Ologies with Alie Ward - Abstract Mathematology (UH, IS MATH REAL?) with Eugenia Cheng

Episode Date: November 22, 2023

Math wants to be friends. Let mathematician, author and Abstract Mathematologist Dr. Eugenia Cheng introduce you to a secret world: the artsy and emotional side of math. Dr. Cheng helps answer the age-old and (recently viral) question, “IS MATH REAL?” We chat about Fibonacci sequences, golden ratios, common core, loving thy neighbor, slide rules vs. calculators, imaginary numbers, the nature of zero, infinite cookies, and more. Turns out that math can change your relationships and permeate your every thought.. if you let it. Also: wtf, Barbie?Visit Dr. Eugenia Cheng’s website and follow her on TwitterBrowse Dr. Cheng’s books including Is Math Real?: How Simple Questions Lead Us to Mathematics' Deepest Truths (2023), The Joy of Abstraction: An Exploration of Math, Category Theory, and Life (2022), and How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics (2016)A donation went to Math Circles of ChicagoMore episode sources and linksSmologies (short, classroom-safe) episodesOther episodes you may enjoy: Quantum Ontology (WHAT IS REAL?), Dolorology (PAIN), Fearology (FEAR), Egyptology (ANCIENT EGYPT), Classical Archeology (ANCIENT ROME), Economic Sociology (MONEY/FREAKONOMICS), Tiktokology (THE TIKTOK APP)Sponsors of OlogiesTranscripts and bleeped episodesBecome a patron of Ologies for as little as a buck a monthOlogiesMerch.com has hats, shirts, hoodies, totes!Follow @Ologies on Twitter and InstagramFollow @AlieWard on Twitter and InstagramEditing by Mercedes Maitland of Maitland Audio ProductionsManaging Director: Susan HaleScheduling Producer: Noel DilworthTranscripts by Emily White of The WordaryWebsite by Kelly R. DwyerTheme song by Nick Thorburn

Oh, hey, it's quite frankly the episode that you never thought you'd click on. And it's the one that I never thought I would do because mathematics, it's an X, it's not anology. But over the years, y'all have begged me to cover this. I swear. And I found anology suitable and anologist who's going to get us emotional about numbers, believe it. And also non-numbers.

Come on a journey. Take this VIP pass. Come slip behind the curtain backstage for a more intimate chill hang with a topic that maybe has seemed a little out of reach, a little intimidating. You're about to meet the really charming and artsy side of math. So thisologist, of course, is a professional

mather, an author and a speaker who holds a PhD in pure mathematics from the University of Cambridge and taught at the University of Cambridge, Chicago and niece, she won tenure and pure mathematics at the University of Sheffield in the UK, has appeared on late night shows, hyping people up about math, has given TED talks and written several books on the topic

such as How to Bake Pie, and her latest one is Is Math Real? How simple questions lead us to mathematics, deepest truths. She's one of us. And the best person possible to cover this topic. So she jumped on a mic from the Midwest where she's currently the scientist in residence at the School of the Art Institute of Chicago. And she's also a concert pianist. You're just going to love her. But first, thank you to patronsatpatron.com slash allergies for submitting your questions. You can join for a bug a month.

And thank you to everyone wearing allergies merch from olatreesmarch.com. Heads up, if you are hoping to play this episode for your kids, this is not an all ages episode, but we do have many of those. They're called smologies, and you'll find them at the link in the show notes. Thank you also to everyone who leaves a review

because you know I look at them with my eyes. So I can say one with my mouth, and this one was left this week by Minecraft Girl, 215837, who wrote, I listen to you every day, and you are so good, but can you make a cookie one? Minecraft Girl, 215837, first off, that's an appropriate number of numbers

in your name, and, we do discuss cookies. So you have no idea how appropriate that is. So let's get into it. Mathematology. Nobody write me and block it this, okay? So many people have used this word. It's just, it's in the air and the universe. We're going for it.

Also, fun that the word math stems from a root meaning simply to learn. So come along with me. Let me hold your hand and guide you to the wings of academia. The behind the scenes of a topic, you did not know you could adore like this. As I hear about Fibonacci sequences, golden ratios, common core, loving thy neighbor, slide rules versus calculators, imaginary numbers, the nature of zero infinite cookies, fingers, toes, knuckles, how math will change your relationships, how math is not just numbers, but dare I say a lifestyle, and how math is weirder and more artsy than you think, and more with author and mathematician and I use Shea.

And you are a pure mathematician? That's right. And an abstract mathematician? Yes, it's kind of the same thing. I mean, maybe one is more specific than the other. Which one is more specific? That's a great question. Do you know I haven't thought about this.

I think that pure mathematics is more than name that it gets given to distinguish it from applied mathematics in formal contexts like in university departments and in funding bodies. I call it abstract mathematics because I think Piro sounds a bit judgmental. It kind of does it kind of implies that there's an impure mathematics which seems like illogical right? Exactly and I think that there's been enough people looking down there and those as other people over mathematics that we can do with getting rid of any of those things wherever we can.

Yeah, it does seem anithetical to your whole mission, which is to make people appreciate and get over their math, right? Or invite them to. Yeah,ite them. Yes. It's a good distinction. Okay, quick aside. What is the difference between the types of math? What makes one kind of math abstract versus applied, if you apply abstract to applied math? How abstract is abstract? It's one of those things where the boundary isn't very clear cut, but the general idea is that abstract mathematics is trying to understand things from the point of view of uncovering logical structures and just exploring how things fit together for their own sake. Whereas applied mathematics is much more about looking at problems in the concrete world around us and coming up with theories to help us understand

those specific problems. So applied mathematics is closer to physics because physics is really about understanding the physical world around us, but applied mathematics uses the techniques that pure mathematicians come up with often, but they are really specifically trying to solve things in their concrete world. Sometimes people say real world, but I are really specifically trying to solve things in their concrete world. Sometimes people say real world, but I don't like that either because you know what's real anyway. Are we real? Is anything real? Am I supposed to, that's what the title of my book is? I don't know. Is math real? Is math real? Am I real? Nobody knows. And so one thing that I love about your book

is just that it's one of those questions that we're all afraid to ask. I think some very intrepid TikToker was doing a Get Ready With Me video. And it's like, how do we even know math is real? And I feel like a year or two ago, it shook the world. I was just doing my makeup for work, and I just wanted to tell you guys

about how I don't think math is real. And I know that like it's real because we all like learn it in school or whatever, but who came up with this concept and you're like, pathatarius. But how? Like he didn't even have plumbing and he was like, let me worry about why equals mx plus b, which first of all, how would you even figure that out? How would you like start on the concept of algebra? Like, what did you need it for? Do you remember that video? Yeah. And you know, that did what that was one of the things that that inspired me to write

this book because I replied to her. I wrote a document and I just stuck it on my webpage and I just replied to each of her questions. And then I did a few radio interviews and people, because people picked up on the fact that I'd replied to her questions. And people emailed me from all over the world saying, oh my goodness, I've wanted to ask those questions all my life. I was stupid and this was the first time I thought maybe I'm not stupid or I thought I was

intelligent in every other way it's set this and I'm sitting in my car crying because you finally validated me after all these years and I thought wow this is really really tapped into something that has hit people all around the world and it's really affected all these grown adults including grown men emailing me to say that they were weeping in their cause because I had finally validated their questions after all these years, people who thought of themselves as otherwise intelligent. And so I thought, okay, maybe I'll write a whole book about this. And so did that spark the book? Did you email your book agent?

