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<v Speaker 1>Oh hey, it's quite frankly in the episode that you

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<v Speaker 1>never thought you'd click on, And it's the one that

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<v Speaker 1>I never thought I would do because mathematics it's an

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<v Speaker 1>X it's not an ology. But over the years y'all

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<v Speaker 1>have begged me to cover this, I swear and I

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<v Speaker 1>found an ology suitable and an ologist who's going to

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<v Speaker 1>get us emotional about numbers, believe it, and also non numbers.

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<v Speaker 1>Come on a journey, take this VIP pass, Come slip

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<v Speaker 1>behind the curtain backstage for a more intimate chill hang

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<v Speaker 1>with a topic that maybe has seemed to all low to

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<v Speaker 1>reach a little intimidating. You're about to meet the really

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<v Speaker 1>charming and artsy side of math. So this ologist, of course,

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<v Speaker 1>is a professional mather, an author and a speaker who

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<v Speaker 1>holds a PhD in Pure mathematics from the University of

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<v Speaker 1>Cambridge and taught at the University of Cambridge, Chicago and Niece.

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<v Speaker 1>She won tenure and pure mathematics at the University of

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<v Speaker 1>Sheffield in the UK. Has appeared on late night shows

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<v Speaker 1>hyping people up about math, has given ted talks and

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<v Speaker 1>written several books on topic, such as how to Bake

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<v Speaker 1>Pie and her latest one is is math real How

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<v Speaker 1>simple questions lead us to mathematics deepest truths. She's one

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<v Speaker 1>of us and the best person possible to cover this topic,

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<v Speaker 1>so she jumped on a mic from the Midwest, where

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<v Speaker 1>she's currently the Scientist in Residence at the School of

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<v Speaker 1>the Art Institute of Chicago, and she's also a concert pianist.

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<v Speaker 1>You're just gonna love her. But first, thank you to

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<v Speaker 1>patrons at patreon dot com slash ologies for submitting your questions.

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<v Speaker 1>You can join for a bug a month. And thank

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<v Speaker 1>you to everyone wearing ologies merch from ologiesmerch dot com.

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<v Speaker 1>Heads up if you are hoping to play this episode

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<v Speaker 1>for your kids. This is not an all ages episode,

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<v Speaker 1>but we do have many of those. They're called smologies

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<v Speaker 1>and you'll find them at the link in the show notes.

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<v Speaker 1>Thank you also to everyone who leaves a review, because

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<v Speaker 1>you know I look at them with my eyes, so

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<v Speaker 1>I can say one with my mouth. And this one

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<v Speaker 1>was left this week by minecraft Girl twenty one fifty

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<v Speaker 1>eight thirty seven, who wrote, I listen to you every

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<v Speaker 1>day and you are so good, but can you make

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<v Speaker 1>a cookie one? Minecraft Girl twenty one fifty eight thirty seven.

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<v Speaker 1>First off, that's an appropriate number of numbers in your name.

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<v Speaker 1>And also we do discuss cookies, so you have no

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<v Speaker 1>idea how appropriate that is. So let's get into it. Mathematology.

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<v Speaker 1>Nobody write me and balk at this. Okay, so many

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<v Speaker 1>people have used this word. It's just it's in the air,

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<v Speaker 1>in the universe. We're going for it. Also fun that

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<v Speaker 1>the word math stems from a root meaning simply to learn.

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<v Speaker 1>So come along with me. Let me hold your hand

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<v Speaker 1>and guide you to the wings of academia, the behind

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<v Speaker 1>the scenes of a topic you did not know you

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<v Speaker 1>could adore, like this as I hear about Fibonacci sequences,

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<v Speaker 1>golden ratios, common core, loving my neighbor, slide rules versus calculators,

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<v Speaker 1>imaginary numbers, the nature of zero infinite cookies, fingers toes, knuckles,

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<v Speaker 1>How math will change your relationships, How math is not

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<v Speaker 1>just numbers, but dare I say a lifestyle? And how

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<v Speaker 1>math is weirder and more artsy than you think, and more.

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<v Speaker 1>With author and mathematician and mathematologist doctor Eugenia.

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<v Speaker 2>Chang, I'm Eugenia Chen and I use sheha.

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<v Speaker 1>And you are a pure mathematician, that's right, and an

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<v Speaker 1>abstract mathematician.

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<v Speaker 2>Yes, it's kind of the same thing. I mean, maybe

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<v Speaker 2>one is more specific than the other.

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<v Speaker 1>Which one is more specific?

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<v Speaker 3>That's a great question, do you know, I haven't thought

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<v Speaker 3>about I think that I think that pure mathematics is

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<v Speaker 3>more the name that it gets given to distinguish it

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<v Speaker 3>from applied mathematics in formal context like in university departments

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<v Speaker 3>and in funding bodies.

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<v Speaker 2>I call it abstract mathematics because I think pure sounds

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<v Speaker 2>a bit judgmental.

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<v Speaker 1>Pure it kind of does. It kind of implies that

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<v Speaker 1>there's an impure mathematic exactly. It seems like illogical, right exactly.

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<v Speaker 2>And I think that there's been enough people looking down

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<v Speaker 2>their noses at other people over mathematics that we can

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<v Speaker 2>do with getting rid of any of those things wherever

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<v Speaker 2>we can.

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<v Speaker 1>Yeah, it does seem anathetical to your whole mission, which

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<v Speaker 1>is to make people appreciate and get over their mathmobia, right.

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<v Speaker 2>Or invite them to invite them.

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<v Speaker 1>Yes, it's a good distinction. Okay, quick aside, What is

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<v Speaker 1>the difference between the types of math? What makes one

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<v Speaker 1>kind of math abstract versus applied? If you apply abstract

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<v Speaker 1>to applied math, how abstract is abstract?

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<v Speaker 2>It's one of those things where the boundary isn't very

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<v Speaker 2>clear cut. But the general idea is that abstract mathematics

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<v Speaker 2>is trying to understand things from the point of view

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<v Speaker 2>of uncovering logical structures and just exploring how things fit

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<v Speaker 2>together for their own sake, whereas applied mathematics is much

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<v Speaker 2>more about looking at problems in the concrete world around

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<v Speaker 2>us and coming up with theories to help us understand

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<v Speaker 2>those specific problems. So applied mathematics is closer to physics,

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<v Speaker 2>because physics is really about understanding the physical world around us,

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<v Speaker 2>but applied mathematics uses the techniques that pure mathematicians come

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<v Speaker 2>up with often, but they are really specifically trying to

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<v Speaker 2>solve things in the concrete world. Sometimes people say real world,

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<v Speaker 2>but I don't like that either, because you know what's

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<v Speaker 2>real anyway? Are we real? Is anything real? And I

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<v Speaker 2>suppose that's what the tide love my book is.

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<v Speaker 3>I who know?

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<v Speaker 1>Is math real? Is math real?

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<v Speaker 3>Am I real?

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<v Speaker 1>Nobody knows, And so one thing that I love about

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<v Speaker 1>your book is just that it's one of those questions

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<v Speaker 1>that we're all afraid to ask. I think some very

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<v Speaker 1>intrepid TikToker was doing a get Ready with Me video

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<v Speaker 1>and just like, how do we even know math is real?

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<v Speaker 1>And I feel like like a year or two ago

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<v Speaker 1>it shook the world.

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<v Speaker 4>I was just doing my makeup for work and I

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<v Speaker 4>just wanted to tell you guys about how I don't

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<v Speaker 4>think math is real. And I know that like it's

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<v Speaker 4>real because we all like learned in school or whatever.

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<v Speaker 4>But who came up with this concept?

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<v Speaker 1>And you're like the farious?

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<v Speaker 4>But how like he didn't even have plumbing and he

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<v Speaker 4>was like, let me worry about why EQ was MX

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<v Speaker 4>plus B, which first of all, how would you even

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<v Speaker 4>figure that out? How would you like start on the

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<v Speaker 4>concept of algebra? Like what did you need it for?

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<v Speaker 1>Do you remember that video? Yeah?

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<v Speaker 2>And you know that did what? That was one of

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<v Speaker 2>the things that inspired me to write this book because

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<v Speaker 2>I replied to her. I wrote a document and I

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<v Speaker 2>just stuck it on my web page and I just

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<v Speaker 2>replied to each of her questions. And then I did

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<v Speaker 2>a few radio interviews and people because people picked up

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<v Speaker 2>on the fact that I replied to all her questions,

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<v Speaker 2>and people emailed me from all over the world saying, oh.

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<v Speaker 5>My goodness, I've wanted to ask those questions from my life.

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<v Speaker 5>I was stupid and this last time I thought, maybe

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<v Speaker 5>I'm not stupid, or I thought I was intelligent and

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<v Speaker 5>every other way except this.

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<v Speaker 2>And I'm sitting.

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<v Speaker 3>In my car crying because you finally validated me after

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<v Speaker 3>all these us.

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<v Speaker 2>And I thought, Wow, this is really really tapped into

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<v Speaker 2>something that has hit people all around the world, and

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<v Speaker 2>it's really effective. All these grown adults, including grown men,

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<v Speaker 2>emailing me to say that they were weeping in their

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<v Speaker 2>cars because because I had finally validated their questions after

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<v Speaker 2>all these years, people who thought of themselves as otherwise intelligent.

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<v Speaker 2>And so I thought, Okay, maybe I'll write a whole

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<v Speaker 2>book about this.

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<v Speaker 1>And so did that spark the book? Did you email

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<v Speaker 1>your book agent? And so listen, I already started on

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<v Speaker 1>a doc.

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<v Speaker 2>Here.

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<v Speaker 1>We got something here.

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<v Speaker 2>Yeah, I mean I already had thoughts about the questions

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<v Speaker 2>that people have always wanted to ask, because I've been

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<v Speaker 2>teaching art students at the School of the Art Institute

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<v Speaker 2>for some years now, and they quite often, quite often

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<v Speaker 2>what we do is like therapy for their past matatural

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<v Speaker 2>and they tell me that all the things that went

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<v Speaker 2>wrong and all the ways in which they were made

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<v Speaker 2>to feel stupid and the question the burning questions they

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<v Speaker 2>had that never got answered because they were told though,

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<v Speaker 2>that's a stupid question, or no, you're not supposed to

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<v Speaker 2>ask that question here, You're just supposed to answer the

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<v Speaker 2>questions that I tell you. And so I'd already been

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<v Speaker 2>building up a kind of catalog of questions that people

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<v Speaker 2>have really wanted to ask and that they never get answered.

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<v Speaker 2>And then when Mattam, I thought, Okay, maybe there is

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<v Speaker 2>scope for this as a whole book.

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<v Speaker 1>Was part of that math Trauma Math Barbie. Do you

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<v Speaker 1>remember math? Do you remember that one?

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<v Speaker 5>Oh?

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<v Speaker 2>No, I mean it's very topical at the moment. I know.

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<v Speaker 5>Anyone boy?

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<v Speaker 3>Howdy?

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<v Speaker 1>Okay? So this team Talk Barbie came out in nineteen

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<v Speaker 1>ninety three and rightly enraged female scientists and mathematicians and

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<v Speaker 1>really any human with a brain who thought sexism was

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<v Speaker 1>weird and that children get brainwashed into gender stereotypes. So

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<v Speaker 1>there's one gorilla group themselves, the Barbie Liberation Organization, and

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<v Speaker 1>they bought a bunch of teen talk Barbies and talking

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<v Speaker 1>Gijo dolls, and they swapped through voice boxes so that

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<v Speaker 1>Barbie said things like troops attack and made machine gun noises,

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<v Speaker 1>and then Gi Joe said, let's go shopping. They did

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<v Speaker 1>this in December of that year, and a lot of

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<v Speaker 1>kids and parents were surprised ad on Christmas morning to

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<v Speaker 1>have a tiny man in combat fatigues lamenting that.

