If you knew that you wanted to learn 10 spoken languages, it would probably be helpful to take a course in linguistics first. Or maybe to have a linguistics course after learning your first or second language. And if the languages are related, it would help to know something about the linguistics of that group […]
When I was writing my post on lemniscate functions yesterday, a line from the Wikipedia article seemed familiar for reasons I cannot place. Defining a tangent-sum operator as a ⊕ b := tan(arctan a + arctan b) gives cl² z ⊕ sl² z = 1. I feel like I’ve seen this tangent-sum used before, but […]
This is the third post in a series on generalizing sine and cosine. The previous post looked at a generalization of the sine and cosine functions that come from replacing a circle with a lemniscate, a curve that looks like a figure eight. This post looks at replacing the circle with a hyperbola. On the […]
Setting up Unicode on my MacBook took some research, so I’m leaving myself a note here if I need to do it again. Maybe it’ll help someone else too. Update: I’ve gotten some feedback on this article that suggest people imagine that I want to use this approach to enter large quantities of text, such […]
Paul Graham said “Programming languages teach you not to want what they don’t provide.” He meant that as a negative: programmers using less expressive languages don’t know what they’re missing. But you could also take that as a positive: using a simple language can teach you that you don’t need features you thought you needed. […]
This post will discuss two scripting languages, but that’s not what the post is really about. It’s really about expressiveness and (or versus) productivity. *** I was excited to discover the awk programming language sometime in college because I had not used a scripting language before. Compared to C, awk was high-level luxury. Then a […]
A common idiom in command line processing of text files is … | sort | uniq | … Some process produces lines of text. You want to pipe that text through sort to sort the lines in alphabetical order, then pass it to uniq to filter out all but the unique lines. The uniq utility […]
I recently evaluated two software applications designed to find PII (personally identifiable information) in free text using natural language processing. Both failed badly, passing over obvious examples of PII. By contrast, I also tried natural language processing software on a nonsensical poem, it the software did quite well. Doctor’s notes It occurred to me later […]
An isomorphism is a structure-preserving function from one object to another. In the context of graphs, an isomorphism is a function that maps the vertices of one graph onto the vertices of another, preserving all the edges. So if G and H are graphs, and f is an isomorphism between G and H, nodes x […]
This post will look at the National Football League through the lens of graph theory, topology, and binary numbers. The NFL has a very nice tree structure, which isn’t too surprising in light of the need to make tournament brackets. The NFL is divided into two conferences, the American Football Conference and the National Football […]