It said, listen, I already started on a doc here. We got, we got something here. Yeah, I mean, I already had thoughts about the questions that people have always wanted to ask because I've been teaching art students at the School of the Art Institute for some years now. And they quite often quite often what we do is like therapy for their past math trauma. And they tell me that all the things that went wrong and all the ways in which they were made to feel stupid and the burning questions they have that never got answered because they were told, oh, that's a stupid question. Or, no, you're not supposed to ask that question here. You're just supposed to answer the questions that I tell you.

And so I'd already been building up a kind of catalog of questions that people have really wanted to ask and that they never get answered. And then when that happened, I thought, okay, maybe there is scope for this as a whole book. Was part of that math trauma, uh, math Barbie? Do you remember? Math class is tough. Do you remember that one? Oh no, I mean, Bob is very topical at the moment. I know. Do you have a crush on anyone?

No, Bob's a tough. Boy, howdy. Okay, so this teen talk Barbie came out in 1993 and rightly enraged female scientists and mathematicians and really any human with a brain who thought sexism was weird and that children get brainwashed into gender stereotypes. So there's one guerrilla group calling themselves the Barbie Liberation Organization and they bought a bunch of Teen Talk Barbies

and talking GI Joe dolls and they swapped their voice boxes so that Barbies said things like troops attack and made machine gun noises and then GI Joe said let's go shopping. They did this in December of that year and a lot of kids and parents were surprised on Christmas morning to have a tiny man in combat fatiques, lamenting that. I do not remember that one, but there was a spoof that appeared a few years ago in my research field. So my research field is category theory, which is considered to be one of the most abstract parts of mathematics. And even abstract mathematicians sometimes think it's too abstract. And so there was this whole series of Barbie cartoons where Ken would say things like,

oh my goodness, what even is a monod, and then Barbie would just go, well, obviously, it's just the monoid in the category of end-of-bunters. Okay, PS, for context, this comic was part of a meme known as feminist hacker barbie, which arose in 2014 like a phoenix from the firebombed ashes of a motel book called Barbie. I can be a computer engineer, which was marketed toward children and featured a teen Barbie learning to computer. And it involved illustrations of Barbie at a laptop and in class. And it was captioned with passages such as, I'm only creating the design ideas. Barbie says, laughing. All needs Stevens and Ryan's help to turn it into a real game. Naturally, computer

people, some of whom were known as women, did not enjoy the existence of this book. And so one of them, Kathleen Tweet, created a meme generator that spawned so many realistic and really sardotic takes on feminist hacker Barbie. And you can read more about it in an article titled, Barbie fucks it up again. So when Barbie explains to her male classmates that a monad is just a monoid in the category of endofuncturs, it's a definition so legendarily opaque

that it's become like a math and programming joke itself. But if you'd like to know a monad in math is an algebraic structure and in programming, it's used to structure computations as a sequence of steps. And a monad can be a thing that describes how something is supposed to be modified, but it isn't really a thing.

And the etymology of monad even means everything or nothing at all. So if it's confusing, that's the joke. And so now we get the joke. If you're seated next to someone at a dinner party and they were to turn to you and say, is math real? Who invented it and how do we trust it? How do you begin in a short interaction to get them to trust that math is real

or at least look at it in a different way? Well, first I would validate that question because often when they're asking those questions, they're already full of doubt, skepticism and past trauma. Sometimes they're trying to say, none of this is real, it's all load of ups, can't say any of those words out loud. Yes, you can. It's all a load of, a cod's wallet. It's all load of cod's wallet, cod's wallet, okay. That's often the subtext of their question and sometimes it's because,

especially in a dinner party situation, they may feel intimidated by finding that I'm in my condition. And unfortunately that happens a lot, especially because I'm not a male person, I'm not a white person, and I'm not necessarily how people expect a mathematician to be, whatever that is. They're quite often people feel intimidated.

And so it depends where those questions are coming from. I also say, well, what do really even mean? And spoiler alert from my book, I don't actually say, math is real. Nor do I say math is not real. What's really more the point is, how does it help us? It doesn't matter whether something is real or not really, if it helps us in some way, that's what I think in the end. So then the question is, does math help us? And does it help us in some way

that you, the person, I'll tell you the question, cares about because people might say, oh, well, sure, if people can use math, they're quite blamed and to make computers work, but that doesn't mean that I have to care about it. And so then I say, try and find out what they care about themselves and whether they care about thinking clearly about the world around them. Do you surf or eat or paint or eat paint or golf or wear clothes?

Math is in the tides. It's in the temperature gauges in your oven, putting angles, rubik's cubes, hair braids, fabric knits, and lasagna guilds. So we all have stuff that gives us butterflies, just nauseated with happiness. And there is a shitload of friendly and helpful and benign and dazzling math involved. And sometimes it, depending on where the person is coming from, when I say that math helps me, empathize with other people. That can be really mind blowing because that is not something that is often presented in math class I think. Yeah, how does it help you empathise? There's two ways I think. First of all, it's a technique for understanding how arguments are

structured. If I want to try and understand somebody who has a completely opposed point of view from mine, then I can do it by understanding where that argument is coming from, because it's always coming from somewhere and it's never going to help if we just sit there and, oh, that person's just not being logical. Their point of view has come from somewhere and one way to empathize with other people is to understand. Their point of view has come from somewhere, and one way to empathize with other people is to understand where that point of view has come from. So being in a math mindset primes your brain for taking something complex and going a step back and breaking it down through logic. How does one get from there to here?

It doesn't mean that we're supporting it, and it doesn't mean that we are claiming it's good, but we are just understanding where it came from from their point of view. abstract mathematics also helps because it's a process of seeing patterns and making analogies between different situations. And so at a basic level, if you say two plus three equals five, what you're really saying is that if you take two plus three equals five, what you're really saying is that anytime you take two object and another three object, as long as we don't kind of spontaneously combust or coalesce,

you will end up with five objects. And that's a pattern that when we teach arithmetic to small children, we show them doing that with objects, physical object, over and over again, until they see the pattern forming in front of their eyes. And that's really a way, I think, to access empathy with people who have different opinions from us, because it's about finding an analogy between our situation and theirs. So between you and the guy who just flipped you off in the Trader Joe's parking lot, there

must be a common denominator. And so it can be quite a far fetched analogy, but because abstract mathematics is really about seeing deep patterns where the surface looks completely different, but if you strip away enough details, you get down to something that's the same underneath. I can do that with people who I really disagree with,

by just stripping away so many details and finding some kind of some kind of analogy even if the topic is completely different thinking about some situation in which I have experienced something that is even remotely abstractly similar. So perhaps where everybody is disagreeing with me about something and getting angry with me for thinking something and it's not getting angry with me for thinking something. And it's not going to help me change my mind. So, for example, if we think about people who don't believe in vaccines and all the ways that people kind of get angry with them to try and get them to believe in vaccines. And then if I think about a situation where a lot of

people are getting angry with me and want me to believe something. Then I can see that that isn't going to help me change my mind. So that kind of that kind of abstraction and analogy helps me understand why people take positions that they take. On that note and stay with me. There was something about this chat in Eugenia's book that reminded me of therapy, of cognitive behavioral therapy. It was funny because I was reading your book thinking about how much math must give you kind of an edge into understanding your own brain and other people's brains by saying, okay, everybody hates me. No one's texted me back today. Is that true?

