Episode 56 - Belin Tsinnajinnie

07/09/20 • 35 min

Evelyn Lamb: Hello, My Favorite Theorem listeners. This is Evelyn. Before we get to the episode, I wanted to let you know about a very special live virtual My Favorite Theorem taping. If you are listening to this episode before July 16, 2020, you’re in luck because you can join us. We will be recording an episode of the podcast on July 16 at 4 pm Eastern time as part of the Talk Math With Your Friends virtual seminar. Join us and our guest Annalisa Crannell to gush over triangles and Desargues’s theorem. You can find information about how to join us on the My Favorite Theorem twitter timeline, on the show notes for this episode at kpknudson.com, or go straight to the source: sites.google.com/southalabama.edu/tmwyf. That is, of course, for “talk math with your friends.” We hope to see you there!
[intro music]
Hello and welcome to my favorite theorem, the podcasts that will not give you coronavirus...like every podcast because they are podcasts. Just don't listen to it within six feet of anybody, and you'll be safe. I'm one of your hosts, Evelyn Lamb. I'm a freelance math and science writer in Salt Lake City, Utah. And this is your other host.
Kevin Knudson: Hi. I’m Kevin Knudson, professor of mathematics at the University of Florida. So if our listeners haven't figured out by now, we are recording this during peak COVID-19...I don’t want to use hysteria, but concern.
EL: Yeah, well, we'll see if it’s peak concern or not. I feel like I could be more concerned.
KK: I’m not personally that concerned, but being chair of a large department where the provost has suddenly said, “Yeah, you should think about getting all of your courses online.” Like all 8000 students taking our courses could be online anytime now... It's been a busy day for me. So I'm happy to be able to talk math a little bit.
EL: Yeah, you know, normally my job where I work by myself in my basement all day would be perfect for this, but I do have some international travel plans. So we'll see what happens with that.
KK: Good luck.
EL: But luckily, it does not impact video conferencing.
KK: That’s right.
EL: So yeah, we are very happy today to be chatting with Belin Tsinnajinnie. Hi, will you introduce yourself?
Belin Tsinnajinnie: Yes, hi. Yá’át’ééh. Shí éí Belin Tsinnajinnie yinishyé. Filipino nishłį́. Táchii’nii báshishchíín. Filipino dashicheii. Tsi'naajínii dashinalí. Hi, everyone. Hi, Evelyn. Hi, Kevin. My name is Belin Tsinnajinnie. I'm a full time faculty professor of mathematics at Santa Fe Community College in Santa Fe, New Mexico. I’m really excited to join you for today's podcast.
EL: Yeah, I'm always excited to talk with someone else in the mountain time zone because it's like, one less time zone conversion I have to do. We're the smallest, I mean, I guess the least populated of the four major US time zones, and so it's a little rare.
BT: Rare for the best timezone.
EL: Yeah, most elevated timezone, probably. Yeah, Santa Fe is just beautiful. I'm sure it's wonderful this time of year. I've only been there in the fall.
BT: Yeah, we're transitioning from our cold weather to weather where we can start using our sweaters and shorts if we want to. We're very excited for the warmer weather we had. We're always monitoring the snowfall that we get, and we had an okay to decent snowfall, and it was cold enough that we're looking forward to warm months now.
EL: Yeah, Salt Lake is kind of the same. We had kind of a warm February, but we had a few big snow dumps earlier. So tell us a little bit about yourself. Like, where are you from? How did you get here?
BT: Yeah. I am Navajo and Filipino. I introduced myself with the traditional greeting. My mother is Filipino, my father is Navajo, and I grew up here in New Mexico, in Na’Neelzhiin, New Mexico, which is over the Jemez mountains here in Santa Fe. I went to high school, elementary school, college here in New Mexico. I went to high school here in Santa Fe. I got my undergraduate degree from the University of New Mexico, and I ventured all the way out over to the next state over, to University of Arizona, to get my graduate degree. While I was over there, I got married and started a family with my wife. We’re both from New Mexico, and one of our biggest goals and dreams was to come back to New Mexico and live here and raise our families where our families are from and where we're from. And when the opportunity presented itself to take a position at the Institute of American Indian Arts here in Santa Fe, it's a tribal college serving indigenous communities from all over the all over the nation and North America, I wanted to take that. I feel very blessed to have been able to work for eight years at a tribal college. And then an opportunity came to serve a broader Santa Fe, New Mexico community, where I also serve communities that are near and dear to my heart, where I've been here for over 30 years. And I'm ...

