Encountering Infinity Twice in a Row

My last few posts have been on life at Cornell, and this one is really not much different. I typically blog about other topics, but this school, this place is so interesting! Anyway, what I cover in this post are two of my classes, Math 2230 and Comp-Sci 1610 (both of which I took two days ago, one right after the other), and how we looked at the idea of infinity in each of them.

Induction

Math 2230 is Theoretical Linear Algebra and Calculus, which covers linear algebra and multivariable calculus. The reason it is theoretical is that the class is very based on theorems and proofs rather than real-world applications. In contrast, Math 1920 is Multivariable Calculus for Engineers. As a math major, I’m in the liberal arts college and not the engineering college, so I get to take 2230.

Anyway, the very first thing we cover is induction. That is, inductive proofs. It is an amazing form of proof because, in just two steps, you can prove that some proposition applies for an infinite number of cases—and often, for all cases.

Essentially, you imagine an infinite chain of dominoes but with a starting domino. If you can show that for any given domino, if it can be knocked over, the next one will also be knocked over, then you have shown that all of them can be knocked over (!). Well, there’s one catch. You have to also prove that some initial domino can be knocked over, usually the first one. Those are the two steps.

It is usually done the other way around. Say I wanted to prove the proposition that 2^n < n! for natural numbers n \geq 4. Let’s plug in a random number to check, say 5. In this case, we have 2^5 = 32 on the left-hand side and 5! = 120 on the right, and 32 is clearly smaller than 120, so the proposition is true. Now suppose n is 10. We then have 2^{10} = 1024 on the left-hand side and 10! = 3628800 on the right, which seems to support the proposition even more. As n goes up, n! is much more than 2^n.

But how do we prove this for all integers of at least 4? Well, we should show that the first domino can be knocked over, i.e., that the proposition is true for n = 4. A quick check gives 16 < 24, so the proposition is true. Now we just need to show that if the proposition is true for a given number k, then it must also be true for k + 1. This requires what seems at first to be a leap of faith. We must assume the proposition is true for k, no questions asked. The proof still makes logical sense, but this part is somewhat unsettling at first.

In this case, we assume that for an arbitrary number k \geq 4, we have 2^k < k!. The next step is to show that this assumption implies 2^{k+1} < (k + 1)!. It’s easier than it seems. It’s because you can rewrite this as 2^k \cdot 2 < k! (k + 1). We certainly know that if we compare the left term of both sides, we will find that the left-hand side is smaller: by assumption, 2^k must be less than k!. It turns out that if we compare the other term, we also find that the left-hand side is smaller: 2 < k + 1, because k must be at least 4. So we’re comparing the product of two smaller numbers against the product of two larger numbers—of course the product of two larger numbers is greater. This shows that 2^{k+1} < (k + 1)!. And it in turn proves that the proposition is true for all n \geq 4.

The domino analogy, in full:

Domino The example
The first domino can be knocked over. The proposition is true for the first relevant value (n = 4).
If any domino is knocked over, the next one will also be knocked over. If the proposition is true for any value k, it is also true for k + 1.
Therefore, all of the dominoes can be knocked over. Therefore, the proposition is true for all n \geq 4.

It’s the conclusion, the third step, that ties induction to infinity. If the proposition is true for 4, it must also be true for 5, which means it must be true for 6, etc. The key is that the positive integers are arranged in order, so we don’t leave out any relevant integers by continuing 4, 5, 6, etc.

Cardinality

Comp-Sci 1610 is Computing in the Arts, and is cross-listed as computer and information science, engineering, music, film, dance, and psychology. If, by any chance, you know what I refer to by “cardinality,” you’re probably wondering, how is THAT related to any of these subjects? Well, it’s not quite related. But the professor spent at least half an hour on this, including the proofs, so I’ll include it here.

Cardinality refers to the size of a set, that is, how many things are in it. The cardinality of “the set of people living in the United States” is a bit over 300 million. What about the set of natural numbers (1, 2, 3, 4, etc.)? It’s infinity. And the set of real numbers (0.25282859…, pi, 32.33…)? Also infinity. But are these two infinities the same? It turns out they aren’t, because if they were, cardinality would become infinitely less interesting.

Actually, it is due to a lack of one-to-one correspondence. If the two sets (the set of natural numbers and the set of real numbers) were the same size, then there would be some way to match each natural number with a real number and vice versa, and not have any of either number left over. Cantor proved this was impossible.

