Evelyn Lamb: Hello, and welcome to My Favorite Theorem, coming at you from the double hurricane part of 2020 today. I mean, I'm not near the Gulf Coast so it's it's not quite as relevant for my life, but that is the portion of the year we are in right now. I am one of your hosts, Evelyn Lamb. I'm a freelance math and science writer in Salt Lake City, Utah. And here's your other host.

Kevin Knudson: Hi. I’m Kevin Knudson, professor of mathematics at the University of Florida. It's just hot here. But you know, there have been, like, fire tornadoes, right, in California? This is all very on-brand for 2020. This year can’t end soon enough.

EL: Yeah, we say that. I feel like I've said that at the end of many previous years, and then it's not great.

Yoon Ha Lee: As a science fiction writer, I have to say never assume it's the worst. It can always get worse.

EL: Yes.

KK: Right, right, right.

EL: Yes. And that is our guest, Yoon Ha Lee. So yeah, would you like to introduce yourself, tell us a little bit about yourself, and maybe talk about your writing a little bit, how you got to writing from the degrees that you have in math.

YHL: So my name is Yoon Ha Lee. I'm from Houston, and I'm a science fiction and fantasy writer. I actually went to Cornell to get a degree in history, and then I realized that history majors starve on the street. So I switched to math, so that I could have an income and ended up not becoming a mathematician. My best-known books are probably the Machineries of Empire trilogy, which is Ninefox Gambit, Raven Stratagem and Revenant Gun. It's space opera, lots of ships blowing up everywhere. And then a kid's book, Dragon Pearl, which is out from Disney Hyperion in the Rick Riordan Presents series. And that one is also a space opera, because ships blowing up is just fun.

EL: Yeah, well, and that's funny. I think I just put together—I had seen the Rick Riordan publishing imprint before, and I just started reading Percy Jackson the other day. And so it's like, oh, that's who that guy is.

KK: And I think I might be the only one among us who is old enough to have seen the biggest space opera, Star Wars, in the theater in its first release.

YHL: Yeah, my parents let me see it on the television when I was six years old, and I was terrified at the point where Luke gets his hand cut off.

KK: That’s Empire.

YHL: I think the second one? I forget which movie it was, but he gets his hand cut off and I had nightmares for weeks. And I'm like, Mom and Dad, Why? Why? Why did you think this was an appropriate movie for a six-year-old? And then I got all the storybooks and I wanted the lightsaber and everything, so I guess it worked out.

KK: Of course, yeah. Well, my movie story—we’re getting off track, but it's it's a good movie story. So when I was six years old, in 1975, my parents thought it would be a good idea to take me to the drive-in to see Jaws. And I had nightmares for months that there was a shark living under my bed, a huge shart that was going to get me.

EL: My husband was born I think right around the time one of them was released. I don't remember which one now. But we were talking with one of his colleagues one time and figured out that on the day he was born, that colleague was going to see that movie, like, the day it came out.

KK: I’m going to guess it was I'm gonna guess it was Jedi. I don't know exactly how old you guys are. But that's that's my guess.

EL: That sounds right. Yeah, I'm not a big star wars person. But yeah, I guess I've always not been sure, like, “space opera.” The term is something that I feel like I know it when I see it. But I don't really know, like, how to describe it. Is it just—do you feel like a categorization of space opera is, like, ships blowing up?

YHL: Ships blowing up, generally bigger, larger-than-life characters, larger-than-life stakes, big galactic civilization types of things. It's basically the Star Wars genre.

EL: Yeah

KK: It works.

EL: yeah. And the Machinery of Empire—the reason that I invited you on here is because I just read Ninefox Gambit a few weeks ago and just thought, you know, this person sure uses a lot of math terms for a novel! So mathematicians might be especially interested in reading this one, it has shenanigans with calendar systems that are based on math and arithmetic and stuff. So yeah, that was fun. So you, in addition to getting a bachelor's degree in math, you got a master's in math education, right?

