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00:00:01

Summary

In this conversation, Gabriel Hesch interviews Kyne Santos, an online creator who combines art, music, and performance in math education. They discuss the intersection of math and music, the controversy surrounding math and drag, and the creative side of math. They also explore topics such as topology, mathematical shapes, and influential books in math. The conversation highlights the importance of challenging traditional definitions and finding new and innovative ways to engage with math education.

Takeaways

- Math and music have a strong connection, and math can be used to analyze, manipulate, and create music.
- Combining art and math education can make learning math more engaging and fun.
- Topology is a branch of mathematics that relaxes the rigid terms used in geometry and focuses on the similarities and differences between shapes.
- Mathematical discoveries can come from playing around and exploring different possibilities.
- Challenging traditional definitions and thinking creatively are important aspects of math education.

Chapters

00:00 Introduction: Best Song Ever Created

02:03 Introduction of Guest: Kyne Santos

03:00 Math and Drag: Combining Art and Math Education

07:45 Addressing Controversy: Math and Drag

08:15 Music and Math: The Intersection

09:14 Mathematical Shapes: Mobius Strip

10:10 Topology vs Geometry

13:01 Holes and Topology

15:14 Topology and Thought Experiments

21:13 Aperiodic Monotiles: New Math Discovery

23:02 New Shapes and Descriptive Rules

25:26 Influential Books: The Quantum Story and Incomplete Nature

27:01 Conclusion and Next Episode Preview

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Transcript

00:00:07

Speaker

What is mathematically the best song ever created? This was a great question. I had to ask you guys on Instagram for your input on this. You guys said Beyonce deja vu, The Beatles, Here Comes the Sun. Both really catchy, legendary pop songs that we'll all be listening to for a long time. A lot of you suggested pieces that used math in their compositions. Bach was famous for this. The Crab Cannon is a song that can be played forwards and backwards at the same time. Kind of like Missy Elliott. Put my thing down, flip it and reverse it.

00:00:41

Speaker

The table cannon was a song that could be played backwards and upside down. It was called a table cannon because you would set the sheet music down on a table, and then two violinists would play it backwards, upside down, standing at opposite ends of the table.

00:00:55

Speaker

There's also Lateralus by Tool, which uses the Fibonacci sequence.

00:01:05

Speaker

But to answer this question, we first have to define song. In our society, we make a big distinction between music and noise. What one person thinks is a musical masterpiece, another person might classify as discordant and noisy. If we only stuck to playing mathematically perfect intervals like Pythagoras would have wanted, we wouldn't have blues or jazz. John Cage used randomness to make music, like stones falling off an ice lager.

00:01:31

Speaker

His most famous song, 4.33, is four minutes and 33 seconds entirely made up of rests. I mean, if zero is a number, can silence be music? What is music? I think what's brilliant is that music is so personal and subjective, and our tastes as a society are evolving, and we keep discovering new innovative ways to make music. We can use math to analyze it, manipulate it, record it, and even create it.

00:01:56

Speaker

but music has a soul to it that you just can't quantify or rank or even define.

00:02:02

Speaker

This is the freaking math podcast and I'm your host, Gabriel Hesh. And I am thrilled today because we are talking to an online creator who brings together art and music and performance all in math education and does so, so well. I am pleased to introduce my guest, Kain Santos. Kain, how are you doing today?

00:02:21

Speaker

Hi Gabe, I'm great. Thanks for having me. Absolutely, absolutely. I couldn't be more excited. Oh man, I have spent the last week and a half reading through your brand new book that'll be out in March, I believe. Is that right? Yes, March 5th. Okay, okay, yeah. And the book was inspired by your online presence where you do math education and it's performed in drag essentially and done beautifully. What gave you the idea to use that form of art in math education?

00:02:51

Speaker

Well, it's funny because I had been a math student in university and just like a drag queen totally separately. Like I was just head of Montana when I was in university. Like I had no idea that anybody else shared this like combination of interests. So I would just like go to school and go to my math lectures during the day and then like go to the bars and do a drag performance by night. And I guess I never thought of combining them until the pandemic.