The proof is by contradiction. He first assumed that the natural numbers could be put in one-to-one correspondence, and then showed that in that situation a paradox occurs, so the assumption must be false.

He basically created a hypothetical list of correspondence between the natural numbers and real numbers between 0 and 1. This is because if there are more real numbers in just the 0-1 interval than the entire set of natural numbers, obviously the entire set of real numbers must also be larger.

1 \leftrightarrow 0.\mathbf{1}234567891011...

2 \leftrightarrow 0.9\mathbf{3}71263636363...

3 \leftrightarrow 0.32\mathbf{7}5218383734...

etc.

Cantor essentially conjures another real number that cannot be in this list. He does this by creating a number that differs by each real number in the list in at least one digit. Note the bolded digits above. We simply add 5 (or subtract 5, as to not go over 9) to each bolded digit, and create a new number out of the modified digits. So the new number’s first digit is 6 (1 + 5), second digit is 8 (3 + 5), and third digit is 2 (7 – 5). Obviously this new number cannot be the first number in the list, because it’s wrong on the first digit. Likewise, it can’t be the second number, because it differs on the second digit. This continues on infinitely. Hence, it is impossible to put the natural numbers and the real numbers in a one-to-one correspondence—there are more real numbers than there are natural numbers.

But that’s obvious, you say. Between 0 and 1, inclusive, there are only two natural numbers and an infinite number of real numbers, so there must be more real numbers.

This is true, but is not the case, however, with rational numbers, i.e., fractions. Even though between 0 and 1 there are an infinite number of fractions (1/2, 1/3, 1/4, 5/8, etc.), it can be proved that the cardinalities of the set of natural numbers and the set of rational numbers are the same, because you can list the rational numbers in order.

Essentially, a rational number is just the ratio of two integers, so you can think of it as a point on a graph, with the x-coordinate being the numerator and the y-coordinate being the denominator. Now it is possible to start at (0, 0) and spiral your way around, touching every integer coordinate.

Spiral GraphEach arrow can have a unique natural number associated with it, the first arrow being 1, the second being 2, etc. And since each natural number corresponds to an arrow, which corresponds to a coordinate, which corresponds to a rational number, we have shown that there is a one-to-one correspondence between the natural numbers and the rational numbers. So the natural numbers have the same cardinality as the rational numbers.

This also means, if you take into account the previous result, that there are more real numbers than there are rational numbers.

Still, this does not answer the question of how this is related to computer science, or psychology, or music, or film. Well, it wasn’t really that related—the professor just went on a tangent. Anyway this has been an interesting introduction to math at Cornell!*

*(I had already learned both induction and a bit on cardinalities, enough to know that the naturals and the rationals have the same size, less than that of the reals. It was fun anyways. Especially seeing the artists/liberal arts people in the second class squirm at Cantor’s diagonal proof.)

Cornell Class of 2014 Orientation

Again, I don’t feel like writing this in any order, so following is a bulleted list:

  • Only at Cornell, it seems, could a 3000-person Rock-Paper-Scissors tournament start and finish within 15 minutes. (And none of the 3000 knew about the tournament beforehand.) The grand prize for winning 12 games in a row was… Cornell bottled water. One bottle.
  • 3000 people gathered around playing RPS is a LOT of people. And that’s just the freshman class. Add in the upper classes and the graduate students, and you get around 20,000 students.
  • Ithaca is GORGES.
  • Cornell’s campus is huge. Texas-style.
  • Mews Hall (dorm where I’m staying) is super-awesome.
  • The Big Red Band (Cornell’s band program, especially the marching band) did the most comprehensive and impressive sidewalk chalking I have ever seen. There were basically arrows and words drawn everywhere. They had some especially funny ones:
    • “BAND” with forward arrow.
    • another “BAND” with forward arrow.
    • quite a few more of those.
    • “YOU MISSED IT // TURN AROUND” with a U-turn arrow once you pass it.
    • “BOTH PATHS // LEAD TO BAND” with a forward arrow and side arrow at an intersection, because the band building was on the opposite corner.
    • “(the most efficient route)” on a diagonal arrow between the two arrows described before.
    • “SUBLIMINAL MESSAGE: // JOIN BAND” all in huge letters.
    • “SEX // NOW THAT I GOT // YOUR ATTENTION // JOIN BAND” with “SEX” in particular large letters.
  • Orientation games don’t seem to help very much in remembering names or knowing people. Then again, they’re quite fun.
  • The food certainly is great.
  • Cornell’s motto is the Big Red. Technically it’s the Big Red Bear, but they have Big Red everything. The store sells things in Big Red Bags, the marching band is the Big Red Marching band, and some Cornell engineers who worked with Spirit and Opportunity insist on calling Mars the Big Red Planet.
  • There’s a freaking waterfall. Yeah, a waterfall. (Which is gorges by the way.) Edit: There are multiple.
  • So far it’s only day two of a 5-day orientation. More interesting news coming next time.