YHL: Yes, at Stanford. And I ended up not using it for very long. I was a teacher for, like, half a year before I left the profession.

EL: Okay, and was it just that your writing was taking off and you wanted to do that more? Were there other reasons?

YHL: A kid came along. That was the big reason. Yeah.

EL: Oh. Yeah. That definitely can take a lot of time.

KK: Ah yeah, just a little bit.

EL: Well, that's great. So what is your favorite theorem?

YHL: My favorite theorem is Cantor's diagonalization proof. And I discovered it actually in high school as a footnote in Roger Penrose’s The Emperor's New Mind. It was really just sort of a sidelight to the extremely complicated and hard-to-follow argument that he was making in that book on the nature of consciousness and quantum physics, which, as a high schooler, you know, it basically went over my head. But I was sitting there staring at this footnote and going “I don't understand this at all.” He said in the footnote that Cantor had proven that the real numbers, the set of real numbers, has a cardinality greater than the set of natural numbers. And of course, I was a high schooler. I hadn't had a lot of math background. So my understanding of these concepts was very, very shaky. But he said if you make a list of, you know—pretend that you have a list of all the real numbers and you put them, you know, 1, 2, 3, 4, you put them in correspondence with the natural numbers, and then you go down diagonally, first digit of the first number, second digit of the second number, third digit of the third number, and so on. And then you shift it by one. So if the numeral in that place is two, it becomes three, if it's nine, it becomes zero, and so on. So you can construct a number that is not on the list, even though your premise is that you have everything on the list. And I think this was the first time that I really understood what a proof by contradiction was. My math teachers had attempted very hard to get this concept into my head. And it just did not go through until I read that proof and meditated upon it. And it's funny, because I spent most of my life as a kid thinking that I hated math. And yet there I was in the library reading books about math, so I guess I didn't hate it as much as I thought I did.

EL: Yeah, I was thinking a high schooler reading that Penrose book is definitely—yeah, you had some natural curiosity about math, it sounds like.

KK: Yeah, I'm sort of sort of surprised that your high school teachers were trying to teach you proofs by contradiction. That's kind of interesting. I don't remember seeing any of that until I got to university.

YHL: I don't know that they got into depth about it. But this was at Seoul Foreign School, which was a private, international school in South Korea. And they tried to make the curriculum more advanced, with mixed results.

KK: Sure. It’s worth a shot.

EL: Yeah, and this, this is really one of those Greatest Hits. Like if you're putting together the like, record that you're going to send out or something, like, Math’s Greatest Hits with would include this diagonalization argument. It's so appealing. And we've had another guest select that too, Adriana Salerno a few months ago and yeah, just people. I think a lot of people who eventually do become mathematicians, this is one of those first moments where they feel like they really understand some some pretty high-concept math kind of stuff. So did you see this this proof later in school?

YHL: No. Ironically, most of what I was interested in doing when I did my undergraduate degree was abstract algebra. So I didn't even take a set theory course at all. But I knew it was sort of out there in the water, and I don't know, one of the things I loved about math and that led me to switch my major to math was the idea that there were these beautiful ideas and these beautiful arguments, and just sort of the elegance of it, which was very different from history, where—I love history, and I love all the battles and things, like the defenestration of Prague and all the exciting things happening. But you can't really prove things in history. Like you can't go back and run the siege of Stalingrad again, and see what happens differently.

KK: Maybe we could though, right? We have the computing power now. Maybe we could do that. This sounds like your next novel, right? So simulation of Stalingrad, and this time, the Nazis win or something? I don't know.

YHL: Oh no. I mean, science fiction writers totally do that. There's this whole strand of alternate history, science fiction or fantasy. Harry Turtledove is one author who, he likes to have the story where aliens invade during World War II and then the Nazis and the allies have to have to team up against the aliens kind of stories there. There is a set there is a readership for these things. Sure.

EL: So you use a lot of math concepts in your writing, your fiction writing. So have you ever tried to work in diagonalization, or this kind of idea, into any of your stories?

