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Math for English Majors with Ben Orlin
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Math & Language: Creativity, Quantification, and Making Math Accessible with Ben Orlin
In this episode of Breaking Math, hosts sit down with Ben Orlin, author of Math for English Majors and Math with Bad Drawings, to explore the intersection of math and language. Discover the unique skill sets required for mathematics and creativity, how math education can be made more accessible, and the role of quantification in empowering individuals across various fields, including literature and the arts. The conversation highlights the historical contributions of women in math, including the impact of Einstein’s wife on his work. Ben also shares insights into his writing process and the challenges of making math relatable to a broad audience. Learn how mathematical thinking can enhance one's appreciation for literature and the world.
Keywords: math, language, skill sets, math education, accessibility, quantification, power of math, women in math, Einstein's wife, math, literature, book, writing, perspective, abstraction, relationships
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Transcript
Introduction and Guest Overview
00:00:00
Speaker
Welcome back to the Breaking Math podcast. My name is Gabriel Heche. I am your host and we are here to talk about the mysteries of mathematics and how it helps us to understand the world. but We'll be interviewing the author of math for English majors. This is in the fine tradition of physics for poets, but it's mathematics for English majors. And we'll be joined by the author, Ben Orland. This is our third time interviewing Mr. Orland. And joining us today, as always, we have my awesome co-host, Autumn Fanef. Autumn, how are you today? I'm well, how are you doing?
00:00:27
Speaker
doing fantastic and I see Ben is already in the room. Ben, thank you for joining us. Pleasure to have you here. Yeah, thanks so much Gabe and Autumn and everyone for welcoming me to the breaking room. but Breaking room. Yeah, yeah, that I like that. I'll use that that that term here. yeah Today we're diving into a book that takes a fresh and witty approach to bridging the gap between numbers and words. Our guest is none other than our very dear friend Ben Orlin, an educator, cartoonist, and author whose work makes math accessible and often hilarious for readers of all stripes. You may know Ben from his previous books, ah Math with Bad Drawings, and the Change is the Only Constant. But today we're talking about his latest work, Math for English Majors. It's a book that's very much a storytelling and language
00:01:04
Speaker
uh as it is about mathematics ben takes the readers on a journey where literary lovers can discover the hidden beauty and logic behind math while math enthusiasts can see how the world intersects with language and literature math for english majors challenges the notion that math is all about cold calculations instead it it is It shows the same creativity and narrative flow that we find in great writing, also in mathematics. Whether you've ever felt like a word person or a numbers person, Ben's book is here to show you that these two categories are more fluid and more fun than you might think. We're excited to chat with Ben about the inspiration behind his book, how he turns math concepts into engaging stories, and why he believes that math can be for everyone, even those who thought they'd left
00:01:44
Speaker
it behind in high
Humor and Storytelling in Math
00:01:45
Speaker
school. So grab your favorite book or maybe your calculator and join us as we delve into math for English majors with Ben Orlin. Let's get started.
00:02:00
Speaker
I'd love for you if you could do a little introduction and tell us about your blog as well as your other books and what you've been up to recently. Yeah, yeah, no, thanks Gabe. I mean, what I do for a living is i I sit down at my desk and I grab sharpies and blank paper and I draw little stick figures making jokes about math. And that that feels like that shouldn't be a job or like maybe there should be one person who has that job, Randall Monroe, um but turns out he's so good at it that it created this whole category of human beings and of which I am one.
00:02:26
Speaker
ah So i get to i yeah I get to write about math and and ideas I find exciting and how to learn math and how to teach math ah and the parts of math that need more of a spotlight, spotlight need to deserve a little more attention. yeah And so I've been doing that on my blog for 10 years now, Math is Bad Drawings, and this is my fourth book coming out in September. um And so yeah, the the books have been about you know sort of each taking a slightly different angle on math. And this one,
00:02:51
Speaker
Yeah, this one feels in some ways the most different from the other three. it's It's about math as a language and about going after the parts of math that have kind of the least glory, the ones that people grumble about the most. Those are the ones I most wanted to give them some some celebration, a chance to a chance to shine and show us that they're actually really weird and quirky and cool. Awesome, awesome. I might ask you ah real quick, with this book in particular, I know you said earlier you have math with bad drawings, which I think takes a look at yeah I would just say a general math curriculum from, oh gosh, kindergarten through, there's even some college in there as well. um Does your first book? Yeah, yeah i mean yeah that that first book in Math is Bad Drawings, it's about different applications of math, right to put it as said blandly as possible. To put it less blandly, it's kind of it's about all the places that math pokes out in the world, places you wouldn't expect to find it. um so you know Places like lottery tickets and analyzing lottery tickets through a thing about expected value or looking at the geometry of the Death Star.
Unexpected Places for Math
00:03:50
Speaker
um or looking at ah scaling factors as organisms grow and so why you know an ant which is teeny teeny tiny like doesn't have any reason to fear falling from heights but has every reason to fear a water droplets whereas we are kind of the opposite if you drop me off a building that's very scary to me if you drop rain on me not so scary um and it's really just about size it's not it's not anything I think special about me versus the ant other than how big we are. Anyways, that's math with bad drawings. A lot of that stuff is nowhere in the curriculum, actually. What I wanted to do is I wanted to gather all these cool tidbits and pieces that that just like aren't there in school math. um School math is doing something else, and so it doesn't hit all those fun ideas. ah And then this book, actually, which is my fourth,
00:04:33
Speaker
I almost wanted to do the opposite. It's not that I didn't want to have fun ideas, I did. But what I want to do is I wanted to reconcile the fact that you can have all these fun conversations about math and be like, oh, look at fractals. These are so fun. Look at the coastline of Britain. Look at ah you know look at chaos theory. Look at triangles in roller coaster architecture. ah And that's all very cool. But there's something there in school. There's something important happening when you sit down and solve equations um or when you sit down and calculate.
00:05:00
Speaker
So it's not the glamorous part of math. It's the part that gets kind of drummed into you in school. And it's it's not the part that we often put math popularizers like me are often celebrating. But there's got to be something going on there. um And I think to expert mathematicians, it's almost invisible. It's sort of like, oh, yeah, we just do that on the side. That's like that's our bookkeeping. um So they don't want to talk about it. And kids don't want to talk about it because it's mystifying and confusing and full of weird notation.
00:05:24
Speaker
And so I was like, OK, how can I dig into this space exactly the stuff that's taught every day in school? And how do we see that with fresh eyes? Nice. Nice. Awesome. And of course, your second book is on calculus and um ah it's it's it's calculus with draw, with withdrawal with ah cartoons, obviously. that that is ah That's another catchy name, of course. um The reason why I bring up the curriculum specifically, I don't mean to dwell too much on this, but um we, the Breaking Math podcast is very, very ah centric with electrical engineering because my degrees are in electrical engineering, which means that we are obsessed with things like Shannon's information theory. um How familiar are you with Shannon's information theory and entropy?