00:03:16

Speaker

And then I just started telling my math riddles in drag, cause I had a YouTube channel and I just had an online presence in drag. And that's just how I wanted to appear on camera. And then people loved it. So, you know, people started messaging me saying that they loved learning math through this new lens. So I was like, you know what, if you guys like this, I have a lot more where that came from. So I guess I'm known now as the math

00:03:42

Speaker

queen.

00:03:42

Speaker

Awesome. Awesome. Fabulous. Now you mentioned math and drag. That title is going to raise a lot of hairs with a lot of our audience. We talked about this before the interview a little bit. I want to address that. For the audience that's uncomfortable with math and drag, this episode is for you. This episode is for you. We have a whole outline prepared and we want to talk about

00:04:04

Speaker

the why people should have free artistic expression as part of their human rights. And that's a huge issue here. In my own family, I have some family members that are...

00:04:19

Speaker

very much in favor of a lot of the laws that are being proposed to limit drag performances in various arenas. So what I wanna do is for, again, our listeners who may be uncomfortable, please, I look forward to hearing from them after listening to this episode, because I wanna talk exactly about what is and what is not a threat or considered inappropriate. I'm sure there's so many more ways for me

00:04:48

Speaker

put this. The point is I want you to listen to the episode. There's also a transcript available and talk to us, engage with us about what's in that transcript and where you stand. So thank you for coming on and talking about this issue. I know it's a pretty.

00:05:04

Speaker

It's a touchy topic. On this math podcast, I love interviewing people who are articulate and passionate about math. And really, as long as things are family friendly, that's the only thing I go for. And there's nothing that's not completely family friendly in your book or in your online presence. Would you say that's true?

00:05:24

Speaker

Yeah, I mean, I would never have guessed that math could be something that is controversial to people but you know they see a drag queen talking about math and all of a sudden you know there's this agenda and I'm trying to recruit kids into this lifestyle but you know, the only message I've ever had was to stay in school and to do your math homework and don't use chat GPT don't cheat.

00:05:45

Speaker

And I just want to share my passion for math. And I want to change people's perspectives that math isn't about always just getting the right answer in school. Sometimes math can be creative and fun. Sometimes there's not always the right answer. Yeah, awesome.

00:06:00

Speaker

Yeah, and we're gonna get to that part real, real soon. And I appreciate just, you know, engaging on the controversial part here. And I only mean controversial as it's perceived, you know. The last part I wanted to mention before we move on and about this episode in particular is I used to teach fifth grade and we had many, many units on various parts of America's history. And it just seems that there's times whether it's, you know, in World War II in Germany,

00:06:27

Speaker

or in America's history with the Jim Crow laws where there's a group of people who are scapegoated. The huge concern, huge concern that I feel right now is that LGBTQ in general are being unfairly scapegoated. And that's my challenge for anybody who's listening to this. I have family that bring scripture and that bring think pieces by, I don't know, Ben Shapiro or

00:06:55

Speaker

Anybody else? I know, right? They have their arguments written out, but what I want to say is, again...

00:07:04

Speaker

regardless of personal belief about things, about whether it's right or wrong, I feel that the LGBTQ community is being scapegoated, and I think that by talking about it, our listeners can read our transcript and say, okay, okay, I agree, I agree, and I also can also agree that free speech should be protected, even though my own religious beliefs or something else may not agree with that.

00:07:30

Speaker

free speech should exist and people should not be scapegoated. Those two are sacrosanct. That's my challenge for our listeners. Now that I've said that, unless there's anything else on this topic, I say we dive into the fun stuff. What do you think?

00:07:43

Speaker

Yeah, let's talk about math and drag. Fabulous.

00:07:46

Speaker

Fabulous. Thank you. I agree. OK. OK. Man, I love the music part. You talk about music a lot in the book. One thing you did talk about as one of your early performances was for David Guetta, Turn Me On. I'm sorry. David Guetta and Nicki Minaj. Nicki Minaj.

