Let’s Talk About Math

Looking at the world around us, it feels like I’m using the word ‘controversy’ wrong when I say that math is a controversial subject. We have controversies on whether it should be taught after a certain age, whether it was invented or discovered, whether PEMDAS is something that people created because we love rules. However, these are topics for another post. I want to look at something specific for this post: math and beauty.

I’m an IB student, and one of the example topics for my math internal was looking at the beauty of Euler’s identity. Don’t worry if you don’t know what that is. Any math you might need to understand, which isn’t a lot because I don’t understand the formula that much myself, I will explain it. Just for your reference, though, here’s the cold-cut formula: e^(π i) + 1 = 0. ‘e‘ is an irrational constant called Euler’s constant that was introduced to calculate continuous compounding, π is an irrational number that defines a circle and is often rounded to 3.14, and i is a notation for ‘imaginary numbers’, or the √(-1).

BBC calls it the most beautiful equation. I didn’t understand it at first, but the eloquence of it stood out to me: the equation to my little, not yet greatly educated brain implied that  e^(π i) is -1. Isn’t that something amazing? You take an irrational number, multiply it by itself π i times, and voila! You get a rational number, an integer nonetheless! If you have a little algebra under your sleeve, you might also be impressed by the fact that the final value is negative. is a positive constant, so it should be impossible to produce a negative value by adding a power to it. Well, that’s where comes in. “But, person,” you ask, “how can something be multiplied by itself √(-1) times?” I don’t know, and we don’t need to, at least for the purpose of this post. I definitely want to know how, and if you are like me, you probably do too*.

What struck out to me was, even if I understood little of the equation, I appreciated the eloquence of it, but is it “beautiful”? Supposedly, yes. According to BBC, Euler was the Mozart of math, and a study conducted in the Frontiers in Human Neuroscience states, “The formula most consistently rated as beautiful (average rating of 0.8667), both before and during the scans, was Leonhard Euler’s identity”. Okay, what? Did they just calculate the beauty of math with more math and numbers, and if so, how? If you didn’t read the article, the quote probably made no sense, and that’s okay.

In short, the researchers let the subjects study a list of 60 equations and rate them as beautiful, neutral, and ugly.  Then, the subjects were scanned using fMRIs to produce images of brain activity when the subjects were shown the various equations. You can read about the results in the article, which is linked above. The rating you see in the quote is from the first part of the experiment (they assigned numbers to the qualitative values, and then averaged the results). Moreover, they found out that the equations the subjects marked as ‘beautiful’ lit up the same part of the brain as when people hear Mozart, or look at Van Gogh’s paintings.

See, the results of this experiment aren’t exactly groundbreaking, but as controversial as this sounds, they kinda are. On one hand, the results imply that understanding something ostensibly has the potential to make the said thing beautiful, but we already knew this. We knew that people who understood an art piece appreciated it more. You can’t show pieces of the minimalist movement to random people and expect them to understand it. Similarly, people with an ear for music will probably be entrapped by the rhythm patterns of Radiohead’s Videotape, even if they aren’t fans of the genre. I don’t listen to Radiohead, but after watching Vox‘s video on the song, I learned to appreciate the syncopation in the song. In fact, if you look at Panic! At The Disco’s I Write Sins, Not Tragedies,  you might notice that the bridge-like chorus has a drum beat that is possibly syncopation too**. These observations probably heighten the experience for you.

Now here’s why the results may be groundbreaking: people tend to hate math because it’s absolute, with no room for emotion. Well, here you go! If you understand it, then it tends to light up the same emotional parts of your brain as when you listen to, look at, or experience something you love.

I don’t really know what the point was, other than showing that I’m not crazy for being enchanted by math’s eloquence.

See ya!

* Here‘s a great link that explains Euler’s identity extremely well. You might, however, need to know some differential calculus to understand all parts of it.
** I’m not sure about this. If any music people are reading this, let me know if I am correct.