00:06:01
Speaker
A little bit, I mean yeah, i mean i could I could give the definition of Shannon entropy. Awesome, awesome. you You already have it though, so you don't need it from me. It's all good man, it's all good, it's all good. But like, when I do the podcast, it's forced me to, um oh, how do I explain this? Learn other areas of mathematics and how they're used in science and understanding the the world in ways that I'm not used to doing. And I kind of feel like, I don't know how much of a video gamer you are, but in i in an RPG, you've got the skill tree, right? And with the skill tree, you decide, you know, what what you're going to work on, whether it's magic or defense or a quick attacks or
00:06:35
Speaker
Whatever. and And there's so many ways ways to play it. And I feel like I'm leveling up on my math skill tree as part of this podcast. But the purpose of this podcast is to have great conversations with other people over the language of math in an accessible way. That brings us back to why I was talking about what your book's great over and and you know what people can expect.
00:06:55
Speaker
with them, you know, just for that reason. This last year, I've had to really delve into statistics as we least've tried to tackle machine learning. And that's not usually a field that I enjoy much. But, but yeah, yeah, we've gotten a lot and into that. So um yeah, anyways, anyways, yeah. and then we said No, that's it's interesting to hear you talk about it, because it's Yeah, we we have this one way of organizing that's very familiar, or you have variations on this one way of organizing math that's very familiar from school. um And that's like a nice way to organize math, but there's lots of other ways to organize math to to chart your path through the ideas. It doesn't have to be that like, okay, you do pre-algebra, and then you do algebra, and then you do these years of themed courses, and then you get to college, and there's sort of these little this little obstacle course you have to follow through the undergraduate degree. um There's like, there's so many other ways to organize and think about math.
00:07:38
Speaker
And so yeah for a medium like audio, you know you get to do a different, it's a different organization that you're presenting here. Yeah, yeah do you know um I've heard that in Great Britain or in um other places, they don't necessarily ah teach it in the same order. I've heard that you might learn a little bit, just like a little bit of calculus you know much earlier than we do here. like it just it's It's sprinkled in here and there as needed. um and i Number one, I've only heard that as a rumor. ah Number two, I don't know if there's a more effective way. Is it better to do it the US way or is it better to do it that that way where you've got a broader knowledge even if not not not as deep? Is there any truth to that rumor I've heard?
Math Education Around the World
00:08:15
Speaker
Yeah, i can I can confirm the rumor that is that is true. GCSE, which is kind of the 10th grade, 9th and 10th grade course in the UK, yeah typically doesn't cover any calculus. But if you do a, um there are sort of like slightly enriched versions of that. and My knowledge is a few years out of date on this that will cover calculus. And then the A level, which is like the junior, senior year curriculum, ah does lots of calculus, but also with lots of other stuff mixed in.
00:08:37
Speaker
um And doesn't i you know they level curriculum, I didn't teach, so I don't know it as well. I taught the IB. But the IB is the same. ah So you know where there's some calculus, and then a mix of other topics. ah the u The US is weird in this sense. I i don't know exactly the history of why the US does these annual themed courses, where it's like, all right, it's geometry year. All geometry, all the time for a year. Like, OK, it's calculus year. We're doing calculus. Nothing but calculus. Calculus from start to finish. other Other countries find that weird, mathematicians from other countries. think that's like weirdly single-minded and narrow. I think it works fine. I think, you know, I like the unity of the year, but ah but it's also, it's definitely not necessary because there's dozens of countries out there doing it differently. Yeah, I hear you. I hear you. That's ah quite something to reflect on. I think that it'd be easier to answer the question, why are we doing this when you have more of ah of an idea of how how everything, you know, how they all, how everything ah
00:09:32
Speaker
Sorry, how everything relates to each to each other. So I think there's some value to doing it that way. So, okay. I have one question for you that readers are going to be wondering and when they see the title of the book. Is it meant for mathematicians or is it meant for people who are English majors? I know that you you have a very long history of combining the two and where did that start?
00:09:58
Speaker
Yeah, yeah it's that's a no it's a very good question. I mean, I wound up giving a longer answer than than would probably be ideal. But yeah, so my one of my favorite pieces of feedback I've ever gotten on one of my books, it's like an Amazon review or Goodreads review, which I don't tend to read, but someone pointed it out to me, where it described my books as basically like Pixar movies in in structure or in approach, that like there's there's jokes there for the grownups, but then there's and grownups here, not literally grownups, but you know, people who know the math already. um And would then though the plot is there for like for the kids, it'll be new, and the kids being just like people to whom the math is is new or surprising could be. Genuinely kids could it just be people who didn't memorize everything they learned in secondary school math. um So that's always been what I've liked doing as a writer, is kind of finding a way to finagle both audiences. um I think for people who don't know math, my books are unusually accessible.
00:10:48
Speaker
um You know, I'm not going to claim that every page and every ah sentence in every book is like going to make sense to immediately, because that's not how learning math works. But I think, um you know, I pride myself on really trying to make my books accessible. And the way I do it is not because I'm a genius at making things super clear. It's like I run it by people and they say, that doesn't make any sense, and then I fix it. It's like my editor, Becky, is great for this, really bright. And it's lots of pop science books. But if I give her a page of nonsense, she's like, that's that's a That's a page of nonsense right there. Just much more politely than I would, but I but i can i can hear what she's saying. um Anyway, so I've always tried to go for kind of the two audiences. I want the books to be... um
00:11:24
Speaker
novel and surprising and exciting to people who don't uh sorry well i want them to be accessible to people who don't know the math i want you to be able to walk in and not have to read it in this painstaking way and not to feel like a math textbook um but i also want the book to be if you do know math which is most of the people who buy math books probably a lot of the people that listen to this podcast like i wanted to have exciting new thoughts you know bits of history and jokes and anecdotes and different ways of explaining things or just little yeah little excursions that you might not have thought about before Um, and this book, I tried to write it that way. Uh, the original pitch for it was basically, um, there's another book each shoots and leaves. yes I don't actually. Oh, okay. Do you want to, what what's your, what's your familiarity with that autumn?
00:12:06
Speaker
I I've seen it a few times. Yeah, um not not terribly in depth, but I've seen it. Yeah, it's a delightful book. So yeah, the the joke. So yeah, it's just and leaves the the joke it's about it's book about punctuation. Lin trust is the author. um And it's just this delightful series of essays about the different punctuation marks in English. um And it's so the the opening joke is ah Panda walks into a bar, has a meal,
00:12:30
Speaker
fires a gun in the air and then walks out and people are like what was that panda doing that's crazy and then they see in the uh there's a book it left behind where it says panda eats shoots and leaves um at the point being that the commas anyway so that's like that's one of the you know there's there's i think i think she she's uh she makes fun of the joke for not being all that funny despite the fact that she put it on her cover um i think it's a good joke uh Anyway, so my pitch was I wanted to do that for for math, I wanted to do punctuation marks, but like, like I want to get you to leaves, but talk about the history of the plus sign and talk about algebraic notation. um And I tried to write that book. And actually, that book isn't writable. And the reason is because if you don't know math pretty well already, you don't have any associations with those marks, maybe plus and and seven, you do. But a lot of the notation of math is just it's just
00:13:20
Speaker
and inscrutable It's like worse than Sanskrit or something. it's It's like a language, not just that is an alphabet you don't know, but it it's not even an alphabet. it like it It connects to the ideas in a different way. um And so it felt like one where I can't i couldn't do my usual trick, where I like sort of explain it for the novice audience, but then include some fun you know other material for the for the more expert audience. um it's It's like early on in writing the book, it's like, okay, I got to make a choice. Who am I writing
Making Math Accessible to All
00:13:47
Speaker
this for?
