“Know how to solve every problem that has been solved.” “What I cannot create, I do not understand.” — Richard Feynman

Micro-lessons

One sharp idea, pulled out of a longer page and made something you do rather than read — a live widget to poke, a worked mechanism, and a prompt to say it back. Born out of the "teach me something" conversations; the kind of thing the terminal is the wrong medium for. 6 so far.

Finite elements

The trick behind finite elements: let the derivative hop Integration by parts moves a derivative from the solution onto a test function — and that half-derivative of slack is exactly what lets FEM use basis functions with corners. distills /finite_elements/weak-form

Gate-level CPU

Every logic gate is a number The half-adder looks like two arbitrary gate choices. It isn’t — and seeing why turns “which gate?” into a counting problem with exactly one answer. distills /gate-level-cpu/arithmetic/half-adder Subtraction is addition in disguise A CPU has an adder but no subtractor — because a signed integer is a clock, and two’s complement makes a − b just a + (−b) on the ring.

Linear algebra

Every matrix has a direction it drags everything toward Multiply any vector by a matrix over and over and it swings to the dominant eigenvector. That loop — power iteration — is the seed of PageRank, PCA, and Lanczos. distills /linear_algebra/power_iteration

Numbers in the machine

Why 0.1 + 0.2 ≠ 0.3 0.1 has no exact binary form, so it’s rounded to the nearest double — and three roundings later, the famous 0.30000000000000004 falls out. Decode the bits yourself.

Probability

The 99%-accurate test that’s a coin flip A test can be 99% accurate and a positive result still mean 50/50 — because the false positives are drawn from a huge healthy pool. A natural-frequency view of Bayes.