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<v Speaker 2>I do not remember that one, but there was a

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<v Speaker 2>spoof that appeared a few years ago in my research field.

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<v Speaker 2>So my research field is category theory, which is considered

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<v Speaker 2>to be one of the most abstract parts of mathematics,

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<v Speaker 2>and even abstract mathematicians sometimes think it's too abstract. And

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<v Speaker 2>so there was this whole series of Barbie cartoons where

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<v Speaker 2>Ken would say things like, oh, my goodness, what even

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<v Speaker 2>is a mona? And then Barbie would just go, well, obviously,

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<v Speaker 2>it's just a monoid in the category of endose.

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<v Speaker 1>Bunxes ps context. This comic was part of a meme

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<v Speaker 1>known as feminist hacker Barbie, which arose in twenty fourteen

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<v Speaker 1>like a phoenix from the firebombed ashes of a matel

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<v Speaker 1>book called Barbie I Can Be a Computer Engineer, which

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<v Speaker 1>was marketed toward children and featured a teen Barbie learning

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<v Speaker 1>to computer and it involved illustrations of Barbie at a

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<v Speaker 1>laptop in class, and it was captioned with passages such

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<v Speaker 1>as I'm only creating the design ideas, Barbie says, laughing,

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<v Speaker 1>I'll need Stevens and Ryan's help to turn it into

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<v Speaker 1>a real game. Naturally, computer people, some of whom were

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<v Speaker 1>known as women, did not enjoy the existence of this book,

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<v Speaker 1>and so one of them, Kathleen Tweet, created a meme

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<v Speaker 1>generator that spawned so many realistic and really sardonic takes

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<v Speaker 1>on feminist hacker Barbie, and you can read more about

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<v Speaker 1>it in an article titled Barbie Fucks it Up Again. So,

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<v Speaker 1>when Barbie explains to her male classmates that a monad

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<v Speaker 1>is just a monoid in the category of endofunctors, it's

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<v Speaker 1>a definition so legendarily opaque that it's become like a

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<v Speaker 1>math and programming joke itself. But if you'd like to know,

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<v Speaker 1>a monad in math is an algebraic structure, and in

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<v Speaker 1>programming it's used to structure computations as a sequence of steps.

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<v Speaker 1>And a monad can be a thing that describes how

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<v Speaker 1>something is supposed to be modified, but it isn't really

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<v Speaker 1>a thing, and the etymology of monad even means everything

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<v Speaker 1>or nothing at all. So if it's confusing. That's the joke.

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<v Speaker 1>And so now we get the joke. If you're seated

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<v Speaker 1>next to someone at a dinner party and they were

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<v Speaker 1>to turn to you and say, is math real? Who

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<v Speaker 1>invented it? And how do we trust it? How do

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<v Speaker 1>you begin in a short interaction to get them to

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<v Speaker 1>trust that math is real or at least look at

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<v Speaker 1>it in a different way.

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<v Speaker 2>Well, first, I would validate that question, because often when

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<v Speaker 2>they're asking those questions, they're already full of doubt, skepticism,

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<v Speaker 2>and past trauma. Sometimes they're trying to say, none of

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<v Speaker 2>this is real, it's all a load of oops, can't

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<v Speaker 2>say any of those words out loud.

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<v Speaker 6>It's all a load of codswallop. It's all a load

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<v Speaker 6>of codswallopd wlop. Okay, that's often the subtext of their question.

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<v Speaker 6>And sometimes it's because, especially in a dinner party situation,

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<v Speaker 6>they may feel intimidated by finding that I'm a mathematician.

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<v Speaker 6>And unfortunately that happens a lot, especially because I'm not

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<v Speaker 6>a male person, I'm not a white person, and I'm.

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<v Speaker 2>Not necessarily how people expect a mathematician to be whatever

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<v Speaker 2>that is. So quite often people feel intimidated and so

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<v Speaker 2>it depends where those questions are coming from. I also say, well,

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<v Speaker 2>what does really even mean? And spoiler alert from my book,

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<v Speaker 2>I don't actually say math is real, nor do I

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<v Speaker 2>say math is not real. What's really more? The point

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<v Speaker 2>is how does it help us? It doesn't matter whether

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<v Speaker 2>something is real or not really if it helps us

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<v Speaker 2>in some way, that's what I think in the end.

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<v Speaker 2>So then the question is does math help us? And

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<v Speaker 2>does it help us in some way that you the

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<v Speaker 2>person asks me the question cares about because people might say, oh, well,

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<v Speaker 2>sure if people can use master wieplanes and to make

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<v Speaker 2>computers work, But that doesn't mean that I have to

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<v Speaker 2>care about it. And so then I say, try and

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<v Speaker 2>find out what they care about themselves, and whether they

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<v Speaker 2>care about thinking clearly about the world around them.

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<v Speaker 1>Do you surf or eat or paint or eat paint

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<v Speaker 1>or golf or wear clothes. Math is in the tides,

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<v Speaker 1>It's in the temperature gauges in your oven, putting angles,

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<v Speaker 1>Rubik's cubes, hair braids, fabric knits, and lasagna gields. So

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<v Speaker 1>we all have stuff. Take kibs with butterflies, just nauseated

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<v Speaker 1>with happiness, and there is a shitload of friendly and

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<v Speaker 1>helpful and benign and dazzling math involved.

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<v Speaker 2>And sometimes depending on where the person is coming from.

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<v Speaker 2>When I say that math helps me empathize with other people,

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<v Speaker 2>that can be really mind blowing because that is not

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<v Speaker 2>something that is often presented in math class.

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<v Speaker 1>I think, Yeah, how does it help you empathize?

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<v Speaker 2>There's two ways, I think. First of all, it's a

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<v Speaker 2>technique for understanding how arguments are structured. If I want

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<v Speaker 2>to try and understand somebody who has a completely opposed

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<v Speaker 2>point of view from mind, then I can do it

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<v Speaker 2>by understanding where their argument is coming from, because it's

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<v Speaker 2>always coming from somewhere, and it's never going to help

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<v Speaker 2>if we just sit there and go, oh, that person

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<v Speaker 2>is just not being logical. Their point of view has

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<v Speaker 2>come from somewhere, and one way to empathize with other

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<v Speaker 2>people is to understand where their point of view has

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<v Speaker 2>come from.

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<v Speaker 1>So being in a math mindset primes your brain for

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<v Speaker 1>taking something complex and going a step back and breaking

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<v Speaker 1>it down through logic. How does one get from there

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<v Speaker 1>to hear?

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<v Speaker 2>It doesn't mean that we're supporting it, and it doesn't

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<v Speaker 2>mean that we are claiming it's good, but we are

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<v Speaker 2>just understanding where it came from from their point of view.

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<v Speaker 2>Abstract mathematics also helps because it's a process of seeing

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<v Speaker 2>patterns and making analogies between different situations. And so at

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<v Speaker 2>the basic level, if you say two plus three equals five,

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<v Speaker 2>what you're really saying is that anytime you take two

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<v Speaker 2>objects and another three objects, as long as they don't

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<v Speaker 2>kind of spontaneously combust or coalesce, you will end up

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<v Speaker 2>with five objects. And that's a pattern that when we

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<v Speaker 2>teach arithmetic to small children, we show them doing that

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<v Speaker 2>with objects, physical objects, over and over again until they

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<v Speaker 2>see the pattern forming in front of their eyes. And

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<v Speaker 2>that's really a way I think to access empathy with

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<v Speaker 2>people who have different opinions from us, because it's about

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<v Speaker 2>finding an analogy between our situation and theirs.

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<v Speaker 1>So between you and the guy who just flipped you

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<v Speaker 1>off in the traders just parking lot, there must be

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<v Speaker 1>a common denominator.

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<v Speaker 2>And so it can be quite a far fetched analogy.

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<v Speaker 2>But because abstract mathematics is really about seeing deep patterns

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<v Speaker 2>where the surface looks completely different, but if you strip

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<v Speaker 2>away enough details you get down to something that's the

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<v Speaker 2>same underneath. I can do that with people who I

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<v Speaker 2>really disagree with by just stripping away so many details

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<v Speaker 2>and finding some kind of some kind of analogy, even

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<v Speaker 2>if the topic is completely different, thinking about some situation

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<v Speaker 2>in which I have experienced something that is even remotely

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<v Speaker 2>abstractly similar. So perhaps where everybody is disagreeing with me

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<v Speaker 2>about something and getting angry with me for thinking something,

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<v Speaker 2>and it's not going to help me change my mind. So,

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<v Speaker 2>for example, if we think about people who don't believe

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<v Speaker 2>in vaccines in all the ways that people kind of

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<v Speaker 2>get angry with them to try and get them to

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<v Speaker 2>believe in vaccines, and then if I think about a

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<v Speaker 2>situation where a lot of people are getting anger with

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<v Speaker 2>me and want me to believe something, then I can

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<v Speaker 2>see that that isn't going to help me change my mind.

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<v Speaker 2>And so that kind of that kind of abstraction and

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<v Speaker 2>analogy helps me understand why people take the positions that

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<v Speaker 2>they take.

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<v Speaker 1>On that note and stay with me. There was something

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<v Speaker 1>about this chat in eugenius book that reminded me of therapy,

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<v Speaker 1>of cognitive behavioral therapy. Here's funny, because I was reading

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<v Speaker 1>your book thinking about how much math must give you

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<v Speaker 1>kind of an edge into understanding your own brain and

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<v Speaker 1>other people's brains by saying, Okay, everybody hates me. No

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<v Speaker 1>one's texted me back today. Is that true? Does everyone

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<v Speaker 1>hate you? What's the logic?

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<v Speaker 2>What is my reason for thinking this exactly? And the

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<v Speaker 2>thing is that I absolutely don't always use logic over feelings.

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<v Speaker 2>I actually do the opposite. I always observe that feelings

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<v Speaker 2>are correct. That's it. Feelings are always true as a

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<v Speaker 2>basic starting point. But sometimes there are other things going

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<v Speaker 2>on as well, and so I've noticed for myself. For example,

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<v Speaker 2>sometimes when I'm feeling terrible because some bad things have

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<v Speaker 2>happened to me, and then they I think about them

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<v Speaker 2>too much. They go around my head and then I

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<v Speaker 2>feel terrible. And sometimes I think to myself, I know intellectually,

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<v Speaker 2>because I have done Callino behavioral therapy, I know that

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<v Speaker 2>if I just go to bed, I will feel better

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<v Speaker 2>in the morning. And what happens after that is that

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<v Speaker 2>I don't want to do it because I don't want

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<v Speaker 2>to just go to sleep and feel better in the morning.

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<v Speaker 2>So then I might say, well, that's not logical, But

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<v Speaker 2>now I think, though that is a true feeling. I

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<v Speaker 2>truly feel this. Okay, Now why am I feeling this,

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<v Speaker 2>and then I realize it's because it seems like cheating.

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<v Speaker 2>I don't want to Then it will feel like it

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<v Speaker 2>will feel like my feelings aren't being validated. If if

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<v Speaker 2>I can just go to sleep and they'll go away.

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<v Speaker 2>So true.

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<v Speaker 1>You're also a musician too. I think we know that

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<v Speaker 1>there's a lot of math in music, but is there

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<v Speaker 1>a lot of emotion in math?

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<v Speaker 2>There's tons of emotion in math. That's such an interesting question.