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Episode 55 - Rebecca Garcia

Evelyn Lamb: Hello and welcome to my favorite theorem. Math podcast. I'm one of your hosts Evelyn Lamb. I'm a freelance math and science writer in Salt Lake City, Utah. And this is your other host.
Kevin Knudson: Hi. I’m Kevin Knudson, professor of mathematics at the University of Florida. How's it going?
EL: All right, it is a bright sunny winter day today, so I really like—I mean, I'm from Texas originally, so I'm not big on winter in general, but if winter has to exist, sunny winter is better than cloudy winter.
KK: Sure, sunny winter is great. I mean, it's a sunny winter day in Florida, too, which today means it is currently, according to my watch, 81 degrees.
EL: Oh, great. Yeah.
KK: Sorry to rub it in.
EL: Fantastic. It is a bit cooler than that here.
KK: I’d imagine so.
EL: So yeah. Anything new with you?
KK: No, no. Well, actually so so my I might be going to visit my son in a couple of weeks because he's studying music composition, right? And the the orchestra at his at his university is going to play one of his pieces, and so kind of excited about that.
EL: Very exciting! Yeah, that's awesome.
KK: Yeah, but that's about it. Otherwise, you know, just dealing with downed to trees in the neighborhood. Not in our yard, luckily, but yeah, stuff like that. That's it.
EL: Yeah. Well, we are very happy today to have Rebecca Garcia as a guest. Hi, Rebecca. How are you?
Rebecca Garcia: Hi, Evelyn. Håfa ådai, I should say, håfa ådai, Evelyn, and håfa ådai, Kevin. Thanks for having me on the program.
EL: Okay, and what—håfa ådai, did you say?
RG: Yeah, that's right. That's how we, that's our greeting in Chamorro.
EL: Okay, so you are originally from Guam, and is Chamorro the name of a language or the name of a group of people, or I guess, both?
RG: It’s both actually. Yes. That's right. And so Chamorro is the native language in the island. But people there speak English mostly, and as far as I'm able to tell I think I'm the first Chamorro PhD in pure mathematics.
EL: Well, you’re definitely the first Chamorro guest on our show. I think the first Pacific Island guest also.
KK: I think that's correct. Yeah.
EL: So yeah, how did you—so you currently are not in Guam. You actually live in Texas, right?
RG: I do. I'm a professor at Sam Houston State University, which is in Huntsville, Texas, north of Houston. And I'm also one of five co-directors of the MSRI undergraduate program.
EL: Oh, nice. That seems like it is a great program. So how did you how how did you get from Guam to Huntsville?
RG: Oh my goodness. Wow. That is a that is a long, long journey.
KK: Literally.
RG: I started out as a as a undergraduate at Loyola Marymount University, and I had the thought of becoming a medical doctor. And so I thought we were supposed to do some, you know, life science or you know, chemistry or biology or something along those lines. And so I started out as one of those majors and had to take calculus and fell in love with calculus and the professors in the math department. And I was drawn to mathematics. And that's how I ended up on the mathematics side. And one of the things that I learned in my undergraduate career was these really crazy math facts about the rational numbers. And so that's one of the things that interested me in mathematics, was just the different types of infinities the concept of countable, uncountable, those sorts of things.
EL: Yeah, those those seem to be the kinds of facts that draw a lot of people into this rich world of creativity and math that you might not initially think of as related to math when you're going through school. So I think this brings us to your favorite theorem, or at least the favorite theorem you want to talk about today.
KK: Sounds like it.
EL: Yeah, so what’s that?
RG: Yeah. So it’s more, I would say, more of a fun fact of mathematics that the rationals first of all are countable, meaning they are in one-to-one correspondence with the natural numbers. And so you can kind of, you know, label them, there's a first one and a second one in some way, not necessarily in the obvious way. But then, at the same time, they are dense in the real numbers. So that to me, just blows my mind, that between any two real numbers, there's a rational number.
EL: And yeah, so you can't like take a little chunk of the real line and miss all the rational numbers.
RG: That’s right.
KK: Right.
RG: That to me just blows my mind. Because—and then you just sort of start, you know, your brain just starts messing with you, you know, between zero and one there are infinitely many rational numbers and yet they're still countable. And it just, it just starts to mess with your mind a little bit. Right?
EL: Yeah. Well, and we were we were talking about this a little bit before and it's this weird thing. Like, yeah, there's, like a c...

