|
|
I explore extending Pascal's Triangle to 3 and 4 dimensions.
2025LinkExploring writing numbers with place value going in two dimensions - as you go right the place value increases by powers of two, but as you go down it increases by powers of three. This ends up making some arithmetic easier. For example, many numbers can be written with only two bits, making multiplication easy.
2024LinkMinesweeper probability is usually talked about in late game, but I find the early positions interesting too. We’ll explore this a little, and talk about probability more generally.
2024LinkWe’re all too familiar with the normal distribution. But why? One may answer that the normal distribution shows up empirically very often. Someone else may answer that the normal distribution plays an important role in the central limit theorem. But I’d argue that the most special thing about normal distributions is their stability, and that these other properties are owing to the stability.
2023LinkThis is an article about the game goofspiel and about designing goofspiel strategies using genetic algorithms.
2023LinkIn this post, I make new trig-like functions using threes. I call them threegonomic functions. These functions have no obvious use, but they’re fun and their construction may help us appreciate the usual trig functions.
2023LinkWe can talk about probability with a shared understanding. But what does it mean to say the odds of rolling a 4 is 1/6? The exact meaning is a little difficult to say. In this blog, I’ll talk about the formal interpretation of probability, why it matters, and why interpreting is difficult.
2022LinkThis article is on “half derivatives,” defined within. Though there are lots of ways to talk about this topic, I’ve chosen to structure this to touch on a few math topics, making potentially surprising connections.
2020LinkThis paper details an algorithm I wrote for the Axelrod library, which efficiently calculates memory lengths of strategies from their finite state machine represenations.
2019LinkThis is a paper to reproduce and explore Axelrod's second tournament. I was added as an author after my contributions in refactoring.
2019LinkAverage age of death over time of prominent individuals, as defined by headlines in the NYT.
2024Link