Does everyone hate you? What's the logic? What is my reason for thinking this? Exactly. And the thing is that I absolutely don't always use logic over feelings. I actually do the opposite. I always observe that feelings are correct. That's it. Feelings are always true as a basic starting point. But sometimes there are other things going on as well. And so I've noticed for myself, for example, sometimes when I'm feeling terrible

because some bad things have happened to me and then they, I think, about them too much, they go around my head and then I feel terrible. And sometimes I think to myself, I know intellectually, because I have done called the pale therapy, I know that if I just go to bed, I will feel better in the morning. I mean, what happens after that is that I don't want to do it, because I don't want to

just go to sleep and feel better in the morning. So then I might say, well, that's not logical. But no, I think, no, that is a true feeling. I truly feel this. Okay, now why am I feeling this? And then I realize it's because it seems like cheating. I don't want to. I then it will feel like it will feel like my feelings aren't being validated. If I can just go to sleep and they'll go away. So true. You're

also a musician too. Yeah. I think we know that there's a lot of math and music, but is there a lot of emotion in math? There's tons of emotion in math, that's such an interesting question. I feel things so deeply when I'm doing and seeing and experiencing math. I try to write that into my books, because on the one hand, the power and the strength of math comes from the fact that it doesn't have emotions in the actual argument of it. So it doesn't depend on emotions, it shouldn't depend on emotions at all to build the argument, but humans are emotional

creatures. And so when we're communicating math, if we don't communicate it with emotions, then I don't think it with emotions, then I don't think anything gets through or at least much less gets through. And I think that's one of the big problems with teaching and learning math is that the idea that math shouldn't have any emotions in it, which is true, but at the same time, all human experiences have emotions in. And if we try and teach someone something without showing the emotional side, or without giving them an emotional connection to it,

then I just don't think it goes in as deeply. So there are many papers on this, but a fresh 2023 study called Emotions and Motivation in Mathematics Education, where we are today and where we need to go. Stated that female students enjoyment of an interest in fashion was found to result in lower engagement in mathematics and prevent them from solving word problems. And I was like, hold up, what? That seems weird. So I checked out the 1994 study they cited,

titled, When Do Girls Prefer Football to Fashion? An analysis of female underachievement in relation to realistic mathematics contexts. And what that study was actually looking at was the tendency for contextual problems in math lessons to make no fucking practical sense at all. Like you're given this long fictional scenario, which you'd approach from an entirely different perspective

in real life. Like the fashion problem in the actual 1994 study was that girls scored lower on the fashion design math calculation than one about football or just an abstract question because the fashion problem made no sense, like in order to divide hours of labor in a mathematically sound way, which is what the problem was about. You'd have to deliver the finished dresses before you sewed them. And this 1994 study concluded that two thirds of girls used their common sense

as well as their mathematical knowledge and then were penalized for doing so. Anyway, there was actually more engagement in the problem, but the problem only made sense on a math test, not in the real world. And research has also shown that figuring out solutions to hands-on actual scenarios gets us more engaged in finding this solution. So it's actually a two-pronged approach to make people actually care. And yes, folks are quick to penalize others without realizing that, hey, they're actually asking really good, important questions. And the problem is more complex and that the emperor, wait a second, is very naked. Why am I seeing his

bear buttocks? Let me put it this way. If you do have an emotional experience when you're doing something, you will remember it more deeply. And so I try to talk about things, first of all, talk about how I feel about mathematics. And secondly, I encourage my students and my readers to have feelings about it. And I try to link it to topics that they already have feelings about. Because if I'm talking about why 1 plus 1 equals 2, someone may have no feelings about that, apart from horror, when they remember they are math lessons from school.

But then if I can find something else, like my wonderful students who came up with thinking about when you mix paints together, when you mix one color of paint with one color of paint, you actually don't get to because you get a new color of paint. And maybe mixing paint is something that some people have much more feeling about. Or if you're making cookies and you've got balls of dough and you decide you're going to make one bigger one instead of two small ones, you take two bits of dough and you stick them together and you make a bigger cookie. That may be something that someone can have a feeling about rather than just it being some abstract concept.

And so the power of abstract mathematics is that it does not involve emotions, but that also makes it difficult to learn and understand. Well, how does an abstract mathematician deal with those balls of cookie dough? I'll see it. So, that's going to trouble me my whole life. Well, it depends, because if you, in one way, if you take two balls of cookie dough, you get two balls of cookie dough, so you take one ball, you take one ball, and that's two. But there's another thing you can do, which is to mish them together and get one bigger

one, in which case you've kind of done one plus one equals one bigger one. And those are two scenarios that are both real. And it's not that one plus one always equals two. It's under what circumstances does one plus one equal to you. And that's where we get to the whole, oh, as long as we don't smush things together and we don't eat the cookie dough because cookie dough is delicious. So in her book, Beyond Infinity, an expedition to the outer limits of mathematics, Eugenia also just stares infinity right the mouth while discussing dividing cookies for all eternity. So many cookies man, hell yeah, yum yum yum, right on. Where in the brain is math coming from? And why when I am stoned do I think I understand math better?

I cannot possibly address that last question. I have absolutely no experience of that whatsoever, and that is for real. However, there's a popular idea that math is on one side of the brain. And the whole left-right brain thing, I think has been mostly completely debunked. Yeah. But I remember it was actually my piano teacher who introduced me to the book drawing with the right side of the brain. And so I think of my head, the idea is that a right side

is the logical side and the left side is the creative side, is that? Is that what they missed was. Right, so I just like to stress that I'm pretty sure it's all being debunked and that both sides of the brain work together and are very highly connected. So while the hypothesis was flipped and the left side of the brain is supposedly logical, the right is supposedly creative, it's been flimflamed by medicine itself. And for more on this, you can read an evaluation of the left brain versus right brain hypothesis with resting state functional connectivity magnetic resonance imaging. And you got to use your whole brain for that study because it concluded from over a thousand scans that there's no evidence that the people nestled

into their brain imaging chambers use one side other pumpkin more than the other. Rather, your whole shebang is interconnected and, quote, the two hemispheres support each other in its processes and functions, which is tender and kind. So if you feel like you need to get it together, don't worry, you have, you are together. And there are people who have either never had one side of their brain or losing use of it and then the other side is able to compensate. And of course there's tons of stuff about the plasticity of the brain learning to do things. But even if one side of the brain were logical

and the other side's creative, that just panders to the idea that math is only logical and not creative. And it's really both together. It's just that when you're doing arithmetic in elementary school or wherever you first do it That might not be extremely creative, but in fact people who came up with arithmetic in the first place That's creative. Oh, I have questions. Yeah, I have so many questions And I don't even remember how old I was when I realized oh Everything's multiplied by 10, because of our fingers. Oh yeah.

Like, it didn't occur to me. The base 10 thing didn't occur to me for so long. But where did math come from? And how many generations has it been passed down? And if we didn't learn it from someone older than us, who raised us, would we even have any capacity to just come up with you know theorems and proofs and calculus and everything out of thin air or is it really does it really just keep building on itself? That's something's fascinating questions, and I think there's a really great question

And so humans did come up with those things, but it took them thousands of years. I mean, people came up with the idea of numbers, thousands of years ago, but it was ancient cultures. While the numbers that we used to do are mostly based on 10 fingers, different cultures based things on different things. And so there are some cultures that based things on eight because of knuckles.

