Short Wave - A Mathematician's Manifesto For Rethinking Gender

Episode Date: September 14, 2020

In her new book, x+y, mathematician Eugenia Cheng uses her specialty, category theory, to challenge how we think about gender and the traits associated with it. Instead, she calls for a new dimension of thinking, characterizing behavior in a way completely removed from considerations of gender. Email the show at [e-mail] pcm.adswizz.com for information about our collection and use of personal data for sponsorship and to manage your podcast sponsorship preferences.NPR Privacy Policy

Hey, everybody, Maddie Safaya here. And Emily Kwong. All right, Kwong. Are you ready for some real talk right now, a little heart to heart? It's my favorite kind of talk. Yes. So just like all of you, the shortwave team is figuring out how to make our way through this pandemic. And making a daily science podcast is hard.

Making one in the middle of a pandemic from our home closets and blanket forts is even harder. So in order to continue bringing you the best. best possible show. We're making a few changes over here. Starting this week, we'll be dropping episodes in your feeds four times a week instead of five. We plan to be back to five days a week soon. You'll still get the pandemic coverage you need. And we promise we'll still get weird and silly with you on a regular basis in the name of science, of course. Because we don't know any other way. Of course. Yeah, we can't really help it. No. It's true. This will allow us to take care of ourselves a little bit better and keep doing what we love most bringing you

this show. Thank you all for understanding. We knew you would. Okay, I'm ready for the show? Oh yeah. It's a good one. You're listening to Shortwave from NPR. So one of the things I most remember from elementary school is all of the math word problems. You know what I'm talking about. The ones that say things like, okay, if Alex has seven cookies and Sam has Three cookies. How many cookies do we need to give Sam to make sure they have the same number of cookies? I would get so excited every time I got the right answer to one of these problems. Anyway, this one is actually pretty easy. Well, we could give four more cookies to Sam, or we could take four cookies from Alex,

or we could make Alex give two cookies to Sam. But for Eugenia Cheng, a mathematician, the better answer is actually. to ask a different question. What if Sam doesn't even like cookies and would rather have apples? See, Eugenia studies this kind of high-level math I'd never heard of, to be honest, called category theory. Yes, category theory is a very abstract part of math,

and it's so abstract that sometimes even other pure mathematicians think it's too abstract. But for me, it's about the core of what makes math tick. And because math, for me, is about the core of what makes the world tick, category theory is like the core core of what makes the world tick. Because category theory is about understanding why things work the way they do. Intrinsic characteristics don't really matter. What matters is how things relate to one another. It started in around the middle of the 20th century. And in a way, it's only a very small, small new idea, but like great ideas, a sort of.

small shift in perspective opens up an absolutely vast array of possibilities because it's like turning on a light. Which is why in her most recent book, X plus Y, Eugenia uses category theory to turn the light on something that at first might seem surprising for a mathematician, something deeply ingrained in many of us, gender. It suddenly illuminates everything and you can see all sorts of things you didn't see before. And so in the same way that we stop focusing on cookies, which not everyone wants, what happens if we also stop focusing on gender constructs, which might not be relevant? Category theory invites us to stop asking if men, women, and non-binary people are equal, and to look beyond the single dimension of gender.

Today on the show, an abstract mathematician's approach to rethinking gender. I'm Emily Kwong, and you're listening to Shortwave from NPR. Okay, so back to Alex, Sam, and their cookie dilemma. The metaphor serves a larger point that our thinking about gender is one-dimensional and doesn't characterize how people really are. Even when we think about gender as a spectrum between masculine and feminine behavior. That's already a problem because it makes it sound wrong. So it makes it sound like men are supposed to be masculine. And if a woman is masculine, then she's somehow going against her nature.

And then if men are seen as being feminine, then that sounds like there's something wrong with them as well. Whereas, in fact, there's no reason to associate gender with character, and everyone can be all sorts of things. If a type of character and behavior is something we value, then why wouldn't we value it from everybody of all genders? So Eugenia started to think about character as a dimension separate from gender, asking how much our society value certain character traits overall. others. And she came up with her own way of categorizing behavior, one that deals with two new traits, she invented, ingressive and congressive. And the idea is that ingressive traits are more about individualism and single track thinking. And Congressive is about bringing things together, bringing people together, bringing ideas together, and thinking about broader communities

and society as a whole rather than individuals. And it's not trying to be a new dichotomy. It's trying to be a way of thinking about behavior and having words, because if you don't have words to think about things, then it's much harder to think about them. Reflecting on her own career, Eugenia realized early on that she forced herself to be aggressive. That is individualistic and single-minded,

and she did land prestigious, jobs in academia. I'm sort of ashamed of it now because I don't like that kind of behavior, but I definitely latched onto the idea that in academia, it's important to make kind of aggressive arguments and show how clever you are and be able to talk yourself up. Because ultimately, she says the academic environment was aggressive and relentless. It was such a kind of ongoing treadmill in my tenured job because it was a very all-year thing. And I remember one August getting ready for the new academic year and feeling like it had been about one minute since the previous academic year.

