One of the most wonderful aspects of math is how deep we can get by studying seemingly trivial questions. Consider the roots of unity, where "unity" simply means the number 1. Basics: roots of unity f

Monte Carlo simulations (or methods) is the technique of applying randomness and the Law of large numbers to the solution of various scientific and engineering problems. One of its first documented us

"Wuthering Heights" by Emily Brontë - good writing, but the protagonists are quite something. There's barely a likable character in the whole story - they are all either crazy, evil, stupid or a combi

Like many programmers, I find Alexis King's Parse, don't validate article fascinating, because it gives a name to an idiom that seems familiar and important - one I've observed and used in the past wi

The following are my notes on discrete-time Fourier series (DTFS), as well as the discrete-time Fourier transform (DTFT). These topics serve as an important theoretical underpinning to the digital pro

The other day, I found myself wondering how big 52! (52 factorial) is, and that led me to ponder how these could be estimated without a calculator or a computer. It turns out there’s some fairly inter

This is part 8 in a series of posts on writing concurrent network servers. In this part, we'll switch to Go and see how it tackles the challenges described earlier in the series. All posts in the seri

This is part 7 in a series of posts on writing concurrent network servers. In this part, we discuss how the challenges described in earlier parts are tackled in the Rust programming language. All post

In Physics simulations or game engines it’s sometimes useful to determine the speed with which two objects are approaching each other. This post will discuss the concept of closing speed, which is the

The Fourier series is a great tool for analyzing periodic functions. But what about functions that don’t repeat? We’ve seen that we can compute Fourier series for a non-periodic function defined on a

The goal of this post is to answer a simple question: why are the following two definitions of the vector dot product in Euclidean space [1] equivalent for vectors \vec{a} and \vec{b}: Component defin

"The Nuremberg Trial" by John Tusa and Ann Tusa - a detailed, meticulously researched account of the Nuremberg Trials. There's not a whole lot of side questing in this book - it's all focused on the t

Recently I came upon Pluggy, a Python library for developing plugin systems. It was originally developed as part of the pytest project - known for its rich plugin ecosystem - and later extracted into

A few months ago I wrote about using LLM agents to help restructuring one of my Python projects. It's worth beginning by saying that the rewrite has been successful by all reasonable measures; I've be

The trigonometric Fourier series is a beautiful mathematical theory that shows how to decompose a periodic function into an infinite sum of sinusoids. These are my notes on the subject, with some exam

This is a brief and simple [1] explanation of how to adjust the standard sinusoid sin(x) to change its amplitude, frequency and phase shift. More precisely, given the general function: \[s(x)=A\cdot s

This week the article Wasm is not quite a stack machine has been making the rounds and has caught my eye. The post claims that WASM is not a pure stack machine because it has locals and is missing som

When I was working on the WASM backend for my Scheme compiler, I ran into several tricky situations with debugging generated WASM code. It turned out that Chrome has a very capable WASM debugger in it

I'm happy to announce the general availability of watgo - the WebAssembly Toolkit for Go. This project is similar to wabt (C++) or wasm-tools (Rust), but in pure, zero-dependency Go. watgo comes with

"Intellectuals and Society" by Thomas Sowell - a collection of essays in which Sowell criticizes "intellectuals", by which he mostly means left-leaning thinkers and opinions. Interesting, though certa