Euler Toys of Tomorrow

Introduction

Obviously, it’s getting harder and harder to solve scientific problems with only pen and paper. Not that people have nothing to do on a Friday evening but write down the state-space of $k$ harmonic oscillators with $n$ energy level per oscillator. Hence, I can’t stress enough the significance of computer in the advancement of science. I can barely perform Gaussian elimination correctly on a 4x4 matrix so imagine a 15x15 matrix of atom coordinates of the simple methane molecule. You gotta leave that to the copmuter. However, as easy as the path to a quick answer may seem to be, the mine field is full of booby traps. Take for example, if you evaluate $f(x)=x^{3}+12 a^{2} x-6 a x^{2}-8 a^{3}=(x-2 a)^{3}$ with the parameter $a = 49999.5$ at $x_{0}=1000000.05$ with 2 different but equivalent transformations, you wil get immensely different results!

x0 = 1000000.05
a = 49999.5
def f1(x):
    return x**3 + 12*a**2*x - 6*a*x**2 - 8*a**3
f1(x0)
7.290025515029768e+17
def f2(x):
    return (x-2*a)**3

f2(x0)
-7.289995018501133e+20

Thus, if you are not careful with numerical calcuation, problems including but not limited to cancelllation, Runge phenomenon may make your algorithm shockingly unstable. With this blog, I hope to lay out some of the pitfalls that I am aware of while simultaneously show you the overwhelming joy of simulating physical and theoretical problems. It’s addictive!

However, I still categorize this blog as a personal instead of an educational one. It’s just my way to organize my school’s stuffs properly. Even though I try to make sure the content of my blog accurate to my best knowledge, please don’t be lazy and just take my word for it. Look through the formulas carefully and read the code line by line. It’s also better for your understanding! If you have a hunch that something in my post is incorrect, there might be a good chance it is so. I’m more than delighted to read anything coming from my readers whether it is critic, feedback, correction or suggestion.

Since it’s a personal blog, I will include some aspects of my life and thoughts that I would love to have them written. Along with some book, music, and play review. You can find these personal posts here in the Home section. For other types of posts, you can find them in the toggleable sliding sidebar via .

The Astronaut

I ran with all my might. I could see all the faces I ran past. There were some familiar ones appearing somewhat blurred under the glare of the parallel streetlights. I kept pushing forward. ‘Do you feel like you are being followed?’. I was staring the window behind him and he snapped me back to the reality. ‘No’, I answered. There was this package that I carried around with me in my backpack for a whole week. I couldn’t bring myself to have it posted. Faces turn into silhouette. I couldn’t stop running. In an amusing way, I think the names of Interstellar’s soundtracks really capture my sentiment precisely and concisely. I put ‘The Cornfield Chase’ on loop and erase the memories.

Calming cat comic

meowy

Berlin

Sometimes I feel like I’m walking on a sphere, a surface of positivity, even though the sky was so gray. For me, the concept of time fails to be tangible. Years of events condense into a tiny spot on the arrow of time. Not a popular opinion but I don’t like taking decent photographs. Like I need to have this strong urge to capture this specific moment, whose composition is so ineffable that it would not reemerge somewhere else ever again. I haven’t experienced that urge. Everything is just passing by interminably. I hardly look back at photos and when I do, the emotions woven in them stay covert to me. On rainy days, I yearn for an armchair and a turntable.