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. e is a positive constant, so it should be impossible to produce a negative value by adding a power to it. Well, that’s where i 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.