Random Thoughts (1)

Random Thoughts (1) （Translated from Chinese, by ChatGPT）

Wishing everyone a Happy New Year! :) Sometimes, when walking alone, a sudden flash of inspiration strikes, and I feel compelled to jot down my thoughts and share them under the title "Essays".

Today, I read an article titled "Calculus and Two Epistemologies" that I found quite fascinating. It discussed the two founders of the calculus system, Newton and Leibniz, from an epistemological perspective. Newton is associated with British Empiricism, which views the human mind as a blank slate that gradually acquires confirmed knowledge through the accumulation of experiences. On the contrary, Continental Rationalism, which Leibniz belonged to, believes that the human brain has an inherent framework from which all knowledge can be deduced and derived. From a certain viewpoint, calculus is a synthesis of these two epistemologies.

Can mere contemplation grasp reality?

Does the human brain inherently possess a framework of understanding about the universe?

Many things happen in the mind that don't clearly manifest in reality. When Johnny is unsure whether his life/work is on track, he tries to step outside of himself, attempting to observe his own situation from a third-person perspective. Another method he uses is to compare himself to an ideal image in his heart. In Johnny's mind, there's an image of someone sincere, kind, and brave. The face is blurred, perhaps not a real person, but some people I meet in real life remind me of that image. If I feel closer to that image, I'm satisfied with my recent life; otherwise, I adjust. This image might represent the concept of "good," which holds powerful sway for someone as emotional as me.

Perhaps the purpose of education is what's called "turning of the soul." The image in my heart seems like a "first principle," and everything else follows naturally. I believe that people who change the world probably have very pure and kind hearts because beautiful things inspire courage while ugly things induce fear and retreat. Only by fully recognizing the beauty can one step out of their comfort zone and make the world a better place.

I've previously written an article titled "The Pursuit of Meaning: A Liberal Arts Student's Journey into Mathematics." I recently dabbled a bit in statistical mechanics and initially struggled, but today I find the simple, universal relationships between abstract quantities in the scaling laws incredibly beautiful (I'll explain more when I have time). The Rushbrooke Scaling Law reminds me of the Euler Formula. The professor, though over sixty, remains vibrant and childlike in his curiosity, his eyes gleaming like crystals, reminiscent of a master with exceptional internal skills in martial arts novels.

I hope my pen can pour forth the infinite beauty perceived by the eye of the soul. Some things inherently contain their own negation, which is what makes them miraculous.

I am the thousand winds that blow

I am the diamond glints in snow

I am the sunlight on ripened grain,

I am the gentle, autumn rain.

As you awake with morning’s hush,

I am the swift, up-flinging rush

Of quiet birds in circling flight,

I am the day transcending night.