Paul Michael Kielstra

It’s final exam season, which means it’s grading season, which means I’ve been looking at student work for nine straight hours and need to blow off steam. So I thought I’d try to get ChatGPT to do something interesting, or, at least, mildly funny. What I got was a surprisingly informative look into the inner workings of large language models, which, once I’ve explained it, will lead me to propose a new Turing test paradigm for determining if you’re talking to a human or a neural network chatbot.

I’m apparently several years late to the party on this one, but I just saw the following tweet:

I’m teaching Math 1A, single-variable calculus, right now. The following problem and solution are for those of my students who found the Intermediate Value Theorem interesting. The problem I got from an entrance test for a university I applied to, which I’m keeping secret in case they still use this question; the solution is my own.

We’re on strike. Here’s what I’ve learned.

Haydn’s The Creation begins with a dramatic instrumental rendition of chaos, followed by a soloist reading from the beginning of the book of Genesis: “In the beginning God created the Heaven, and the earth; and the earth was without form and void; and darkness was upon the face of the deep.” The chorus stands, backed by strings: “And the Spirit of God moved upon the face of the waters.” The orchestra falls silent, and the chorus sings, alone except for quiet instrumental echoes between the phrases: “And God said: Let there be light.”

I’m currently studying for the language exam for my master’s degree, which will involve translating a page of mathematics from French into English. I speak conversational French, but that still leaves me with the need to learn mathematical vocabulary. For this we have the ultimate memory tool. That’s right. I made a set of flashcards to learn mathematical French.

I still haven’t taught a university course yet, and won’t for several years, but I’ve taken opportunities to teach where I’ve found them. I just finished teaching a week-long seminar for Chinese high-school students, entitled The Art of Mathematical Proof but mostly consisting of an introduction to group theory, at the Harvard Summit for Young Leaders in China (HSYLC). This post is my attempt to write down what I’ve learned, on the grounds that I would have had a much easier time if someone had pointed me to a post like it beforehand.

“Oh no,” said Adam. “We’re taking this too seriously. But surely it’s not non-degenerate?”

A friend of mine and I recently decided that it would be a good use of our time to determine how many dragons the USA could support. While exact numbers are obviously hard to come by, it turns out that the answer is about 4500. Here’s how we got there.

Internet, meet Civet. It’s a piece of software I wrote that lets you write very simple scripts to run programs over and over again with different parameters. It came out of a project I’m working on that involves profiling the performance of an algorithm to solve differential equations. I realized that it would be useful to have code that could run through dozens or hundreds of different setups and determine how many iterations the algorithm took to solve each, but without the overhead of a full testing or CI system. If you need to do repetitive experiments with computer software, you should check it out. But that’s not why I want to talk about it now.