00:13:47
Speaker
um And I said, okay, I wanna write this for the for the new people. um And then weirdly, I got deep enough into it that I could step back and be like, this this is a weird explanation. I'm talking about math in ways that I've actually never talked about it before. Just trying to animate the weird life behind the written language of math. um Actually, they like when I would explain it to math friends, you have friends who are mathematicians, they'd be like, huh, really? Like a variable is a pronoun?
00:14:14
Speaker
Okay, okay. like It's not how you think of a variable, but yeah, that's kind of right. A variable is a pronoun. it's you know It's a way of referring to a number without needing to say it by name, um and it opens up a nice kind of linguistic approach to mathematics. There we go. The idea that plus isn't a verb, it's like, oh, it is, because you add things. It's like, well, no, in English, add is a verb, but plus isn't a verb. Two plus three, nobody's doing the plus. It's just it's more like a preposition, two with three.
00:14:42
Speaker
two and three, a conjunction maybe. um Anyway, so I found myself like, despite choosing to go for the more novice audience, um as an expert mathematician, i'll put expert in scare quotes, like I found myself a little surprised by what I came across. So I think I think the book does wind up You know, it it really genuinely is written for English majors. I'm an editor as an English major. My agent is an English major. I was really like, I did have some specific English majors in mind. um But but I think it actually is, it it will be a little weird and surprising in the same way that when you really look closely at English and things you do naturally as an English speaker, you're like, what? Oh, wow, I never realized I was doing that. um I think I think this book will give fluent speakers of math the same feeling about math.
00:15:23
Speaker
Nice, nice. I gotta say one thing real quick. Well, a couple of things. You had mentioned um an early draft of or an early idea of this book about math symbols and the inaccessibility would be that people don't know those symbols. As you said earlier, it's like strange Sanskrit. A bunch of symbols in Greek letters, you're like, I don't even know what this means. um What's so funny is one of the books that we were just given, like we get more books a month than we know what to do with. Oh, did you know that Prince University Press just published a new one. Is this the ah is this the one you think of?
00:15:48
Speaker
it might be ah the book on the history of all the symbols of math yeah yeah yeah looks looks like a nice book yeah i have the so yeah um but i was going to say it that would be an amazing book oh yeah yeah i've just i've just skimed so really nice one i mean and that and that one i think the it it looks like a lovely book from what i can tell and they just they just took the opposite fork at that that that early fork in the road where I said okay I gotta make this accessible to novices I want to make this I want to make this for people like my stepmom who talks about how it very bright lady she ran into algebra one and she like yeah she took it a year early or something and just like has hated math ever since it just never made sense or she hasn't liked it since. But if you go the other way and you're like, okay, let's let's talk to people before I show you the math background, then you can get into those that history. So i think that's that's I'm really glad that book is out there. um Also glad I didn't accidentally accidentally write it. its You never want to have two people writing the same book. They take a long time to write. If one person's writing it, then just let that person go write it. Yeah. Awesome. um Awesome. All I'm saying is that just like in you you know in hip-hop albums, you get a really good mashups.
00:16:47
Speaker
adamt curiosity ah how did you decide which concepts to include and what did you leave out or was there something Yeah who really wanted to talk about that you left out Yeah, yeah, no, it's great. Your questions are going like right at my, exactly the process for this book. Weirdly, I wrote this book using the greedy algorithm. um I went back and smoothed it out afterwards. I'd never written a book like this. I'm a very top-down thinker. So I like to outline and then say, okay, here are the five sections and there will be the three chapters in each section. like I really like to really plan it out like that. And this book, I tried that for a while. This book much took much longer to write than my others. so And so what I did, finally, what made the book work and start clicking was I sat down like, okay,
00:17:29
Speaker
What's the first thing I should tell you about math? And I wrote a chapter about counting. um and about how to count is to is to come up with a system for naming numbers. Like that's what counting is. It's like, you throw back to like Genesis, right? and And Adam's first move is to like name the animals, right? Like that's counting. Counting is naming the numbers. It's giving the numbers names so we can talk about them. um And we have a weird system for doing that. The one I ah start with in the book actually is in Welsh, where I was hiking in Wales and came across this little plaque that just listed the numbers in old Welsh.
00:18:03
Speaker
And the one I love, uh, it's in the teens. So you get 15 is kind of looks like five and 10 kind of, and then 16 is 15 and one. Which like makes sense. that That's 16. 17 is 15 and two. But 18 is not 15 and three. Like if you kind of translate the word literally 18 is two nines. It's like double nines. Why?
00:18:25
Speaker
Because that's a great name for 18. Isn't that a cool name for 18? I don't know. like i wish I wish I had. you know like You turn double nines. Now you can vote. um I don't know. I like i like i like double nines. And it's like a better you know if you think about it, what does 18 mean? right The 8 is 8, and the teen is 10. That's the etymology. So like that's a weird way to call 18. Why would you call it 8 and 10? That's not the nicest. like Call it 9 and 9. That's a nicer way to think of 18.
00:18:49
Speaker
um But of course you can't, it's actually really hard to learn to count in Welsh, because you gotta learn these wild names that are switching back and forth. It's much easier, like Mandarin, as I understand, speak Mandarin, but it's even simpler than English in the sense, because it's sort of like you get to 10, and then it's 10-1, 10-2, 10-3, 10-4, and the more irregular your names are, the harder they are to learn.
00:19:11
Speaker
Anyway, so that's that's where I started it. So I wrote that chapter about about counting and and naming numbers. um And then it just kept going. I was like, I think the next one I ever sat down, I was like, you know, that's a start, but we need to talk about negatives now. And I don't know why that was the thing I want to talk about first before we talk about fractions, before we talk about equations, negative numbers, we got to talk about that, because I think that's something you encounter very young.
00:19:31
Speaker
And negatives embody a really different perspective on math. um It's not about labeling things out there in the world. It's about, because they you you know don't have negative free dogs. It's not how the game works. So it's about negatives are about creating a system um where things fit together nicely, where like opposite directions can be unified on one number line.
00:19:52
Speaker
um Anyway, so I did that, and then then I did that for like 40 chapters. They're all really short. um and And then I had to go back and kind of smooth it over. ah But that was that was pretty much the book. So it was, um it was yeah, the greedy algorithm is the way I described it. It was just like every day I would sit down and be like, all right, what is the next thing that I should write about? What's the next thing if I was talking to a reader who's only ever going to read this about math? I've told them these six things. What's the next thing I should tell them? um And it it led me to places that like weren't the places I usually dwell in math.
Creative Writing Process
00:20:22
Speaker
So yeah, it was a fun way to write it. What did I leave out? I think those Japeron functions that I cut, I think functions are a really potent idea and a notation that's really easily confused, but it was a little outside the kind of path that I had been carving in this book.
