5 minutes with Nat Alison, polyhedra enthusiast

One Glitch use case that we absolutely love to highlight, is the situation that occurs when folks play around with Glitch to figure out creative solutions to problems. Which brings me to Nat Alison, a software developer and one such Glitch creator. If you’re anything like me, when you see graphs and x-and y-axis points, your eyes go wonky and you get flustered. Not so for Nat, who introduced me to a totally different world of solving interesting problems with math—and Glitch. Please enjoy our recent conversation, hopefully, as much as I did.

Jenn: How did you discover Glitch?

Nat: I honestly don’t remember! It’s either

Do you have a favorite project you’ve seen on Glitch?

I think it’s less of a specific project and more of a sense of joy whenever I see a Glitch project pop up in the wild! It’s always something quirky or interesting, and reminds me of the good ol’ StumbleUpon days where the internet wasn’t just four websites recycling content. I try to carry that spirit in my work, and I think Glitch does a good job at it too.

Why polyhedra? What do they signify for you?

Do you have a favorite addition to CSS in the past year, and is there anything not-widely-supported that you're hoping will be soon?

Oh man there are so many! Container queries, “:has” selectors, new color spaces. I just checked and they’re adding trigonometry to it. CSS had gotten so powerful recently it’s amazing! The problem is I can’t legitimately can’t tell you which features have been “added” in the past year or which ones are still not widely supported. I was going to answer offset-path but it turns out everything but Safari implemented it in 2020 or earlier!

**Is there an unsolvable puzzle out there that haunts you? **

The Classification of Finite Simple Groups. “Groups” are abstract objects that represent symmetries, like the moves of a Rubiks Cube, or the rotations or reflections of a polyhedron! These symmetries can be broken down into “atoms” called “simple groups”, just like molecules, and by a lucky coincidence there are 18 infinite families just like in the periodic table!

Oh and there are 26 of them that don’t fit into any family, the largest of which is called The Monster and lives in 196,883 dimensions. Like if there were just 26 random atoms made out of strange and charm quarks and one of them was almost as big as the observable universe. Oh and the proof takes more than ten thousand pages. And it has something to do with the most efficient way to pack spheres into 24-dimensional space. And the fact that eπ√163 is almost an integer. Why are they there?? It’s all extremely Cursed Algebra.

Where did you come up with the idea for a permutation group visualizer?

Honestly it was kind of a joke! I was studying the sporadic groups–those 26 groups that are just there for some reason? I plotted one of them to see what it looked like, and let’s just say, the results are not very aesthetically pleasing. Why does it look like that? If this is one of the fundamental atoms of symmetry, why does it look so un-symmetric? I knew I had to make something interactive to show others how baffled I was. Later I found a “prettier” representation of the same group, but my fascination still stands!

This is my introduction to permutation groups - what’s there to know and what's done with this knowledge?

Permutation groups are ways to represent ways to rearrange objects, like a deck of cards or people around a table. They’re the most tactile way to represent a group, whether it’s the transformations of a square or the arrangements of a Rubik’s cube, and it’s often easier to “see” the underlying object they represent. For example, for the symmetries of a square, you can tell the permutation group represents turning and flipping a square. It’s harder to do that with, say, a matrix representation. When I’m looking at something more abstract that doesn’t have a real-world equivalent, it’s a fast way to get a “feel” of how a group works.

Some people’s perception of work in mathematics/abstract algebra looks more like dense research papers and static diagrams—do you consider clean, accessible, interactive work like this to be something to like... fight that, or is there a cohort/movement that you’re working within that deserves more exposure to outsiders?

Definitely! I think, at its core, mathematics is play—exploring abstract concepts, asking weird questions, yeeting numbers—but the notation or the way it’s taught gets in the way of a lot of people getting to enjoy that.

As for cohorts, I’m part of the Explorable Explanations community, which is a group of creators combining play and learning. If you like my stuff you should check out other stuff on their page!

It seems rare to find tools useful for mathematicians that are so fun to click around, is this on purpose?

Haha, I don’t think there’s a secret cabal of mathematicians going “we need to keep math BORING.” I think it’s more that a lot of math tools are meant for research, and so the focus is on utility rather than style. It’s harder to make fun visualizations for a lot of higher level, more complicated math, both because it’s rarer to find someone with UI/UX knowledge that the material and there are usually more prerequisites so it’s hard to convey the point across to the layperson! …though that doesn’t stop me from trying!

What JavaScript dependencies make building stuff like this on the web possible?

I’m using React because it’s what I’m most familiar with but honestly it’s more important to find a toolset that’s right for you and just start making things.

Speaking of the web, what is your favorite thing about the internet?

It’s really hard to say, especially since so much of the Web has been gutted in recent years. Flash is dead, forums have been abandoned for closed off message boards, even your freaking parking meter wants you to sign up for an app… But you can still make a Geocities-style website, or a blog, or a weird math app! And there are places (like Glitch!) that make doing it super-easy now. I remember in college wanting to make an online puzzle game of sorts but was so confused on how to make a website that I… just did it over Google Forms. It’s also the most accessible place to share what you’ve made. I love making web apps because I can show them to anyone on their phones without them needing to download an app, or buy it from a Steam page or what have you.

What’s next for you?

I want to make more math apps! There are more cool things in abstract algebra I want to visualize. My dream is to figure out some way for people to even get a bare glimpse of comprehension of something as complicated as the 196,883-dimensional Monster, and I’m going to do it one math toy at a time.

I’m also looking for a Renaissance-style Patron to fund my strange artistic endeavors (or you know, a normal job would be fine too).

Where can we find you online?

My personal website is https://tesseralis.site. All my socials are there, but I’m mostly (somehow) on Twitter at @tesseralis.

_Software developer and ride or die for polyhedra, Nat’s previous work explores the relationships between math, puzzles, componentry, and Pokémon. _