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<v Speaker 2>I feel things so deeply when I'm doing and seeing

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<v Speaker 2>and experiencing math, and I try to write that into

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<v Speaker 2>my books because on the one hand, the power and

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<v Speaker 2>the strength of math comes from the fact that it

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<v Speaker 2>is it doesn't have emotions in the actual argument of it,

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<v Speaker 2>so it doesn't depend on emotions. It shouldn't depend on

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<v Speaker 2>emotions at all to build the arguments. But humans are

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<v Speaker 2>emotional creatures, and so when we're communicating math, if we

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<v Speaker 2>don't communicate it with emotions, then I don't think anything

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<v Speaker 2>gets through, or at least much less gets through. And

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<v Speaker 2>I think that's one of the big problems with teaching

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<v Speaker 2>and learning math, is that there's the idea that math

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<v Speaker 2>shouldn't have any emotions in it. Which is true. But

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<v Speaker 2>at the same time, all human experiences have emotions in

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<v Speaker 2>and if we try and teach someone something without showing

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<v Speaker 2>the emotional side, or without giving them an emotional connection

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<v Speaker 2>to it, then I just don't think it goes in

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<v Speaker 2>as deeply.

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<v Speaker 1>So there are many papers on this, but a fresh

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<v Speaker 1>twenty twenty three study called Emotions and Motivation in Mathematics Education,

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<v Speaker 1>Where we Are Today and Where we Need to Go,

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<v Speaker 1>stated that female students enjoyment of and interest in fashion

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<v Speaker 1>was found to result in lower engagement in mathematics and

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<v Speaker 1>prevent them from solving word problems. And I was like,

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<v Speaker 1>hold up, what that seems weird? So I checked out

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<v Speaker 1>the nineteen ninety four study they cited titled When Do

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<v Speaker 1>Girls Prefer Football to Fashion? An Analysis of Female underachievement

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<v Speaker 1>in relation to realistic mathematic contexts, And what that study

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<v Speaker 1>was actually looking at was the tendency for contextual problems

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<v Speaker 1>in math lessons to make no fucking practical sense at all,

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<v Speaker 1>Like you're given this long fictional scenario which you'd approach

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<v Speaker 1>from an entirely different perspective in real life, like the

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<v Speaker 1>fashion problem in the actual nineteen ninety four study was

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<v Speaker 1>that girls scored lower on the fashion design math calculation

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<v Speaker 1>than one about football or just an abstract question because

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<v Speaker 1>the fashion problem made no sense, like, in order to

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<v Speaker 1>divide hours of labor in a mathematically sound way, which

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<v Speaker 1>is what the problem was about, you'd have to deliver

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<v Speaker 1>the finished dresses before you sowed them. And this nineteen

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<v Speaker 1>ninety four study concluded that two thirds of girls used

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<v Speaker 1>their common sense as well as their mathematical knowledge and

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00:21:32.559 --> 00:21:35.240
<v Speaker 1>then were penalized for doing so. Anyway, there was actually

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00:21:35.279 --> 00:21:38.359
<v Speaker 1>more engagement in the problem, but the problem only made

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<v Speaker 1>sense on a math test, not in the real world.

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<v Speaker 1>And research has also shown that figuring out solutions to

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<v Speaker 1>hands on actual scenarios gets us more engaged in finding

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00:21:48.319 --> 00:21:51.480
<v Speaker 1>this solution. So it's actually a two pronged approach to

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00:21:51.519 --> 00:21:54.359
<v Speaker 1>make people actually care. And yes, folks are quick to

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00:21:54.359 --> 00:21:58.200
<v Speaker 1>penalize others without realizing that, hey, they're actually asking really good,

404
00:21:58.240 --> 00:22:01.599
<v Speaker 1>important questions and the problem is more complex and that

405
00:22:01.680 --> 00:22:04.680
<v Speaker 1>the emperor wait a second, is very naked. Why am

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<v Speaker 1>I seeing his parabot X.

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<v Speaker 2>Let me put it this way, if you do have

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<v Speaker 2>an emotional experience when you're doing something, you will remember

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<v Speaker 2>it more deeply, and so I try to talk about things.

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<v Speaker 2>First of all, talk about how I feel about mathematics,

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<v Speaker 2>and secondly, I encourage my students and my readers to

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<v Speaker 2>have feelings about it, and I try to link it

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<v Speaker 2>to topics that they already have feelings about, because if

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<v Speaker 2>I'm talking about why one first one equals to someone

415
00:22:34.400 --> 00:22:37.039
<v Speaker 2>may have no feelings about that, apart from horror when

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<v Speaker 2>they remember their math lessons in school, all right down.

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<v Speaker 2>But then if I can find something else, like my

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<v Speaker 2>wonderful students who came up with thinking about when you

419
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<v Speaker 2>mix paints together, when you mix one color of paint

420
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<v Speaker 2>with one color of paint, you actually don't get to

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<v Speaker 2>because you get a new color of paint. And maybe

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00:22:53.480 --> 00:22:56.160
<v Speaker 2>mixing paint is something that some people have much more

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<v Speaker 2>feeling about. Or if you're making cookies and you've got

424
00:23:00.920 --> 00:23:02.720
<v Speaker 2>balls of dough and you decide you're going to make

425
00:23:02.880 --> 00:23:04.880
<v Speaker 2>one bigger one instead of two small, and you take

426
00:23:05.079 --> 00:23:06.559
<v Speaker 2>two bits of dough and you stick them together and

427
00:23:06.599 --> 00:23:09.039
<v Speaker 2>you make a bigger cookie, that may be something that

428
00:23:09.079 --> 00:23:12.759
<v Speaker 2>someone can have a feeling about rather than just it

429
00:23:12.920 --> 00:23:16.920
<v Speaker 2>being some abstract concept. And so the power of abstract

430
00:23:16.920 --> 00:23:19.640
<v Speaker 2>mathematics is that it does not involve emotions, but that

431
00:23:19.759 --> 00:23:22.079
<v Speaker 2>also makes it difficult to learn and understand.

432
00:23:22.519 --> 00:23:27.599
<v Speaker 1>Well, how does an abstract mathematician deal with those bars

433
00:23:27.640 --> 00:23:31.079
<v Speaker 1>of cookie dough. What's the answer that's going to trouble

434
00:23:31.119 --> 00:23:32.000
<v Speaker 1>me my whole life.

435
00:23:32.759 --> 00:23:35.359
<v Speaker 2>Well, it depends because if you in one way, if

436
00:23:35.400 --> 00:23:37.039
<v Speaker 2>you take two balls of cookie dough, you get two

437
00:23:37.039 --> 00:23:38.440
<v Speaker 2>balls of cookie dough. So you take one boy and

438
00:23:38.440 --> 00:23:40.359
<v Speaker 2>you take one ball, and that's two. But there's another

439
00:23:40.359 --> 00:23:42.000
<v Speaker 2>thing you can do, which is smash them together and

440
00:23:42.039 --> 00:23:43.920
<v Speaker 2>get one bigger one, in which case you've kind of done.

441
00:23:43.920 --> 00:23:46.599
<v Speaker 2>One plus one equals one bigger one. And those are

442
00:23:46.599 --> 00:23:49.759
<v Speaker 2>two scenarios that are both real and so it's not

443
00:23:49.839 --> 00:23:53.279
<v Speaker 2>that one plus one always equals too, it's under what

444
00:23:53.519 --> 00:23:56.960
<v Speaker 2>circumstances does one plus one equal to And that's where

445
00:23:57.000 --> 00:23:58.519
<v Speaker 2>we get to the whole. Oh, as long as we

446
00:23:58.640 --> 00:24:02.119
<v Speaker 2>don't smash things together, we don't eat the cookie dough

447
00:24:02.119 --> 00:24:03.519
<v Speaker 2>because cookie dough is delicious.

448
00:24:03.640 --> 00:24:06.920
<v Speaker 1>So in her book Beyond Infinity, An Expedition to the

449
00:24:06.960 --> 00:24:12.160
<v Speaker 1>Outer Limits of Mathematics, Eugenia also just steers infinity right

450
00:24:12.240 --> 00:24:16.599
<v Speaker 1>the mouth while discussing dividing cookies for all eternity. So

451
00:24:16.640 --> 00:24:19.279
<v Speaker 1>many cookies, man, Hell yeah, yeah, maam, yam right on

452
00:24:19.599 --> 00:24:23.039
<v Speaker 1>where in the brain is math coming from? And why

453
00:24:23.200 --> 00:24:26.839
<v Speaker 1>when I am stoned? Do I think I understand math better?

454
00:24:28.759 --> 00:24:33.400
<v Speaker 2>I cannot possibly address that last question. I have absolutely

455
00:24:33.559 --> 00:24:37.519
<v Speaker 2>no experience about whatsoever, and that is for real. However,

456
00:24:38.039 --> 00:24:41.640
<v Speaker 2>there's a popular idea that math is on one side

457
00:24:41.640 --> 00:24:43.960
<v Speaker 2>of the brain. I'm a whole left right brain thing

458
00:24:44.039 --> 00:24:49.279
<v Speaker 2>I think has been mostly completely debunked. But I remember

459
00:24:49.720 --> 00:24:52.079
<v Speaker 2>it was actually my piano teacher who introduced me to

460
00:24:52.119 --> 00:24:54.279
<v Speaker 2>the book drawing with the right side of the brain,

461
00:24:54.599 --> 00:24:57.200
<v Speaker 2>and so I think, of my head, the idea is

462
00:24:57.200 --> 00:25:01.039
<v Speaker 2>that the right side is the logical side and the

463
00:25:01.160 --> 00:25:05.000
<v Speaker 2>left side is the creative side. Is that is that

464
00:25:05.079 --> 00:25:07.559
<v Speaker 2>I think the myth was right. So I'd just like

465
00:25:07.599 --> 00:25:09.400
<v Speaker 2>to stress that I'm pretty sure it's all being debunked

466
00:25:09.400 --> 00:25:11.160
<v Speaker 2>and that both sides of the brain work together and

467
00:25:11.200 --> 00:25:12.359
<v Speaker 2>are very highly connected.

468
00:25:12.640 --> 00:25:16.000
<v Speaker 1>So while the hypothesis was flipped and the left side

469
00:25:16.039 --> 00:25:19.799
<v Speaker 1>of the brain is supposedly logical, the right is supposedly creative.

470
00:25:19.880 --> 00:25:22.799
<v Speaker 1>It's been flim flammed by medicine itself. And for more

471
00:25:22.799 --> 00:25:24.960
<v Speaker 1>on this, you can read an evaluation of the left

472
00:25:25.000 --> 00:25:29.720
<v Speaker 1>brain versus right brain hypothesis. With resting state, functional connectivity,

473
00:25:29.839 --> 00:25:32.559
<v Speaker 1>magnetic resonance imaging, and you got to use your whole

474
00:25:32.559 --> 00:25:35.799
<v Speaker 1>brain for that study, because it concluded from over a

475
00:25:35.880 --> 00:25:39.480
<v Speaker 1>thousand scans that there's no evidence that the people nestled

476
00:25:39.480 --> 00:25:43.160
<v Speaker 1>into their brain imaging chambers use one side other punkin

477
00:25:43.759 --> 00:25:47.400
<v Speaker 1>more than the other. Rather, your whole shebang is interconnected

478
00:25:47.759 --> 00:25:51.119
<v Speaker 1>and quote, the two hemispheres support each other in its

479
00:25:51.160 --> 00:25:55.279
<v Speaker 1>processes and functions, which is tender and kind. So if

480
00:25:55.319 --> 00:25:58.000
<v Speaker 1>you feel like you need to get it together, don't worry.

481
00:25:58.119 --> 00:25:59.720
<v Speaker 1>You have you are together.