00:20:39
Speaker
um Yeah, yeah. that was and And also, like, everything else. and Any book is sort of like a depressive writing that you discover. There's 99 books that you that could go in here, and then it's about finding the one that that does, the one that fits and coheres. With that, do you have a favorite analogy or metaphor throughout the whole thing? Yeah. One of the ones I was very proud of, and actually I showed it to a linguist who who also liked this metaphor, which which made me feel good about it. Are you guys familiar with the term creolization?
00:21:12
Speaker
No, I'm familiar with the language. Oh, great. yeah The Creole, right? Exactly. yeah Okay, so so this is where Creole comes from. um So it's over. I mean, it's it's a brutal history, but but an interesting one. um So what you get is you get a bunch of people thrown together. In the case of like Haitian Creole, we're talking about people who were abducted from their homes and brought across the Atlantic and slaves. But that can happen in other settings, too, that are a little less cosmically horrible, um where you get people thrown together who speak all different languages, but they're adults, and it's really hard to learn each other's languages as adults, and also, like, whose language would you learn anyway? And so what they do is they'll basically speak what's called a pigeon, um not, like, the bird, but P-I-D-G-I-N, um which is, like, not it's not, according to linguists, it's not really a full language. It's it's more like a phrasebook. There's, like, a set of things you can say in the pigeon,
00:22:00
Speaker
And those are the things you can say. um So it doesn't have the feature that English or Haitian Creole or or American Sign Language or any any full language has, which is you can, it has a full grammar. You can you can sort of express almost any thought um and generate sentences of like layered complexity. um So this will come back to math in a moment. um But so so with the way a pigeon becomes a Creole is that the next generation is born.
00:22:28
Speaker
And the human brain, for reasons I certainly don't understand, maybe maybe some linguists do, um is just thirsty for grammar. And so what kids will do is they'll hear that language, so it's not a language, they'll hear that pigeon, and they will just speaking amongst themselves, breathe life into it, and it will turn into a full language.
00:22:49
Speaker
um So that's how a Creole develops is is the grammar is this this structural richness brought by the next generation. um And you go from something that's sort of simplistic and and just a phrasebook into something that's got this generative complexity. um Anyway, so long metaphor, but that's my kind of pivot point in the book. The first half two thirds of it are ah essentially about arithmetic.
00:23:14
Speaker
So you know what does it mean to count? What does it mean to talk about numbers between the counting numbers? you know What are our languages for doing that? um The operations, you know when we add, when we subtract, when we take square roots, like what are we doing? What is that all about? um And that gives you arithmetic. But arithmetic is almost more of a pigeon. Because you can only ever talk about specific numbers that way. You can say 7 and 2 make 9. Or 7 times 2 makes 14. I almost said 18. I don't know why I was talking about 18 earlier. you You could say seven times too, it makes 18. It would be a silly thing to say. anyway yeah you know but they may Maybe we can find out. Is there a base in which it... Probably not. um ah Anyway, but so so but you can only say so much. And if you want to say things like, when you multiply any two numbers...
00:24:02
Speaker
It doesn't matter whether you reverse the order, right? A times B is always B times A. You'll notice I have to slip into algebra. um Algebra is the Creole. that's That's my metaphor, is that algebra takes this kind of list of numerical specifics.
00:24:18
Speaker
And it turns it into this full language where you can talk about the language itself. You can talk about bigger patterns. You can talk about anything. yeah You can't have literature in a pigeon. You can have literature in a creole. ah And so anyway, that's that's a long metaphor. I've got to learn not to give a minute answers to questions. I have to I have to confess on them real quick here. I did not read the entire book. And because I have five kids, I'm going to use the I have five kids many times here. but I read all of I read almost all of the last chapter and I read a few random pages throughout the rest of it.
00:24:47
Speaker
Everything you just told us is utterly, spectacularly fascinating. And I'm wondering, is this did you write what you wrote, what you just said in this book? or Or is this just facts that you knew that you're you're spitting bars here now that you're on the podcast? that that that one So that that what I just recited there is is possibly actually a wordier version, but it's essentially the same idea as um the introduction to the third section. So the book is in the book is in four sections. um The last one, I'm glad you turned straight to that one, because that one's the most browsable and kind of flip through a bowl. It's like a phrase book of different um like fun mathematical terms that I think yeah can make cool everyday usage. ah But yeah, the the first two sections are arithmetic, so it starts a section on numbers and then a section which is called nouns, a section on arithmetic, which is called verbs, and then that section where you get to algebra and like algebraic thinking, which was really, that's what I was aiming at. that's like that's That's really what the book was about, but it took a while to get there. I couldn't i couldn't jump straight into that.
00:25:40
Speaker
ah that's that's It's at the start of that section called Grammar is where you get the ah the pigeon into Creole metaphor. It's magnificent. And I only bring this up because um in math of computation, and we get into Goedel, Escher, Bach. And um I bring this up because this leads into a conversation on language. Our fifth episode of this podcast we ever did is called Word, where we sat down and we talked about the evolution of of language with a colleague of ours who was a linguist.
00:26:04
Speaker
um And it was fascinating. We then did a follow-up episode, I think probably 12 or 20 episodes later. Sorry, I forgot which one, called Language and Entropy. And it was literally it was literally about the continuing evolution of language and just about the concept of entropy itself. Now it was, um I think,
00:26:21
Speaker
proper linguists would probably not be a super big fan of that episode because this is ah folks who are not on the field pontificating about the field. Full disclosure. But but still, you know what I mean? like like if If concepts like entropy rule the universe, I'm sure there are ways in which entropy can be used to describe the evolution and change of language itself.
00:26:39
Speaker
ah so So this has been a continuing um ah discussion, is like meaningful communication, ah communication systems, language and entropy, it's fascinating stuff. um Yeah, so so I was wondering, did you- I love that stuff, and i and I'll alsoll say also, in defense of people pontificating about things beyond their field,
00:26:58
Speaker
Yes, you know, it's sort of there's there's a trade off here because like I want math to be a a communal possession. I don't want people to feel like math is something only for people with a doctorate in it, particularly given that I don't have a doctorate. That would be be a dangerous party line for me to espouse. um But but the the phrase of that is like people will you know, people don't always say things that are the experts would agree with and like you know what that's okay when a communal possession like you know you you want people listening to the experts but you also want them forming their own ideas and some of the price of that is like you know maybe people are like a little more into the golden ratio than I think is strictly ah sensible it's like hey no that's that's okay that's like that's that's that's what you get when when map is opens its doors a little wider
00:27:36
Speaker
say tolerance for imperfection. Maybe we've reached the internet age of Aquarius where suddenly there's this tolerance for imperfection. Yeah. ah If you ever thought of um um discussing this book over a podcast with some linguists, I know a few.
00:27:51
Speaker
That would be really fun. No, I would love to do that. I've been meaning to reach out to Gretchen McCulloch, who I read um her book, Because Internet, and try to see if she would be so kind as to receive a copy. And then the front cover blurb is David Crystal, another linguist, whose whose books I've enjoyed. Ben, one thing that I have to say is, you don't need a PhD, you went to Yale.
