Friday, March 17, 2017

数学 (Mathematics)

When I was a kid growing up in suburban Chicago, I though I was good at math. I got good grades in school, went to advanced math class, could do arithmetic in my head, everything just clicked and it was fun. Geometry was fun, it was all about proving things and getting one answer, like a mystery that you knew had a pot of gold at the end of the rainbow. Algebra was fine; find out what x is using whatever means necessary, sometimes even y and z. No sweat. But then starting to get into calculus and advanced math concepts late in high school, that's when it got hard (I still got a 5, the highest score, on my AP Calculus exam though!) and then going to college and understanding there were so many smart people in the world and many smarter with me coincided with taking a really hard math class right at the beginning of my college experience that took the ambition and willpower out of me. Math was no longer fun, math was no longer easy, I no longer could understand how to solve the mystery and sometimes didn't even know what the mystery was. Math left me behind in the dust, and I abandoned math (unfortunately, cuz apparently people who really understand math can set themselves apart from others).

As an adult, though, I now realize how much math is in our everyday life. One could argue everything about life is about math. How much money one can afford to buy a house, how much one's money will accrue in a savings account, how many payments one has to pay off the car, etc. But it's not just money. Everyday events like how much gas to fill up require math, how much salt and vinegar to put into one's dish. And honestly, love and finding a romantic partner, is in a sense, related to mathematical topics (a little bit of a stretch), but those algorithms that dating websites use to match people up with each other really contain math and use statistics to come up with combinations. The concept of love itself might be math-related: at some point, after going through so many different potential partners with different combinations of character traits, one finds someone who is compatible. (Just ask every The Bachelor or The Bachelorette contestant what it's like to play the numbers game). It relates to sample size, setting enough of a sample and only needing one unit out of that set, the chances of finding someone in a set of 25 is not 100% but pretty high. It's like if you put 30 people randomly into one room, the chances of someone having the same birthday as someone is really high, really close to 100% from what I read. I'm fascinated by this stuff, how the easy math concepts can relate to average life. I used to sit idly sometimes and just think about math and how the numbers relate to each other, how people even created numbers, and how they work magically, like somehow you can have an infinite amount of numbers, but if any of them are multiplied by zero, they go back down to zero. It's like the biggest eraser/ wet towel ever, zero, yet the concept of zero is so fascinating in that there's no quantity in it, it has to exist only because there's no other way to describe the absence of any other numbers. The concept of the smallest minutest thing can become the biggest, limitless amount just by changing the question, like the distance between 0 to 1 seems small but then you realize you can create an infinite number of numbers between there, like 0.199999999..............etc, etc.

Anyway, I brought this up because in filling out March Madness brackets, I learned that I still hadn't perfected the craft of setting up a March Madness bracket, which on its surface doesn't seem that complicated: a 64-team tournament, pick who wins and you get a point. But IT IS very complicated when you're in a March Madness pool of about 100 people and want to try to maximize your chances of winning the pool, without knowing beforehand how other people will make their picks. It's something that normal people (so not me, apparently) do very normally and just have fun with it, but I like to think more about it, get to the bottom of the mystery as part of the mystery-solving carryover from my youth, even though some mathematician has probably derived the perfect solution. The dilemma is this: in a 100 people bracket, you want to WIN the pool, finish No. 1, and it doesn't matter what other places you finish in. So how do you maximize your chances to win? The first obvious answer might be to pick the team that has the highest chance to win (hard to say, obviously, in sports, but for the sake of argument let's say somebody crunched all the strength of schedule, rankings, and intangibles, and Kansas this year has a 15% chance to win it all). If you take Kansas, the odds-on favorite, you have a good chance that Kansas might win it all, but then 25 other people in the pool who picked Kansas ALSO had Kansas and you would need to do especially well and lucky to win the pool within the Kansas pickers. As opposed to picking someone like Michigan, a 7 seed wild shot in the dark with about a 2% chance to win, whom everyone stayed away from, if on a long shot Michigan were to win, you would most likely win because picking the winner is the key. But is it worth it to go for that and be on your own than take Kansas, which has a much higher likelihood of actually winning? And what's to say before seeing other people in the 100 entry bracket that other people didn't have the same idea and pick Michigan, and 5 other people picked Michigan? Then you're screwed and the odds are totally against you, even on the 50 to 1 long shot Michigan wins, you'd have to compete against 4 other entries on other factors, not a good shot. So long story, there's so much going on with game theory, psychology, but mostly MATH that makes this practice so fascinating, and makes me as giddy as when I was a little kid adding up grocery prices at the supermarket. It's quite thrilling to seek the answer, even if there might not be a definite answer (Life, the difficult concept that it is, unlike math, sometimes doesn't give a clear answer).

I picked Gonzaga to win it all. Let the madness begin!

Fantasize on,

Robert Yan

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