Edit (8/24/10): Well, orientation is just about done! It’s been awesome getting used to the place. The last two days though, it has been very rainy and not as scenic. Today it was a little better. Classes will start tomorrow. A few additional things:

  • I had to wear a jacket in August. That’s certainly one difference from Austin.
  • The band is so epic.
    • After a first rehearsal, we went to Collegetown and sang some really bizarre songs. One of them amounted to saying “Penn sucks” about 30 times, and another questioned the sexual nature of Yale people. Profanity was pretty much a requirement for a song.
    • If you think that was bad, imagine how the trumpet section made it even more awesome.
      • Actually, I suggest you don’t imagine that.
    • The Cornell trumpet section owns the website www.trumpets.org.
    • Regarding marching, the time required to cover fundamentals, forward/backward marching, slides, dress/cover, box drill, and spin maneuvers at my high school was 3 days of strenuous band camp. At Cornell it took 15 minutes. (Actually it took much longer for most sections, but the trumpet section did it in 15 minutes.)
  • An umbrella is a must-have accessory. It rained on and off for two days.

Cortlandville, NY and How I Got There

Last time I said my next post would be coming from Ithaca, NY. I’m afraid that’s not going to be true, for I am blogging right now from Cortlandville, NY, an even smaller town than Ithaca. It turns out all the hotels in Ithaca are booked up due to the influx of students, so we’re staying about 20 miles away in Cortlandville.

Anyways, the last 24 hours or so have been somewhat hectic. Back in Austin, around 11 pm, I was trying to print something that just didn’t print. After restarting the computer and printer several times, still nothing happened. I ended up using another laptop (which was already packed, but had to be unpacked) to print it successfully. This wasted an hour.

From midnight to 1 am, I couldn’t really sleep. I reminisced over Austin and the people I have met, and would not see again for some months, or at all. This ended with me pulling out the Westwood yearbook and looking through the all signatures one last time before departing. Of course that didn’t cover all of you, but I was finally able to sleep.

Wake up at 4 am. Say some goodbyes to my room and our house, and leave for the Austin airport at 5 am. The plane left at 7 am. By the way, the route was Austin to Charlotte to New York (La Guardia) to Ithaca. That was easily explainable: Charlotte is a hub for United Airways, and Ithaca is, well, in the middle of nowhere, so only a few regional flights could connect to it.

Austin to Charlotte in itself was very nostalgic. Before Austin, we lived in Greenville, SC, and it the first time since September 2000 that I had stepped foot in one of the Carolinas, even if it was only an airport.

And also, my seat neighbor on the flight happened to be a Dartmouth graduate who had studied physics, math, and compsci. Guess what I listed for my top 3 choices for major on the CommonApp? Yep: physics, math, and compsci, though with math and compsci before physics.

It was actually somewhat awkward, because we didn’t start talking until halfway through the flight. She and I were both kind of napping the first half. Anyway, there was a flight attendant fail moment during landing, when electronic devices are to be shut off. The Dartmouth girl had a Kindle, and when a flight attendant came over to us, she told her to shut down the Kindle. The catch was, the Kindle was already shut off. The screen just displays text regardless.

We didn’t have much time in Charlotte, so we just moved on to the next flight, to New York La Guardia. That trip wasn’t as interesting, other than that there was a Princeton graduate sitting next to me. Jeez, why do I have to be put next to Ivy graduates?

(By the way, the Princeton guy snored while he was napping.)

But it gets better. It was the third flight, New York to Ithaca, that was the most surprising. My neighbor appeared at first to be just an old lady, but she revealed herself to be the mother-in-law of the Dean of the College of Arts and Sciences at Cornell. Out of the seven undergraduate colleges at Cornell, that’s the one I’m going to. And I get to hear this dean speak in a few days at Convocation.