YHL: This one? No. I mean, occasionally, I remember writing a story in college, actually, called Counting the Shapes. And it was just everything in the kitchen sink, because I was taking point-set topology, and so I used it as a metaphor for a kind of magic that worked that way, and other ideas, like, I don't know, I had recently read James Gleick’s Chaos. So I was really interested in chaos theory and fractals. And I don't know that I was super systematic about it, and I sort of suspect that a real mathematician would look at it and poke holes. You know, I'm using this as a magic system, not as rigorous math, more as a metaphor, I guess, or flavor.

KK: Oh, but I mean, writers do that all the time, right? So I, I taught math and lit class with a friend of mine in languages a few years ago. And, you know, Borges, for example, you know, this sort of stuff is all over his work, these ideas of infinity and, and it's even embedded in Kafka and all this stuff, and it can be a wonderful way to to get your readers to think about something from a point of view they might not have thought of before.

YHL: Well, the interesting thing about Ninefox Gambit and the math terminology that I used for flavor is that 20 publishers turned the book down because they said it had too much math. And I my joke about this is that they saw the word diagonalization in the linear algebra matrix context, and they didn't know what that meant, and they ran away from it. Which was extremely discouraging when my agent at the time, Jennifer Jackson, and I were going out on submission with this book. And it's like, it's basically a space opera adventure where people blow each other up. You don't have to worry about the occasional math term. It's just there as flavor for the magic system. But a lot of people—I’m sure you have encountered the fact that a lot of people in the US have math phobia, and this really does affect the readership as well.

KK: Really?

EL: Yeah, that’s funny, because in some way, I mean, you definitely use the the math language to give a certain flavor to the system that this universe is in, but you could sub it out for, like, any Star Trek term,

YHL: Exactly.

EL: t’s just like, oh, yeah, you could put tricorders and dilithium crystals, or, you know, anything in to serve that that because you know, you're it's not a math textbook, no one's learning linear algebra from reading Ninefox Gambit.

YHL: No, exactly. I actually, when I was originally writing the book, like the rough draft, I had my abstract algebra textbooks out and ready to go. And I was going to construct sort of a game engine, a combat engine of how these battles were going to work in an abstract algebra sense. And my husband who, he's not afraid of math, he's actually a gravitational astrophysicist, and he's arguably better at math than I am. But he sat me down and said, “Yoon Ha, you can't do this. You're not going to have any readers because science fiction readers who want to read about big spaceships blowing each other up do not want to have to wade through a math textbook to get to the action.” And I mean, it turned out that he was absolutely correct. So I ended up not doing that and just using it as, you know, “the force,” except with math flavor.

KK: Linear algebra is the force. All right!

EL: That’s so interesting. I noticed on your website that you have a section for games. So do you also like to design games?

YHL: I do design games. And by design games, I mean tiny little interactive, interactive fiction text adventures or really small tabletop RPGs in the indy sense. You know, three page games for five people, no GM, that kind of thing. So I do enjoy doing that. And it is related to math, I think, but it's certainly not something that we learn to do in any of our math classes.

EL: Yeah, well, I mean, personally, I think it would be very cool. Have you have you written up this potential game, the abstract algebra game thing into an actual game? Or was that kind of abandoned on the editing floor while you were putting the book together?

YHL: It got abandoned on the editing floor. Also because it would have been a tremendous time suck. And, you know, it would have been a fun idea. But if I wasn't going to use it in a book, and it certainly wasn't going to be used in like a computer game or some something like that, there just didn't seem to be enough incentive to go ahead and do it.

EL: Yeah, probably the market of math mathematicians who read sci fi is, you know, not a tiny market but maybe not quite the demographic you're looking for. But I'm just imagining, like, hauling out the Sylow theorems to, like, explode someone’s battle cruiser or something. Just saying that, you know, if you were bored some time and wanted to sink a bunch of time into that.

YHL: if somebody else wrote it, I would definitely buy it and read it, I have to say.