And then there are some people who use the spaces in between their fingers as well. And there are some people who use the spaces in between their fingers as well and there are some cultures who based on 20. 20 fingers and 20 toes. And the number system in French has traces of that where 80 is Kathe van with 420s and then 90 isn't 90 it's 420s plus 10 because it's as if you're counting up in 20s. So there are different things but then this base 10 thing has really taken over. So base 10 systems have been used for probably as long as we've had 10 fingers. And though the written records go back to 3000 BCE in Egypt, it wasn't until between 100 and 400 years into the common era that the

Hindu Arabic numeral system of 0 to 10 kind of won out. And this number system has only been in use in Europe for like the last 1000 years. But yeah, it goes far, far beyond that in different forms, but staring at your hands for a while, that's math people. And there were some ancient cultures, I think it might be in my encounter, that used base 60, which is why there are 60 minutes in an hour and 60 seconds in a minute. No.

Right, so many of our things are intense. The lovely American system still uses Fahrenheit, but it doesn't fit well with hundreds of things. No, it does not. But we have this thing with 60 seconds in a minute and 60 minutes in an hour. And 60 is a great number to use because it has a lot of factors. And so you can divide an hour into a lot of really nice chunks, whereas if we went decimal

on time, I think there's some fantastic society somewhere that thinks we should go metric on time and have 100 minutes in an hour. We would actually not be able to divide it up into quite so many handy units, because we wouldn't be able to do a third in quite a handy way. So we can divide an hour into half, third, quarters,

fifth, tenths, 12th. I mean, we can do all sorts of things. And so, 60s are pretty good number for that. But the whole 10 finger thing eventually took over. And to answer your question about, if we grew up and nobody older than us taught us enough, would we be able to come up with all of it? Well, I, here's what I think, and this is just pure speculation. I think it would

be hard to do that in a single lifetime. It did take humans thousands of years to get to the point we are. And I think it's amazing how fast an individual human is now able to learn all of those things that it took humans thousands of years to learn. And it's because we communicate with each other. And so it's really dependent on people who already know it passing it down to the next generation. If we each had to develop it from scratch, it would take a really long time and I don't know how far an individual would get. Well, do you think there's any maths systems that have been completely forgotten that some people cultivated for a

couple thousand years and then just wasn't a record of it and we just have no idea that there's a whole math system based on pie or the Feminology sequence or like seven or something. Almost certainly, especially because so many cultures passed things down from generation to generation and then maybe died out or got killed off by what you're getting people or are living uncontacted somewhere. And I think that there are certainly pieces of math

that are obsolete now because we've developed more technology. So for example there's the whole map of the slide rule. My parents' generation had to learn how to use a slide rule, which is a really clever device for multiplying large numbers together using logarithms. And the thing is we just really don't move that anymore because we've got calculators. So that slide rule system was invented by a dude named Edmund Gunter in 1620. And that was the same year that the Mayflower crashed the party that's now known as North America. And the slide rule was technically an analog computer and it had this ability to glide to different positions to reveal these complex mass solutions.

This is how folks conquered big multiplication and division of numbers until about the 1970s when electronic calculators just be pooped their way onto office desks next to ash trays and diapypsy and became accessible and commonplace. Now as for this so-called slipstick, it became obsolete, partly because you could not write boobies upside down with it. And so the Slido has become obsolete. I don't know how to use one myself. I expect my parents had it drummed into them so hard that they could still do it.

It's a good answer to them with a slide rule. I'm sure there's somebody out there who still loves using their slides rule. I mean, I remember the anxiety of how to afford a Texas instruments, TI-87 or a graphical calculator. Yeah, like needing one of those in high school, being like like I need $109 for a calculator size of a brick

How much that's maybe that's not used anymore, but maybe it is in testing situations, but I know I know you get asked this all the time but who is good at math? How much is it aptitude? How much is it attitude? How much is it access? And why are we so afraid of it? Why do so many people just throw their hands up and say, no, a suck by like, you split the bill, I'm not dealing with it. So, first of all, I think it's mostly access and how much help you have. And how much that help was specifically helpful to you. All the scientific research at the moment points to brain being spectacularly plastic. Neural plasticity,

it's extraordinary how much brains can change according to how they are used and how they are stimulated. So you can coax your brain toward a better life, which means maybe one day I will be good at dancing. And so there is almost no evidence. There's basically no evidence to show that there's some kind of hard-wiring birth that means that some people are destined to be better at math and others. And in my previous book, X plus Y and mathematicians manifest over rethinking gender, I talked about this a bit because there are still some people who think that maybe there's just some biological reason that for men to be better than women at math and therefore there's nothing we can do about it. And the evidence, the scientific evidence for that is just so thin that it's actually laughable. I mean, I laugh at it, that means it's laughable, right? And so, because how can

we even tell that something is hard-wired at birth except by testing newborn babies? But how do you even test newborn babies? They don't do anything. You can't. You can't get them to do anything. It's hanging around. And so the idea that anything you can get a newborn baby to do is going to be indicative of their future mapability. It's just ludicrous to me because mapability is a really complicated combination of things. It's not just about being how fast you can do arithmetic. And so I always say that the things that you can test in lab controlled situations are necessarily very restrictive. Just like you can test how far

people can sprint the hundred meters. And I don't think anybody really argue with the fact that men can, the fastest men can run the hundred meters faster than the fastest women. It's to do with 40 strength and stuff like that. But ultramarathons, women have been beating men at ultramarathons. I can't remember how long an upcance is an ultramarounsel. But it might be 250 miles or something. Okay, so technically everything over 26.2 is an ultramarathon. But the longest and the most grueling is the Hong Kong 298K, with no stopping or sleep or support on the trails. Just two to three days of continuous running.

Why? Why? Why? Why? Why? But take a gander at this one article from 2021 titled, Why Women Are Faster Than Men in Long Runs? And you'll learn that the men, among us, tend to have larger hearts to pump oxygen for powerful sprints and more muscle mass to power those bursts of energy. However, that's the gander.

The geese in this situation, lady athletes, excel at endurance due to a multitude of factors, such as a higher body fat percentage that helps when they hit a wall, figuratively, more slow twitch muscle fibers, and yes, emotional resilience, in general. Because some of these bodies have thrust a whole person out of their more sensitive aperture, so maybe an ultramarathon is like a walk in the park, but just without ever stopping until you've collapsed at the end. And that's a really complicated combination of skills, much more complicated than running

the hundred meters. We didn't say running the hundred meters isn't hard, it's just a much more focused thing. Where the naut larger mouth involves planning, strategy, self-knowledge, pacing, and mouth is like that because mouth isn't just about memorizing things or manipulating large numbers. Math is about spotting patterns and being able to perform abstractions in order to see patterns that previously weren't visible. And having ideas for how to group objects together to make structures that will be useful to us,

it's a bit like designing a useful tool for building a house except for bits and abstract tool for building ideas. Okay, so it's like a hammer to drive nails versus the idea of a hammer to drive the idea of a nail, which can be applied to the mathematics of the physics of the fabrication of the tool to drive the nails, which becomes the real hammer. Woodworkers, you love math. So how do you measure a biological predisposition for doing that? Why not skills that are just something that you can be born with? How are we going to test whether a newborn baby can do that? We can't.

Well, what do you think about Common Core? Because I don't have kids, but all I know is that my friends with kids seem horrified or confused by Common Core. I don't quite understand what it is, but why has there been this shift in the way that we're teaching math and I guess like the last ten or so years? The reason I've been a shift in the way we're teaching math is because most people have acknowledged that it wasn't going very well. It's just that people haven't really agreed on what to do about it.

