Math and Physics
I am slowly sifting through and summarizing all of the miscellaneous knowledge that’s out there on the subject of “Geometric Algebra”. GA is a quirky subfield of math that is obviously terrible yet obviously on to something, and I haven’t quite figured out what it is but I also don’t think anybody else has either. So far I am avoiding using the GA term directly because I don’t want to be associated with it, but long-term the goal is to tackle GA head-on. So far I’ve got:
- Oriented Areas and the Shoelace Formula
- 1. Matrices and Determinants
- 2. The Inner product
- 3. The Hodge Star
- 4. The Interior Product
- 5. EA as Linearized Set Theory?
- 6. Oriented Projective Geometry
- 7. Simplex Volumes and Boundaries
- 8. All the Exterior Algebra Operations
I’m also searching for some kind of weird calculus that involves delta functions, pseudoinverses, and dividing by zero.
I’m also slowly working through my undergraduate math and physics curriculum and trying to “compress” it in a way that makes sense to me. This is because I want to learn QFT to understand how the universe works, but (IMO) the foundations are so shaky that there’s no point. I suspect everyone else is in the same boat but, unlike me, distrusts themselves instead of distrusting the foundations.
- Some Intuition For Entropy
- Geometric Mean and Standard Deviation
- All About Taylor Series
- The Essence of Complex Analysis
- The Essence of (the math of) Quantum Mechanics
Every once in a while I write other miscellaneous math-related musings.
- Meditation on Taylor Series
- Infinite Summations and You
- Aphantasia, or how not to do math in your head
- A possible derivation of the Born Rule
I also write myself references which, dunno, could be useful somebody else I guess. These are generally less polished and might just be wrong in places, watch out.