00:28:08
Speaker
well they say yeah i try not to My bachelor's degree is from Yale. i try I try not to trade too much on it, though. I'm just turning 37. And there's something, I don't want to be too much, like, if you're a 37-year-old who still needs to talk about what but you were doing from ages 18 to 21. Like, I mean, one thing, if if I'd been in the Olympics, that would be cool. Like, I think when Simone Biles was 37, I would encourage her to keep talking about what she did during 18 to 21. That was pretty cool stuff. I watched it on TV. um For me, it wasn't, you know, anyway. but but but But thank you, Autumn. I appreciate your your vote of confidence in my ah in my pedigree. Just knowing you long enough and seeing the evolution of your writing,
00:28:40
Speaker
and yeah And also knowing your partner as well. You know, just saying. Well, yes, my wife is my wife is what I would call a real mathematician. She's a research mathematician. So, yes. Right. As first hand. Yeah. So, you know, but that does have some trade off where you can just throw ideas. Yeah. Right. No, that's right. Yeah. Yeah. and And certainly, yeah. Being married to a mathematician means that even though actually I managed to squeeze through my bachelor's degree, never taking technically taking a real analysis course, it's easier over that kind of time scale than to pack it into a semester. It's a trade off.
00:29:10
Speaker
Yeah. Okay, I want to ask, do you have a a favorite part of chapter four? Oh, and also let's explain what chapter four is for our listeners. It's where yeah um I think that it's a great chapter to learn new language and to, I don't know, I felt really smart reading it. It gives you math terminologies. And it's like a thesaurus comical usage of the math terminologies. Do you have any favorite parts of chapter four?
00:29:34
Speaker
Yeah, yeah. So the idea with that that section, that fourth section of the book is um it sort of comes from this one moment at um oral argument at the Supreme Court. So there was some lawyer, actually, I wish I should know the name of the lawyer. I don't know his name, um who used the word orthogonal. He was he was speaking for the justice. This was 15 years ago, maybe, 2010, 2011. And he used the word orthogonal, which stra as ah as if you've done work with vectors, you know, means perpendicular, right, the inner product zero. um And two of the justices, it was Roberts and Scalia, who was on the live and on the bench at the time, like, what was that word you just used, orthogonal? And the lawyers like, get ah yeah, yeah, I mean, it's like unrelated, right, because it was a word that was just kind of starting to creep probably via tech circles from the math classroom into popular usage. And Roberts and Scalia, I think, particularly Scalia, who was a real wordsmith, um like oh orthogonal i like that i like that there's like that these you know these very powerful spring process is just really into this mathematical word um anyway so that was my template for like you know there's more words obviously exponential has has taken off some
00:30:33
Speaker
Possibly at the beginning it was even exponentially the way it took off.
Math in Everyday Language
00:30:36
Speaker
um Logarithmic you hear, although often misused. Orthogamals on the rise. Inflection point, which I'm not sure I love the way it gets used, but but it's nice to hear a math word out in the wild. Anyway, so it was like, okay, let me let me go through math.
00:30:48
Speaker
take i say maybe 80 or 100 terms in there um and just find ones that I think are really ripe for kind of fun usage out in the world and then do a little definition that's accessible to someone who doesn't know the math, gives you a little context, and then a little cartoon showing how it could be used. um yeah One of my favorites in that section is brute force. There's a little a little subsection on um like problem-solving methods and heuristics and algorithms. And brute force, as any mathematician knows, is like, I don't have any clever ideas for how to solve this problem. I am just going to try every single case. And so the example I give is two people in a parking lot full of sort of identical-looking cars. And one of them is like, do you remember where we parked the rental car? And the other one is like, nope. We're going to have to brute force this. Just start walking around, pressing the key, and seeing what makes a noise.
00:31:38
Speaker
Um, meat I don't remember the exact phrasing yet. The equivalent of that analogy for real life is, uh, for anyone who knows the UMass Amherst, uh, Smith College, Hampshire College area, the number of Subarus that you will go into the parking lot coming out of Whole Foods. You will mistakenly walk into another blue Subaru.
00:32:04
Speaker
when you are coming out um of the store or Trader Joe's. It was a Trader Joe's in Berkeley. I was borrowing my aunt's car, her her silver Prius in Berkeley, California in 2010. I came out and like I was like, oh no. i like I had to look for the bumper stickers was the only way I could identify ah which was the right silver Prius in the in the yeah Berkeley, California parking lot.
00:32:27
Speaker
Okay, I'm reading this right here. I found one that I like, but asymptotically, it's a really fun one, really fun one. as eternity as As eternity unfolds, you to describe an outcome that we don't necessarily reach, but to which we come progressively closer. um Yeah, I use that back in algebra one. Is that right? Something like that? That's a fun one. I don't know.
00:32:46
Speaker
Yeah, albra algebra II courses probably would tend to give some asymptotic behavior. um Certainly calculus, it really yeah comes up a lot. Yeah, it's one that's one that like really catches the eye. that that one know that That one has already, I think, kind of slipped into the public imagination from the the math textbook. um There's a journal like some a literary journal of translations, I think, that's called Asymptote. um The idea being that when you translate a work of literature,
00:33:11
Speaker
You're never quite, it's like it's never going to be the same as the original, right? Like to translate is to change. But a skilled translator can sort of approximate the experience of reading the original more and more closely in some kind of asymptotic way. You can never quite get there. It's never going to be the same. um But you can get real, real close. OK, fair enough. I remember shortly after I got my degree, it was a colleague of mine and I were talking about dating apps and just like ah Ambiguous signals that are just in the dating game all the time and we used a lot of electrical engineering Terminologies and concepts to describe that like ah what's the signal-to-noise? Ratio with with what you're picking up from her and you know, just oh gosh, what were the other ones? That was the main one um but yeah that's a right Yeah, noise is huge, right? Yeah, right and again going back to your interest in in entropy and communication Yeah. Oh, yeah. Yeah, it was it was fun. So so yeah, yeah cool book here cool cool cool book and cool ah
00:34:05
Speaker
Thesaurus, your own mathematical terms. out of curiosity what did you did you find anything new when writing this book between math and literature question this one so every book i've written i found new things you know there have been things that surprised me um yeah the games book which was my third book is probably the one where it was the most novel um there was the least in that book that when i sat down to write it i already knew um because what it did is yeah i sort of went out and searched for lots and lots of games so there's like dozens and dozens of games and they're from all different you know some of them a couple of them are games that were played in classrooms but mostly they're sort of like little clever hobbyist games that people had shared on board game geek or ones that were getting passed around or once the kids were playing on schoolyards but no one was really writing about
00:34:51
Speaker
um Anyways, that one, there's tons of new stuff that I found writing it. This one, I was almost trying to rein in my desire for novelty and my interest in going and looking for new stuff because because I wanted to really laser focus on core, core mathematics. um So like writing a chapter on addition, you know, the hard part for me wasn't actually going out and finding new stuff to say about addition. It was like stopping myself, as you can hear the length of my answers, stopping myself from saying 45 minutes worth of stuff on edition when I'm just trying to say, you know, I'm trying to do 800 words. I'm not trying to to do write a whole book on edition. So that said, right, I'm sure there was there was stuff that was there was new and surprising as I as I searched. I think.
