Articles, thoughts, and opinions about math, science, game dev, and more.
1. Introduction The existence of AI tools has caused a jump in the ever-shifting speed-rigor equilibrium we all use to evaluate projects, and our intuition needs to follow that jump. In this article we'll argue that the purpose of project documentation has subtly changed; it is
Or: Bring Back the APL Keyboard. No, Wait—Don’t. But Maybe, Kind Of. This series is a deep dive into operators and their overloading—how they work, how they don’t, why so much confusion surrounds them, and how we might disentangle that. We have
Dark matter is one of the most discussed topics in popular science, often framed with the clickbait: "Was Einstein Wrong?" Well, no. No, he wasn’t. This is Betteridge's Law of Headlines, and in general, articles about gravity fall into a few predictable categories: the
Diagrams are amazing—whether it’s a signal flow diagram, UML, or an electronics schematic. There’s something special about creating a concise, elegant, and high-information-density representation of a system. If you agree, then this is the article for you! Many types of diagrams have
If you are reading this, you probably know how to multiply two matrices together, but if you haven’t taken a Linear Algebra course, you might not realize that that is just one way to do it. Without a Numerical Analysis course, you might not know how useful these
Ghost has its ActivityPub integration in (private) beta! I'll be re-publishing a few things using it, but since it's in beta, please be aware that replies, comments, boosts, and even whole articles may disappear or reappear in strange, sci-fi, consternation-inducing ways. This is
"Why are LLMs so good at summarization tasks?" The deep dive on using compression ideas as a bridge is a little longer than I wanted it to be. So, in keeping with the theme, I asked GPT-4o for an editorial one-page version. If you didn’
"...extending a prompt with a controlled, often zero, amount of additional random entropy per symbol." Introduction I often hear LLM generators described as "just statistical—they can only regurgitate what they've seen!" or, slightly better, "auto-complete on steroids." These descriptions
This blog is made possible partly thanks to a modern large language model, but not in the way you might think. Let me explain: I'm dyslexic. Okay, that's an understatement. I'm horrendously, depressingly, appallingly dyslexic, sometimes to the point of incomprehensibility. One of my
I first saw this kind of chart in a nice www.edwardtufte.com forum thread about project management charts. Specifically, the NASA Launch schedule slip chart caught my eye. It shows how, and with annotations why, project milestones and deadlines moved. It is cleanly focused on milestones and, in my
Every so often, the DCQE (Delayed Choice Quantum Eraser) makes the rounds on various internet places. There are many good explanations of how it works and why it DOES NOT require weird explanations, like time travel. However, these often seem to miss or gloss over a couple of important points
My hack used walking a Hilbert Curve to order the border crossings of the circles used to denote each tree's sun-collecting area and then building work lists that grow (pun intended!) sufficiently slowly ( so “≤log(N)” ) to maintain a viable maximum memory size. All
Yes, but my solution nearly breaks my own rules about Euler integration, and the contrived ways ray marching figures out which surface is intersected creates quite a mess. Consequently doing more than one bounce for each reflection or refraction really hurts performance. Overview Shader Toy is kind'a awesome.
At a high level, the specification or requirements for a project can often be distilled into a single question of the form “How do I get X, without Y, ignoring Z”. In the real world, ignoring Z always comes back to bite your butt, and “without”
Hi, my name's Ian McEwan. Welcome to my little corner of the internet where I hope you will find interesting articles on various topics that I've worked on over time. I'm an applied mathematician, which means I love getting into the details of why