482
00:26:00.240 --> 00:26:03.119
<v Speaker 2>And there are people who have either never had one

483
00:26:03.160 --> 00:26:05.799
<v Speaker 2>side of their brain or lose the use of it,

484
00:26:05.839 --> 00:26:08.200
<v Speaker 2>and then the other side is able to compensate. And

485
00:26:08.240 --> 00:26:10.559
<v Speaker 2>of course there's tons of stuff about the plasticity of

486
00:26:10.559 --> 00:26:13.640
<v Speaker 2>the brain learning to do things. But even if one

487
00:26:13.720 --> 00:26:16.279
<v Speaker 2>side of the brain were logical on the other side's creative,

488
00:26:16.519 --> 00:26:19.759
<v Speaker 2>that just panders to the idea that math is only

489
00:26:19.799 --> 00:26:24.119
<v Speaker 2>logical and not creative, and it's really both together. It's

490
00:26:24.200 --> 00:26:28.079
<v Speaker 2>just that when you're doing arithmetic in elementary school or

491
00:26:28.400 --> 00:26:31.400
<v Speaker 2>wherever you first do it, that might not be extremely creative.

492
00:26:31.599 --> 00:26:33.759
<v Speaker 2>But amo the people who came up with arithmetic in

493
00:26:33.799 --> 00:26:36.640
<v Speaker 2>the first place, that's creative.

494
00:26:37.279 --> 00:26:40.039
<v Speaker 1>I have questions. Yeah, I have so many questions. And

495
00:26:40.079 --> 00:26:43.200
<v Speaker 1>I don't remember how old I was when I realized, oh,

496
00:26:43.519 --> 00:26:48.200
<v Speaker 1>everything's multiplied by ten because of our fingers. Yeah, like

497
00:26:48.319 --> 00:26:51.039
<v Speaker 1>it didn't. It didn't occur to me. The base ten

498
00:26:51.079 --> 00:26:54.440
<v Speaker 1>thing didn't occur to me for so long. But where

499
00:26:54.519 --> 00:26:59.400
<v Speaker 1>did math come from? And how many generations has been

500
00:26:59.440 --> 00:27:02.799
<v Speaker 1>passed down? And if we didn't learn it from someone

501
00:27:03.000 --> 00:27:06.839
<v Speaker 1>older than us who raised us, would we even have

502
00:27:06.920 --> 00:27:11.920
<v Speaker 1>any capacity to just come up with, you know, theorems

503
00:27:11.920 --> 00:27:14.559
<v Speaker 1>and proofs and calculus and everything out of thin air

504
00:27:14.680 --> 00:27:18.759
<v Speaker 1>or does it really just keep building on itself.

505
00:27:18.039 --> 00:27:20.720
<v Speaker 2>That Those are fascinating questions, and I think those are

506
00:27:20.759 --> 00:27:24.039
<v Speaker 2>really great questions. And so humans did come up with

507
00:27:24.079 --> 00:27:26.519
<v Speaker 2>those things, but it took them thousands of years. I mean,

508
00:27:26.680 --> 00:27:28.759
<v Speaker 2>people came up with the idea of numbers thousands of

509
00:27:28.839 --> 00:27:32.599
<v Speaker 2>years ago, but it was ancient cultures. While the numbers

510
00:27:32.599 --> 00:27:34.960
<v Speaker 2>that we use today are mostly based on ten fingers,

511
00:27:34.960 --> 00:27:37.680
<v Speaker 2>different cultures based things on different things. And so there

512
00:27:37.680 --> 00:27:41.200
<v Speaker 2>are some cultures that base things on eight because of knuckles,

513
00:27:41.559 --> 00:27:43.640
<v Speaker 2>and then there are some people who use the spaces

514
00:27:43.680 --> 00:27:45.720
<v Speaker 2>in between their fingers as well. And there are some

515
00:27:45.880 --> 00:27:49.000
<v Speaker 2>cultures who based on twenty.

516
00:27:48.720 --> 00:27:51.319
<v Speaker 4>Twenty fingers and twenty.

517
00:27:50.960 --> 00:27:55.119
<v Speaker 2>Twos, and the number system in French has traces of that,

518
00:27:55.680 --> 00:28:01.160
<v Speaker 2>where eighty is catravan with four twenties. Ninety isn't ninety,

519
00:28:01.200 --> 00:28:03.920
<v Speaker 2>it's four twenties plus ten because it's as if you're

520
00:28:03.960 --> 00:28:07.440
<v Speaker 2>counting up in twenties. So there are different things. But

521
00:28:07.480 --> 00:28:10.000
<v Speaker 2>then this base ten thing has really taken over.

522
00:28:10.400 --> 00:28:13.319
<v Speaker 1>So base ten systems have been used for probably as

523
00:28:13.319 --> 00:28:17.440
<v Speaker 1>long as we've had ten fingers, And though the written

524
00:28:17.480 --> 00:28:21.839
<v Speaker 1>records go back to three thousand BCE in Egypt, it

525
00:28:21.960 --> 00:28:25.559
<v Speaker 1>wasn't until between one hundred and four hundred years into

526
00:28:25.559 --> 00:28:29.079
<v Speaker 1>the Common era that the Hindu Arabic numeral system of

527
00:28:29.200 --> 00:28:31.839
<v Speaker 1>zero to ten kind of won out. And this number

528
00:28:31.880 --> 00:28:34.519
<v Speaker 1>system has only been in use in Europe for like

529
00:28:34.559 --> 00:28:37.920
<v Speaker 1>the last one thousand years. But yeah, it goes far

530
00:28:38.039 --> 00:28:42.000
<v Speaker 1>far beyond that in different forms. But staring at your

531
00:28:42.000 --> 00:28:44.119
<v Speaker 1>hands for a while, that's math, people.

532
00:28:44.519 --> 00:28:47.359
<v Speaker 2>And there were some ancient cultures I think it might

533
00:28:47.400 --> 00:28:50.400
<v Speaker 2>have been Mayan culture that used base sixty, which is

534
00:28:50.400 --> 00:28:53.480
<v Speaker 2>why there are sixty minutes in an hour and sixty

535
00:28:53.680 --> 00:28:59.680
<v Speaker 2>seconds in a minute. No, right, So many of our

536
00:28:59.759 --> 00:29:05.000
<v Speaker 2>things are in tens. The lovely American system still uses fahrenheit.

537
00:29:05.119 --> 00:29:06.920
<v Speaker 2>That doesn't fit well with hundreds.

538
00:29:07.079 --> 00:29:07.880
<v Speaker 5>You, no, it does not.

539
00:29:09.480 --> 00:29:11.680
<v Speaker 2>But we have this thing with sixty seconds in a

540
00:29:11.720 --> 00:29:14.240
<v Speaker 2>minute and sixty minutes in an hour, and sixties are

541
00:29:14.279 --> 00:29:16.319
<v Speaker 2>great number to use because it has a lot of

542
00:29:16.359 --> 00:29:20.559
<v Speaker 2>factors and so you can divide an hour into a

543
00:29:20.559 --> 00:29:23.559
<v Speaker 2>lot of really nice chunks. Whereas if we went decimal

544
00:29:23.640 --> 00:29:27.240
<v Speaker 2>on time. I think there's some fantastic society somewhere that

545
00:29:27.240 --> 00:29:29.640
<v Speaker 2>thinks we should go a metric on time and have

546
00:29:29.680 --> 00:29:31.880
<v Speaker 2>one hundred minutes in an hour, we would actually not

547
00:29:31.960 --> 00:29:34.079
<v Speaker 2>be able to divide it up into quite so many

548
00:29:35.119 --> 00:29:37.440
<v Speaker 2>handy units, because we wouldn't be able to do a

549
00:29:37.480 --> 00:29:39.839
<v Speaker 2>third in quite a handy way. So we can do

550
00:29:39.920 --> 00:29:45.839
<v Speaker 2>we can divide an hour into half thirds, quarters, fifths, tenths, twelfth,

551
00:29:45.960 --> 00:29:47.720
<v Speaker 2>I mean, we can do all sorts of things, and

552
00:29:47.759 --> 00:29:50.160
<v Speaker 2>so sixties sixties are pretty good number for that. But

553
00:29:50.200 --> 00:29:53.519
<v Speaker 2>the whole ten finger thing eventually took over. And to

554
00:29:54.319 --> 00:29:57.559
<v Speaker 2>answer your question about if we grew up and nobody

555
00:29:57.559 --> 00:29:59.480
<v Speaker 2>older than us taught us enough, would we be able

556
00:29:59.519 --> 00:30:02.680
<v Speaker 2>to come up with all of it? Well, I here's

557
00:30:02.720 --> 00:30:05.559
<v Speaker 2>what I think, and this is just pure speculation. I

558
00:30:05.559 --> 00:30:07.200
<v Speaker 2>think it would be hard to do that in a

559
00:30:07.240 --> 00:30:10.519
<v Speaker 2>single lifetime. It did take humans thousands of years to

560
00:30:10.559 --> 00:30:12.440
<v Speaker 2>get to the point we are, and I think it's

561
00:30:12.519 --> 00:30:16.160
<v Speaker 2>amazing how fast an individual human is now able to

562
00:30:16.279 --> 00:30:19.400
<v Speaker 2>learn all of those things that it took humans thousands

563
00:30:19.440 --> 00:30:22.759
<v Speaker 2>of years to learn. And it's because we communicate with

564
00:30:22.839 --> 00:30:26.160
<v Speaker 2>each other, and so it's really dependent on people who

565
00:30:26.240 --> 00:30:28.799
<v Speaker 2>already know it passing it down to the next generation.

566
00:30:29.440 --> 00:30:32.519
<v Speaker 2>If we each had to develop it from scratch, it

567
00:30:32.559 --> 00:30:35.960
<v Speaker 2>would take a really long time, and I don't know

568
00:30:36.000 --> 00:30:38.240
<v Speaker 2>how far an individual would get.

569
00:30:38.559 --> 00:30:41.720
<v Speaker 1>Well, do you think there's any maths systems that have

570
00:30:41.759 --> 00:30:45.839
<v Speaker 1>been completely forgotten that some people cultivated for a couple

571
00:30:45.920 --> 00:30:48.359
<v Speaker 1>thousand years and then just wasn't a record of it,

572
00:30:48.599 --> 00:30:50.559
<v Speaker 1>And we just have no idea that there's a whole

573
00:30:50.559 --> 00:30:54.599
<v Speaker 1>math system based on pie or the Fibonacci sequence or

574
00:30:54.640 --> 00:30:56.920
<v Speaker 1>like seven or something.

575
00:30:57.359 --> 00:31:04.039
<v Speaker 2>Almost certainly, especially because so many cultures passed things down

576
00:31:04.079 --> 00:31:08.000
<v Speaker 2>from generation to generation and then maybe died out or

577
00:31:08.839 --> 00:31:13.279
<v Speaker 2>got killed off by white European people or are living

578
00:31:13.400 --> 00:31:19.359
<v Speaker 2>uncontacted somewhere. And I think that there are certainly pieces

579
00:31:19.400 --> 00:31:26.160
<v Speaker 2>of math that are obsolete now because we've developed more technology. So,

580
00:31:26.200 --> 00:31:29.119
<v Speaker 2>for example, there's the whole math of the slide rule.

581
00:31:29.319 --> 00:31:34.200
<v Speaker 2>For my parents' generation had to learn how to use

582
00:31:34.400 --> 00:31:37.440
<v Speaker 2>a slide rule, which is a really clever device for

583
00:31:37.599 --> 00:31:43.640
<v Speaker 2>multiplying large numbers together using logarithms. And the thing is,

584
00:31:43.680 --> 00:31:47.480
<v Speaker 2>we just really don't need that anymore because we've got calculators.