KK: All right. The challenge is out there, everybody. Everybody should get on this.

EL: Yeah, very cool. Yep.

KK: So another thing we do on this podcast is we ask our guests to pair their theorem with something. So what pairs well, with Cantor's diagonalization argument?

YHL: Waffles.

KK: Waffles? Oh, well, yeah.

YHL: Because sort of that grid shape. I know, this is super visual. But the waffles I'm thinking of, my husband did his postdoc at Caltech, so we lived in Pasadena. And when we were there, there was this delightful Colombian hotdog place. And they also made the best waffles with berries and fruit and syrup and whipped cream. And those are the waffles I think of when I think of the diagonal slash proof.

KK: Right. And so the grid is actually fairly small. Is it one of those waffle makers?

YHL: Yeah.

KK: Yeah. Okay, so I have a Belgian waffle maker, and it's fine. It makes four at a time, but those holes are pretty big. Right? I'm thinking of, like, the small, Eggo style, right? You can put a lot of digits.

EL: You could also, like, I guess, maybe a berry is too big to fit in them, but I'm just thinking you can put different things in all of them, make sure no two waffles have the same arrangement of syrup and berries and cream.

KK: This is a good pairing. I'm into this one a lot.

YHL: I’m hungry now.

KK: Yeah.

EL: Yeah. I just had lunch, so for once I don't leave this ravenous. So would you like to let people know where they can find you online?

YHL: Online I’m at yoonhalee.com. I'm also on Twitter as @deuceofgears and also on Instagram as @deuceofgears.

KK: Deuce of gears. Is there a story there?

YHL: It’s the symbol of the crazy general in Ninefox Gambit. Okay. And also, because I'm Korean, there are five zillion other Yoon Ha Lees. So by the time I joined Twitter, all the obvious permutations of Yoon Ha Lee had already been taken, so I had to pick a different name.

EL: Yeah, and if I'm remembering correctly, there are sometimes cat pictures on your Twitter feed. Is that right?

YHL: Yes. So the thing that I post periodically to Twitter is that my Twitter feed is 90% cat pics by volume. There are people who, you know, they tweet about serious things, or politics, or so on, and these are very important, but I personally get stressed out really easily so I figure people could use an oasis of cheerful cat pictures.

EL: Yes, I just wanted to make sure our listeners have this vital information that if they are running low on cat pictures, this is a place they can go. It's definitely been an important part of my mental health to make sure to look at plenty of cat pictures during this—these stressful times as they say.

KK: Yeah, on Instagram, I follow a lot of bird watching accounts. So I just get a feed of birds all day. It's better for my mental health.

EL: Well maybe Yoon’s cat would like that,

KK: I suspect yes, that's right. That's right. Yep.

EL: Yeah, we were talking to a friend who said that they have some bird feeders outside, they just have indoor cats. And the cats will meow to get them to open the windows in the morning so they could watch the birds outside. It’s like, “Mom, turn on the TV.”

YHL: I tried putting on a YouTube video of birds, and my cat was just completely indifferent to the visuals. But she kept looking at the speaker where the bird sounds were coming from.

KK: Hmm.

EL: Interesting. I guess maybe hearing is like more of a dominant sense or something? Cats have pretty good vision, though, I think.

YHL: Yeah, I think she's just internalized that nothing interesting comes out of the moving pictures.

EL: Yeah. Well, thanks for joining us. I really enjoyed talking with you.

KK: This has been good.

YHL: It’s been an honor.

On this episode of My Favorite Theorem, we were happy to talk with Yoon Ha Lee, a sci-fi and fantasy writer with a math background, about his favorite theorem, Cantor's proof of the uncountability of the real numbers. Here are a few links to things we mentioned in the episode:
Yoon Ha Lee's website, Twitter account, and Instagram account

Our episode with Adriana Salerno, who also loves this theorem
Roger Penrose's book The Emperor's New Mind

James Gleick's book Chaos
Harry Turtledove