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. 🙂

On the Occurrence of Improbable Events

Many events are extremely improbable, but are almost guaranteed to occur. For example: winning the lottery, being struck by lightning, or, as a real-world example of what happened today, seeing snow in Austin.

I wanted to go into a metaphysical or mathematical rant on this, but I’m not quite sure how to proceed into either. Weather is, right now, at best a probability—it’s a chaotic system. The famous Butterfly Effect illustrates that a butterfly flapping its wings can cause a tempest elsewhere in the world.

From Caltech on this phenomenon [Michael Cross, 8/18/2009]:

The “Butterfly Effect” is often ascribed to Lorenz. In a paper in 1963 given to the New York Academy of Sciences he remarks:

One meteorologist remarked that if the theory were correct, one flap of a seagull’s wings would be enough to alter the course of the weather forever.

By the time of his talk at the December 1972 meeting of the American Association for the Advancement of Science in Washington, D.C. the sea gull had evolved into the more poetic butterfly – the title of his talk was:

Predictability: Does the Flap of a Butterfly’s Wings in Brazil set off a Tornado in Texas?

So, a tiny change in initial conditions can alter the overall environment in the future. Now what does the Butterfly Effect have to do with snow in Austin? Simple. It means we have no idea what could have caused the snow. It could have been a butterfly in Brazil. No—it was the one next to it. Or was it a butterfly in Mexico? Was it a butterfly at all?

Okay, I’ll admit that’s extending the facts a little bit. In fact, I’ve been tricking you. The principle that allowed snowfall in Austin is not the Butterfly, but rather, the Law of Large Numbers. This law more or less states that the average value will approach the expected value after a large number of trials. For example, say the probability of appreciable snow on any given day in Austin is 0.1%. This means that we expect one day in every thousand to have snow. But this does not mean that in any given 1000 days, there must be at least one day with snow.

In fact, we can perform a simple calculation to find the chance that there are no days with snow in a 1000-day interval. The probability that there is not snow on a given day is 99.9%. For two days in a row, we multiply this number by itself, and we end up with a number near 99.8%. For 1000 days, we simply raise 0.999, the probability, to the 1000th power; this gives 36.8%. This is the probability that in 1000 days, there is no day with snow, even though we expected one day to have snow. To find the chance that there is at least one day with snow, we subtract the probability from one; this gives 63.2%. With further calculation (using the binomial distribution, or more specifically the Poisson distribution, for those concerned with the math), we find that the probability of X days of snow in 1000 is:

Days with snow Probability
0 36.8%
1 36.8%
2 18.4%
3 6.12%
4 1.53%
5 0.304%

These numbers added together give over 99.9%, meaning the chance that there are six or more days of snow is extraordinarily small. Let us now go to a cumulative probability, which will be more useful here. This means we’re going to sum all the probabilities up to that number.

Days with snow Cumulative probability
0 36.8%
1 73.6%
2 92.0%
3 98.1%
4 99.6%
5 99.9%

What does this mean? Basically, it says there is a 36.8% chance there are zero days of snow, 73.6% chance there is at most one day of snow, 92.0% that there are at most two days of snow, etc.

Let us take the next step: say we measure over 10,000 days. From pure probability, we would expect 0.1% of those 10,000 days to have snow, or 10 days. We again take a cumulative probability:

Days with snow Cumulative probability
0 0.00452%
1 0.0497%
2 0.276%
3 1.03%
4 2.92%
5 6.70%
6 13.0%
7 22.0%
8 33.3%
9 45.8%
10 58.3%
11 69.7%
12 79.2%
13 86.5%
14 91.7%
15 95.1%
16 97.3%
17 98.6%
18 99.3%
19 99.7%
20 99.8%

Now here is the important part. We want there to be on average 1 day of snow for every 1000 days. To make the first case even considerable, we must allow a give or take of 100%. We’ll allow anywhere from 0 days of snow to 2 days of snow for every 1000. Then the probability of this is 92.0% in the 1000-day case, but 99.8% in the 10,000-day case. So in the smaller experiment, there was an 8% chance to deviate by a 100% error, but in the second case, only 0.2%. So it’s more likely to be close to the expected value as the number of trials increases.

There is another way to analyze this. We shall cut the allowed deviation in the previous analysis from 100% to 50%. Basically, we want the chance there is one out of every 1000. For the 1000-day case, this chance is 36.8%, from the very first table. For the 10,000-day case, we look at the numbers from the last table for 5 through 15 days of snow. Subtracting 6.70% from 95.1%, we obtain 88.4% chance that there are between 5 and 15 days of snow in 10,000 days. And 88.4% is much higher than 36.8%. It is then much more likely that the outcome approaches the expected value when the number of trials increases. We may try cases with 100,000 days or 1,000,000 days, and the trend will continue.

So, over a 10,000-day period, there will probably be near 10 days of snow, but in any given run of 1000 days, there is no guarantee of even a single day of snow.