585
00:31:47.720 --> 00:31:50.519
<v Speaker 1>So that slide roll system was invented by a dude

586
00:31:50.720 --> 00:31:54.799
<v Speaker 1>named Edmundculter in sixteen twenty, and that was the same

587
00:31:54.880 --> 00:31:58.240
<v Speaker 1>year that the Mayflower crashed the party that's now known

588
00:31:58.279 --> 00:32:03.559
<v Speaker 1>as North America. Slide rule was technically an analog computer,

589
00:32:03.759 --> 00:32:06.720
<v Speaker 1>and it had this ability to glide to different positions

590
00:32:06.759 --> 00:32:10.519
<v Speaker 1>to reveal these complex math solutions. And this is how

591
00:32:10.559 --> 00:32:15.480
<v Speaker 1>folks conquered big multiplication and division of numbers until about

592
00:32:15.480 --> 00:32:19.440
<v Speaker 1>the nineteen seventies, when electronic calculators just be booped their

593
00:32:19.480 --> 00:32:23.920
<v Speaker 1>way onto office desks next to ashtrays and diepepsi and

594
00:32:24.039 --> 00:32:29.680
<v Speaker 1>became accessible and commonplace. Now, as for this so called slipstick,

595
00:32:30.119 --> 00:32:33.720
<v Speaker 1>it became obsolete partly because you could not write boobies

596
00:32:33.759 --> 00:32:34.559
<v Speaker 1>upside down with it.

597
00:32:34.839 --> 00:32:39.400
<v Speaker 2>And so the slide rule has become obsolete. I don't

598
00:32:39.400 --> 00:32:42.519
<v Speaker 2>know how to use one myself. I expect my parents

599
00:32:42.559 --> 00:32:44.480
<v Speaker 2>had it drummed into them so hard that they could

600
00:32:44.480 --> 00:32:47.920
<v Speaker 2>still do it with a slide rule. I'm sure there's

601
00:32:48.000 --> 00:32:51.720
<v Speaker 2>somebody out there who still loves using this slide rule.

602
00:32:52.119 --> 00:32:56.880
<v Speaker 1>I mean, I remember the anxiety of how to afford

603
00:32:57.240 --> 00:32:59.680
<v Speaker 1>Texas instruments TI eighty.

604
00:32:59.480 --> 00:33:01.519
<v Speaker 2>Seven graphical calculator.

605
00:33:01.839 --> 00:33:04.000
<v Speaker 1>Yeah, like meeting one of those in high school, being

606
00:33:04.039 --> 00:33:07.960
<v Speaker 1>like I need one hundred and nine dollars for a

607
00:33:08.000 --> 00:33:12.359
<v Speaker 1>calculator size of a brick, you know, like how much

608
00:33:12.440 --> 00:33:14.720
<v Speaker 1>it's maybe that's not used aaymore, but maybe it is

609
00:33:14.759 --> 00:33:17.880
<v Speaker 1>in testing situations. But I know, I know you get

610
00:33:17.880 --> 00:33:21.279
<v Speaker 1>assets all the time, but who is good at math?

611
00:33:21.640 --> 00:33:25.000
<v Speaker 1>How much is it aptitude? How much is it attitude?

612
00:33:25.240 --> 00:33:29.000
<v Speaker 1>How much is it access? And why are we so

613
00:33:29.119 --> 00:33:31.240
<v Speaker 1>afraid of it? Why do so many people just throw

614
00:33:31.240 --> 00:33:34.240
<v Speaker 1>their hands up and say nope, a sack by like

615
00:33:34.319 --> 00:33:36.000
<v Speaker 1>you split the bill I'm not dealing with.

616
00:33:36.519 --> 00:33:40.000
<v Speaker 2>So, first of all, I think it's mostly access and

617
00:33:40.119 --> 00:33:42.960
<v Speaker 2>how much help you've had and how much that help

618
00:33:43.119 --> 00:33:47.559
<v Speaker 2>was specifically helpful to you. All the scientific research at

619
00:33:47.599 --> 00:33:53.599
<v Speaker 2>the moment points to brains being spectacularly plastic. Neuroplasticity, it's

620
00:33:53.720 --> 00:33:57.759
<v Speaker 2>extraordinary how much brains can change according to how they

621
00:33:57.759 --> 00:34:00.279
<v Speaker 2>are used and how they are stimulated, so.

622
00:34:00.319 --> 00:34:03.240
<v Speaker 1>You can coax your brain toward a better life, which

623
00:34:03.279 --> 00:34:05.559
<v Speaker 1>means maybe one day I will be good at dancing.

624
00:34:06.079 --> 00:34:10.440
<v Speaker 2>And so there is almost no evidence, there's basically no

625
00:34:10.599 --> 00:34:12.920
<v Speaker 2>evidence to show that there's some kind of hard wiring

626
00:34:12.920 --> 00:34:15.880
<v Speaker 2>at birth that means that some people are destined to

627
00:34:15.880 --> 00:34:18.679
<v Speaker 2>be better at math than others. And in my previous

628
00:34:18.719 --> 00:34:22.519
<v Speaker 2>book X plus Y and Mathematicians Manifesto for Rethinking Gender,

629
00:34:22.800 --> 00:34:25.159
<v Speaker 2>I talked about this a bit because there are still

630
00:34:25.239 --> 00:34:28.880
<v Speaker 2>some people who think that maybe there's just some biological

631
00:34:28.920 --> 00:34:32.360
<v Speaker 2>reason that for men to be better than women at math,

632
00:34:32.400 --> 00:34:34.320
<v Speaker 2>and there's therefore there's nothing we can do about it.

633
00:34:34.679 --> 00:34:37.840
<v Speaker 2>And the evidence, the scientific evidence of that is just

634
00:34:38.119 --> 00:34:42.679
<v Speaker 2>so thin that it's actually laughable. I mean I laugh

635
00:34:42.760 --> 00:34:44.719
<v Speaker 2>at it. That means it's laughable, right.

636
00:34:44.599 --> 00:34:44.679
<v Speaker 1>And.

637
00:34:46.280 --> 00:34:48.960
<v Speaker 2>So, because how can you even tell that something is

638
00:34:49.719 --> 00:34:53.199
<v Speaker 2>hardwired at birth except by testing newborn babies? But how

639
00:34:53.239 --> 00:34:55.800
<v Speaker 2>do you even test newborn babies? They don't do anything,

640
00:34:56.679 --> 00:35:00.320
<v Speaker 2>you can't you can't get them to do anything. And

641
00:35:00.360 --> 00:35:02.599
<v Speaker 2>so the idea that anything you can get a newborn

642
00:35:02.639 --> 00:35:04.639
<v Speaker 2>baby to do is going to be indicative of their

643
00:35:04.639 --> 00:35:08.800
<v Speaker 2>future mathability. It's just ludicrous to me because mathability is

644
00:35:08.840 --> 00:35:13.639
<v Speaker 2>a really complicated combination of things. It's not just about

645
00:35:13.639 --> 00:35:16.199
<v Speaker 2>being how fast you can do arithmetic. And so I

646
00:35:16.199 --> 00:35:18.480
<v Speaker 2>always say that the things that you can test in

647
00:35:18.559 --> 00:35:23.199
<v Speaker 2>lab controlled situations are necessarily very restrictive, just like you

648
00:35:23.239 --> 00:35:25.519
<v Speaker 2>can test how far people can sprint the one hundred meters.

649
00:35:25.960 --> 00:35:29.480
<v Speaker 2>And I don't think anybody really argues with the fact

650
00:35:29.480 --> 00:35:32.480
<v Speaker 2>that men can the fastest men can run one hundred

651
00:35:32.519 --> 00:35:34.519
<v Speaker 2>meters faster than the fastest women. It's to do with

652
00:35:34.559 --> 00:35:39.440
<v Speaker 2>body strength and stuff like that. But ultra marathons. Women

653
00:35:39.519 --> 00:35:42.480
<v Speaker 2>have been beating men at ultra marathons. I can't remember

654
00:35:42.480 --> 00:35:44.280
<v Speaker 2>how long it counts as an ultramathm, but it might

655
00:35:44.320 --> 00:35:45.960
<v Speaker 2>be two hundred and fifty miles or something.

656
00:35:46.199 --> 00:35:49.039
<v Speaker 1>Okay, so technically everything over twenty six point two is

657
00:35:49.039 --> 00:35:52.559
<v Speaker 1>an ultra marathon. But the longest and the most grueling

658
00:35:52.800 --> 00:35:55.079
<v Speaker 1>is the Hong Kong two hundred and ninety eight k

659
00:35:55.840 --> 00:35:59.559
<v Speaker 1>with no stopping or sleep or support on the trails,

660
00:35:59.800 --> 00:36:03.320
<v Speaker 1>just two to three days of continuous running. Why why

661
00:36:03.360 --> 00:36:06.719
<v Speaker 1>why why why? But take a gander at this one

662
00:36:06.920 --> 00:36:10.119
<v Speaker 1>article from twenty twenty one titled why women are faster

663
00:36:10.239 --> 00:36:13.159
<v Speaker 1>than men in long runs, and you'll learn that the

664
00:36:13.280 --> 00:36:16.760
<v Speaker 1>men among us tend to have larger hearts to pump

665
00:36:16.800 --> 00:36:21.400
<v Speaker 1>oxygen for powerful sprints and more muscle mass to power

666
00:36:21.400 --> 00:36:24.639
<v Speaker 1>those bursts of energy. However, that's the ganders the geese

667
00:36:24.639 --> 00:36:28.239
<v Speaker 1>in this situation. Lady athletes excel at endurance due to

668
00:36:28.320 --> 00:36:31.960
<v Speaker 1>a multitude effectors, such as a higher body fat percentage

669
00:36:32.039 --> 00:36:35.679
<v Speaker 1>that helps when they hit a wall figuratively, more slow

670
00:36:35.719 --> 00:36:40.440
<v Speaker 1>twitch muscle fibers, and yes, emotional resilience in general, because

671
00:36:40.440 --> 00:36:43.199
<v Speaker 1>some of these bodies have thrust a whole person out

672
00:36:43.199 --> 00:36:46.559
<v Speaker 1>of their more sensitive aperture. So maybe an ultra marathon

673
00:36:46.679 --> 00:36:48.440
<v Speaker 1>is like a walk in the park, but just without

674
00:36:48.480 --> 00:36:50.920
<v Speaker 1>ever stopping until you've collapsed at the end.

675
00:36:51.280 --> 00:36:55.239
<v Speaker 2>And that's a really complicated combination of skill, much more

676
00:36:55.280 --> 00:36:59.159
<v Speaker 2>complicated than running one hundred meters, which you have to say,

677
00:36:59.199 --> 00:37:01.719
<v Speaker 2>unne hundred meters and hard. It's just a much more

678
00:37:01.760 --> 00:37:08.880
<v Speaker 2>focused thing, Whereas an ultra mouth involves planning, strategy, self knowledge, pacing,

679
00:37:09.239 --> 00:37:12.159
<v Speaker 2>and math is like that because math isn't just about

680
00:37:13.000 --> 00:37:17.960
<v Speaker 2>memorizing things or manipulating large numbers. Math is about spotting

681
00:37:18.039 --> 00:37:22.880
<v Speaker 2>patterns and being able to perform abstractions in order to

682
00:37:22.920 --> 00:37:27.199
<v Speaker 2>see patterns that previously weren't visible, and having ideas for

683
00:37:27.280 --> 00:37:31.960
<v Speaker 2>how to group objects together to make structures that will

684
00:37:31.960 --> 00:37:34.719
<v Speaker 2>be useful to us. It's a bit like designing a

685
00:37:34.880 --> 00:37:37.760
<v Speaker 2>useful tool for building a house, except that it's an

686
00:37:37.800 --> 00:37:39.559
<v Speaker 2>abstract tool for building ideas.

