stillthinking

A personal blog. Making sense of the world, one small part at a time.

July 2026

Jul 2 math

Connections in Math: the two kinds of random

Two files of a million digits, statistically identical, and yet one compresses to three lines and the other never will. Chasing that gap splits the idea of 'compressible' into two very different things — and leads to a strange wall: you can always prove a thing can be compressed, but never that it can't.

June 2026

Jun 27 math

Connections in Math: deriving the SVD from scratch

Most books state the Singular Value Decomposition as a finished theorem. Here we arrive at it naturally, without even aiming for it — letting the structure of any linear map hand us the factorization for free.