoming game, and I suppose attending a sports event was something I had not done for over half a year. But besides that, the intriguing part happened when a fellow trumpet player and I left a bit after half time, only to find the band room locked on all exits.

For the next part, I will let other people remain anonymous, though I doubt the Cornell police are reading this. And if you are, you need not be alarmed as there was neither criminal intent nor damage done.

The person with me is quite good at knowing how things work, so he naturally assembles a makeshift lock-picking set from some handy materials. This includes a trumpet lyre, a Cornell Homecoming pin button, and an iPhone. The iPhone was used solely as a flashlight (this was at nearly 9 pm), the lyre was used as a “torsion wrench,” and the pin from the pin button was used as a pick, i.e. the thing that any lock-picker in a movie uses to poke into the keyhole.

After perhaps 15 minutes of attempts, it is clear that the lock is too sophisticated. He mentions how he could only set the first “tumbler” in place but that the lock had five tumblers. Heck, I didn’t even know those things in locks were called tumblers.

While this was going on, I reflected on the nature of problem solving, and realized that the problems I solve in classes, whether they be physics questions that assume surfaces are frictionless, or math questions that deal with uncountably infinite sets—I realized that such problems didn’t help the slightest bit when I faced this real world problem of a locked door. Even the highest levels of theoretical math and physics wouldn’t help now.

I even joked at how, if this were some action movie, one of us could climb through the ventilation system and pop down inside the room and open it from the inside. Unfortunately, it is an old building and there is not a ventilation shaft to fit into.

That physical locked door in front of me was the ironic manifestation of the hypothetical locked door. Neither my friend nor I had the key. And without the key, there was no getting past it.

I exit the building temporarily to go to the Statler, and on my way out, I see some other familiar band people coming in. I tell them we tried to lock pick the door, and continue walking. When I came back a few minutes later, a remarkable thing had occurred: the door was open! My friend and the other band people were inside, and yet none of us had a key.

It turns out that one of the people I ran into on my way to Statler had done the impossible: he climbed through a ridiculously small opening in the top corner of the room where some utility pipes passed through, and successfully landed and opened the door from the inside. Of course, in the room where we spend so long lock-picking, there just happened to be a ladder.

It’s been a nice semester so far. The weather is so much better than in Austin, where temperatures are still surpassing 100°, and it feels great not being a freshman—I actually know where things are!  Classes I’m taking:

• Math 4130 (Honors Introduction to Analysis I): Mostly review so far. It’s only been a week, I’m pretty sure it will get harder as the semester goes on. But I definitely think Math 2230/2240 are great preparation.
• Phys 1116 (Mechanics and Special Relativity): Also mostly review.
• Gerst 1210 (Exploring German Contexts I): Intense immersion learning. I feel like I’ve learned more German in the past week than I learned in my first month of Spanish in middle school. This makes perfect sense, since college is quite a step up from middle school.
• Econ 3010 (Microeconomics): We’re covering some of the underlying theory of economics, which is intrinsically heavy on math. Particularly, a lot of what I learned in Math 2230 last year is coming into use. Having independently studied some game theory over the summer, I found this introduction very interesting; things are clicking already.
• CS 2110 (Data Structures and Object-Oriented Programming): Almost all review. In yesterday’s section we covered linked lists, which seemed to baffle at least half the group. The 25-hour assignment due next week does not look fun though.

Of course, I am also in the band, which has started up. Once again I am impressed by the speed at which it learns the show. Everyone seems ready for performance after a mere one rehearsal.

My residence for this year is 14 South Avenue, which is on the southwest corner of campus. This is a total change from last year, when I was on the northeast side of campus. The change of perspective is certainly nice.

Here is my schedule from Schedulizer:

“You are guilty of being innocent of being Jack Sparrow.” Really?

An entertaining successor to the first three films in the Pirates series, On Stranger Tides makes up in comical brilliance and swashbuckling action for what it lacks in ingenuity.

Seriously—the creativity all but evaporated half an hour into the movie. Or perhaps, as an avid fan of the Pirates series, I had unrealistically high expectations. Whichever the reason, the plot of this film is a huge disappointment.

The introduction is great. We see a hilarious court scene and then Jack Sparrow fooling around with the king. The part leading up to Jack’s duel with Angelica is pretty interesting too. But once Jack is seaborne, the movie turns very unoriginal:

• Jack is searching for the Fountain of Youth, and later finds out that he must also find two chalices. He searched for the “dead man’s chest,” among other things, in earlier films.
• Blackbeard’s foretold death from a one-legged man, his power to magically control the Queen Anne’s Revenge, as well as other supernatural events in the movie. The first three films were full of the supernatural.
• They must secure a mermaid and keep her captive for a certain ritual. In At World’s End, they similarly held Calypso. And of course, in Curse of the Black Pearl, Elizabeth Swann is kept captive for a ritual.

In addition, this film did not see the return Will and Elizabeth, two major characters in the earlier films.

That said, there were many impressive positive features of On Stranger Tides. For one, the music was outstanding, combining the epic original theme with a fitting Spanish atmosphere.

Also, the actors Johnny Depp (Jack) and Geoffrey Rush (Barbossa) performed superbly. When you watch them for just five seconds, you know they’re pirates. The portrayal of Blackbeard and Angelica is convincing too, but they were clearly not veteran pirates.

And then there’s humor. The best part of the movie is Jack Sparrow’s remark about jumping off a cliff: “You know that feeling you get when you’re standing in a high place… sudden urge to jump?… I don’t have it.” Granted, I saw this quote in the trailer, but it’s just so perfect.

Rating: 7/10

The reason is, I’ve sorta been avoiding technology this summer. I set my personal record for number of consecutive days without Facebook, and also a record for number of days without blogging.

On the other hand, I’ve used StumbleUpon much more and following certain sites more consistently. So it’s probably a lie that I’ve avoided technology—I’ve just been avoiding certain parts of technology. More reading and less writing.

Now that I’m back at college, I feel more compelled to write, like last year. I’ll probably start with some of the movies I watched this summer, and move on from there.