687
00:37:39.840 --> 00:37:42.880
<v Speaker 1>Okay, so it's like a hammer to drive nails versus

688
00:37:42.920 --> 00:37:45.559
<v Speaker 1>the idea of a hammer to drive the idea of

689
00:37:45.599 --> 00:37:48.480
<v Speaker 1>a nail, which can be applied to the mathematics of

690
00:37:48.559 --> 00:37:51.119
<v Speaker 1>the physics of the fabrication of the tool to drive

691
00:37:51.119 --> 00:37:56.039
<v Speaker 1>the nails, which becomes the real hammer. Woodworkers, You love math, So.

692
00:37:56.079 --> 00:37:59.639
<v Speaker 2>How on earth do you measure a biological predisposition for

693
00:37:59.719 --> 00:38:02.840
<v Speaker 2>doing that? They're not skills that are just something that

694
00:38:03.320 --> 00:38:04.800
<v Speaker 2>you can be born with. How are we going to

695
00:38:04.800 --> 00:38:07.400
<v Speaker 2>test whether a newborn baby can do that? We can't.

696
00:38:08.440 --> 00:38:11.119
<v Speaker 1>Well, what do you think about common core? Because I

697
00:38:11.159 --> 00:38:14.079
<v Speaker 1>don't have kids, but all I know is that my

698
00:38:14.199 --> 00:38:18.280
<v Speaker 1>friends with kids seem horrified or confused by common Core.

699
00:38:18.400 --> 00:38:21.039
<v Speaker 1>I don't quite understand what it is. But why has

700
00:38:21.079 --> 00:38:24.000
<v Speaker 1>there been this shift in the way that we're teaching math?

701
00:38:24.079 --> 00:38:26.440
<v Speaker 1>And I guess like the last ten or so years.

702
00:38:26.800 --> 00:38:28.639
<v Speaker 2>The reason there's been a shift in the way we're

703
00:38:28.639 --> 00:38:32.920
<v Speaker 2>teaching math is because most people have acknowledged that it

704
00:38:32.960 --> 00:38:36.639
<v Speaker 2>wasn't going very well. It's just people haven't really agreed

705
00:38:36.800 --> 00:38:39.719
<v Speaker 2>on what to do about it. And I think one

706
00:38:39.719 --> 00:38:44.119
<v Speaker 2>of the problems with changing the system is that a

707
00:38:44.159 --> 00:38:48.199
<v Speaker 2>lot of teachers don't get autonomy over what they're allowed

708
00:38:48.199 --> 00:38:49.800
<v Speaker 2>to teach. They get it planked on them and say,

709
00:38:49.880 --> 00:38:51.599
<v Speaker 2>now you have to teach like this and that's that,

710
00:38:52.119 --> 00:38:54.559
<v Speaker 2>and then you have to prepare people for standardized tests,

711
00:38:54.639 --> 00:38:56.719
<v Speaker 2>and then you get judged on how they do in

712
00:38:56.719 --> 00:39:01.400
<v Speaker 2>those standardized tests. And I think that that any time

713
00:39:01.599 --> 00:39:07.159
<v Speaker 2>that we're aiming to teach people content like can you

714
00:39:07.239 --> 00:39:09.119
<v Speaker 2>do this thing at the end of it, then that

715
00:39:09.239 --> 00:39:13.480
<v Speaker 2>is going to be less successful than teaching them basically

716
00:39:13.480 --> 00:39:17.679
<v Speaker 2>the appreciation and allowing teachers more autonomy to teach the

717
00:39:17.719 --> 00:39:19.440
<v Speaker 2>things that they care about in the way that they

718
00:39:19.480 --> 00:39:22.920
<v Speaker 2>care about. And as the world changes, some basic things

719
00:39:22.960 --> 00:39:26.039
<v Speaker 2>become less important, just like the slide rule is not

720
00:39:26.079 --> 00:39:29.559
<v Speaker 2>important anymore and controversial idea, but I don't think that

721
00:39:29.679 --> 00:39:34.119
<v Speaker 2>long multiplication is important anymore. They've got calculators and it's

722
00:39:34.199 --> 00:39:37.519
<v Speaker 2>just like learning to ride a horse. Isn't important anymore,

723
00:39:37.760 --> 00:39:40.039
<v Speaker 2>which doesn't mean no one should learn to ride a horse.

724
00:39:40.079 --> 00:39:42.639
<v Speaker 2>If someone learns riding a horse, great, but it's not

725
00:39:43.039 --> 00:39:45.679
<v Speaker 2>an important it's not a crucial skill for most people's

726
00:39:45.719 --> 00:39:50.320
<v Speaker 2>daily lives. And I think that sometimes parents get really

727
00:39:50.360 --> 00:39:54.039
<v Speaker 2>upset if they don't understand the work that their children

728
00:39:54.039 --> 00:39:56.159
<v Speaker 2>are being asked to do. And I've talked to many

729
00:39:56.159 --> 00:39:58.679
<v Speaker 2>math teachers who say that the parents complain to them

730
00:39:58.800 --> 00:40:00.559
<v Speaker 2>that it's not like it was when they were young.

731
00:40:00.880 --> 00:40:02.800
<v Speaker 2>But then the teachers say to them, well, did you

732
00:40:03.000 --> 00:40:05.599
<v Speaker 2>like math, and they go, no, I hated it. They go, well,

733
00:40:05.639 --> 00:40:07.679
<v Speaker 2>why do you want me to do that to your children?

734
00:40:08.079 --> 00:40:11.000
<v Speaker 1>Oh, it's sympathetic.

735
00:40:12.280 --> 00:40:14.400
<v Speaker 2>And sometimes people say, oh, it's terrible, I can't help

736
00:40:14.400 --> 00:40:16.960
<v Speaker 2>my children with their homework. And sometimes I want to go, well,

737
00:40:17.000 --> 00:40:19.360
<v Speaker 2>don't help them with their homework, then it's their homework.

738
00:40:19.639 --> 00:40:21.440
<v Speaker 1>Okay, this just didn't It turns out that I had

739
00:40:21.480 --> 00:40:24.639
<v Speaker 1>no idea what common core really meant because I don't

740
00:40:24.639 --> 00:40:26.280
<v Speaker 1>have kids and I don't listen.

741
00:40:26.320 --> 00:40:26.559
<v Speaker 2>Well.

742
00:40:26.800 --> 00:40:31.119
<v Speaker 1>So common Core was adopted in US states around twenty ten,

743
00:40:31.320 --> 00:40:35.400
<v Speaker 1>and it's actually the set of standardized assessments measuring where

744
00:40:35.480 --> 00:40:38.639
<v Speaker 1>kids should be for every school year. But that term

745
00:40:38.800 --> 00:40:42.159
<v Speaker 1>common core, often mistakenly is applied to just this new

746
00:40:42.199 --> 00:40:45.599
<v Speaker 1>way of teaching math that's more intuitive and is actually

747
00:40:45.599 --> 00:40:48.400
<v Speaker 1>a very old way of doing math. So instead of

748
00:40:48.559 --> 00:40:51.000
<v Speaker 1>going and fetching a piece of paper to figure out

749
00:40:51.039 --> 00:40:54.840
<v Speaker 1>what's sixty three minus forty two and then borrowing some

750
00:40:54.960 --> 00:40:58.280
<v Speaker 1>numbers and stacking figures on top of each other, kids learn, well,

751
00:40:58.320 --> 00:41:01.519
<v Speaker 1>if you add one to forty two, than sixty three

752
00:41:01.639 --> 00:41:04.320
<v Speaker 1>minus forty three would be twenty. So it's twenty plus one,

753
00:41:04.440 --> 00:41:07.079
<v Speaker 1>which is twenty one. Because we all have pocket computers

754
00:41:07.239 --> 00:41:11.079
<v Speaker 1>for the bigger arithmetic issues, teaching these quicker and less

755
00:41:11.079 --> 00:41:14.760
<v Speaker 1>fussy ways of handling numerical concepts is more valuable and

756
00:41:14.880 --> 00:41:17.639
<v Speaker 1>future generations will probably thank us when it comes to

757
00:41:17.679 --> 00:41:21.880
<v Speaker 1>adding tips to dinner bills, that is, if American restaurant

758
00:41:21.880 --> 00:41:24.239
<v Speaker 1>workers are still making minimum wage and at the mercy

759
00:41:24.280 --> 00:41:26.840
<v Speaker 1>of groutsey customers to actually pay for the rent. We

760
00:41:26.920 --> 00:41:30.280
<v Speaker 1>thought we'd have flying cars, but really just one healthcare Well,

761
00:41:30.320 --> 00:41:33.159
<v Speaker 1>I wonder how do you think the world will change

762
00:41:33.440 --> 00:41:36.440
<v Speaker 1>with a new generation learning math in a different way.

763
00:41:36.480 --> 00:41:41.440
<v Speaker 1>Do you think we'll have more mathematicians, more statisticians, more scientists,

764
00:41:41.559 --> 00:41:46.599
<v Speaker 1>or do you think will progress even faster through mathematics.

765
00:41:46.639 --> 00:41:49.239
<v Speaker 2>Is that a good thing. I'm much more worried about

766
00:41:49.280 --> 00:41:51.400
<v Speaker 2>the people who fall off and get put off and

767
00:41:51.440 --> 00:41:53.800
<v Speaker 2>get traumatized by it. What I would like to see

768
00:41:53.960 --> 00:41:57.400
<v Speaker 2>is not more mathematicians and more scientists. It's fewer people

769
00:41:57.400 --> 00:41:59.960
<v Speaker 2>who hate it. That's what I really want to see.

770
00:42:00.280 --> 00:42:04.639
<v Speaker 2>And partly because when there's half or more of adult

771
00:42:04.760 --> 00:42:09.039
<v Speaker 2>humans who either hate math, are traumatized by it, or

772
00:42:09.039 --> 00:42:13.519
<v Speaker 2>who are actively hostile towards math and science, we've got

773
00:42:13.559 --> 00:42:17.360
<v Speaker 2>problems with persuading people that things like vaccines are real,

774
00:42:17.559 --> 00:42:19.960
<v Speaker 2>that the pandemic is real, and that we need to

775
00:42:20.000 --> 00:42:23.119
<v Speaker 2>do something about it, that climate change is definitely something

776
00:42:23.159 --> 00:42:25.679
<v Speaker 2>that we need to worry about. I think that that's

777
00:42:25.719 --> 00:42:28.639
<v Speaker 2>a big problem for the way that society is going,

778
00:42:28.679 --> 00:42:31.719
<v Speaker 2>if people are ready to just believe those kind of lives.

779
00:42:32.000 --> 00:42:35.440
<v Speaker 2>And I do think that my background and training in

780
00:42:35.480 --> 00:42:40.119
<v Speaker 2>abstract mathematics really helps me to not be manipulated by

781
00:42:40.159 --> 00:42:41.800
<v Speaker 2>people who are lying to me, and it helps me

782
00:42:41.880 --> 00:42:45.400
<v Speaker 2>always to be aware of the frameworks for finding out

783
00:42:45.440 --> 00:42:49.519
<v Speaker 2>whether information is good or not and deciding whether something

784
00:42:49.719 --> 00:42:53.480
<v Speaker 2>that someone is saying is probably true or not. And

785
00:42:53.559 --> 00:42:57.639
<v Speaker 2>I think that that is all part of what I

786
00:42:57.639 --> 00:43:00.840
<v Speaker 2>think education should be aiming for. Not can you multiply

787
00:43:00.840 --> 00:43:03.559
<v Speaker 2>these large numbers together, and can you calculate this thing

788
00:43:03.559 --> 00:43:05.400
<v Speaker 2>and get the right tanswer? And can you solve this equation?