00:08:02

Speaker

I almost choreographed an entire eighth grade dance routine to that song. So I was so excited that you brought it. It's a great song. Yes, yeah. The video for that song inspired me to get into computer graphics. And we did two whole math podcast episodes about the mathematics in CGI and how ray tracing works and all that. Because that video for Turn Me On, it's Nicki Minaj being assembled as a robot. And it's almost like the beginning of

00:08:32

Speaker

Ghost in the Shell, I believe, where you see the robot being assembled into this girl. And it made me fascinated because that's also where art and math come together. I'm doing too much talking and I'd rather do some listening and hear about you. So let's talk about, if you don't mind, some of your favorite videos that you've done so far on the platform. I asked you for a collection of them and we have all of them. This is a Mobius strip. It's a very important shape in math because it's a one-sided surface.

00:09:00

Speaker

All you have to do to make it is take a long rectangular strip, twist one end, I'll show you what's gorgeous, and attach the end to it. To prove to you that it only has one surface, you can take a marker and draw a straight line down the middle. Okay, not very straight at all. And neither is this line. But you'll see that we ended up right back where we started and the marker touched both sides without ever leaving the paper because they're the same side. But here's something even crazier. Look what happens.

00:09:27

Speaker

If I try to cut this down the center, you end up with one super long strip. You'll see that there's multiple twists in this, so it's no longer a mobius strip. But what do you think would happen if instead I cut it a little bit off center about a third of the way into the edge? We end up with this. Two separate strips interlocking with each other.

00:09:54

Speaker

Wow, that's awesome. I never get tired of Mobius strips. My daughter in third grade came home. They just talked about that in her gifted class, I believe. And that is a really good segue. I think the mathematical branch is called topology. Is that right?

00:10:09

Speaker

yes yes and you know what's funny that video um i think is like the most viewed video ever on my page it got like 14 million views and i think you know people online they just like to see um math that's creative and that's different that is sort of mind-boggling because most people's opinion of math is

00:10:27

Speaker

okay, you solve this trig identity, you solve for x, you plug in these numbers into a calculator, and they don't really know how to sort of connect the dots. But I think that the TikTok channel is proof that math is fun and it is appealing to young people especially. You sort of just have to package it in a way that shows them the highlights of math.

00:10:49

Speaker

Yeah, I think you agree. We tried to do that a little bit when the Breaking Math podcast was first created. My co-host, Sophia, designed an app that would create a colorful rainbow hypercube. I don't know if you're familiar with the rotating hypercubes. We've all seen pictures of hypercubes. Those are pretty bad right now.

00:11:04

Speaker

She designed an app where you could input how many dimensions you wanted, so four or five. The computer kind of fried at 17, so you want to keep it under about 15 or so, but then it would rotate in all those dimensions, and then you could press another button, and then it would toggle a trail. So just imagine this 3D rotating hypercube rainbow thing. It was incredible. We called it our version of a lava lamp.

00:11:29

Speaker

And again, all it was was the single interesting point of mathematics and beauty. So, you know, that's really cool. But yeah, that's a really fun topic to talk about. I want a quick question about topology. It's funny. I know a lot about electrical engineering mathematics. I don't know a lot about other fields of mathematics. I've been using topology and geometry interchangeably. Are they technically different things or are they the same?

00:11:56

Speaker

They're different. So basically, topology, it relaxes a lot of the terms that we use in geometry. In geometry, you have circles, you have triangles, you have squares. But a topologist might look at all of those and sort of think of it like a chain. If you have a chain necklace, you can shape that into a circle. You can shape that into a triangle. You can shape it into a square. So those shapes would be

00:12:22

Speaker

topologically the same. So topology is about relaxing a lot of the rigid terms that we might use in geometry and thinking, if we zoom out and really relax a lot of these requirements, what things do these things have in common? So a topologist might look at something in graph theory. And in graph theory, we look at networks and see how things are connected. So it's a little bit more abstract than geometry.

00:12:51

Speaker

Thank you. That gives me a lot to think about, that the term topology has been used a lot in my conversations with other machine learning experts, where they talk about topological connections, and then they'll show a shape. And I'm just like, is that the fancy word for geometry? The data? Yeah. And also, as you were talking, that reminded me, sort of, you know, people are first, first learning something about, like, say calculus, and you learn about

00:13:16

Speaker

the area under a curve, and you approximate it by drawing a bunch of rectangles, and then the rectangles get smaller and smaller. So that approach, I don't know. Again, it's kind of geometry and topology, sort of. I think my thoughts are still forming, so I may not be able to articulate quite correctly, but I want to do a blog post inspired by this question,

00:13:36

Speaker

so I do thank you for that.