We had a really interesting conversation. The flight had a scheduled boarding time of 5 pm and a departure of 5:30 pm. Due to delay, we boarded at 5:45 pm. She told me that United Airways fails like this a lot when going to Ithaca. At about 6 pm, they suddenly come in and say that one person needs to leave this plane and board the next plane, at 9:59 pm, due to weight restrictions. They offer a $200 stipend.

One man makes a bold self-sacrifice, but a few minutes later, the gods are still unsatisfied, and demand additional tribute. After about 10 minutes of asking and getting no response, the flight attendant threatens that this plane can’t go anywhere until someone leaves. Finally, two women make the ultimate sacrifice, and leave the plane.

It is about 6:10 pm. The plane starts moving, and after maneuvering the runway for a while, it STOPS. No problem, we’re just waiting for a few planes in front of us to go, right?

At 6:40 pm, with the plane still on the ground, the pilot announces that it is “rush hour” for aircraft traffic and that when we entered the queue, we were 25th. Wait, what? TWENTY-FIFTH. Jeez, so we had to wait for 24 planes to depart ahead of us. In this same announcement, the pilot assures us that since then, most of the planes have left, and that we are in the top ten, and that it would take at most another 10 minutes.

At 7 pm, the plane finally leaves the ground, a full hour-and-a-half after scheduled time. In the meantime, the old lady and I (actually, it was mainly her) were bashing United Airways. Oh yeah, it was also a propeller plane, not a jet.

The pilot announces that the estimated flight time was 42 minutes. Haha.

At about 7:45 pm, we land in Ithaca. The airport is rather small. It’s a brick building with two terminals. Yes, two entire terminals.

We get our rental car and drive to this Ramada hotel in Cortlandville, where I wrote this post. The drive was fairly uneventful, and it turned dark very fast, so I can’t yet comment about the scenery. But I will say, there are a lot of trees!

Tomorrow (or rather, today, given that it is already early morning), we will be visiting Ithaca and the Cornell campus, one day prior to Orientation. I’ll keep ya posted!

Off to Ithaca

As I am leaving for college, I originally intended this post to be a reminiscence of and a goodbye to Austin, but when I tried to write it, the words would not easily come out. Therefore, this is not solely a farewell to Austin, but an anticipation of where I’m heading next.

Austin has been my home for 10 years, almost exactly. We moved here from Greenville, South Carolina in September 2000, and it is now late August 2010.

Even though I wasn’t born in Austin, I consider Austin to be my primary hometown. Besides relatives, nearly all the people I know I have met in Austin. I was too young to remember people from Greenville or earlier places.

I also received most of my primary and secondary education here in Austin, from third grade straight through twelfth. I attended Forest North Elementary School, Laurel Mountain Elementary School, Canyon Vista Middle School, and Westwood High School (’10).

And I almost continued this with University of Texas (’14):

UT TowerYet, I chose Cornell University instead. I have nothing against UT. In fact, logically I should have gone with UT, for it was a little bit cheaper, and I was in two honors programs (Dean’s Scholars and Plan II) to boot.

But for me, it lacked only one thing: fresh air. Don’t get me wrong—Austin is one of the cleanest cities in the nation, and is reputed one of the best places to live. What I mean by “fresh air” is, I have lived in Austin for 10 years, and it was time for a change. Between familiarity and uncertainty, I had to choose the latter:

Cornell TowerIt was certainly not an easy choice. Since most of the people I know are in Austin, I would miss them all. Furthermore, no one else from my high school class is going to Cornell (though I do know a couple of people in a different grade). And from my high school, a million (okay, more like at least 50) people in my class are going to UT. So those are the numbers. And, oh yeah: Winter? Snow? What’s that? 😀

We’re flying tomorrow morning. Today is my last day in Austin. I feel like I have a lot more things to say, but I don’t know what order, so I’ll just make a list:

  • I’m going to miss all those “Keep Austin Weird” bumper stickers.
  • An online shoutout to the Westwood Class of ’10!
  • And to the Cornell Class of ’14!
  • I am moving from a liberal city to an apparently even more liberal town.
  • Ithaca, at 7.92%, has the highest percentage of residents holding Ph.D.s in America. [Source: Forbes on MSNBC]
  • Perhaps Austin and Ithaca won’t be too different. Who knows?
  • I still have some final packing to do, and my room is nowhere near clean.
  • We’ve said so many goodbyes in the last few days as we’re going off to college. I would love nothing better than to say goodbye to all my friends in person, but that is obviously impossible. To all those whom I didn’t catch in person: Goodbye! And to those whom I did: Goodbye again!
  • Even this morning, the UT McCombs School of Business entrepreneur-in-residence Gary Hoover commented on this blog out of the blue, and gave me a goodbye present. That was very pleasant, thank you.
  • This blog WILL continue to be updated as I become a college student.
  • Cleaning out my room and finding old things is creating a lot of nostalgia. Right now there are about 253 things on the floor, so I’d best get back to cleaning. My next post shall come from Ithaca. 🙂

