A “weeknote”, I am told, is best written on a Friday, and yet here I am putting this second one up on Sunday night. I am sovereign of my domain name, I shall do as I see fit.

A “weeknote”, I am told is not like a blog post, and yet here I am putting this first one on my blog. I am sovereign of my domain name, I shall do as I see fit.

This is a second post about hither, a little stack-based programming language I wrote. In this post I want to talk about the code behind hither a little bit.

“Forth” is the name of a stack-based programming language. I’ve been curious about what goes into writing a programming language for a while now, and after a little prompting from a friend, I decided to give writing one a try. The purpose of this post is to talk a little about what the language I wrote, which I’m calling “hither”, is like. In a future post I’d like to talk about some interesting things I learned along the way.

A sad fact that every topologist should be surprised about at some point in their career is that many apparently "nice" CW complexes are not actually metrizable. The purpose of this post is to introduce CW complexes and talk about metrizing them.

In mathematics, if you squint, the word “real” has a kind of eldritch quality. Although calculus students work confidently with them, and they enable all kinds of nice behavior in topology, the definition of a real number is, well, surreal. The title of this blog post is a pun. You might ask why we need the real numbers, and one answer is “for completeness”. For the same reason, I thought a blog post would be useful.

In this post, I want to kind of bring together the theme of curvature and the theme of affine or projective geometry.

The purpose of this post is to pick up where the last one left off: the story of curvature from a, like, “geometer’s geometer” standpoint.

As a geometric group theorist interested in “CAT(0)” and “hyperbolic geometry”, I appear to care very deeply about notions like “curvature”, but I have to admit my understanding of what it means is not that deep. This post is an attempt (one of likely several) to deepen my understanding. I’d like to bring you along for the ride.

This is a post about affine or projective geometry. It's also a post about intersections. Like, suppose you take two line segments and you want to ask: do these line segments intersect? And suppose you're a little obsessed with linear algebra. So let's use it if we can. As I mentioned in my last post, one useful aspect of the affine or projective perspective on geometry is that it turns affine subspaces, like points and lines that don't have to go through the origin, into linear subspaces of one larger dimension which do contain the origin and thus can be reasoned about and manipulated with matrices and the tools of linear algebra.