the more i know, the more i realize i don’t know.

The more I learn about Calc, the more I realize I don’t actually know anything about Calc. I have violin lessons every week, and have been since I was basically 6 years old. Yep, you guessed it: I don’t know SHIT, even though I wish I knew everything there was to know. Every time I run a track workout I feel a pain slightly worse than the previous 100 times. Every time I learn something new about what I can handle, both mentally and physically.

Think to whenever you last learned something knew. Isn’t it crazy how we think we know so much, but in reality we really, truly, do not? Like I could bang out some difficult integrals, do some disgusting derivatives, and still only know, like, not even 1% of what Calculus is. It’s the foundation of something just completely indescribable, interconnected, and infinitely more complex than it looks to be on the surface. It’s not just math; it’s literally a language, a way of thinking, a lens through which the world suddenly looks bigger and more as if it was designed by some greater being.

formal definition of derivative (killed me already just by looking at it)

Gaussian integrals. Woke me up from death and then killed me again. Try proving those.

Since we’re talking about Calculus already, why not talk about it more!

This is about to sound really nerdy, but I’m going to say it anyways. There’s something just so beautiful about mathematics in general. It’s a language that describes the world around us. It’s something can give us a glimpse into that tiny piece of the kaleidoscope that is universe. What I’m trying to say is, math is one of the only things that helps us understand why we are, what we are, and how the universe came to be. Now this may not make sense if you haven’t taken calculus, and if you’re just a math hater, I don’t blame you (that much). I was a huge one up until this semester as well. But math truly is what I say it is now! It exists everywhere in nature and yet we all look over it like it’s nothing. Don’t believe me? Take this as an example.

Credit: This guy on stack overflow.

Yes, that is Barnsley’s Fern, if you didn’t know. It looks like a plant. But here’s the catch: It’s a fractal, or an amazingly complex mathematical pattern, and in this case, it closely resembles something in nature. Here’s the code for creating it with Python and matplotlib if you were curious:

from PIL import Image
import random
import matplotlib.pyplot as plt
A=[]
mat=[[0.0,0.0,0.0,0.16,0.0,0.0,0.01],
    [0.85,0.04,-0.04,0.85,0.0,1.6,0.85],
    [0.2,-0.26,0.23,0.22,0.0,1.6,0.07],
    [-0.15,0.28,0.26,0.24,0.0,0.44,0.07]]
x=0.0
y=0.0
for k in range(0,100000):
    p=random.random()
    if p <= mat[0][6]:
        i=0
    elif p <= mat[0][6] + mat[1][6]:
        i=1
    elif p <= mat[0][6] + mat[1][6] + mat[2][6]:
        i=2
    else:
        i=3

    x0 = x * mat[i][0] + y * mat[i][1] + mat[i][4]
    y  = x * mat[i][2] + y * mat[i][3] + mat[i][5]
    x = x0

    ptn=[x,y]

    A.append(ptn)

plt.figure(figsize=(20,30))
plt.scatter( *zip(*A),marker='o', color='g',s=0.1)
plt.show()

But here’s the thing: all of this knowledge out there that we simply can’t know isn’t a reason to give up. No! Absolutely the opposite! It’s a reason to keep going. The more we acknowledge how little we know, the more open we become to growth, criticism, and learning! It’s just a little, not-so-gentle reminder that learning isn’t about arriving at a destination; it’s about embracing the journey. Sure, it’s frustrating to realize how much you don’t know. But it’s also exhilarating because every question leads to another answer, and every answer leads to another question. It’s a never ending series.

So here’s to not knowing! Here’s to staying curious and willing to admit that we’ll never know it all. And maybe that’s the whole point.

Till next time.

PS - I apologize for my sloppy writing and lack of creative prose! This is not my best writing, and I’ll do better next to time to take more time on my articles to make them more fun to read!

PPS - IF and only if you are interested in philosophy, tech, and honestly whatever, and just want to have fun discussions and what not, literally just for fun, whenever you want, then consider joining this discord server.

You definitely don’t have to, but it could be just a fun way for people to talk to each other about various issues so we can all come to a better understanding of the world around us (I will participate of course, so if you want to talk to me personally, that’s the best way to get in touch!).

Here’s the link: https://discord.gg/44FBCjNe