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!

Why I Agree With Jill Filipovic

Say I take a sample of 500 people in a thousand people population, and I ask them if they loved pepperoni. 25% say yes, so I can conclude that about 25% of the 1000 people population would say that they loved pepperoni. This works the other way too, no? I250 of 1000 people are pepperoni-lovers, I can assume that 25 of every 100 individuals in the population are pepperoni-lovers. Now, say I gathered a group of 100 people and asked them how many identified as female. 51 people would answer yes, so I would conclude that 51 of every 100 individuals in the population identify as female, and because this is such a broad category, there are very few sample conditions in which this should prove false, such as if I asked a sample in which all of them are lesbians (100%). Thus, you would think that if I asked 100 people from the workforce how many are female, 51 would say that they are, right? Yeah, no. You probably knew that, because you aren’t living under a rock. According to the United States Department of Labor, women comprise only 47% of the workforce.  This isn’t even talking about specific jobs. In highest paying jobs, women make up about 5%-13% of the labor force. That’s one of the thousand reasons I call myself a feminist. As a feminist, I think that it’s important to talk about the article What Victory Will Look Like for Feminists in 2018 by Jill Filipovic and outline why I agree with her. 

Although the years of female disfranchisement seem farther away with every second, women in the US are still held back by society’s chauvinistic standards. While feminists, people who support the ‘radical’ notion that women are people too, were ostensibly getting closer towards their goal, the 2016 election seems to be a tremendous setback. As it appears as if the ‘role models’ of this generation are dismounting the “feminist mantle”, author Jill Filipovic highlights the feminist goals and struggles today (post make-or-break election) in her article “What Victory Will Look Like for Feminists in 2018”. The author begins to outline the catastrophic 2017, during which the feminists were increasingly “on the defensive”, but she also brings the immensely influential movements that demand accountability for sexual harassment and assault; this, the author believes, might not have happened had the results of the 2016 election turned out different.

Not only does Filipovic highlight arguments against Republican men, but she also gives due credit to Republican women and supposedly ‘left’ members. She shines light on the popular ‘class before gender struggle’, satirically adding that empowering the working man would end misogyny somehow. She moves on to criticize Tom Perez for welcoming pro-life members in the Democratic party. The author also bashes Kellyanne Conway’s incorrect interpretations of feminism and claims to be an “individual feminist” who works for a man known for his misogyny; Filipovic continued on to criticize Ivanka Trump’s empty promises and non-insightful statements in Women Who Work. Finally, the author once again brings the aforementioned movements and their effectiveness to light.

Personally, I believe that feminism and women’s rights are issues of utmost importance that really should never have been questioned. I think that if people didn’t want women fighting to receive treatment as humans, they should’ve treated women as people. I especially find it fascinating that a group of people fighting for equal rights for everyone are labelled as anti-male or misandrists. I’m often surprised to find women who are against feminism. To me, it seems like a prisoner who refuses to have their shackles removed. Furthermore, I’m annoyed that women are constantly suppressed: when Trump supporters claim that he helps the working class, they refuse to acknowledge that women are part of the group too. The odds are always stacked against women. As Ivanka Trump puts it, “[balance]’s never a scale that stays equal for very long.” I think that feminism works to equal that scale, and I agree with Jill Filipovic when she says that Ivanka Trump did little to help “architect” the balance, despite her grandiose promises. As Ivanka Trump and Tom Perez stand as examples, even people feminists perceive as allies may turn their backs.

I’m sorry

Do you ever feel like your world’s falling beside you? You know your parents care, but it feels like they don’t give a shit, and all they care about is you making them proud. Honestly, you stop giving a shit too. Who cares if staring at a black and white screen all day is unhealthy? It means you’ll focus more on test prep, so screw colors! You have momentary lapses of caring for yourself, but you catch yourself before it gets in the way of that 1600! Really, you’re not even actually studying. You fool yourself into believing you’re being productive, when really you get one section done in two hours, because the smart part of your brain stopped giving a shit too. To recap, the “care for yourself” part of you shut down to give way to the “smart test-taker” part of you, but that part stopped functioning, so you’re a lifeless body that gives no shit, eats food that is considered shit for your body, and actually shits. The worst part is, you’re considered a mentally healthy person and you have no excuse to be so horrible at life. Physically, you’re supposed to healthy, but you eat the aforementioned shit and don’t really care enough to exercise, so your cholesterol levels might be too high for the overweight body of yours. Again, you have no reason to be so horrible at living, so you decide to wallow in your misery. You want to scream, but you don’t have the energy to put into that scream, so you content yourself with the piercing internal screams. You do this while the cruel part of you flashes everything you’ve said so that you can scrutinize your shortcomings in holding a conversation. You tell it to shut up, but it just keeps going, and you’ve got a full on conversation in your head, and then a third voice joins, and you just have your alter egos talking while you wonder which one is really you. Are you the prejudiced shithead or the voice correcting the prejudices?

If you said yes, WE HAVE SO MUCH IN COMMON! Congratulations; you probably don’t give a shit.


If you haven’t heard about the controversies surrounding guns, there’s one of very few things happening: You haven’t been on the internet, or really any place where people talk, at all for the past few months (honestly, the entire year); you’ve spent all your time on the ‘fluffy bunnies and rainbows’ side of the internet; you’re lying to yourself. What’s wrong with guns? Nothing. Except that they’re one of the most used weapons to kill CHILDREN. Oh, but it’s not always the case, you say? You know what is the case? A child, an 18-year old at best or a 5-year old, could lose their life in a place for learning. When it comes to a point at which I’m genuinely scared at code red drills, it’s a problem.

During the last drill at my school, a police officer whose voice we did not recognize ended the drill over the PA. I can tell you that a significant number of people (including myself) were terrified when we first heard the voice. You know the last time drills were this serious? The Cold War, when there was a genuine threat of nuclear warfare. So you know what the solution was? Better laws concerning this. At what point will people understand that lives are more important than protecting what they believe is the second amendment.

Speaking of which, here’s what the second amendment actually entails: “A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed.” Militias have been disbanded since 1903 by the Militia Act of 1903. If you’re keeping up and agreeing with me (which you don’t have to, by the way) here, you might’ve arrived at the following conclusion: people would rather protect a baseless privilege that never should have existed over the rights of others to live. It’s a fight between privilege and life.

Now, you may fall into the group of people who believe that you could use guns for defense against other attacks. I may be wrong, but here’s why I don’t agree with you: say there’s a little barbecue and the kids are playing with the frisbees. One child (let’s say Kathy) throws a frisbee at another (let’s call him Alex) and injures the child. At this point, the parents notice this, and they not only punish Kathy but they will also most likely just take away the frisbees. An adult won’t stand over Alex with a frisbee for protection, and they won’t teach Alex how to injure Kathy and anyone else with a frisbee. Why can’t this be translated to guns too?

When a state bans Nerf guns and can arrest children for carrying toy guns, why are actual AR-15s so simply available. When are we going to stop blaming toys and video games that involve guns and start focusing on the actual guns?

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.