789
00:43:05.519 --> 00:43:08.760
<v Speaker 2>But can you think clearly about the world around you.

790
00:43:08.840 --> 00:43:13.159
<v Speaker 2>Can you make sure that people don't manipulate you and

791
00:43:13.360 --> 00:43:16.800
<v Speaker 2>can't lie to you about things just so that they

792
00:43:16.840 --> 00:43:19.920
<v Speaker 2>can get your vote or your money. And can we

793
00:43:20.000 --> 00:43:23.079
<v Speaker 2>make a contribution to the world that benefits more people

794
00:43:23.119 --> 00:43:24.199
<v Speaker 2>and not just ourselves.

795
00:43:24.400 --> 00:43:27.039
<v Speaker 1>The way that social media is, I feel like we're

796
00:43:27.079 --> 00:43:31.320
<v Speaker 1>going toward kind of a quantitative rather than a qualitative

797
00:43:31.360 --> 00:43:35.320
<v Speaker 1>assessment of our lives. And maybe there creates a little

798
00:43:35.360 --> 00:43:37.840
<v Speaker 1>bit of an anxiety around math there too. And we

799
00:43:38.159 --> 00:43:40.559
<v Speaker 1>look at how many followers, how many likes something has

800
00:43:40.719 --> 00:43:44.679
<v Speaker 1>we've really started to introduce numbers to things that are

801
00:43:44.800 --> 00:43:46.280
<v Speaker 1>much more qualitative.

802
00:43:46.639 --> 00:43:50.519
<v Speaker 2>Oh that's a really interesting point. Yeah, right. I think

803
00:43:50.559 --> 00:43:53.480
<v Speaker 2>it's because society is trying to rank everything all the time.

804
00:43:53.960 --> 00:43:54.199
<v Speaker 1>Yeah.

805
00:43:54.239 --> 00:43:57.519
<v Speaker 2>And it starts in school because the system tries to

806
00:43:57.599 --> 00:44:00.719
<v Speaker 2>rank students. But then we get into this this frame

807
00:44:00.760 --> 00:44:03.280
<v Speaker 2>of mind where everything has to be ranked by a number.

808
00:44:03.639 --> 00:44:06.440
<v Speaker 2>And it might sound funny because I'm a mathematician. I'm

809
00:44:06.440 --> 00:44:10.519
<v Speaker 2>saying shouldn't rank things point number anymore, but tays in

810
00:44:10.559 --> 00:44:13.440
<v Speaker 2>point is that at the School of the Art Institute

811
00:44:13.559 --> 00:44:17.199
<v Speaker 2>where I teach, we don't have grades, and so there

812
00:44:17.239 --> 00:44:20.360
<v Speaker 2>is an understanding that we are not trying to rank

813
00:44:20.400 --> 00:44:23.880
<v Speaker 2>everybody by a gping because there are no grades, and

814
00:44:23.960 --> 00:44:26.400
<v Speaker 2>I just think that's wonderful, so we can focus on

815
00:44:26.719 --> 00:44:28.320
<v Speaker 2>educating rather than ranking.

816
00:44:28.559 --> 00:44:30.239
<v Speaker 1>For more in this you can see the twenty twenty

817
00:44:30.280 --> 00:44:34.239
<v Speaker 1>one paper grade Less Learning, The Effect of Eliminating Traditional

818
00:44:34.239 --> 00:44:38.239
<v Speaker 1>grading practices on Student Engagement and Learning, which notes that

819
00:44:38.360 --> 00:44:42.000
<v Speaker 1>throughout their study, it became clear that students want to learn.

820
00:44:42.320 --> 00:44:45.119
<v Speaker 1>Accurate feedback is a vital part of the learning process,

821
00:44:45.239 --> 00:44:48.440
<v Speaker 1>it says, but grades are not. The traditional grading system

822
00:44:48.559 --> 00:44:51.840
<v Speaker 1>pits students and teachers against one another, often leading to

823
00:44:51.880 --> 00:44:56.199
<v Speaker 1>either side bickering over fractions of percentage points, which I

824
00:44:56.199 --> 00:44:59.039
<v Speaker 1>guess is applied mathematics. But I don't think that's the

825
00:44:59.119 --> 00:45:02.199
<v Speaker 1>lesson here, and I wanted to ask a little bit

826
00:45:02.239 --> 00:45:04.880
<v Speaker 1>about some basics for people who maybe are not math majors.

827
00:45:04.920 --> 00:45:11.920
<v Speaker 1>But when things go from numerical to letters, we're in

828
00:45:12.119 --> 00:45:16.519
<v Speaker 1>the learning process of math, from like arithmetic to pre

829
00:45:16.559 --> 00:45:20.039
<v Speaker 1>algebra to algebra to precalculus to calculus, Like where do

830
00:45:20.159 --> 00:45:26.760
<v Speaker 1>things start turning from numbers into letters? Why does that happen? Oh?

831
00:45:26.760 --> 00:45:28.360
<v Speaker 2>Thank you? That is one of the questions that I

832
00:45:28.400 --> 00:45:30.280
<v Speaker 2>address in the book because it is something people say

833
00:45:30.320 --> 00:45:32.559
<v Speaker 2>to me a lot like. And so we're not with

834
00:45:32.639 --> 00:45:36.039
<v Speaker 2>kind into letters exactly, and so we're thinking about the

835
00:45:36.079 --> 00:45:38.760
<v Speaker 2>idea of a person, and so we don't name them

836
00:45:38.800 --> 00:45:40.960
<v Speaker 2>because we don't know who they are, and so that's

837
00:45:40.960 --> 00:45:43.239
<v Speaker 2>why we do that with numbers as well. It's possible.

838
00:45:43.239 --> 00:45:47.239
<v Speaker 2>But I also introduced it like a murder mystery where

839
00:45:47.559 --> 00:45:49.360
<v Speaker 2>someone is a murderer and you're trying to find out

840
00:45:49.400 --> 00:45:50.960
<v Speaker 2>who they are, but you can't refer to them by

841
00:45:51.000 --> 00:45:53.679
<v Speaker 2>naming it because you don't know who they are, a

842
00:45:53.679 --> 00:45:55.679
<v Speaker 2>whole load of evidence about them and then you pin

843
00:45:55.760 --> 00:45:59.360
<v Speaker 2>them down and go ah ah. It was actually changed

844
00:46:00.599 --> 00:46:02.239
<v Speaker 2>or often in math, we're trying to find out what

845
00:46:02.320 --> 00:46:05.360
<v Speaker 2>something is, but we don't know what it is yet,

846
00:46:05.440 --> 00:46:07.280
<v Speaker 2>so how can we refer to it? So we use

847
00:46:07.280 --> 00:46:09.960
<v Speaker 2>something like a pronoun, but it's a letter because that's

848
00:46:10.000 --> 00:46:12.760
<v Speaker 2>what we do in math instead of a pronoun, And

849
00:46:12.800 --> 00:46:15.480
<v Speaker 2>then we gather evidence about it and so we say, oh, well,

850
00:46:15.519 --> 00:46:17.840
<v Speaker 2>it's related to this other thing like this, and when

851
00:46:17.840 --> 00:46:19.920
<v Speaker 2>we do this to it, it behaves like that, and

852
00:46:19.920 --> 00:46:21.840
<v Speaker 2>when we do this to it. So it's like twenty questions.

853
00:46:21.840 --> 00:46:23.440
<v Speaker 2>You say, what happens when you do this? What happens

854
00:46:23.480 --> 00:46:25.000
<v Speaker 2>when you do this to it? And then you find

855
00:46:25.039 --> 00:46:28.760
<v Speaker 2>all these relationships. And so that's what solving equations is about.

856
00:46:28.840 --> 00:46:30.840
<v Speaker 2>It's about putting that thing, you don't know what it

857
00:46:30.880 --> 00:46:34.079
<v Speaker 2>is yet, into a relationship where you found out various

858
00:46:34.119 --> 00:46:37.000
<v Speaker 2>aspects of its behavior. And now you find out now

859
00:46:37.039 --> 00:46:40.679
<v Speaker 2>you can pin down what that thing actually is. And

860
00:46:40.800 --> 00:46:43.599
<v Speaker 2>that is the point of using letters, and that is

861
00:46:43.679 --> 00:46:47.360
<v Speaker 2>the point of solving equations. It really is like a

862
00:46:47.480 --> 00:46:50.000
<v Speaker 2>murder and mystery. So anyone who enjoys any kind of

863
00:46:50.119 --> 00:46:52.960
<v Speaker 2>murder mystery, I think that that's I think it's math.

864
00:46:53.280 --> 00:46:55.800
<v Speaker 1>One thing that does not embarrass me is asking really

865
00:46:55.840 --> 00:46:57.920
<v Speaker 1>basic questions for me and for the good of all

866
00:46:57.960 --> 00:47:00.480
<v Speaker 1>of us, such as, what is the difference between a

867
00:47:00.519 --> 00:47:04.000
<v Speaker 1>logarithm and an algorithm? They sound alike, are they friends?

868
00:47:04.360 --> 00:47:07.559
<v Speaker 2>A logarithm is very different from an algorithm. Okay, A

869
00:47:07.559 --> 00:47:12.519
<v Speaker 2>logarithm is a particular function, and it I'm now doing

870
00:47:12.519 --> 00:47:16.159
<v Speaker 2>hand motions that doesn't help on an audio. So the

871
00:47:16.280 --> 00:47:19.360
<v Speaker 2>graph of a logarithm, it starts down at infinity and

872
00:47:19.440 --> 00:47:22.280
<v Speaker 2>it goes up really fast, and then it tails off.

873
00:47:22.480 --> 00:47:24.599
<v Speaker 2>So it's kind of like the opposite of an exponential

874
00:47:24.639 --> 00:47:26.719
<v Speaker 2>so much so that it actually is the opposite of

875
00:47:26.800 --> 00:47:30.280
<v Speaker 2>an exponential, So it's the inverse of an exponential function,

876
00:47:30.760 --> 00:47:34.360
<v Speaker 2>and so that tails off as it goes along. That's

877
00:47:34.360 --> 00:47:38.480
<v Speaker 2>completely different from an algorithm. So an algorithm is a

878
00:47:38.519 --> 00:47:42.320
<v Speaker 2>method for doing something, and it's a particular form of method,

879
00:47:42.400 --> 00:47:46.360
<v Speaker 2>like a really really step by step recipe, the step

880
00:47:46.360 --> 00:47:49.440
<v Speaker 2>by step process that you could tell a computer to do. So,

881
00:47:49.519 --> 00:47:53.480
<v Speaker 2>for example, the dreaded long multiplication is an algorithm. It's

882
00:47:53.519 --> 00:47:57.360
<v Speaker 2>a step by step process whereby you can follow these

883
00:47:57.440 --> 00:48:01.559
<v Speaker 2>steps and multiply large numbers together by following the steps

884
00:48:01.599 --> 00:48:04.480
<v Speaker 2>all the way through. But the algorithm says, if this happens,

885
00:48:04.480 --> 00:48:06.559
<v Speaker 2>to do that, now, if this happens to do that now,

886
00:48:06.639 --> 00:48:09.960
<v Speaker 2>it's like flow chart. And so that's not really math.

887
00:48:10.119 --> 00:48:12.039
<v Speaker 2>And that's why I say that we don't really need

888
00:48:12.079 --> 00:48:14.679
<v Speaker 2>long malved creation anymore, because it's an algorithm. It's a

889
00:48:14.719 --> 00:48:17.599
<v Speaker 2>handy algorithm for doing something, but it's not really math.