00:13:38

Speaker

Hey, how many holes does a straw have? Two. The top and the bottom. No, it has one. The top and the bottom are the same hole. Who are you living at? No, you go in one and out the other. If an animal dug a hole into the ground and came up somewhere else, you'd say there were two holes in the ground. And if you buried one of them with dirt, you'd say there's only one hole left. So, two separate holes.

00:13:58

Speaker

Okay, but if you pierce your ears, the earring goes in one side and out the other. So that counts as two separate holes. But that logic, a pair of scissors has four holes in it. No, a hole has to be long enough for it to count as two separate holes. How long? How long do you want? What if there were zero holes in this? If it had a hole in the side, you wouldn't be able to drink out of it properly. You'd say, I want a new straw, this one has a hole in it. Therefore, an unpunctured straw has zero holes.

00:14:21

Speaker

No, a straw with one extra hole in the side, you could form that into a Y-shaped straw. So pretty much like a pair of pants. And that's obviously three holes. Remove one of them, you get two holes. No, a straw has one hole, a pair of pants has two holes. Now I'm really confused. What did you see here of this question?

00:14:38

Speaker

I think I read about it first in Jordan Ellenberg's book, Shape, where he sort of touches on some topics of geometry and topology. Actually, that's another question that a topologist might talk about is how many holes does a straw have? Because basically in topology and in a lot of mathematics, really mathematicians are asking in what ways are these things similar and in what ways are they different?

00:15:03

Speaker

of course a straw is something that you you know sip a drink through and a donut is a piece of food but topologically they both have one hole okay incredible i i love real quick as you're saying that again the top of the word topology

00:15:18

Speaker

You know, it was mostly foreign to me, but I keep hearing the discussions happening in education, whether it's a Mobius trip or a straw in the phrase topology. So I love that these questions are still being introduced in some fun ways at young ages and they give kids time to think on it. These are unplanned stories, so I hate hogging the mic, so I appreciate you listening while I'm saying this, but it's relevant. It's relevant.

00:15:43

Speaker

We talked a little bit about zero, one, and infinity in our Socratic discussions. And I can see with topology, as shapes are changing and suddenly you could conceive of a single hole or no holes or an arbitrary or up to infinity amount of holes, so to speak, it's very relevant.

00:16:03

Speaker

The way it was phrased in, this is a sixth grade class, was the question began, if you take two circles and if they don't touch at all, they intersect at zero points. If they touch, they intersect at one points. If they overlap, then they intersect at two points. But here's the interesting one. If you have two circles overlap completely, how many points do they intersect at?

00:16:29

Speaker

And I think- Infinitely many. Yeah, yeah. We had kids arguing for infinity and for one, depending on how you define the point. And then they said, okay, well then play that thought experiment again, but you're with spheres. If you have two spheres, they touch at one point, they overlap at an infinite amount of points, but then they completely overlap at how many points?

00:16:49

Speaker

also infinity. Yeah, that's, that's fun. Yeah, yeah, yeah. It's a good thought experiment. And I only bring that up because talking about, you know, constructing a straw, you already have, you know, it challenges traditional definition. Oh, the whole theme of math and drag. It challenges traditional definitions of things in math. And, and, you know, how do you define things and for what purpose and

00:17:13

Speaker

Oh, it was amazing. So yeah, another blog idea. So again, thank you for my hugging the mic. I had to. Yeah, let me say, this mathematician, Edward Frankel, I think is his name, he has a great analogy and he says that the way that we teach math in schools is like if you taught an art class by making kids paint fence.

00:17:37

Speaker

And you never showed them the works of Michelangelo or Leonardo da Vinci or Picasso. They wouldn't come out of that class thinking, wow, I love art. I'm such an art person. That's how most people teach math. Most people are learning math by learning the basic rules, memorizing the times tables, and they're not really seeing the fun side of math, which is about challenging traditional definitions. It is about

00:18:04

Speaker

debate, and sometimes there isn't a clear answer until you sort of work through it and parse through it. And really, that's what the book is about. It's showing people the fun side of math, which is about creativity and challenging those traditional definitions, which is what real mathematicians do. Mathematicians are pushing those modern boundaries and finding new original thoughts. They're not just sitting at a blackboard punching numbers into a calculator.