00:35:35
Speaker
One, it was a surprise that I found before writing the book, actually, and then went into the book. But one of my favorite little discoveries was the word logaram. This is David Crystal, the linguist I mentioned. He has this book called The Disappearing Dictionary.
00:35:50
Speaker
And ah it's a collection of words from kind of around the British Isles that are fading from usage, like words that were just little colloquialisms used in a local dialect, but that people like aren't using as much anymore because everybody just watches TV and goes on TikTok and just imbibes the general culture. ah And one of those words was logaram, which meant nonsense. It was like, oh, I was talking logaram. We're like, oh, stop stop speaking logarams. And it comes from logarithm, like the idea of like ah like well like what's the what's the icon of nonsense?
00:36:19
Speaker
a logarithm. Like, ah stop stop talking logarithms. like you sat You sound like you're speaking in logarithms. um So it's like a dismissive way to say someone was was talking nonsense. that what That one I thought was was ah a fun a fun discovery. I remember the moment I found that, I was like, oh, that's really fun. I gotta pass that along.
00:36:34
Speaker
I had a question for you, but I got you know i think our conversation so far has almost answered it just to just in the way you've been sharing your your thought process. I was going to ask you, how do you feel like mathematical thinking specifically can enrich a person's appreciation of literature or vice versa?
00:36:49
Speaker
Yeah, yeah, yeah. I mean, what I love about math, the reason I love writing about math is it just, it gets its tentacles and everything. It's like a, um or the tentacles is maybe a little bit of a scary term. People don't want math to be a little sea monster creature that's getting its tentacles everywhere. But think of math as like maybe a river that feeds a whole landscape with these little kind of creeks and tributaries, which tributaries go in, estuaries go out, running away from the river. And so just like math, it it seeps in everywhere.
00:37:16
Speaker
um which is a little different from saying, I think sometimes I'll hear people trying to preach for math, say like, ah, math is the perspective you need for everything. It's the one like it's the one true way of thinking about stuff. I think that's definitely not true. um yeah But what I love about math is it is it fits so nicely alongside other things. um It's a very purified and simplified form of thinking, but that makes it a great partner for other disciplinary perspectives. um So, yeah, literature. there's in In my first book, I did a chapter on um kind of digital humanities and attempts to take, it was all before a large language models arose, but attempts to take text and boil it down to numbers and then do stats on the numbers and then learn something about the text. And I came across in doing that chapter, came across a lab, I don't know if they're still publishing new papers, I bet they are, called the Stanford Literary Language. No, that doesn't sound right.
00:38:14
Speaker
Stanford Digital Humanities Lab, something along those lines. they did But they had lovely papers, you know one where they were kind of like found a way to quantify a genre and they pulled out like the most gothic sentence they could find in any of the hundreds of novels they'd sent into the computer. And it was funny because you looked at it and you're like, oh yeah, that is the most gothic thing I've ever heard. It was like somebody walking into a creepy courtyard on an autumn moonlit night and there were cobwebs and shadows. They're like, oh yeah, this is really gothic. um stanford But it was sort of interesting. but There we go. Stanford Literary Lab, thank you. Yeah, I mumbled my way through that. Thank you, Autumn, for being my memory. It's Google. Yeah, well, yeah, but but but you're the one who who summoned the the genie of Google. um ah Yeah, Stanford Literary Lab. So anyway, that so stuff like that. um Yeah, oh, I'm im um drifting away from your your good question, I think, Abe. But you know what does math give you as a thinker?
00:39:07
Speaker
um The danger is that it makes you think of everything as quantities, right? That anything can be boiled down to numbers and then operations on numbers. And that's just not true about reality. Like much of what May has made, like I had a nice day today, you can't quantify a lot of it numerically. Like I went for a run and you can quantify how far I ran, you can quantify how fast I ran. But like the little moment when the mist kind of came off and I couldn't tell if it was raining or just water falling off of the trees from an earlier rain,
00:39:37
Speaker
That's not a seven or something, right? That's not a 19. There's no numbers for that. So most of what makes human life rich and exciting is is not quantifiable. And that's a danger of mathematics. But the the possibility of mathematics, what makes it exciting and worth everybody learning, um is a thing that people don't think they like, but they do when they get to know it, the abstraction. It's the fact that math is about these very abstract and very general relationships. And they give you ways, math gives you ways of of conceiving of the world, um of thinking about the world as is as the simplest way I can put it. um And that's sort of what that last section of the book is about, all those little you know jokes about orthogonal and and brute force. um That math, because it's about very abstract relationships, it's sort of about everything, right? Like you talk about noise to signal ratio, and like that's relevant if you're transmitting something across phone lines, but it's also relevant if you're trying to figure out if a potential romantic partner is is interested. It's the empty set.
00:40:37
Speaker
there go right yeah yeah We were just having a conversation about this before jumping on the call. Right, that's a tough one. Yeah, I can't remember the exact joke I made. right One of the things that you get in in in ah in those sorts of things is thinking about, maybe that's my intersection joke, is that if like someone's like, well, look, i just want ah yeah I just want an affordable place and I want to live in walking distances in San Francisco. And it's like, yeah, that's that's the empty set, the intersection of those two things. is that is a um Yeah, pretty much. I have a theory here because I learned more about machine learning. I have this great idea and then I realized it's complete nonsense and that's happened so many times. It's been jarring, but I've gotten better at it. So I think about a really skillful comedian, any comedian at all who can read an audience or just one of your funny friends that can really read something. I still think there's a quantifiable measurement happening even if if we all don't share that skill set.
00:41:30
Speaker
and somehow he can anticipate things where he says the right thing at the right time that that, that, um, what's the word I'm looking for about expectations? Like it's subverse expectations in a way that we all find funny and delightful. I still think there's an accounting happening, and there's a measurement, and there's some kind of a skillful process, but it's more about the exchange exchange of ideas. It still involves math though, at least I argue.
00:41:52
Speaker
yeah yeah i think so i think Yeah, what I would say is that the lesson I take from large language models and from other generative AI is that ah quantification is way more powerful than I would have guessed. That just like kind of naively assigning numbers to things and throwing them into a neural network.
00:42:09
Speaker
um gets you much, much further than I would ever have imagined. um yeah And it can do different media. And you could do like, I played around with the music one, it's really fun. Or you feed it some lyrics, and it makes a song like, <unk> it's crazy stuff. Like, I find it astounding what these what these things can do. Yeah, downright scary in some ways. Yeah. Now that's it. I still what it what it makes me think of, though, is there's the power in quantification, but then there's the there's the temptation to see everything as quantifiable. And I think it just, you don't, it doesn't actually work that way. Like like the simplest example I can give um is you think about the choice between like, say you and your partner have a free night, um got a babysitter, and it's like, okay, what do we want to do? Do we want to go out to some, see a show or something? yes so Something kind of a little, you go to a club or something, that I don't have to go to clubs, but she put something a little more exciting.