Starcraft II: Wings of Liberty

StarCraft II

Starcraft II: Wings of Liberty is a real-time strategy game and yet another impressive gem from Blizzard.

Overview

This post is a review in all but the usual sense. I’m not here to assign the game a number from 1 to 10 (though if I were, it would be very high); instead, I am going for a “review” in a more academic sense—a study of the game.

Which means I’m not trying to praise or condemn the game, but rather, to gain an almost artistic appreciation for it, like I would of a film or book.

Gameplay Background

The real-time strategy genre is a type of chess where you can move all your pieces at once and you don’t take turns. What the original Starcraft (1998) did was create totally different factions. Instead of each side’s army consisting of a king, a queen, two rooks, two bishops, two knights, and eight pawns, one side could have four pieces that moved like knights and pawns, another two like rooks with limited range, two more like bishops that could jump over pieces, and a piece that could teleport to another unoccupied square within two rows, but only once every three turns.

Call the standard 16-piece setup A, and this new 9-piece setup B. Each piece in B might be more powerful than in A, but B has less pieces. In Starcraft, if the Terran (humans) are A, then the Protoss (an alien race) would be B, for they use smaller numbers of stronger and costlier units.

The Zerg (the other aliens) are the opposite of the Protoss. Perhaps their chess setup would have 16 pawns, four pieces that moved like kings (but don’t obey the rules of check), four knights, and a queen. This is a total of 25 pieces.  This allows swarming with larger numbers of weaker and cheaper units.

Of course this is a drastic oversimplification of the game style (I’ve left out important things as resource collecting, production buildings, scouting, etc.), but that covers it essentially. Starcraft II continues the same gameplay, just with different units.

Plot Background

In Starcraft II’s single-player campaign, you follow the actions of Jim Raynor, a rebel leader against the Terran Dominion and its evil leader Arcturus Mengsk. You learn that Raynor is a friend of many Protoss factions, and that he is especially on good terms with the dark templar Zeratul. And the Zerg are led by Kerrigan, the Queen of Blades.

This alignment did not occur from accident.

Starcraft: The Terran Confederacy in the Koprulu sector in the Milky Way suddenly encounter technologically advanced Protoss warships that incinerate some Terran fringe colonies. They find that the Protoss have done so to prevent the spread of a parasitic race called the Zerg.

At this point, Jim Raynor is a Marshall on the planet Mar Sara, which is attacked by the Zerg. The Confederacy is slow to help, so Raynor puts himself in charge of saving as many colonists as he can. When he destroys a structure that has been infested by the Zerg, the Confederacy arrests him, and to evade arrest, Raynor has no choice but to join the Sons of Korhal, a terrorist group led by Arcturus Mengsk.

To overthrow the Confederate capital world of Tarsonis, Mengsk sends his second-in-command, psionic agent Sarah Kerrigan to place a psi-emitter on the planet. This device lures the Zerg, who will overrun the human population on Tarsonis. When the Protoss under Tassadar come to destroy the Zerg, Mengsk orders Kerrigan to stop the Protoss, but when she does so, Mengsk abandons her on the planet to the Zerg. Raynor, disgusted by the betrayal of Kerrigan, defects from Mengsk, and in the fall of Tarsonis and the Confederacy, Mengsk creates the Dominion and crowns himself Emperor.

The Overmind, ruler of the Zerg, had actually decided not to kill Kerrigan. She was instead infested to be an agent of the Zerg Swarm. The Protoss dark templar Zeratul assassinates the Zerg Cerebrate Zasz, but this act reveals to the Overmind the location of Aiur, the Protoss homeworld. The Overmind quickly mounts a direct assault, and embeds itself into the planet.

