• ## But what really is symmetry? (Apparent vs. Actual Structure)

First post in a while: a fairly short one on some thoughts I had about symmetry. As I see it, symmetry is an artifact of us considering apparent instead of actual structures when analyzing systems. I talk about this and various examples. There are two other stories about symmetry I also hope to cover in […]

• ## Natural Units

I’m back! I decided to blog this because it didn’t feel substantial enough to have notes on its own and I couldn’t find a proper place for it elsewhere so here I am. Today, I wanted to discuss natural units i.e. the system under which , , etc. It became apparent to me that many […]

• ## A Natural Limit Definition

Often, the first exposure one gets to rigorous mathematics is the definition of a limit. Let’s consider what this is for a sequence. We say if This, at first sight, is ugly. It takes a while to even understand what it’s saying, longer to see why it works, and much longer to apply it. It’s […]

• ## Philosophy of Quantum Mechanics

Quantum Mechanics since its inception has been one of the most philosophically controversial concepts in all of physics. But what really is so confusing about quantum mechanics? The answer lies in two fundamental principles: locality and realism. Locality – locality asserts that all information and matter in the universe is limited by the speed of light. No […]

• ## Quaternions Revisited

It has admittedly been quite a while since my last post over a year ago. I thought I would restart the posts by revisiting one of the first topics I discussed on the website: quaternions. My previous post, upon review, seems to be quite uninformative on what the nature and use of them are which […]

• ## Calculus of Variations Part 2: Lines, Bubbles, and Lagrange

In the first part, we discussed the idea of a functional, what it means, and how to find its extrema using the calculus of variations. However, those equations don’t really capture how amazing and applicable calculus of variations really is so the following will be some examples of this. In fact, the drawn out results from […]