00:43:02
Speaker
Would you go to the one you have with the math lounge the logger rhythm so yeah, yeah, we're soft brown lager rhythm absolutely absolutely i say well the right life i've done I don't like a flavorful beer. So lager is perfect for me. Okay, you know that the A's are too much ah Anyway, but so so there's like a choice between just let's take to like, you know It's going out kind of having an adventurous night or doing something really casual go into like your favorite.
00:43:26
Speaker
restaurant that's like really close by, you know the menu, you don't even have to look at it, like something really safe and comfortable. um Which one is better? right like if and If things are quantifiable, then quantity of quantification usually starts with comparison. right Before you can establish some kind of linear scale for things, you need um you need inequalities. right so like in the In the foundations of microeconomics, to establish what a utility function is, you sort of bootstrap it from a set of preferences.
00:43:53
Speaker
So, so like microeconomics in microeconomic theory, we assume these preferences, um, like hardcore utilitarian similarly, we'll assume that you can rank order any experiences like that. So this should be a right answer, right? Like I as an individual should have a right answer. Should I go out and do the slightly more tiring thing, but a little more stimulating and novel and down the road. I'm i'm more likely to remember that in a year or two, you know, like that, that night we did that thing, as opposed to just going to the restaurant we love and and doing it again, which will probably kind of fade in memory. um Like the comfort food versus the trying something new, which that could be, could go well, could not go well. Like I think genuinely there's not a right answer there. Like you can choose a preference. You can exert your will and make a choice. But there's just not, it's not gonna be the case that one is better than the other necessarily. Or if if you on a given night do feel like one is better than the other, well, you know, pick a different night or change the options a little bit. I think everyone can find two options where you go, well, I don't know, that one's better in some ways and worse in some ways. And like, there's not a right answer as to which one is better.
00:44:49
Speaker
um and like that's a very sort of like trivial thing to say in some sense that like not all things can be compared and rank ordered um but in a in a world where like things are changing as fast as they are right now a triviality like that can actually be kind of a profound thing you need to hold on to um so like it just it just isn't the case that Everything can be all experiences can be rank ordered um or that there's a natural quantitative scale underlying all human experience. It's like quantitative skills are great, but they're simplified models. um And so it's astounding what the simplified models can do, right? Like now those simplified models as we let them get more complex and we add more dimensions.
00:45:26
Speaker
um and you know like dimensions are great so you keep adding dimensions to your model and you're up to like a million dimensional model and it's almost almost starts to feel like reality and you start thinking well maybe reality is just a billion dimensional space and if we can capture it all then we'll have it all um and like that's just not when i think about human psychology and experience i i just don't think I don't think it is, I don't think it is a dimensional thing at all. It's something more ineffable than that. There's something more elusive. And so quantitative models can be like are are so powerful, right? Like we wanna use them. But but i yeah, I don't wanna imagine, I should say I don't wanna imagine, it but if if that were the way it is, that's the way it is. But like looking at the world and my experience of it, I see where quantification just falls short at sort of elementary tasks.
00:46:13
Speaker
Okay. It's always a simplification. It's always a rounding. It's always an approximation. Yeah, yeah. front of Okay, so next question. um This involves what we've been talking about, languages and, you know, the human experience in mathematics. And this is, why why do you think that people often draw such a stark line between math and the humanities?
00:46:33
Speaker
Yeah, like that that that line in the sand, right? um sure Yeah, yeah. I mean, I think ah where I see it drawn most sharply is by people who really felt like they thrived in one and got really frustrated with not feeling like they thrived in the other. So, you know, often that's people who are um like successful in school and the humanities classes, and they go into math and they just feel they feel confused about it. They like can look over and see a different kid finishing the worksheets faster than they are. um And it's like an alienating experience to feel like I pride myself on my success in these subjects. And then here's this one that like i can't I can't do. So I think that's that's where you get like the I'm not a math person quote coming from. is people who like it's It's not actually people who like didn't like school at all. Because if you didn't like school at all, you're like, I don't know. A math was fine. English was fine. Whatever. I'm glad I don't have to do it anymore. like There's no real need to draw that distinction. It's people who actually really were invested in their academic career.
00:47:25
Speaker
um you know, people who often go into sort of professional work, you know, white collar work, ah for whom like school was an important formative experience, and their success in school was important for them. um And that's where you have to draw the line, because if you succeed, felt like you succeeded in one, it didn't feel like you succeeded in the other, it's important for you to kind of put a fence between them and say, Oh, yeah, but that stuff, that's that's different stuff.
00:47:46
Speaker
um and then yeah And then I think it happens less often, but but also happens the other way, where people who really feel like they thrive in quantitative disciplines, the kind of reasoning and thinking and and and arguing and and work that you do and in more humanistic subjects, they may feel like, I don't know, that's always felt so fuzzy and I didn't know where I was supposed to stand. It felt like I had nothing, no firm ground underneath me. um And so they will draw the line in the other way. It's like a yeah literature, cook who needs it?
00:48:14
Speaker
um with that Out of curiosity, how do educators, how can they use this book to help students who don't excel in math, but excel in the language
Integrating Math with Other Disciplines
00:48:27
Speaker
arts? How can they use this to help narrate that path? Yeah, yeah, no, I appreciate that question. right yeah Yeah, everything is narratives. Yeah, I think one of my hopes for the book is that it can become like just sort of an essential piece of equipment, a nice little guidebook for K through five teachers in particular, but also K through eight teachers. I was just like, here it all is in one spot. Here's like a one little friendly volume that
00:48:53
Speaker
ties the ideas together so it doesn't feel like it's this disparate collection of skills. You can kind of see the threads that will lead your your students through math education. um So I hope it can be equipment for them. I think like teaching needs to be done by teachers. So I never like into my writing about education or giving people advice about education. I try never to be like, and here's the right way to do it because like that the right way that worked for the kids I taught might not be the right way for the kids you're teaching. It's like it it takes flexibility. It's an art.
00:49:18
Speaker
um exactly So that's one, yeah, yeah. So thats that's one hope I have for the book. um And then the other one, right, you you asked, like, where what what can can kids get from it? What can students get from it? um One thing, and and particularly for those English kids, you know, the sort of the proverbial English major. um ah To me, one of the things that emerges is that math, math is a narrow language. It's only one lens for looking at the world. It's a very specialized language that takes some intuitions you have in childhood, you know, of like quantifying things and comparison and and shape, and it shows that those seemingly kind of simple intuitions can bring you to really fabulous places. um But I guess I would take away that like math isn't everything there there are things that that are beyond the purview of math.
00:50:00
Speaker
um and so Yeah, and I think the the sense of the scope of math. What is math for and not for? What does it do for us and what does it not do for us? I think um i think to make it approachable, it's important to have acknowledge math doesn't do everything. it's like that's ah it's not nope No tool does everything. What math does is astounding. um but it's But it's got its place on the shelf.
00:50:22
Speaker
um And I think ah think that can make it seem less like this amorphous entire worldview that you have in Adopted or something, even though it it sort of is a whole worldview. um but But we all have lots of worldviews that we can switch between, um and math is one worth having.