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Episode 57 - Annalisa Crannell

Evelyn Lamb: Welcome to My Favorite Theorem, joining forces today with Talk Math With Your Friends. I'm Evelyn Lamb. I co-host this podcast. I'm a freelance math and science writer in Salt Lake City, Utah. And this is your other host.
Kevin Knudson: Hi, I'm Kevin Knudson, professor of mathematics at the University of Florida, where it is boiling hot today, and I’m very happy to be in this—how would they put this on on TV?—crossover event, right?
EL: Yeah.
KK: So like, I think last night on NBC, on Wednesday nights, there are all these shows that take place in Chicago: Chicago Med and Chicago PD and Chicago Fire, Chicago Uber, who knows what. Anyway, sometimes they'll just merge them all into one three-hour super show, right? So here we go. This is the math version of this, right?
EL: Yes. And I realized today that our very first episode of My Favorite Theorem, we published that in late July 2017. So this is our early third birthday! And we're so glad that people came to join us! And we are very happy today to have our guest Annalisa Crannell with us. Hi, Annalisa. Can you introduce yourself and tell us a little bit about yourself?
Annalisa Crannell: So hi, my name is Annalisa Crannell. I profess mathematics at Franklin and Marshall College, which is in south-central, southeastern Pennsylvania. It's a small liberal arts college. I got my PhD working in differential equations, partial differential equations, nonlinear differential equations, switched into discrete dynamical systems, topological dynamical systems, but for the past 10 or 15 years have been really thinking hard about projective geometry applied to perspective art.
KK: That’s quite the Odyssey.
AC: Yeah, I was really influenced by by Paul Halmos saying that one of the marks of a really good mathematician is that they can change fields. And so yeah, I feel like I'm trying to enjoy so many different aspects of what this profession allows us to do.
EL: And a fun story, at least it was fun for me, is that one time you were here in Utah giving a talk at BYU, which is down the street. And we went to an art gallery and you pulled out your chopsticks and showed me how you use your chopsticks to help you know where to stand to best appreciate art, and it was just so amazing to me that that was this thing that you could do. So that was that was a lot of fun. And I think it just, to me, sums up the Annalisa experience.
AC: Thank you. Yeah, summing, I guess, is a good thing for mathematicians. I think everybody should carry chopsticks with them. I mean, it's great. It's frugal. It helps you avoid to trash, but it also helps you do really cool mathematics. So what's what's not to love about them?
EL: Yeah. So what is your favorite theorem?
AC: So if you had asked me about five years ago, I would have said the intermediate value theorem. But today, I am going to say no, Desargues’ theorem. So Desargues’ theorem first came into human knowledge in the 1640s. And it's a theorem that sounds like it's sort of about planar geometry, but I really think of it as being about perspective. So is this when I'm supposed to tell you what the theorem says?
KK: Yes, please.
EL: Yeah. Okay, should we all get out our—so this is one, I feel like I always need like a piece of paper. (I’m trying to hold it up, but I’ve got a Zoom background.) But I got my piece of paper out so I can hopefully follow along at home.
AC: Yeah. If you had a piece of paper or a chalkboard right behind you, you could imagine that you would have a triangle, like, standing up on a glass pane. And then on one side of this glass pane would be maybe a magician or somebody holding a light. Maybe your granddaughter drew the magician. (Okay, for people in the podcast, I'm showing a picture that my granddaughter drew on the chalkboard.) If this light shines on the triangle, then it casts a shadow, and the shadow is also a triangle. And so we say those two triangles are perspective from a point, the point is the light source. And we say that because the individual corners, the corresponding corners, are colinear with the light source. So A and the shadow of A are collinear with a light. B and the shadow of B are colinear with a light. But it turns out that those shadows, the triangle and its shadow, are also perspective from a line. And what that means is that if you think not about the points on the triangles, but the three lines on the triangles, and you really think of them as lines, not line segments, so going on forever, then the corresponding lines will also intersect along a line. And you can think of that second line, which we call the axis, as the intersection between the plane of glass that's sitting up in the air and the ground. So the interesting thing to me about Desargues’ theorem is that it pretends like it's a theorem about planar geometry, because this theorem holds when the two triangles are both in the same plane, in...