eigenℝesidue

hi! welcome to my study blog. my name is jon, i’m an engineering and mathematics major currently in their junior year. i have a crude sense of humor but i try to be thoughtful every now and then. i also really like talking so send a message 📨

[eigenresidue]

YOU KNOW WHAT I JUST DID????

YOU KNOW WHAT I JUST FUCKING DID???

I DID THE FOURIER TRANSFORM ON THE LAPLACIAN TO SOLVE A POISSON PDE!!!!

I DID A FOURIER TRANSFORM. ON AN OPERATOR. I MADE AN OPERATOR INTO A FREQUENCY VARIABLE.

WHAAAT THE FUUUUCCKIN FUCK

[poorsignaltonoiseratio]

i saw the milky way and thousands of stars and they were beautiful

[eigenresidue]

haha wow

[eigenresidue]

MY CODE WORKS OH MY GOD FINALLY IT WORKS OH MY GOD

[eigenresidue]

what business does Elmo have to be connected to my university’s lecture streaming platform :(

[eigenresidue]

Applying(?)/finding connections between the concept I learned an hour ago(Euler-Lagrange) and something I saw very briefly like 4 months ago (coordinate transform using a Jacobian matrix). Found a connection between a transpose and a conjugate that I will be exploring later?

I’ll try to explore this more rigorously somewhere later

[eigenresidue]

7/12/2025 9:49AM --------------------- photos 1-4 After hovering over numerous different topics in mathematical physics, I decided to finally start learning calculus of variations to support my further study downstream in classical mechanics. I have always really struggled with going from physics -> math and upon reading a junior-level classical mechanics textbook three weeks ago, I felt like an actual Physics major -- constantly lost and confused at what I'm reading or doing. So, I decided to study the mathematical theory behind it first before tackling anything (which is just simply something I should have done to begin with since I've known that works...) I first got the idea because my friends in Physics learned classical mechanics last semester and I found it very interesting - but could barely follow whatsoever. Granted I only showed up to two of their courses halfway through the semester, I still found a common theme of 'optimization' or at least efficient calculation in order to determine some parameter or value. It immediately resonated to a memory I had in high school, when we were learning about basic optimization theory in calculus AB and I found myself absolutely bewildered. I mean, coming from a purely middle-school geometric and algebraic standpoint, it was insane to me that you had such a simple process to the maximization of some parameter. I mean, to me, this is the heart of applied calculus - sure it can get complex, but it will always be something as simple as f'(x) = 0, f''(x) > 0r f''(x) < 0. Even in a multivariate sense this rings true, ∇f = 0, ∇⋅∇f/H and its properties, etc. I decided to use the little analysis I learned last semester and apply the basic ideas we learned (and honestly I might not have applied them correctly, I might have written something wrong or weird, you can detonate a bomb within 2 km of me if you want) and attempt to prove or the very least provide an outline on what I think you would need to prove things like the extreme value theorem or f'(x) = 0. My general philosophy on life and take is a novelty-based approach, and I've always been incredibly impatient when it comes to experiencing things I've already experienced before and provide no value, but applying the analysis to see things I already knew in a different light or way was satisfying and sort of a message to myself that it's okay to go back and redevelop your foundations. It's never a bad idea and in fact, I'm pretty sure neuroscience supports this position of *meaningful* repetition being the optimization of learning (haha). So, whenever you can, change your basis -- the result might be the same but the new process can be quite enlightening. (This is still consistent with my approach on life, see? I love new things) Resources I am using: https://youtu.be/6HeQc7CSkZs?si=-5AJtuXTkTbh7AqZ Classical Mechanics by John Taylor Fractals Everywhere by Michael Barnsely, which covers precisely the same exact sequence (haha) and concepts that I learned in my proofs + analysis course, was a good review and nice read. Might read a little more later. 5th image is just me trying to understand ray angles and construct them for some software I am making at work. 6th was my work outfit because this is my Tumblr and I can be as slutty and weird as I fucking want. Bye

[bootleg-nessie]

I FUCKING LOVE INFORMATION!!! I WANT TO LEARN EVERYTHING AND KNOW EVERYTHING!!!!! I WANT TO UNDERSTAND EVERYTHING ABOUT LIFE, THE UNIVERSE, AND EVERYTHING!!!!!! I AM UTTERLY CONSUMED BY MY THIRST FOR KNOWLEDGE!!!!!!!!!!!!

[eigenresidue]

What is beauty anyway?

--------------- It is odd to think that an aperture of the universe can individualize itself enough to the point where it can consider itself as a separate entity of the universe, though everything it experiences and understands can only be a consequence of the construct that it is inherently part of.

Have we become that detached?

It is an even stranger thought to think that we, fragments of the universe (yet still the universe), can categorize other fragments as separate from itself, but additionally within this idea of beautiful or ugly. Purely, the idea of what is and what isn’t does not concern itself with these measures, yet we have become so far detached from the idea that we are all a holistic experience that we have even constructed classifications that we obsess over.

And from that, we can then understand that becoming an individualistic experience can be likened to narcissism - an aperture of the universe finding another aperture to be aesthetically pleasing while they are of the same thing. ---------------

>written from the perspective of an open individualist or panpsychism, nov14 2023. fun lil thought experiment. although you can definitely tell i don't share the same beliefs as you read (i pose some strange questions and lines of thought i imagine someone who adopts this framework wouldn't ask or talk about) >what do you think about panpsychism? do you think it's a better explanation for consciousness by explaining or describing an idea that typical frameworks do not? or does it lose accuracy in its romanticism