And I think one of the problems with changing the system is that a lot of teachers don't get autonomy over what they're allowed to teach. They get it plonged on them. They're like, now you have to teach like this and that's that. And then you have to prepare people for standardized tests and then get judged on how they do in those standardized tests. And I think that any time that we're aiming to teach people content, like, can you do this thing at the end of it, then that is going to be less successful than teaching them, basically, appreciation and allowing teachers more autonomy

to teach the things that they care about in the way that they care about. And as the world changes, some basic things become less important, just like the slide rule is not important anymore. And controversial idea, but I don't think that long multiplication is important anymore. We've got calculators, and it's just like learning to write a horse isn't important anymore. Which doesn't mean no one should learn to write a horse. It's someone who loves writing a horse. Great! But it's not a crucial skill for most people's daily lives.

I think that sometimes parents get really upset if they don't understand their work that their children are being asked to do. I've talked to many math teachers who say that the parents complain to them that it's not like it was when they were young. But then the teachers say to them, well, did you like math? And they go, no, I hated it. They go, well, why do you want me to do that to your children? Oh, sympathetic. Sometimes people say, oh, it's terrible. I can't help my children with their homework. And sometimes I want to go, well, go and help them with their homework, then it's their homework. Okay, this just in. It turns out that I had no idea what Common Core really meant,

because I don't have kids and I don't listen well. So Common Core was adopted in US states around 2010 and it's actually the set of standardized assessments measuring where kids should be for every school year, but that term Common Core often mistakenly is applied to just this new way of teaching math that's more intuitive and is actually a very old way of doing math So instead of going and fetching a piece of paper to figure out what's 63 minus 42 and then Borrowing some numbers and stacking figures on top of each other kids learn well if you add 1 to 42 then 63 minus 43 would be 20 so it it's 20 plus one, which is 21. Because we all have pocket computers

for the bigger arithmetic issues, teaching these quicker and less fussy ways of handling numerical concepts is more valuable. And future generations will probably thank us when it comes to adding tips to dinner bills. That is if American restaurant workers are still making minimal wage and at the mercy of ground sheet customers to actually pay for the rent.

We thought we'd have flying cars, but really just one healthcare. Well, I wonder, how do you think the world will change with a new generation learning math in a different way? Do you think we'll have more mathematicians, more statisticians, more scientists, or do you think we'll progress even faster through mathematics? Is that a good thing? I'm much more worried about the people who fall off and get put off and get traumatized by it. What I would like to see is not more mathematicians and more scientists. It's fewer people who hate it. That's what I really want to see. And partly because when there's half or more of adult humans who either hate math or

traumatized by it or who are actively hostile towards math and science, we've got problems with persuading people with things like vaccines are real, but the pandemic is real and that we need to do something about it, but climate change is definitely something that we need to worry about. I think that that's a big problem for the way that society is going. If people are ready to just believe those kinds of lies, and I do think that my background in training and abstract mathematics really helps me to not be manipulated by people who are lying to me, and it helps me always to be aware of the frameworks for finding out whether information is good or not.

And deciding whether something that someone is saying is probably true or not. And I think that that is all part of what I think education should be aiming for, not can multiply the larger numbers together. And can you calculate this thing and get the right answer and can you solve this equation? But can you think clearly about the world around you? Can you make sure that people don't manipulate you and can't lie to you about things just so that they

can get your vote or your money? And can we make a contribution to the world that benefits more people and not just us all? The way that social media is, I feel like we're going toward kind of a quantitative, rather than a qualitative assessment of our lives, and maybe there creates a little bit of an anxiety around math there too, and we look at how many followers, how many likes something has. We've really started to introduce numbers to things that are much more qualitative. That's a really interesting point. Yeah.

Right. I think it's because society is trying to rank everything all the time. Yeah. And it starts in school because the system tried to rank students, but then we get into this frame of mind where everything has to be ranked by a number. And it might sound funny because I'm a mathematician I'm saying we shouldn't rank things by number. But I mean, a case in point is that at the School of the Art Institute where I teach, we don't have grades and so there is an

understanding that we are not trying to rank everybody by a GPN because there are no grades. And I just think that's wonderful, so we can focus on educating rather than ranking. For more on this, you can see the 2021 paper, Grade List Learning, the effect of eliminating traditional grading practices on student engagement and learning, which notes that throughout their study, it became clear that students want to learn. Accurate feedback is a vital part of the learning process. It says, but grades are not.

The traditional grading system pits students and teachers against one another, often leading to either side, bickering over fractions of percentage points, which I guess is applied mathematics, but I don't think that's the lesson here. And I wanted to ask a little bit about some basics for people who maybe are not math majors,

but when things go from numerical to letters, where in the learning process of math, from like arithmetic to pre-algebra to algebra to pre-calculus to calculus, like where do things start turning from numbers into letters? Why does that happen? Thank you. That is one of the questions that I address in the book because it is something

people fake me a lot. Like, oh, it's fine with Mac and go, when number's time is a lot of, what do we do exactly? And so we're thinking about the idea of a person. And so we don't name them because we don't know who they are. And so that's why we do that with numbers as well. It's possible, but I also introduced it like a Murder mystery where someone is a murderer and you're trying to find out who they are But you can't refer to them by name it because you don't know who they are A whole load of evidence about them and then you pin them down and go ah ah it was actually James

Often in math. We're trying to find out what something is But we don't know what it is yet. So how can we refer to it? So we use something like a pronoun, but it's a letter because that's what we do in math instead of a pronoun, and then we gather evidence about it. And so we say, oh, well, it's related to this other thing like this. And when we do this to it, it behaves like that. And when we do this to it, so it's like 20 questions, you say, what happened when you do this? What happens when you do this to it? And then you find all these relationships. And so that's what solving equation is about.

It's about putting that thing, you don't know what it is yet. Into a relationship, when you found out there is aspects of it behavior, and now you find out, now you can pin down what that thing actually is. And that is the point of using letters. And that is the point of solving equations, and that is the point of solving equations. It really is like a murder mystery.

So anyone who enjoys any kind of murder mystery, I think that that's, I think it's that. One thing that does not embarrass me is asking really basic questions for me and for the good of all of us, such as, what is the difference between a logarithm and an algorithm? They sound alike, are they friends? A logarithm is very different from an algorithm. A logarithm is a particular function. And it, I'm now doing hand motions, that doesn't help on an audience.

So the graph of a logarithm, it starts down at infinity and it goes up really fast and then it tells off. So it's kind of like the opposite of an exponential. So much so that it actually is the opposite of an exponential. So it's the inverse of an exponential function. And so that tails off as it goes along, that's completely different from an algorithm. So an algorithm is a method for doing something. And it's a particular form of method like a really really step-by-step recipe.

The step-by-step process that you could tell a computer to do. So for example, the dreaded long multiplication is an algorithm. It's a step-by-step process whereby you can follow these steps and multiply large numbers together by following the steps all the way through. But the algorithm says, if this happens to do that, now if this happens to do that, now it's like flow chart. And so that's not really math. And that's why I say that we don't really need

a long lot of creation anymore, because it's an algorithm, it's a handy algorithm for doing something, but it's not really math. And when people say the algorithm, are you talking about the internet? Yeah, the algorithm is showing my videos or the algorithm wants me to listen to the news.