Even as the Zerg take over Aiur, the Protoss Conclave insists on conventional, honorable fighting against the Zerg, even though the Protoss are hopelessly outnumbered. The Conclave also seeks to arrest the high templar Tassadar, who has tried to free Zeratul—only dark templar energy could defeat the Overmind. After a brief Protoss civil war, the combined forces of the Protoss under Tassadar and Zeratul, and Raynor’s rebel group, defeat the Zerg, and Tassadar sacrifices himself to slay the Overmind.

Brood War: Not terribly important to the storyline of Starcraft II, except that Kerrigan becomes the sole leader of the Zerg.

Story and Storytelling: The Single-Player Campaign

Blizzard has come a long way in storytelling. In Starcraft, the plot unfolds in-game as well as in mission briefings. Key cinematics also illustrate critical points. The plot was linear, meaning one mission directly followed another.

The campaign of Starcraft II is, by contrast, nonlinear. You often have different missions to select from (though you end up playing through most or all of them anyways), and have choices to make in upgrades and research. Three times in the campaign, you will have to make a binary choice that either affects the plot or what you’ll face the next mission. These choice selections were very interesting, and lead to interesting replay options.

In one choice, you must decide whether to help Tosh break out a group of Specters or help Nova stop the Specter operation. If you help Tosh, you’ll have the ability to create Specters in later missions, whereas if you help Nova, you’ll have the ability to create Ghost. The two missions where you either help Tosh or Nova are my favorite in the campaign.

Besides the nonlinear story, the story itself was greatly enhanced by the various methods of storytelling. Besides mission briefings, in-game actions, and cinematics, the story takes place interactively on the Hyperion, Raynor’s ship. The most amusing method was the television broadcasts, which show Donny Vermillion and/or Kate Lockwell. Donny often cuts off Kate’s report of the real news, reporting his own biased information.

As always, the story is full of surprises and plot twists. The most shocking part of the story was Zeratul’s appearance on the Hyperion, and his visions that Raynor later viewed. It turns out the Overmind in Starcraft was more than it had seemed.

To soften the overall serious tones of alien invasion and saving the universe, Blizzard added plenty of references and humorous dialog. My favorite is the part when Tychus jokes to Raynor that using the Xel’Naga artifact could destroy the space-time continuum, to which Raynor responds, “This isn’t science fiction!”

Favorite Mission: “Ghost of a Chance”

This one is intense on micromanagement. You control no base, only Nova and a few reinforcements. The positioning of units and usage of abilities is key. The mission is like an epic version of “The Dylarian Shipyards” from Brood War.

Next Favorite Mission: “Breakout”

Essentially an Aeon of Strife game, like DotA. You control only one unit, Tosh, and try to control the tide of a battle. As in “Ghost of a Chance,” the key is positioning and using abilities. It is similar to the mission “The Search for Illidan” in Warcraft III: The Frozen Throne. Also, the parts where Raynor constructs bases in areas you capture is the opposite of “Twilight of the Gods” in Warcraft III, where the enemy Archimonde constructs bases in areas that he conquers.

Battle.net and Multi-Player

Also a great improvement. Battle.net is a state-of-the-art online system, and the lack of LAN is not a big issue. This is because the new Battle.net has very little lag, and whatever use for LAN can be done on Battle.net.

Besides that, the gameplay is excellent and well polished. The only qualm I have is that the Terran and Protoss seem more fun to play than the Zerg. Note that I’m not saying they’re imbalanced or easier to play; they just seem to have so many more options. Protoss with their Warp Gates are extremely fun.

Favorite Protoss Unit: Stalker

An very flexible unit that can hit air and ground. It is extremely mobile with its blink ability, and the option to use Warp Gates to warp in many of them at once is amazing. Massed stalkers with upgrades seem to be very effective.

Terran Favorite Unit: Viking

It has a very long-range air-to-air attack that is perfect against capital ships or Overlord hunting, and it can transform to ground mode, making it a viable ground-to-ground mech fighter. The ship upgrades work for both modes.

Zerg Favorite Unit: Baneling

There’s nothing more satisfying than watching your opponent’s army decimated by a massive blob of rolling green spheres.

Balance

As an amateur player I cannot speak much about this, but Starcraft II seems very well balanced. Each race has a distinct feel, but together they are matched up quite well. The game has come a long way from the early days of the beta (in which I did play), when several cheap strategies could win consistently. Even now, the Void Ray rush is super effective, at least at lower levels.