And I thought, oh, it's just going to be like this until I retire now. And then, honestly, what happened was I started looking around at the people around me who were close to retirement. And I thought, oh, no, I'm becoming like them. And I didn't want to. to. And I thought I have to get out of this before I become sort of fossilized into this kind of behavior that I don't like. So she left the traditional tenure track and became a professor at the School of the Art Institute of Chicago as their scientist in residence. That's right. Eugenia

began to teach math to art students. She wanted to make math more relevant to them. And then came the 2016 election, a moment that brought issues of gender and race into focus. And it was like I flipped a switch in my mind and I thought, you know, silence is complicity. If I don't talk about these things, then am I complicit with these things? It's too important not to talk about it. And I thought actually every academic discipline is there to help us understand the world. And what is the most important thing in the world that we need to understand right now? It is this social and political situation that we're getting ourselves into. And so then I felt like I really had to talk about it all the time. So the question for her became, how do I get my

students to unlearn all of the ingressive, competitive, answer-driven math they've been taught for so many years, especially when there are so many concepts to learn and so little time. And Eugenia kind of figured it out by making sure that everyone in the class learns together, aka, congressively.

Take, for example, this hands-on activity she does to teach them about platonic solids. And I don't tell them what the platonic solids are. And so, in case, you can't remember or never knew. The platonic solids are the three-dimensional shapes that are maximally symmetric. And some of them are built out of triangles.

And so they sit down and they build things together and they talk to each other while they're doing it and it's therapeutic because it's cutting and sticking things together. And some of them build platonic solids. And some of them build things that are almost platonic solids that have a lot of symmetry but aren't quite platonic solids. And then someone will build a dinosaur. and the thing is that if you build a dinosaur, right, if you build a dinosaur, then what you discover

is that pentagons are a really terrible shape for building a dinosaur, whereas triangles are a fantastic shape for building a dinosaur. You can build practically anything with triangles, and that's a profound mathematical fact. Triangulations are really a really important tool in high-level research, And so whatever they do, they will learn something. And when we pool everything we've built as a class, we will get all of these things, even if not every individual person, built every individual platonic solid.

And so that is one way that we can do Congressive explorations, rather than sitting down and sort of memorizing, these are the platonic solids, these are the properties they have. This one is called this, and it has this many faces and this many vertices, and this many edges.

I've been in those classes. Yeah. In this way, like you're holding up the dinosaur and you're discovering something together about platonic solids through this joint exercise. Right. And in her class, she uses concepts from math

to probe the relationships between people. And the thing about a Congressive classroom is that students are able to probe back. Ask how all of this applies to say different types of privilege in society. And that moment was something that I would never have come up with that idea about privilege and factors of numbers and the geometry, if my art student hadn't asked me these questions and push things further and further,

because when you're teaching congressively, I think it's important to find what motivates the students and tap into that. When you're teaching ingressively, you try and bend their will to yours to try and show them, this is the right way of thinking. This is the way. Instead of meeting them somewhere, which is a congressive way. The key for Eugenia is to make math a process of mutual discovery, one that's truly inclusive and not competitive. Her classroom is a place where in the same breath that students are learning math,

they can have frank conversations about the role of race and gender in society. If you ask them to stop thinking about it when they come into the math classroom, then they won't be interested in anything I say. And the people who think that we should stop talking about it in math, for them, it's not part of their life all the time because they're part of their life. of a group that doesn't have to think about it all the time. And so that's the reaction I get. Mostly it's amazement from people who really, really resonate with these issues.

But you might be wondering, what about people who are more aggressive? Aren't they getting lost in the shuffle? Some people worry that I'm now making it non-inclusive towards aggressive people. And I've had this query sometimes. And it's an interesting one because the thing is, I do think, I do, value Congressive behavior more than ingressive behavior. But if you think of it as, for example, ingressive people are obstructive towards others in the classroom. So then what we're saying is that I'm not going to be inclusive towards obstructive behavior in the classroom. And I think that's

okay. I don't feel any reason to include obstructive behavior in my classroom. And so inclusivity is subtle. I don't think it means that we need to include all things. I don't need to include violence in my classroom. I don't need to include intellectual violence and I don't need to include behavior that obstructs and squashes other people either. And I don't think that means I'm not being inclusive. I think it means that I'm valuing things that are helpful to our community and I am not valuing things that are obstructive to our community. We have talked about everything in this conversation. I'm just, I showed up, you know, we're going to talk about math and we're talking about relationships, we're talking about how we learn

and how we teach, how communities work. I mean, it's just, it kind of encompasses so much of actually what's really going on right now in society around race and gender too. So I guess the only other thing I really want to ask you is what is like the single most powerful thing that listeners can take to become more progressive in their lives and create progressive situations at home. And yeah. I think to notice when we're fabricating competition that doesn't have to be a competition,

competition comes from a scarcity of resources. And we do not live in a world of scarcity of resources at the moment. It has been fabricated to have a scarcity of resources. And then we fabricate competitions like music competitions. Music of all things is a thing that doesn't need to be a competition. Education doesn't need to be a competition because what we're learning is understanding and knowledge and wisdom and there isn't a limit on that resource. We can all have it. We don't have to prevent somebody else from having it

in order to have it ourselves. And conversations end up being competitive where the idea seems to be to win an argument. Whereas why are we trying to win in an argument? And if we try and iron out contrived ingressive situations in individual personal interactions, then we can build up from there, because the world is made of little interactions that build up into big ones. And I really think that even if we start small, we can build up to change the whole world to be a better place for everybody of all genders. Eugenia's latest book, X plus Y,

a mathematician's manifesto for rethinking gender, is out now. Today's episode was produced by Rebecca Ramirez. She and I fact-checked it, and Viet Le gave it a masterful edit. I'm Emily Kwong, and this is Shorwave from NPR.