Oh, yes. So that's a particular, really it's a particular algorithm that the internet, or most places we interact with on the internet, use some process for deciding how to show you something next. And it's a bit murky exactly what their process is. And that many people think that there's something the ferry is doing on the hind it, which there probably is, and it's probably

based on money. So they have applied some step-by-step algorithm, and that one really is implemented by computer to say, based on this person's previous activity, follow these steps and show them this next thing. That's kind of capital A, the algorithm. So this is the math that expertly hooks us with engaging, but ultimately never satisfying, and infinity-like scroll of content,

just harvesting our tastes and churning out more like it back with this boggling speed. Now, Twitter looks at half a billion tweets every day and then decides exactly what to show you. And one article titled The TikTok Algorithm, New My Sexuality Better Than I Did, pretty much says it all. So we cover more of this in, yes, the TikTokology episode with your favorite psychomer on there, Mr. Hank Green. And yeah, we will link that in the show notes. There are many other algorithms and algorithms. And sometimes algorithms are great because they help us conserve our brain energy.

And I think that's really important because our brains are finite and very puny. And so if we can conserve that energy as much as possible, that's really helpful. So I personally have all sorts of algorithms for helping me run my life, and this may be me as a mathematician speaking, but it's because I don't want to use up my brain energy on something that's kind of irrelevant. What do you have? Yeah, tell me, tell me, tell me. Oh, for example, I have algorithms for where I buy more coffee, for example. Okay, tell me everything. So I buy five pound bags of beans, but then I keep a pot of them on the counter. So I refill the pot on the counter from the bag of beans, and then once the last bit of the bag of beans has filled the pot, then I immediately buy another bag of beans so that

it's ready by the time I get to the end of the pot. And I don't have to think about that. Now maybe one day I can have a smart coffee bean port which will automatically order it for me. But that is my algorithm for coffee beans. I love that those are algorithms. Can you tell me some other places where we don't realize there's math just everywhere. I know a video going viral. I know you've seen sign waves in your wraps and burritos. There's math in And there's math and braids and hala. Hala.

Where are some of the unexpected places where math is like really making our lives amazing? Well, one thing that I do when I'm walking across Chicago, which is on a grid, is that thing where I walk in one direction until I hit a stop sign. And so if I don't get a crosswalk, the light on the crosswalk, then I turn and take the crosswalk going the other way, and then I keep going in that direction until...

So that's my algorithm for walking across Chicago. And there's some map in there that's telling us that wherever we turn, it doesn't matter. So if I need to go five blocks east and ten blocks north, then it doesn't matter where I turn, it will still be the same distance of walking, as long as I consider that turning doesn't exhaust me. And that's actually a part of metric spaces. And so a metric is a more general form of distance, and we think about distance usually as distance as the crow flies, but you don't fly like a crow when you're walking

across Chicago, there are buildings in the way. And so the distance we actually need to go to get somewhere is not the distance of the crow fly. It's the distance along this grid. And so we need to know that it doesn't matter, it doesn't matter where we turn. And that's intuitively kind of clear, right? And then you can do things like say what's a circle if we're using this form of distance? Because a circle doesn't quite look like a circle anymore. It looks more like a diamond shape, but that counts as a circle because it's all the points that are four blocks away from you. And I think that's kind of hilarious because I like things that challenge the received wisdom which makes me sound like a pointless rebel. But I like the point full rebel because

mouth is about not making assumptions that you don't need to make. And I think that that's really important in life as well because a lot of the problems with society come from people making assumptions about other people that you don't need to make. Which doesn't mean we shouldn't make any assumptions about people because actually that's impossible. As soon as we meet someone, we have to start somewhere and that we have to have an instinctive intuitive got response to them. But the really important thing is to be ready to change it when we get new information. And math is really about that. You can be aware you made them so that if they turn out not to be right, you can change them and then get a different result. It seems like once you embrace math, you understand that it can be very empowering and that can offer a lot of clarity.

That is certainly what I think. So if that's the impression I've given you, that's fantastic. And I think I just realized I don't think I really addressed the part of your question earlier where you said, why are people so put off it and afraid of it? And this is what makes me sad because I think it's there to help us. And I think that it's not presented like that enough. Mm-hmm. Okay, I have some questions from listeners. They know that you specifically are coming on. But first, let's raise the bottom line of a cause of theologist choosing Nugini at Pointed Us toward mathcirclesofChicago.org,

whose mission statement says, we offer engaging, flexible, and free math programs to students in grades three through 12, and focus on reaching black and Latino communities and other communities where most children live in low income households. You can find out more at mathcirclesofChicago.org and that will be linked in the show notes and that donation was made possible by sponsors

of allergies. All right, let's divide and conquer your queries. One wonderful one that was asked by Mallory Skinner, Doug Pace, Maddie S, Talia Dunjak, Emily Staufer, Devon Naples, Devon S. I will ask separately. I'll ask this similar question. Oh wow. Want to know, please explain infinity in a way that my brain can really comprehend.

Oh. Well, you know, infinity is really difficult. And so if your brain, if you feel like your brain isn't comprehending it, then maybe it is. Oh, wow, go on. It's supposed to be mind-blowing. If people who think they understand infinity are kind of just deleted. And so, I think that the correct feeling is to feel like it's too mind-boggling to get your head around.

That's the whole point of it. It's bigger than anything that we can think of. It behaves in really weird ways. And I think what often makes some people, mathematicians and some people, math-phobic, is embracing the feeling of not understanding something, rather than taking it as a sign you're bad, taking it as a sign that there's something really interesting going on. If you go to the edge of a cliff, I don't like looking over the edge of a cliff because I'm worried I will fall and die. Same. And I think that there's a similar kind of vertigo that sometimes people get when thinking about math concepts and people have been so humiliated and traumatized by their past

math experience, but that it feels like it's they're going to get hurt if they look over that cliff. And what I want to say is that you're not going to die anyway by looking over the mathematical cliff. You might get some emotions dug up from some past negative experiences. But the good thing is that you won't physically die by looking over the math cliff. And the thing that's over the math cliff is something that maybe kind of gives you intellectual vertigo. I don't run away from those things. And I think that's the only difference.

It's not that I'm better at it or something. It's just that I have decided that I'm interested in it. And that it's not a sign that I'm bad at it, if I don't understand it. I don't understand anything if I think about it hard enough. The number one, what even is that? I can't understand the number one. If I don't understand the number one,

how am I going to understand in 50? But that's what drives us to do more research. It's the feeling that there is always more there to understand and we want it to understand it. We don't go, oh, I can't understand this. We go, oh, I want it to understand more. I'm never going to understand all of it, but that doesn't mean I'm going to give it. We don't go, oh, I can't understand this. We go, oh, I want to understand more. I'm never going to understand all of it, but that doesn't mean I'm going to give up. I'm just going to keep trying to understand more all of the time I can. Some people call this a growth

versus a fixed mindset. And fixed mindsets tend to be afraid to try and fail, but growth is like, you know, whatever happens, I learn some. And from personal experience, two of the smartest people I've ever encountered, my friends, doctors, Kasey Hanmer and Christine Corbett, have worked at NASA. Kasey now heads terraform industries, working on these new ways to capture atmospheric carbon and turn it into natural gas. And one thing about the two of them and their merit is that they just try stuff.