Achievements

How do you enhance the replay value of any game? Add achievements. I’m not sure whether this is new for the real-time strategy genre, but Blizzard certainly has success with the achievement system in its World of Warcraft. I’ve read an article somewhere about how achievements scientifically make a game addicting. But Starcraft 2 doesn’t even need the psychological effect.

For example, in the campaign missions, there are two bonus achievements, and it can sometimes be difficult if not nearly impossible to grab both awards in one play of the mission. One achievement might be to kill every last structure on the map, while the other might be to finish the mission in under 20 minutes. You’d have to play the mission at least twice, once to get the first achievement, another to get the second. Plus, there are de facto achievements such as finding research points on the field that can be used for valuable upgrades for later use in the campaign.

This system is very addicting for perfectionists like myself. Even without achievements, I would search every corner of a map for hidden stuff (e.g., in Warcraft III, especially the expansion, there were secret items and tomes everywhere if you looked for them). The achievement system makes you want to do this even more.

Graphics

While I don’t consider graphics to be the most important part of a game, I am fairly impressed by the graphics of Starcraft II, mostly the ability to generate in-game cutscenes and rendered movies in the campaign. Also, the real movies are in much higher resolution and detail than those in previous Blizzard titles such as Warcraft III.

Map Making

Blizzard’s map editors have been incredible, and during the beta I have already discussed the basics of the Starcraft II map editor. I haven’t found time to really experiment with it yet, but when I do, I’ll keep you updated.

The Fun Factor

To be honest, Starcraft II is one of the funnest games I have ever played, if not the most. It is because they made it much more than a game—they made it an environment, and a very immersive one at that. My only real concern here is that it might be too immersive, and be another World of Warcraft, a very addictive game due to its fun factor. World of Warcraft is what happens when you make a game too good.

Then again, there is no monthly subscription fee for Starcraft II, so Blizzard needs not make it as addicting. But once you get the game, it will be very hard to put down, at least for a while.

Concluding Remarks

Starcraft II is incredibly polished and incredibly fun, and it proves that the real-time strategy genre is not dead—it just needed another kick. And Blizzard gave it this kick.

I Write Like…

George Orwell, Arthur C. Clarke, Ursula K. Le Guin, Isaac Asimov, and Chuck Palahniuk, according to this funny online tool called “I Write Like.”

Actually, what I did was, I fed into the “I Write Like” analyzer the first five chapters of my Mirror novel, one at a time, and got these five different authors. I recognized Orwell, Clarke, and Asimov, but had no clue who Le Guin or Palahniuk were, so I wiki’d them. Considering my story is dystopian/science fiction, the results are pretty accurate for the content.

Chapter One: George Orwell

George Orwell

English writer best known for the novels 1984 and Animal Farm.

The opening of George Orwell’s 1984:

It was a bright cold day in April, and the clocks were striking thirteen. Winston Smith, his chin nuzzled into his breast in an effort to escape the vile wind, slipped quickly through the class doors of Victory Mansions, though not quickly enough to prevent a swirl of gritty dust from entering along with him.

I’m not going to give any spoilers on my novel, but the first paragraph won’t hurt:

A dark and sweltering city, where light shined from only one cluster of buildings: the chief luminosity came from a circular structure of steel and glass, rising twenty-two stories into the sky. On the roof was a grid of solar panels that, in the daytime, rotated to the Sun. Inside the structure, a maze of plants freshened and purified the air. The building, like most around it, was completely sustainable, running on its own power grid, producing not a breath of carbon dioxide. It was, in every sense of the word, environmental.

(Note: I used the entire chapter for the analysis, not just this paragraph. If I just enter this paragraph, it gives Arthur C. Clarke, whom I match for my second chapter.)

Not the clearest comparison, but at least the subject matters are somewhat similar.

Chapter Two: Arthur C. Clarke

Arthur C. ClarkeEnglish science fiction writer best known for the novels Childhood’s End and 2001: A Space Odyssey.

Also, I should mention that of the five authors, Orwell is the only one I’ve actually read. Being a sci-fi person, I’ve obviously heard of Clarke and Asimov, but am not familiar with them.

An excerpt from 2001: A Space Odyssey by Clarke:

Bowman was already up, pouring himself some coffee from the dispenser, when Poole greeted him with a rather worried “good morning.” After all these months in space, they still thought in terms of the normal twenty-four-hour cycle – though they had long since forgotten the days of the week.

