Picture Yourself as a Worm by Paige B. '24

The way we interact in our three-dimensional world is frankly kind of confusing, especially considering how many different visualizations there are possible.⁠01 It's important to note how I am defining dimension here. By dimension, I refer to the number of independent directions on your space. The most clear understanding of this may be through the directions on Earth: up/down, left/right, and forwards/back. The number of these directions is (vaguely) the dimension of what you're considering.

On the one hand, we can understand our three-dimensions through lower dimensions. For instance, the Earth is locally homeomorphic to R^2, by which I mean, it looks like a plane at a given location (if you suppose that you can only see a short distance away). This isn’t to say that flat-earthers are by any means correct, but I think the misconception’s origins do, to some extent, make sense. A perhaps less controversial way to understand this can be seen through the use of cameras; taking a photo of our three-dimensional world results in a two-dimensional image of what can be seen from where you point the camera. But I digress.

These examples motivate numerous areas of study in math, in particular single-variable and multivariable calculus. But there are similarly interesting ways to understand our world through higher dimensions, however weird that may seem.

The most common example of this is found in physics, in which we consider the fourth dimension of time. Some might disagree with this notion, given that time is independent of our “space”,⁠02 i.e. the notion of time <strong>and</strong> space but for the purposes of this blog, I will not be worrying about this distinction. I promise that soon this blog will become less technical and the metaphor will come through but this is the set up.

When I was at my most existential, I used to worry that humans were pieces of four-dimensional beings. When I brought this up with my friend, he said (understandably) “what the heckers?”– but hold on, I will explain what I mean. Consider cutting an apple into thinner and thinner slices. The more thin you make these slices, the more 2-dimensional it becomes. Of course, in our real world we could never actually get to something 2-dimensional, given that the slices of apple will always have some non-infinitesimal thickness, but in math this notion works out quite nicely. In math, a “slice” of a three-dimensional object is two-dimensional. And in fact the higher up in dimensions we go, the more this is true. A slice of a four-dimensional object, is three dimensional. So when I was at my most existential, I worried that there might be some higher-dimensional-being that I’m merely a slice of. A fragment of. An infinitesimal part of.

As it turns out, for some reason, this is a concept that also comes up in philosophy.⁠03 I'd like to thank Ana Sanchez '22 for telling me about this somewhat cursed but also beautiful concept This concept is known as McTaggart’s “B model of time”, and vaguely follows like this.

Picture yourself as a worm (a four-dimensional one at that).⁠04 don't you love it when the title of a piece is in the text? I love when that happens. If you take a slice of this worm at a given time, you obtain a three-dimensional slice of your life. It’s like the most detailed picture you can possibly imagine. Your worm contains all the versions of you, throughout time and space, continuously growing, and changing, and evolving with you.

You may wonder what the point of this is– what the concept of a four-dimensional worm actually gives you in a philosophical sense. And while there are many possible take-aways from this concept in the Philosophy of Time and numerous other areas of study, I’m interested in the worm’s relationship with identity.

Identity changes and shifts over time, but identity in the past is an integral part of who you currently are. As someone who’s trans, I think about this quite a lot (though I’m certain you can find a part of your identity that is similar). I am a woman– that is my identity, right here, right now. But the fact that I grew up understanding my identity to be a masculine one no doubt plays a role in who I am today. It plays a role physically, for instance how I’m  6’1″~.⁠05 I am now the tallest blogger take that @ Alan But it also plays a role emotionally, in worrying about being too tall, or wondering what childhood experiences I missed out on. And while it plays this role in my identity, it doesn’t change the fact that my four-dimensional worm is a woman.

This visualization of the human experience is a bit obscure, but I find it comforting. Something along the lines of “I stand on the shoulders of the giants I once was” or another. It makes me feel like I’m not stagnant– I’m growing with my worm over time, though at any point of the worm the world is (locally) three-dimensional (i.e. homeomorphic to R^3, vocab word of the day).

Now for the part of the blog in which I get more into why the hell I’m writing about this.⁠06 alas it isn't just to cause an existential crisis with your morning dose of college applications

Picture yourself as numerous four-dimensional worms,⁠07 one simply wasn't enough for this blog post  where each worm is a part of your identity. One worm might love crocheting, another love building things, another love teaching. (Yes, this is once again a blog about struggling with numerous parts of my identity.) What happens to these worms when parts of your identity start to fade out?

This summer I wrote that I wanted to spend this summer focusing on being an academic. Focusing purely on my math, and math research, and whatever the hell it means to “be a mathematician”. I felt like this would be the only real way to know if I would like being a graduate student. Because as a graduate student, it may be hard to find the time to work on hobbies/side interests you find interesting. I recognized that this is the case, and wanted to see if I would like who I become if I stop putting in the effort to satiate the various other parts of my identity (the other worms, if you will). I planned to essentially starve out the worms that like writing and teaching so that the academic one could thrive (now I’m picturing a worm doing research, a funny thought).

Then, I got into the semester, and you know what happened? I found myself still making time for these interests of mine. I kept hopping on calls with OCW, I became a blogger, I started being the UA⁠08 undergraduate assistant for 18.101,⁠09 Analysis and Manifolds I created a club to explore maths communications between undergraduates (more on this soon), and all of these worms kept existing.

I’m certain in the process some parts of my identity have died down a little. I no longer do puzzles quite like I used to, and I haven’t been working as closely with The Tech as I did last year. These parts dying down for a little bit don’t mean they are gone forever. The slices of the worms in the past still exist, and who knows, after college I might be able to bring them back to life. And these parts of my identity dying down certainly doesn’t mean they aren’t a part of me. They are a part of my past self, and they may be a part of my future self.

Right now, I’m just a four-dimensional worm; growing, evolving, and changing with time. Who I was in the past is a part of who I am now, and who I am now will be a part of who I am in the future. I find that quite exciting.

For now, I will save the existential crisis on “If my four-dimensional worms are slices of five-dimensional beings” for another day.

P.S. If you want to learn more about understanding four-dimensions through the use of three-dimensions, or three through two, etc., I highly consider the book Things to Make and Do in Four Dimensions by Matt Parker, as well as this maths-comedy special by Matt himself. This was actually one of the things I wrote about in my MIT application way back when, and here I am now studying n-dimensions and projection theory. More on that research at another time.