Strange Symmetries

The project really morphed as I got more into it, just like all creative projects seem to. At first, I started building digital diatoms based on the drawings of Ernst Haeckel, who made thousands of scientific drawings during a three-year ocean voyage on the H.M.S. Challenger in the late 1800's. I'd find a picture of a creature in one of his books, or a photograph from a real microscope field and try to understand its symmetry well enough to describe it, then iterate to create it.

But it turned pretty quickly into a study of mathematics and symmetry rather than trying to recreate the look of real biological creatures digitally.

After a particularly intense set of meetings I built maybe a dozen in my hotel to relax and unwind. This session is where some of my favorite creatures came from, like the Ribbon Weaver and the Penrose Growth Rings. It was meant to be fun and meditative, letting me explore concepts and shapes I liked.

I didn't set out to build an app at all. I started just making these little mathematical creatures for myself, somewhere to spend time with the mathematical ideas I liked without needing them to be useful, the way you'd enjoy a favorite piece of music.

But when I posted a few on social media, someone commented that they looked like they were from a book. It made me wonder: Could I make a book like that? And if so, what kind of a book would that be? A field guide for mathematical creatures? I thought that was a pretty compelling idea!

It gave me a different challenge to: now I had to think of it in terms of the whole of mathematics, what a comprehensive taxonomy might actually look like. That was interesting because there are so many different topics within mathematics, many of which I had barely explored, and others I felt I knew well, like regular tilings.

I challenged myself to see if I could make a dozen. It turned out to be easier than I thought—there are so many breathtaking mathematical concepts waiting to be revealed through beautiful styling. I kept adding more and more ideas, scouring academic papers and math wikis and tessellation groups for ideas. Soon I was nearing a hundred.

I made myself a little field to scroll around to look for my favorites, and you could tap them to watch their animation play. But I had no idea what I wanted to actually do with them, except that I just loved looking at them.

It's not a math app. I think it's the opposite of a math app, actually. It's whatever the opposite of homework is, or the opposite of, remember those math worksheets where you had to do calculations in class as fast as possible? No, no, this is completely different, philosophically. This is about exploration, and wonder, and contemplation.

I wanted to share my personal experience with these creatures. The more time I spent scrolling around the field, the more I started wondering whether the joy I felt coming across one of my favorite beautiful creatures would be fun for other people too. Even, or especially, people who don't consider themselves math people.

I think mathematics works the same way art does. You can fall for the wild branching of a fractal or the texture of a specific tiling without being able to say why, and that's not a lesser kind of understanding. After all, so much art and beauty has a mathematical component. But looking at most mathematical drawings, they're flat and boring, not captivating or awe-inspiring.

I wanted to build a sanctuary where mathematics was beautiful, and discovering these concepts is joyful and calm. For me first, and now, maybe, for you too.

I hope so, actually. I want to replace that anxiety with joy. It's funny, don't think I ever heard the term "math anxiety" growing up, but I completely get it. It's no wonder people have bad experiences with math, so much of the curriculum is just utilitarian skills-building where mathematics is completely stripped of its beauty. You have to memorize the quadratic formula to find roots and do it a hundred times without being able to feel what's happening, so you never build any intuition around it and as a result it becomes tedious or boring or both. Where's the joy? The wonder?

I want everyone to feel that. It's the same with so many other things: music, art, wine... In fact I think it is really quite like wine. Every sommelier can remember a moment with a special wine they enjoyed before they could describe the color or the nose or the palate in detail. We know that we don't need to explain why a wine moves us to know the moment still counts. Being drawn to something—before you know why, before you have the words—is already a real way of appreciating it.

Magic squares! It just completely left me in awe. You have these squares of numbers in a grid and every row, every column, and every diagonal adds up to the same number. I learned that you can make them with a specific algorithm. I was in about grade 6 or 7, and it was like magic to me, like how is that possible, for the symmetry to be so perfect. And it was a simple idea, just adding, but I'd never learned anything like that in class, that's for sure.

The next time was a lot later: Godel's Incompleteness Theorem, which is a theorem about proofs - so kind of meta. The tl;dr on that one is that it's a proof that there are things that are true but that can't be proven. As in, just because something is true doesn't make it provable. It's such a wild, unexpected result.

Math dreams.

Yes. Math dreams. I used to have them all the time when I was in undergrad, when I was studying. A little bit in grad school, too. But basically they are these dreams that are completely conceptual, they are like a feeling and maybe a little bit of a visual but more like a pull of intuition about the truth about something abstract, like the feeling of a certain kind of symmetry. Now that I have spent so much time building and contemplating the creatures in the app, I've been having them again, and they make me wake up with such a feeling of calm and awe that really sets the tone for the whole day.

Most of the biomes I created with a palette in mind because I wanted to visuals to mean something beyond "pretty colors." Many of them are inspired from favorite music videos or paintings or art pieces.

The name is a playful nod to the history of mathematics, which is full of fascinating, archaic terms I wish we'd bring back—like fluents and fluxions, which are the original terms that Newton used in describing calculus. A fluxion is the derivative, and come on, which sounds more interesting?

But you asked about zenzicube. In the 16th century, mathematicians used words like zenzic (for a square) and surd (for a root). A zenzicube was the term for the sixth power of a number (the square of a cube). And they kept going, too. There are zenzizenzics and zenzizenzizenzics and one and one. It's just so much fun to say, there's so much whimsy in it. I wanted to lean into that, so in the app, you'll actually find a couple zenzicube-inspired creatures! They are some of my favorites. And in fact, the logo is a projection of a 6-dimensional cube, which has an "area" of s to the sixth.

I believe this whole "you're a stem person" or "you're an artistic person" is completely false. In fact I think that a lot of technical fields are extremely creative, and I believe that to be a great artist you need analytical skills. But what happens? People go to university and they take classes that are all the same type of focus, and if you don't practice, if you don't build those intellectual muscles then they don't stay strong.

But the work I care about most has always lived at the boundaries between things. The strange symmetries kept pulling me toward questions that didn't belong to any single discipline. Zenzicube is one place they've led.