They want to learn something, they just die right in. As a result, Dr. Corbett has an extra master's in creative writing and just got a black belt in kung fu. They are smart people who ask smart people sometimes basic questions and Casey once told me the key to how much they get done is that they just learn shamelessly from any failure. They get it, they keep moving, so they are heroes. They are not zeros, which reminds me that Brenna had a question. On that note, Jenny Lowrodes, Maggie Morgan, Star, Lillian Wright, Christine Pixstein,

Meg C. Lillian, Hagadon, and Brenna Pixley. I'll have questions about zero. Jenny wants to know how long has zero been a thing? Maggie's like, is zero a number? Great questions. I do know that it has troubled people for thousands of years about whether it really ought to count as a number or not. My recollection is that maybe the Greeks or the Romans, one or the other, or maybe both,

that were really unconvinced that zero should count as a number, still affoquially bothered them. And that really helped them back because here's the thing you can decide whether you want zero to count as a number or not. But the question is how does it help us? There are often no right and wrong answers to these things. Mathematicians say, okay, here's a world in which this thing is true and here's a different world in which something else is true, which one is going to help us? So we can make a world in which zero isn't a number. We're not going to be able to do very much there. Zero is a really helpful number to have around because if we're going to represent nothing,

what are we going to represent it with? If we subtract 5 from 5, what do we get? If we don't have a number called 0, we can't do that. And then we can't really make negative numbers either. If we can't make negative numbers, there are all sorts of things we can't do. And so if we do call 0 a number, then we do get to do all these things. And so that's why mathematicians generally have decided that 0 should get counted as a number, just so that we can do all of those things. It's just language. So, as long as we can manipulate zero in some way, we can get to do those things.

If you feel like you don't want to call it a number, then that's fine. Don't call it a number. As long as you can still manipulate it in those ways, because it's really helpful to do it. So zero, we can wrap our brains around that. Some of you had a weirder concept, plaguing you, such as Anna Thompson, Jennifer Lemmon, Ariel Van Sant, Christina Kunz, Elinura, Renaud Banville, CJ Wyatt, Tony Vessel, Sarah Val McElvie,

Felicia Chandler, Valerie Bertha, and first time question ask her Bill LeBranch and Christina Kunz asks, imaginary numbers, what the fuck? What is an imaginary number? What's going on? Yeah, this is great. And this is a great thing to say after is zero a number because sometimes people go, are it not really numbers a number? So, market conditions really don't like having rules imposed on them. And this makes me sad that one of the things that puts people off mouth is that there seems

to be all of these rules that you have to follow. Whereas market conditions go, wait, okay, those rules, we have to follow those rules in this world. But I don't want to follow. Whereas, mathematicians go, wait, okay, those rules, we had to follow those rules in this world, but I don't want to follow them anymore. Can I build a different world in which I don't have to follow those rules? And so, one of the rules mathematicians don't like having to follow, and I do talk about this in the book, is you can't take the square root of a negative number. Well, why can't you take the square root of a negative number? Because if you try squaring numbers, square rooting is the opposite of squaring, right?

So you're saying, is there any number such that when I multiply it by itself, I get negative one? Well, let's think about that. If I multiply a positive number by itself, I get a positive number. If I multiply a negative number by itself, I also get a positive number. You are employing a double negative. So we seem to be out of options for things we could multiply by themselves and get a negative number. But mathematicians go, never mind, I'll just make something up and say what happens? And so it's called an imaginary number because we sort of just imagined it.

And the wonderful thing about abstract concepts is as soon as you imagine them, they become something that exists because it's an abstract concept. And so I would love to imagine my dinner and for it just to exist. That doesn't work like that. Or you imagine some dollars in my bank account. Oh, there they are.

But I love that about now. You can just imagine something into existence. So you just imagine that there is something and you take it square and it is negative one. So what is it? But it doesn't really matter. Because in the now, it doesn't matter what something is. It only matters what it does.

And I think this is a wonderful thing to think about in the life as well. Because really, it shouldn't matter what somebody is. No, it shouldn't matter what the color of their skin is or what they look like or how large they are or what gender they are or anything that it should really matter what they do. Are they a nice person? Are they helpful? Are they kind? Are they generous? Those kinds of things. And so in that, we kind of put aside the question of what that imaginary number is. We just say what does it do? And it's like when children make up a game, they will make up a whole world and they will play that game. And that's what math is. But then it goes once at first. Because it goes, oh, is this helpful? Cryping, it actually is. So it starts off as being just some kind of ludicrous game that

we're playing in our heads. People turn out to be really helpful for solving problems in physics. It's extraordinary. I just think it's extraordinary that this thing that we made up that doesn't have any physical reality to it is helpful in physics. Because what happens is that you draw pictures of it. And when you have ordinary numbers, you draw them on a number line, right? We put numbers on a line and it's one line. A line is very flat, it's one dimensional.

But if you add imaginary numbers into that mix, where do you want imagining numbers go? Well, they're not on the line, so they just have to go in a different direction. So you can just make them sort of go up the page. And then when you mix all those things up, you get a two-dimensional space instead of a one-dimensional space.

And you know, in two-dimensional space, you can see beautiful patterns that you can't see a one-dimensional space. And you know in two-dimensional space, you can see beautiful patterns that you can't see in one-dimensional space because it's so incredibly thin. A line is just too thin, you can't see pattern. Whereas in the two-dimensional space, you can see gorgeous pattern. And that's how it's helpful in things like physics, because you see, you work out the patterns using the two-dimensional space, and then once you apply it to the real world again, you just take the part that's on the line, but it's just that you can recognize what the patterns are because you were exploring them in two-dimensional space.

It's kind of like, if you're clearing out your closet, you kind of need to take everything off the rail and spread it out on your bed before you put it back on the rail again. So behind every perfectly Marie Condo closet is the chaos and the pain and the discovery and the beauty of purging and whittling what's hiding in the universe's crevices and corners. Well, kind of on that note too, Felicia Chandler and James Dean Cotton

want to know about the Fibonacci sequence and Felicia asked, why do we see it so much in nature? I imagine that Dan Brown's the Da Vinci code really put the Fibonacci sequence on the map. I'm into something here that I cannot understand. What does math have to say about that particular like equation in nature? So perhaps I should remind everyone

that the Fibonacci sequence start 1, 1 and then you add up the two previous numbers to produce the next number. So you get 1 at 1, which is 2, and then you add that to the previous number, 1 at 2, which is 3, then you get 5, and then you get 8, and then you get 13, and so on. Okay, so just a quick primer. Fibonacci Leonardo Pizzano was an Italian guy who around the year 1200 wrote a book about math and popularized the standard Hindu Arabic numerals in Europe. Everyone loved him for it, thought he was dope at math,

and they died, and everyone forgot about him for like 400 years until they 1800s. Two things. He didn't actually invent or discover the Fibonacci sequence. That dates back to at least 300 BCE when this Indian poet, Bengala, was already down with it. Not Fibonacci's fault that we named the sequence after him. Another thing is that Fibonacci was from Pisa, which is where the leaning tower of Pisa is, and it was built around 1200 during his lifespan. So where was he when it came to applied mathematics? Yeah, I'm super busy these days.

Also, I didn't intend this, but worldwide Fibonacci Day is this week, occurring on the same day as the dog holiday wolfanute and American Thanksgiving. But every year you can celebrate Fibonacci by eating artichokes and romanesco and pineapple, because 1123 is Fibonacci-esque, even though again it wasn't him to discover the sequence. Also, I need you to know that I only found out about Fibonacci-day because I googled was Fibonacci-hot and I happened upon a blog that mentioned 1123 and that there is little known of his physical appearance. I don't know, I just have a hunch, I bet he was hot, maybe like a 10. I think the first thing to say is that it is not quite a problem as

it's popularity may suggest. Okay. Good to know. It's like the golden ratio, which isn't nearly as prevalent as it's popularity would would indicate either. But I think the reason is that nature, I don't want to anthropomorphism or by nature too much, but nature is trying to do as much as it can with the smallest starting point as possible, because that's kind of efficient. And why that is the case is a whole deep philosophical or possibly biological question, but it may be to do with survival of the fittest and evolution, the things that survived were the ones which did the most possible stuff with the smallest possible amount of information. And so sometimes it really is a sheer mathematical situation.