00:18:33

Speaker

following a list of equations. You know, they are challenging traditional definitions. A lot of people don't know that Filipino used to only refer to Spanish people born and raised in the Philippines. I'm here in the walled city of Intramurosk in Manila. Up until the 1900s, this used to be the center of the Spanish Empire in Asia. And we can see the Spanish influence all over from the architecture to this Catholic Church, San Agustin, where my parents got married.

00:18:58

Speaker

When the Spanish colonized these islands, they named them the Philippines after King Philip of Spain. The natives were exiled from the city and these walls only housed the Spanish elite. It used to be that the name Filipino could only refer to people with Spanish heritage born and raised here in the Philippines. The natives were called Indios or Negritos. It wasn't until the Philippine Declaration of Independence in 1898 that the name Filipino could be used for everybody in these islands regardless of ancestry.

00:19:22

Speaker

Very cool. Now, I noticed this was one of the videos with a bit more of a socio-historical context. Can you tell me why? Yeah. You know, I started doing these videos, these short form videos, about three, almost four years ago now. And I think they've evolved from just talking about math to really talking about everything that interests me. And, you know, I'm a Filipino Canadian. I moved to Canada when I was quite young and I feel like I didn't really get a chance to learn a lot about my history and my heritage.

00:19:52

Speaker

And I feel like a lot of Filipinos out there are like me. And so, you know, if I have a platform, I want to share that with the world because I feel a lot of people don't really know about Filipino history. So the channel has turned into something that's just math videos to math and science and history, Filipino history, queer history, just things that I think more people should learn about. And I think that the channel is for everybody who just wants to learn something new.

00:20:20

Speaker

Oh, awesome. Fantastic. Fantastic. A few of my favorite channels have gone that exact same route and it excites me because as a math podcaster, I'm not only into math, you know, I'm into a whole bunch of things too. Yeah, exactly. I did a whole show last year just on 3D art. I was going to be the digital version of Bob Ross and I worked so hard on that show.

00:20:39

Speaker

Well, there's a channel called Asianometry that does high-tech videos about advancements in silicone chips, but then it'll talk about Japanese history and Taiwanese history of the last 20th century, and it interweaves between those two things. So I think it's really cool. I think it's really cool.

00:20:58

Speaker

This year, mathematicians discovered a new shape. Actually, it wasn't even a mathematician who discovered this. It was a hobbyist who loved jigsaw puzzles. One day, he cut this out of paper and accidentally stumbled across the answer to a decades-old unsolved problem in math. Some shapes can be used to tile flat planes like squares, hexagons, triangles,

00:21:18

Speaker

Actually, there are infinitely many shapes we can use to tile the plane like this, but all of these have repeating patterns. They're what we would call periodic. If we pick up this entire plane and shift it all one square over, it looks the exact same. Of course, we could also just take a grid of squares and put a single rectangle in the middle. And this is technically aperiodic because you can't shift it around anymore without it looking different. But this patch still looks the exact same as this patch and that patch.

00:21:44

Speaker

What we're really interested in is tilings where every patch of the plane looks aperiodic. So the question became, can we use just a finite set of tiles to tile an infinite plane aperiodically? Initially, the answer was no. If you just start out with a finite set of tiles, eventually the pattern is going to have to repeat itself.

00:22:02

Speaker

In 1966, Robert Berger found a way to do it, using 20,426 tiles. Then he condensed it down to just 104. In the 70s, Roger Penrose found a way to tile the plane with only two tiles. For a while, we thought that was the best we were gonna get.

00:22:17

Speaker

November 2022 when David Smith discovered the hat tile. He noticed you could piece them together like a puzzle, but not in any repeatable or predictable patterns. So he contacted Craig Kaplan, a prof at the University of Waterloo, and two other mathematicians, and they proved that this hat tile is the very first aperiodic monotile. You can tile the entire infinite plane, and every patch looks a little different from every other patch.

00:22:43

Speaker

despite all being composed of one tile. And not only that, but it even admits an entire continuum of infinitely many aperiodic monotiles. Wow. So November of 2022, so like a year, two years ago? A year and some months ago, that's it. Yeah. So brand new math, folks. Mathematics is not, it's funny. So yeah, we think that math is like breaking math. Yeah, thank you.