00:50:39
Speaker
Let me ask you this. ah Going back to my analogy earlier where I talked about RPG skill trees, obviously this book, both the ability to to do mathematics, to understand mathematics, and to communicate mathematics, those were all different skills. i' I've had teachers that were brilliant mathematicians but could not communicate and relied on a script that was prepared from other people to write on the chalkboard line by line. They just they couldn't explain their thinking.
00:51:04
Speaker
Now, all that said, ah how would you rate rank or how would you describe your own um artistic ability or or creativity versus your mathematics? I've got an answer, too, but I'd like to hear that from you. Oh, i miss you you have an answer for yourself, an answer for me.
00:51:21
Speaker
I have an answer for myself. Absolutely. I'll share it. I'd like to share it, but I'll, or I could share it first, uh, as a, for example, perhaps. by the way yeah ah Sure. Yeah. I'll go to share first. So actually I am very, very much an artist, uh, like, like literally an artist and a painter and a storyteller who learned how to do mathematics and, and the, and the slow process of learning it. Once I got it, I feel like I got it pretty well, but I was always, uh, slower in math until I made it through engineering school and in one day, you know, just I kind of felt like I had a shift in how I was thinking and I had to experience that it was it was uncomfortable, but when I got it and I understood it and I i knew what to expect, I feel like I did pretty well. So now I feel like I've got natural skills and creativity and ah hard work and earned skills in mathematical modeling and learning how to calculate and think about things analytically, which is very different than than creatively.
00:52:16
Speaker
Yeah, yeah, yeah, that's interesting. Yeah, I've read, I'm curious to hear yours too, Autumn, but yeah, might like my own skill tree, um I think I'm definitely not a hands-on person. I will put it that way. is Like I'm very comfortable with ideas and navigating spaces of ideas. That's where I love to live. um And like drawing a picture on a piece of paper, that's tough. That's that's hard work. That's that's why why it was Math of the Bad Drawings was the the way I began and and why that's still kind of my brand and who I am.
00:52:43
Speaker
um Yeah, yeah. do That is the simplest way to put my my own skillset. Math didn't ever feel as separate from other subjects to me as um as it felt to other people. i think I think math fit in very naturally for me among other academic subjects. And I think you see that in my writing, that like I move between them quite fluidly in a way that someone who's a more singular advocate for math might not. um But but yeah, where i've I've always seen a temper to myself of like, I'll be like trying to help my daughter my five year old with crafts. And like, just like getting the needle through the thing getting I don't know, getting the glue to stick to the thing. It's like, like, element like stuff that, ah you know, a reasonably competent eight year olds can do. That's like, that's about my level. I'm like, not on athletic, I like I'm reasonably coordinated when it comes to sports. but But but like, a little fine motor, I don't know, making the finicky stuff work. I've i've always been very, very bad.
00:53:33
Speaker
But your gift of gab is on point. I mean, in the best way, like your ability to to to speak captivatingly. And again, there are mathematicians who don't have that. And what's actually really astonished me. And you know what? Before I continue, we've got a scientist that we've got two minutes left in studio. So I'll ah be quick here.
00:53:50
Speaker
um I also want to hear, Autumn, your answer to this as well. I'm going to make time for you as well. Reading ah the autobiography of Oppenheimer, and I forgot what the book was called, American Prometheus, I believe, he talked explicitly how at in Los Alamos Labs, among all the busy physicists, you know Richard Feynman and Niels Bohr, you know when when he was there, or or just other physicists, there are idea people and there are are um engineer people. there There are, as they called it, the brick makers and the brick layers, and they're very different. Oppenheimer was an idea person. He was not a hands-on person.
00:54:27
Speaker
either Okay, there's lots more labs there are physicists who? That lab is named after if he was the engineer he was the one that made the cyclotron You know like very much hands-on so I find it even among you know geniuses There's different types different tools alright, and I'd love to hear you your your skill tree discussion autumn if I may um I'm actually very skilled as an Oregonist. And yeah, so I can do the intricate folds for and that like all of the mathematics. I can see how things are built structurally. And I'm also what the people ah listening to the podcast don't say is I am a very talented artist.
00:55:13
Speaker
Yes, you are. You absolutely are. so I like that I'm ah easily the worst artist on this call. here but but but here here's the thing I can build whatever engine it is or whatever structure. If you ask me a technicality and a proof,
00:55:32
Speaker
Nope, I'm gone. Throw it out the window. sting it's It's polar opposite. So I can build you the whole concept, tell you how to write it, but sometimes the technicalities of things, I don't care.
00:55:48
Speaker
Interesting. Interesting. I'm the person that makes sure that it works. Yeah. I know this is a bit of a strange ah a strange topic and I don't want to get too much into it because I don't want to get too much of the comparison here. But when you read about Albert Einstein, for example, and you read about his one year, what there's a term for the year that he published those four papers. What what was that? Ennis Mirabalos, a miracle year. Yeah. You can read it. at And you get these brilliant physicists who read it and say, this guy was the smartest man that ever lived to see these connections. But then you get into the less popular mathematicians like Enrico Fermi, or or ah Paul, Paulie, I'm sorry, there's Paulie, there's Fermi, there's Dirac, there's these names that unless you're a physicist, you may not hear and you see the way they did their math. And I would say they were much more powerful mathematicians than Einstein.
00:56:38
Speaker
They ran circles around Einstein, but I wouldn't say that they they saw the connections in different fields the same way, if that makes sense. so so again yeah yeah just Just a little thing. Sure. When Einstein published all of his papers, those were considered his golden years. Do you know why? Why? Because his wife was the one who wrote a lot of it. Oh, man. Okay. Okay. That's often not spoken. Every great man is an exceptional woman.
00:57:06
Speaker
absolutely absolutely yes in their in their divorce proceedings i want to say i think i remember it's in it's in the isaacson biography some some part of the condition of the divorce was sort of when he wins the nobelle she will get she got the bulk of the money or something like that yeah that was part of their their agreement for the course oh my gosh yeah which i would yeah i'm i'm not sure i don't think that was specifically about credit or something yeah that's that that's like kind yeah she couldn't take the courses and the university wouldn't allowed her to sit in the classes for such a long time. Wow. So she wrote all of the papers and everything. Wow. And that's right that's where like 80% of his time is. Yeah. And i'm I'm sorry to end it here, but the studio needs to kick me out because I'm just borrowing their studio here. But Ben, it's been too long and it's been an absolute pleasure um because I'm very busy. I give full reign to Autumn. Autumn, if you ever want to have been on again for any reason and any episode, please do so. Just give them a call. Get them on. That'd be great. No, I'd love it. I'd love it. Yeah. Absolutely. Let's take full advantage. And Autumn, I don't say thank you to you specifically enough. You to take the reins and you make this show what it is. It couldn't be what it is without you. So thank you so much. And I mean that. And I just, all the work you put into putting this episode together, you put the outline together, you are editing everything behind every great man as a great woman. So thank you so much.
00:58:25
Speaker
Yeah. Sorry. No, it's true. I just got to get it, you know. Yeah. No, no, no. And and and think about Autumn ontto and Dave. It's really it's fun. Fun chatting with you both. And I was I admire the work with you were doing with the with the podcast with the the Breaking Math Empire.