Now an excerpt from my novel’s chapter 2:

Spek left the room in disgust. As he walked out into the unlit night street a lash of warm air caught him for a moment before he started walking again. It was a hotter March than ever. Global warming. It reminded him of the difficulty in modeling the weather, of adding in all the cycles, inputs, and outputs. And how chaotic it was: if there was one wrong piece of data in one frame of the simulation, it would cause the next frame to be wrong as well, causing eventually the entire simulation to fail.

Note: I’m trying to pick passages of similarity.

Chapter Three: Ursula K. Le Guin

Ursula K. Le GuinAmerican author notable in fantasy and science fiction, known for the two universes of the Hainish Cycle and Earthsea.

Based on what I saw find online, I couldn’t find a matching excerpt, so I’ll just insert a paragraph from A Wizard of Earthsea:

The island of Gont, a single mountain that lifts its peak a mile above the storm-racked Northeast Sea, is a land famous for wizards. From the towns in its high valleys and the ports on its dark narrow bays many a Gontishman has gone forth to serve the Lords of the Archipelago in their cities as wizard or mage, or, looking for adventure, to wander working magic from isle to isle of all Earthsea. Of these some say the greatest, and surely the greatest voyager, was the man called Sparrowhawk, who in his day became both dragonlord and Archmage. His life is told of in the Deed of Ged and in many songs, but this is a tale of the time before his fame, before the songs were made.

Excerpt from my novel’s chapter 3:

An asteroid collision sixty-five million years ago shuffled the gene pool, wiping out the great beasts who had clawed their way to the top, and leaving behind a new competition for survival. But this time, there was to be no competition to determine which species would succeed the human. There would be no other species. Maybe a few microbes, he thought. But that was it. Nothing capable of intelligence.

Chapter Four: Isaac Asimov

Isaac AsimovA prolific American writer considered a master of science fiction, and most known for the Foundation series.

From Wikipedia: “One of the most common impressions of Asimov’s fiction work is that his writing style is extremely unornamented.”

An excerpt from Asimov’s short story “The Last Question”:

The energy of the sun was stored, converted, and utilized directly on a planet-wide scale. All Earth turned off its burning coal, its fissioning uranium, and flipped the switch that connected all of it to a small station, one mile in diameter, circling the Earth at half the distance of the Moon. All Earth ran by invisible beams of sunpower.

As usual, from Mirror, this time chapter 4:

Almost as soon as she put the thermometer in place, the level began to rise. 26, 27, 28 within seconds. Unbelievably, the temperature was increasing.

That wasn’t due to the sun, in case you were wondering.

Chapter Five: Chuck Palahniuk

Chuck PalahniukAmerican; Wikipedia describes him as a journalist and “transgressional fiction novelist.” Turns out that this genre is the one in which a character feels confined by social expectations and breaks out of them. His writing style is also described on that page as “minimalist.” Known for the novel Fight Club, which was made into a famous film.

From Fight Club:

And this is how Tyler was free to start a fight club every night of the week. After this there were seven fight clubs, and after that there were fifteen fight clubs, and after that, there were twenty-three fight clubs, and Tyler wanted more. There was always money coming in.

And chapter 5:

He saw, as it passed overhead, a dark, high-flying bird that didn’t flap its wings. The sound was loudest as the bird passed overhead. And then it became quieter and quieter, until it was gone. A strange sight—but strange things happened every day. He continued rowing.

And the Winner Is… George Orwell

If I analyze the five chapters together, the result is George Orwell. Clarity for the win!

Other Matches, According to “I Write Like”

  • The essay in my previous blog post, “Do Androids Dream of Science Fiction?,” matches the writing style of H. P. Lovecraft.
  • My IB Theory of Knowledge essay matches H. P. Lovecraft. Hmm, it seems my nonfiction writing matches him a lot, even though I have never read anything by him.
  • The “Plot Similarities in Blizzard Games” post matches Arthur C. Clarke again.
  • The play Lewis’s Adventures in Wonderland (or at least, the 50% of it that I have so far written) unsurprisingly matches Lewis Carroll.
  • My review of Toy Story 3 matches… H. P. Lovecraft. Again?
  • A spoof of Othello (Shakespeare) written in the style of Tom Stoppard’s Rosencrantz and Guildenstern Are Dead matches James Joyce. What?!
  • The essay “Video Game Physics: A Case Study on the Falcon Punch” matches Ursula K. Le Guin again.
  • The post about my novel matches Dan Brown.

Next I just need to add some wit and get Oscar Wilde.