Hello World

You probably guessed this, but uh… Hi! If you’d ever tried learning coding, you might’ve assumed that the title of this post was default, but it isn’t. Not in the technical definition of default, anyway. It wasn’t just there, and I didn’t just leave it there. So no, it’s not default. However, the title “Hello World” is a go-to when you’re introducing yourself online, no? Maybe because it’s in a limbo state between “you’re awesome!” and “you, sir/ma’am/person, have blinded me with the brilliance that is your existence.” In other words, it’s not completely informal like “Wassup?”, but it isn’t exactly a cordial, royal greeting to the world either. Moreover, it puts the writer out to the world. If this had been a platform that’s meant to convey a sense of privacy or a one-on-one, then this title makes no sense. “Hello World” suggests that the writer (I, in this case) is letting the world know their thoughts. Now, this might not necessarily be the case. In fact, looking at statistics, it’s highly unlikely that the even a fraction of a percent of the world will see this, but it is on the internet, and that means that a lot of the world’s population has access to it.

Let’s be honest here, this post isn’t just to praise the title “Hello World”. I mean sure, it’s awesome, but just praising it is pointless. This post has more to do with its default-ness (not a word, I know). Using default things seem to spark criticism almost all the time. One of the major ways Android users criticize Apple users is that Apple users choose to stick to the default. I don’t get why using default things is such an issue. Moving from phone analogies, let’s zoom into using defaults in platforms where people make content for others. Yes, sometimes there are millions of better alternatives that convey the idea better, but sometimes the default convey the idea perfectly, and there is no reason to change it. In first case, using the default may show a lack of care, and probably warrants change–examples would be this blog’s header and icon (I’m working on it). However, it’s possible that the content-maker doesn’t percieve that object as the key focus of the page and doesn’t think it matters. Unless this is the case, using the default when it barely fits the topic isn’t exactly something we can defend. Now let’s look at the second case: if the default conveys the idea perfectly already, why change it? It’s a little like “If it ain’t broke, why fix it?”

So yeah, long rant aside, HELLO WORLD! I just want to put out my thoughts on things with the blog, and as unlikely as this is statistically, I hope someone will read them and let me know their thoughts back. Hey, a person can dream , right?

See ya!

Standardized Testing: why I think it sucks

In the mood of the topic, I’m going to be using words that I think may show up on the SAT.

Okay, so my SATs are coming up, and I sort of want to shove a metal rod into my eye. See, I think that a test like the SAT has potential, but all of it has been squandered by the sheer dissimilarity shown in scores. I attend an SAT prep class, and quite honestly, it has been quite effective in increasing my scores. Here’s proof created from the diagnostic tests we take:

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In showing you this, note that I am not advertising SAT prep. I’m actually doing the opposite. Allow me to clarify. This class that I take costs $1,600. That’s not an inconsequential amount to most people. In fact, the median household income in my state is $48,273. So, you may wonder, why don’t they just study using cheaper materials. To you, dear reader, I say the following: this particular class (let’s call it My Prep* for convenience’s sake) improves scores by about 200 points. My first diagnostic score was after I studied on Khan Academy’s free resources. So I should really be getting a score around 1200, without any prep.

Now take a look at someone who is less fortunate and cannot afford to pay for tutoring. Not to mention, My Prep requires students to work for about 6-8 hours a week in order to reach the +200 threshold. This may be an issue for a vast majority of high schoolers, who often have to support the household income with jobs. Thus, a student who has the raw potential to score 1300 is overshadowed by my expensive-prep-produced 1460 or higher.

Quite honestly, I am wrong to admonish prep classes. The truth is, the major problem with these tests is the content they test. While the math section may be forgivable, the Writing and Language section is absolutely a waste of time. Sure, while prepping, I learned that a sentence written like this one has a mistake, it is a comma splice. Sure, I learned that this sentence is a run-on and run-ons produce high yield questions. Sure, I learned that two independent clauses can be joined by a coordinating conjunction, but I do not understand how that will ever help me.