In the case of Austin, we expect there to be several days of snow every decade, but we don’t know in which years they will fall. On the other hand, if I go to a college in the North…

Concerning Football and Competitive Behavior

Last evening, the Texas–Alabama football game evoked impassioned feelings everywhere, especially from the city of Austin. I could see the excitement building everywhere. I would not consider myself a football fanatic, but I must admit that this game was intense. All year I watched like two college football games, and this was one of them. It showed just how people could become so competitive-minded, and yet, at the same time, still show exemplary sportsmanship. I use this as the springboard for today’s topic—competitive behavior.

What sparked this inquiry was Jooyeon’s blog post (on Tumblr) yesterday, before the game started, asking why there was so much hype:

I don’t know about anyone else, but I’m like dying from school right now. I just can’t get myself to focus or motivate myself to do well. And it makes me really wonder how I survived last year when I had so many other things on my plate. I think I might crash right after I finish this post.

Anyways, so tonight is the National Championship game, and my Facebook newsfeed is gonna be flooded with statuses about the game. Man, that’s gonna be annoying. I really don’t give a crap about football. People are making such a big deal about this, like it’s gonna be the end of their lives if UT doesn’t win tonight. And it’s kind of ridiculous. There are good citizens on both sides but people are treating this like war. You know, if I happened to be living in Alabama right now, it’d be the exact same case except with Alabama. And people also hurt each other in football. They hurt each other big time. Why would you cheer and cry out of happiness when you have just witnessed someone physically hurting someone else? I know “it’s fun” and all, but I guess the spirit of football has never really soaked into me. I’m aware that I am sort of being a hypocrite right now, because I’ve cried about many things other people wouldn’t give a crap about. So I guess it’s all about perspective. I apologize for my lack of spirit, but for me it looks like tonight’s just going to be another normal school night.

I agree—I’m not a huge supporter of football either. I watched the game because it was something out of the ordinary for me. It also might have been the last major Texas football game I ever watch while in Austin. I enjoyed it. But afterwards, I thought about your post, and realized that what underlies the hype is not the little details, but the big picture.

If we view the game as a bunch of large men running into each other and one of them holding a football, we won’t get very far. But that’s what football is! So why is it so popular, so fanatical, so compelling? The answer, I found, concerns competitive behavior.

Football is full of it. In fact, the hype for just about any competitive game, from football, to StarCraft, to chess, though varying in degree from game to game, rests upon the nature of human behavior.

But this behavior among humans (i.e. competitive behavior) was not originally for winning games amongst themselves; rather, it was for survival amongst nature’s hostilities. Because of this relationship with the surrounding environment, competition among early humans was not competition for the sake of competition, but rather, competition for the sake of life. So we weren’t consciously competitive—our intentions were just to live—but our actions gave the appearance of competition. In other words, in evolution, competition was an emergent property, and not a phenomenon in itself.

Humans changed that. Sure, we initially fought for our survival. But in early agricultural societies that created sufficiencies and surpluses, we began competing for other items besides food. Any survey of ancient civilization will tell you that. Times changed. By the Egyptian era, we had developed not only an appetite for tangible materials, but also knowledge. Fast forward again, and you have the Greeks, who greatly developed mathematics, history, philosophy, and politics.

Leap ahead, and we loom in the shadows of the Dark Ages. Competitions among religions were extreme. The Islamic expansions and the Christian Crusades demonstrated the use of war not as an instrument of survival, but as an instrument to spread divine beliefs. These were competitions of ideologies.

Jump again, this time to the Renaissance. Machiavelli is the prime point of investigation here. “The ends justify the means.” That changed the world. It might not be so true right now, as for a modern leader seeking power, almost each one of these “means” is closely followed and made public, but nonetheless, Machiavelli was the acknowledgment that competition was the ultimate war.

Today we find boundless examples of competition. Games (as aforementioned) are competitions. Politics is virtually a competition. The business world is an enormous competition. School, in many places (ahem), is a competition. Football games seem mild in comparison. Sure, they attract hundreds of thousands of fans, but the impacts of their results are undoubtedly nowhere near as relevant as those in politics or business.

Football is, of course, more entertaining than other competitions. It is a symbol of the human experience, for there are many lessons to be learned from it—yesterday’s game especially. The maxim of the game: Don’t give up. After losing Colt McCoy, and subsequently being 18 points down after the first half, Texas and its fans had every reason in the world to make excuses, blame Garrett Gilbert, or a combination of the two. The players must have been at a huge morale loss—they were against the number one ranked team, and they lost their star quarterback. What could they do? They could have given up, but instead, they fought as hard as they could, and nearly managed to bring back the game. They showed everyone that even if they lost, they lost it in style.

That is the essence of the big-picture perspective. In detail, football consists people running around on a giant field, but of course, there is much more it than that. In it, the highly-praised values of teamwork, dedication, sportsmanship are always there. It gives a sense of identity. It generates the feeling of community. It creates awe. For me, I don’t watch football very often, but I did learn something last night: The spirit of competition is greater than the competition itself.