Articles

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:

• 0. 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.

• How To Invert Anything
• Delta Function Miscellanea
• Divergences and Delta Functions
• Delta Functions via Inverse Differentials

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
• Simple Examples for 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
• The Case Against Geometric Algebra

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References

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.

• Bayesian Inference
• A particular calculation for the Pauli Hamiltonian in QM
• A long WIP reference on Fourier transforms
• Some notes on Survival Analysis
• Quaternions
• The various forms of the Triangle Inequality
• Trigonometric Formulas
• Vector and Matrix notations