00:23:07

Speaker

Breaking math, exactly, exactly. That brings us back to our name.

00:23:11

Speaker

We're totally writing the coattails of Breaking Bad, the show that takes place in Albuquerque, New Mexico, which is where we're filmed. So that's kind of what we're thinking anyways. But yeah, that's breaking math. It's new math that exists. So now the math part of me is very, very curious about

00:23:26

Speaker

If that's a new shape, are there others that have been discovered that are similar since that time? Have we figured out the descriptive rules for what allows that shape to do what it does?

00:23:40

Speaker

Well, what's really interesting is it wasn't discovered by a mathematician thinking, you know, here are the descriptive rules of what an aperiodic monotile should look like. It was discovered by somebody who was sort of just playing around and cutting out pieces of paper. And that is how that discovery was born. And I think it speaks to the fact that mathematicians love doing things for fun.

00:24:05

Speaker

And not every math discovery has to have this like real life application, which is always the immediate question that everybody wants to ask. Sometimes we are just playing around with something and we can discover something completely original. And as the video said, once we found that shape, it admitted a whole continuum of shapes. If you sort of tweak the shape a little bit, those properties would still stay the same. So technically there's infinitely many

00:24:32

Speaker

new acreage monotiles. That's also interesting because we talk a lot about the next part of the podcast. I want to talk about some influential books and just playing around is talked a lot about in evolution and intelligence.

00:24:47

Speaker

and in machine learning, actually, where you've just got random trials and try it and see and see what works. And that's how engine that's what drives machine learning. That's what drives evolution. That's what drives creativity. So, yeah, it's it's pretty cool. I'd like to talk to you about and to anyone who listens. This book is hard to get through and worth every ounce of effort. It is called The Quantum Story, a History in 40 Moments by Jim Baggett. I was initially skeptical based on the cover

00:25:16

Speaker

I don't know why, but anytime something is like colorful, I don't associate it with serious math. It has to have a boring number. I don't know why. I don't know why, but by far, this book, and I've probably read hundreds of books I could rattle off between 500 and 1,000, I want to say, and this book is the top of the charts for all of them. The way I describe it is just start on chapter one in the first three pages. It's about the crisis in physics with Max Planck.

00:25:44

Speaker

trying to describe what he observed with light in the ultraviolet catastrophe. This book is a forever inspiration because it's like a log that burns forever and ever and ever, and I can make content from this. There's only one other book that I'll mention similarly because I want to be respectful of the time on this podcast. This one was written by an anthropologist who's also very articulate about chemistry and biology, and the book is called Incomplete Nature.

00:26:12

Speaker

Um, I don't know anybody who's finished it. That's another slow burn and everyone usually, so two things in full disclosure, everyone will read the entire Wikipedia page for incomplete nature. Uh, and then maybe get through a 10th of the book or, you know, or just really slowly. It's again, the same style as girdle Escher Bach, where it, it talks about

00:26:33

Speaker

Is it possible to have, you know, awareness and meaning and consciousness emerge from things like matter? And I know that's a very scary, uncomfortable question, but it approaches it in a beautiful way. So, yeah, if you want something, you know, to spend some time on and to really ponder over, I recommend even the Wikipedia page, but please support. Yeah, support the author recommendation. No. Yeah, I'll have to look into that. Oh, fabulous.

00:27:01

Speaker

And that was the first half of my interview with Kine, the content creator known as OnlineKine and the author of the book, Math in Drag. Next week we'll have part two and next week we'll have a whole section, a whole section to talk about just for science content creators and for educational content creators in general. So if you've been thinking about sharing your hobby in gardening or knitting or

00:27:25

Speaker

automotive mechanics or anything like that and you want to become a content creator, tune in next week. We'll talk about how to get started. I'm Gabrielle Hesh and you can find the Breaking Math website at breakingmath.io. All episodes are available with no commercials on the Patreon starting at our $3 tier. And if you have any questions, if you'd like a copy of the transcript for this episode or anything else, send us an email at breakingmathpodcast at gmail.com. Thank you very much.