So for example, the spirals on a pineapple are typically fever-narchy numbers. And so if you count how many spirals there are in each of the different directions, there are three different directions that spirals on a pineapple can take. There's the kind of really vertical direction. There's the more obvious slanted direction, and then there's the really, really, really slanted direction. That's less obvious. And the thing is that geometrically,

the two smaller numbers have to add up to the bigger one, that you can work that out on any shape at all. Why they typically turn out to be fever-narchy numbers, maybe something to do with the way that the little fruitlets grow, and it's the same with the leaves on the stem of a plant, that they grow at different angles spiraling around the plant, possibly to get as much sunlight as possible. And the angles, the way that the angles work in a Fibonacci sequence, is sort of to try and make sure the next time a leaf lines up with the one beneath it, it's as far away as possible. But it's often only a very small part of the Fibonacci sequence. So it's just like two consecutive numbers or something.

And so that's why I think it's not quite so prevalent. If you have, if you have leaves spiraling around, and it happens to be in a pattern three and five, that's only two numbers out of the Fibonacci sequence. So I wouldn't go, oh wow, it's a Fibonacci sequence. And maybe it's just three and five, and it's not gonna do the Fibonacci sequence at all. And sometimes the reason that something

that's constructed very simply in now pops up all over the place is a beautiful and maybe slightly mysterious thing. And that's one of the things that's wonderful about it. And that is maybe not an answerable question. And this is why sometimes people believe in a higher being because it seems like some higher being created that. But I personally don't feel the need to say that it was a higher being,

a specific kind of delineated higher being. I just think that math is a higher being. Math is my co-pilot. This one was on the minds of Jim Pompeo, Milan Ilyniki, Mushroom Morgan, Rachel Gardner, Taylor, the Ren You Know, Karina Reagan, Felix LaCell, Claire Nirk, and listener Victoria Souther,

who wrote via patreon.com, suchologies. I'm so excited you're talking to you, Jania Chang. I have huge math crush on her. I have two of her books. Victoria writes, as a teacher, I believe math is for everybody, and I try to make clear that math isn't an isolated subject when we use it to understand all parts of the world.

Suggestions to bring math into the living room, so to speak. That's a little juicier, Victoria writes. Last question from listeners. So many people wanted your expert advice, and Elta Sparks wanted to know any recommendations for teaching number sense to very young students. Blessed are the cheese makers. Asked math professor here. Do you have any advice for college professors or any teachers who want to improve their teaching? So any advice to people teaching or learning math

that you feel like has been empowering to people. Well, see her book. This is why I write all my books, to try and give people ideas and help people get over their past traumas. I think that one of the messages that I most want to say to everyone who's learning math and therefore I want everyone who's teaching it to also pass that on is that if you find it hard that doesn't mean you're bad at it. You're probably just right, it is hard and that that's not a reason to be put off it. And if you look around you and it seems that other people are finding it easier, they might just be talking out of their armpit. So to speak. In order to

intimidate other people because most mathematicians, in fact, every mathematician I know thinks they're stupid and finds everything very difficult. Is that true? Yes, I think that is a real look. It's a correct impulse to think it hard because it is hard. But the point is we can keep understanding more of it all the time. And I think that celebrating the questions that children ask and not being afraid if it's a question that you don't know how to answer because then you can celebrate them for having asked a question You don't know how to answer and then we can all learn about how you discover answers to questions And then if it's a question that nobody knows the answer to like why does the phenology sequence come from nature

Then you can say to a child if you become an expert in that field, you could be the one who answers it. And then you could be the one doing on this podcast explaining it to other people. Please do. What about, I always have to end with these, but what's your least favorite thing about what you do as a professional abstract mathematician? I think it is overcoming people's misconceptions and it's the fact that the misconceptions are so deeply embedded culturally and that's what I'm trying to overcome.

I'm not trying to get everybody to love math because we don't all have to love the same things, right? I'm just trying to show it for what it really is. If everyone saw it for what I think it is and they still didn't like it, then you know fine, we can all like different things. It's the fact that people see some really, really narrow shallow side of it and then write it off from their lives. When I think it can help everybody, that I find that frustrating but that's the challenge it's to overcome those deeply embedded misconceptions and it's been so great talking to you about it because it doesn't sound like you have those things but sometimes even getting something published can be difficult

because the people who want to publish something have their own misconceptions and go well I want you to write that mouth but this isn't mouth and so then I have to persuade them that this is mouth What about your favorite thing or your favorite number your favorite theorem your favorite moment What has just made your heart sing the most in your career? my favorite thing is Being able to help people understand something they didn't previously understand. And seeing their gossips of delight when some mathematical thing has got them to be as excited as when I see it. That is what gives me the most joy in math. I think is being able to give that joy to other people. I wonder if there's a word in any

language for that moment when something clicks, when you are figuring it out, figuring out, figuring out, you don't get it, you don't get it, and I've sat in calculus classes before, I don't get it, and then suddenly something changes over, and you're like, I get it, I get it, I get it. Whether it's a joke or whether it is a theorem or something, I wonder what is happening in the brain because that moment is just unlike anything else when you finally get it. And it really feels like pieces falling

physically into place, doesn't it? It does, yeah. I'm fascinated by the brain. I'd love to try and do brain scans while I'm doing things like that to try and see what's going on. This has just been such a joy. Oh, I've been really enjoyed it too. Thank you so much.

So you have it. Ask the simplest questions, and you'll learn the deepest truths. And for more on that, you can see Dr. Eugenia Chang's freaking book titled Is Math Real? How Simple Questions Lead Us to Mathematics Deepest Truths, which is linked in the show notes alongside her website and her social media.

We are at Alligies on Instagram and I guess Twitter, but I'm at Alliward with one L on both. And Alligies Merch is available at Alligies Merch.com in case you need holiday gifts. Smalligies are available for free. They are a G-rated. They're at Alliward.com. Slash Smalligies. Those are kid-friendly versions of classic episodes. To join Patreon, ends it up at your questions before recording. Head to patreon.com slash allergies. Aaron Talbert admins the allergies podcast Facebook group Emily White of the Wordery makes our professional transcripts.

Noel Dilworth is scheduling producer Susan Hale is our major managing director who also assisted in research for this episode. Kelly Arndt Dwyer makes the website secret regust Thomas and Jared sleeper of mind jam media worked on small jizz alongside our lead editor of this episode and of Ologies, the infinitely talented Mercedes-MateLint of Maitland audio. Nick Thorburn wrote the theme music and if you stick around after the show, I'm telling you a secret. Okay, so this week I used to make cocktail recipes for cooking sites. I used to write about nightlife way back when. So I'm pretty versed in making cocktails.

Like at a party, people would be like, we got some peppermint schnapps and a cantaloupe and a pixie stick and some Tabasco makes that mad at it. And I could usually whip something up. But I'm not much of like a make cocktails at home, kind of person these days, pretty chill. But I just found myself making a beverage and he used like some lemon powder and some peach emergency and a heaping scoop of metamusel. And I had it in a now gene and I was just shaking that thing up because you have to.

And I realized that the muscle memory of the cocktail shaking is still there. It's still strong, but just a very different contents and very different vibe. But hey, you got a hydrate, got to get those electrolytes, colon motilities important. And so is math, math is real.

But nothing's real, and life is very beautiful. And met a useful can be tasty. All right. Bye bye. Meteorology, nephrology, nephrology, seriology, and synagogology. Nephrology.