At this point, most of us know how to get our points across in a meaningful structure. If not, we have software like Grammarly, Hemmingway, and God forbid, Google. Moreover, we make large amounts of stylistic choices in literature. In fact, the SAT’s Reading passages contain innumerable grammar mistakes that the SAT writes off as “stylistic choices”. Sections like Writing and Language are purely based on knowledge, something that the SAT was created to eliminate. These sections pave way for classes like My Prep, Princeton, PrepScholar, etc.

*This is a fictional name, and if you do know a My Prep, note that I am not talking about it.










Making Discrimination Mortal

I think that most people here will agree with me when I say that discrimination is immoral, that it’s unethical, that it should be stopped, and that most of you will never discriminate in your internal sense of the word. But I’m going to say something that a lot of you might not agree with. Discrimination is seemingly immortal. Now before you climb up to my face and scream that it will end and that it can be combated, know that I agree with you, 100 percent, but give me a small portion of your time and let me explain what I mean. I’m telling you that if things don’t change, discrimination will be immortal, and the main culprit would be our definition of discrimination.

When people think of discrimination, they think of the Apartheid, segregation, slavery, the Trail of Tears, women’s suffrage, the Holocaust etc. and these are horrific examples that never should’ve occurred, but they did occur. However, these events in history showcase the most extreme of discrimination. They don’t show the once subliminal discrimination that led to these monstrosities. They don’t show the growth of discrimination, they just show the final outcome This leads to a purely, forgive my choice of words, black and white definition of discrimination that is incorrect to the core. People think that discrimination is just kicking someone out because of their race, gender, sexuality, origin, disability, etc. But the truth is, discrimination is so much more than that. Discrimination is saying that someone can’t do something because a majority of a group they belong to can’t so the said thing. Discrimination is saying that someone will do something because people in the group they belong to did the said thing. Discrimination is making jokes at other people’s expense and saying “you used to have a sense of humor” when confronted. Discrimination is using gay as an insult and throwing around the n-word as if it’s yours to toss without knowing if it’s okay with the African Americans around you. Discrimination is whispering to your friends or family that the boy over there shouldn’t be there because he doesn’t belong to a group you belong to. Discrimination is saying that girls should get hair curling irons while boys should get curling irons that they build muscles with. Worst of all, people use science and statistics to support their preposterous claims that one group is better than the other. It doesn’t matter if boys biologically have stronger chests, or if a study showed that girls are more emotionally sensitive, girls can lift weights if they wanted to and guys can cry if they needed to. The problem with the definition of discrimination is how constrained it is. Yet, somehow, people find a way to demonize the victims and the movements to reduce discrimination.

Throughout history, people change the goals of a movement. For example, people take the feminist movement, a movement about equality for all men and women, and somehow make it out to be against men. People take the Black Lives Movement and somehow turned its meaning against people of other races. This is wrong on all bases. I’m not black and let me tell you that not only am I not the least bit offended by the movement but that I’m a staunch supporter of the movement.

And by the way, it’s a popular thing to say that discrimination arises from fear. Let’s look at that for a second. There are countless meaningless phobias that aren’t phobias whatsoever, but we can ignore most of them because they don’t harm anyone. What I cannot comprehend or forgive is the existence of homophobia, xenophobia, Islamophobia, etc. How on Earth can you be genuinely afraid of a sexuality, of immigration, or of a religion? These aren’t phobias, they’re excuses. And I believe that as long as these excuses exist, discrimination will be immortal.

The first step to making discrimination mortal is destroying prejudices, for its prejudices that caused the worst forms of segregation and it’s prejudices that are still causing discrimination. Our society got better, yes, but why are we stuck? It’s because we hold onto internal prejudices, and even grow them when we speak our prejudices out loud. And although this is easier said than done, if someone tells you that what you said was offensive, stop saying it. This world should be a place where everyone feels welcome, and the first step to destroying this seemingly immortal, but definitely immoral act is destroying our internal prejudices and changing the definition of the word ‘discrimination’.