890
00:48:17.840 --> 00:48:20.599
<v Speaker 2>And when people say, the algorithm. Are you're talking about

891
00:48:20.639 --> 00:48:21.639
<v Speaker 2>the Internet.

892
00:48:21.800 --> 00:48:25.119
<v Speaker 1>Yeah, the algorithm is showing my videos, or the algorithm

893
00:48:25.159 --> 00:48:27.800
<v Speaker 1>wants me to listen to the new Yes.

894
00:48:27.960 --> 00:48:31.760
<v Speaker 2>Right, So that's a particular Really, it's a particular algorithm

895
00:48:31.840 --> 00:48:35.880
<v Speaker 2>that the Internet, or most places we interact with it

896
00:48:35.920 --> 00:48:39.159
<v Speaker 2>on the Internet, use some process for deciding how to

897
00:48:39.199 --> 00:48:42.119
<v Speaker 2>show you something next. And it's a bit murky exactly

898
00:48:42.119 --> 00:48:45.559
<v Speaker 2>what their process is, and that many people think that

899
00:48:45.599 --> 00:48:48.519
<v Speaker 2>there's something nefarious going on behind it, which there probably is,

900
00:48:49.000 --> 00:48:52.639
<v Speaker 2>and it's probably based on money. So they have applied

901
00:48:52.719 --> 00:48:55.320
<v Speaker 2>some step by step algorithm, and that one really is

902
00:48:55.400 --> 00:48:59.760
<v Speaker 2>implemented by computer to say, based on this person's previous activity,

903
00:49:00.280 --> 00:49:03.400
<v Speaker 2>follow these steps and show them this next thing. That's

904
00:49:03.480 --> 00:49:06.599
<v Speaker 2>kind of capital T capital a the algorithm.

905
00:49:06.920 --> 00:49:09.920
<v Speaker 1>So this is the math that expertly hooks us with

906
00:49:10.039 --> 00:49:15.480
<v Speaker 1>engaging but ultimately never satisfying, and infinity like scroll of content,

907
00:49:15.840 --> 00:49:19.360
<v Speaker 1>just harvesting our tastes and churning out more like it

908
00:49:19.400 --> 00:49:23.000
<v Speaker 1>back with this boggling speed. Now Twitter looks at half

909
00:49:23.039 --> 00:49:26.559
<v Speaker 1>a billion tweets every day and then decides exactly what

910
00:49:26.679 --> 00:49:30.440
<v Speaker 1>to show you. And one article titled the TikTok Algorithm

911
00:49:30.599 --> 00:49:33.079
<v Speaker 1>knew my sexuality better than I did. Pretty much says

912
00:49:33.079 --> 00:49:35.840
<v Speaker 1>it all. So we cover more of this in Yes,

913
00:49:35.920 --> 00:49:39.719
<v Speaker 1>the tic Tocology episode with your favorite sycomer on there,

914
00:49:40.000 --> 00:49:42.000
<v Speaker 1>mister Hank Green, and yeah, we will link that in

915
00:49:42.000 --> 00:49:42.599
<v Speaker 1>the show notes.

916
00:49:42.840 --> 00:49:47.119
<v Speaker 2>There are many other algorithms algorithms, and sometimes algorithms are

917
00:49:47.119 --> 00:49:52.760
<v Speaker 2>great because they help us conserve our brain energy. And

918
00:49:52.880 --> 00:49:55.800
<v Speaker 2>I think that's really important because our brains are finite

919
00:49:56.360 --> 00:49:59.679
<v Speaker 2>and very puny, and so if we can concert that

920
00:50:00.159 --> 00:50:03.280
<v Speaker 2>as much as possible, that's really helpful. So I personally

921
00:50:03.320 --> 00:50:07.199
<v Speaker 2>have all sorts of algorithms for helping me run my life.

922
00:50:07.400 --> 00:50:09.119
<v Speaker 2>And this may be me as a math magician speaking,

923
00:50:09.159 --> 00:50:11.000
<v Speaker 2>but it's because I don't want to use up my

924
00:50:11.119 --> 00:50:13.840
<v Speaker 2>brain energy on something that's kind of irrelevant.

925
00:50:14.079 --> 00:50:16.400
<v Speaker 1>What do you have? Yeah, tell me, tell me? Tell me?

926
00:50:16.760 --> 00:50:19.679
<v Speaker 2>For example, I have algorithms for where I buy more coffee.

927
00:50:19.760 --> 00:50:23.840
<v Speaker 2>For example, Okay, tell me everything. So I buy five

928
00:50:23.840 --> 00:50:27.079
<v Speaker 2>pound bags of beans, but then I keep a pot

929
00:50:27.400 --> 00:50:29.960
<v Speaker 2>of them on the counter, So I refill the pot

930
00:50:30.000 --> 00:50:33.159
<v Speaker 2>on the counter from the bag of beans, and then

931
00:50:33.239 --> 00:50:36.119
<v Speaker 2>once the last bit of the bag of beans has

932
00:50:36.159 --> 00:50:38.800
<v Speaker 2>filled the pot, then I immediately buy another bag of beans.

933
00:50:38.880 --> 00:50:40.280
<v Speaker 2>So that it's ready by the time I get to

934
00:50:40.280 --> 00:50:42.440
<v Speaker 2>the end of the pot, and I don't have to

935
00:50:42.440 --> 00:50:44.159
<v Speaker 2>think about that. Now, maybe one day I can have

936
00:50:44.199 --> 00:50:47.480
<v Speaker 2>a smart coffee bean pot which will automatically order it

937
00:50:47.599 --> 00:50:50.159
<v Speaker 2>for me. But that is my algorithm for coffee beans.

938
00:50:50.400 --> 00:50:52.719
<v Speaker 1>I love that those are algorithms. Can you tell me

939
00:50:52.760 --> 00:50:56.519
<v Speaker 1>some other places where we don't realize there's math just

940
00:50:56.599 --> 00:50:59.840
<v Speaker 1>everywhere I know a video going viral. I know you've

941
00:50:59.880 --> 00:51:05.639
<v Speaker 1>seen sine waves in your wraps and rado. There's math

942
00:51:05.719 --> 00:51:09.679
<v Speaker 1>in braids and halla. Where are some of the unexpected

943
00:51:09.679 --> 00:51:12.719
<v Speaker 1>places where math is like really making our lives amazing.

944
00:51:13.239 --> 00:51:18.079
<v Speaker 2>Well, one thing that I do when I'm walking across Chicago,

945
00:51:18.119 --> 00:51:21.039
<v Speaker 2>which is on a grid, is that thing where I

946
00:51:21.119 --> 00:51:23.480
<v Speaker 2>walk in one direction until I hit a stop sign,

947
00:51:23.559 --> 00:51:26.440
<v Speaker 2>and so if I don't get a crosswalk the light

948
00:51:26.519 --> 00:51:28.960
<v Speaker 2>on the crosswalk, then I turn and take the crosswalk

949
00:51:29.000 --> 00:51:30.760
<v Speaker 2>going the other way, and then I keep going in

950
00:51:30.800 --> 00:51:33.760
<v Speaker 2>that direction until So that's my algorithm for walking across Chicago,

951
00:51:34.119 --> 00:51:36.719
<v Speaker 2>And there's some math in there that's telling us that

952
00:51:37.079 --> 00:51:39.519
<v Speaker 2>wherever we turn it doesn't matter. So if I need

953
00:51:39.599 --> 00:51:42.239
<v Speaker 2>to go five blocks east and ten blocks north, then

954
00:51:42.280 --> 00:51:44.880
<v Speaker 2>it doesn't matter where I turn, it will still be

955
00:51:44.920 --> 00:51:47.159
<v Speaker 2>the same distance of walking, as long as I consider

956
00:51:47.199 --> 00:51:51.039
<v Speaker 2>that turning doesn't exhaust me. And that's actually a part

957
00:51:51.400 --> 00:51:56.039
<v Speaker 2>of metrics spaces, and so a metric is a more

958
00:51:56.079 --> 00:51:59.480
<v Speaker 2>general form of distance. And we think about distance usually

959
00:51:59.480 --> 00:52:02.519
<v Speaker 2>as distance as the crow flies, but you don't fly

960
00:52:02.639 --> 00:52:05.119
<v Speaker 2>like a crow when you're walking across Chicago. There are

961
00:52:05.119 --> 00:52:08.119
<v Speaker 2>buildings in the way, and so the distance we actually

962
00:52:08.159 --> 00:52:10.400
<v Speaker 2>need to go to get somewhere is not the distance

963
00:52:10.400 --> 00:52:13.000
<v Speaker 2>of the crow flies. It's the distance along in this grid.

964
00:52:13.559 --> 00:52:16.320
<v Speaker 2>And so we need to know that it doesn't matter,

965
00:52:16.599 --> 00:52:20.559
<v Speaker 2>it doesn't matter where we turn, and that's intuitively kind

966
00:52:20.559 --> 00:52:24.679
<v Speaker 2>of clear, right, And then you can do things like say,

967
00:52:25.239 --> 00:52:28.440
<v Speaker 2>what's a circle if we're using this form of distance,

968
00:52:28.960 --> 00:52:32.920
<v Speaker 2>because a circle doesn't quite look like a circle anymore.

969
00:52:33.400 --> 00:52:36.199
<v Speaker 2>It looks more like a diamond shape. But that counts

970
00:52:36.199 --> 00:52:39.320
<v Speaker 2>as a circle because it's all the points that are

971
00:52:39.360 --> 00:52:43.039
<v Speaker 2>four blocks away from you. And I think that's kind

972
00:52:43.079 --> 00:52:48.679
<v Speaker 2>of hilarious because I like things that challenge the received wisdom,

973
00:52:49.000 --> 00:52:51.440
<v Speaker 2>which makes me sound like a pointless rebel, but I

974
00:52:51.559 --> 00:52:55.039
<v Speaker 2>like to a point full rebel because maths about not

975
00:52:55.119 --> 00:52:58.559
<v Speaker 2>making assumptions that you don't need to make, and I

976
00:52:58.599 --> 00:53:01.519
<v Speaker 2>think that that's really important life as well, because a

977
00:53:01.559 --> 00:53:03.679
<v Speaker 2>lot of the problems with society come from people making

978
00:53:03.719 --> 00:53:06.480
<v Speaker 2>assumptions about other people that you don't need to make.

979
00:53:06.760 --> 00:53:09.239
<v Speaker 2>Which doesn't mean we shouldn't make any assumptions about people,

980
00:53:09.280 --> 00:53:12.360
<v Speaker 2>because actually that's impossible. As soon as we meet someone,

981
00:53:12.480 --> 00:53:14.199
<v Speaker 2>we have to start somewhere, and so we have to

982
00:53:14.239 --> 00:53:17.440
<v Speaker 2>have an instinctive, intuitive, gut response to them. But the

983
00:53:17.599 --> 00:53:20.000
<v Speaker 2>really important thing is to be ready to change it

984
00:53:20.679 --> 00:53:24.360
<v Speaker 2>when we get new information, and math is really about that.

985
00:53:24.519 --> 00:53:26.239
<v Speaker 2>You can be aware you made them so that if

986
00:53:26.280 --> 00:53:28.079
<v Speaker 2>they turn out not to be right, you can change

987
00:53:28.119 --> 00:53:29.480
<v Speaker 2>them and then get a different result.

988
00:53:30.800 --> 00:53:34.719
<v Speaker 1>It seems like once you embrace math, you understand that

989
00:53:34.760 --> 00:53:37.800
<v Speaker 1>it can be very empowering and that could offer a

990
00:53:37.840 --> 00:53:39.039
<v Speaker 1>lot of clarity.

991
00:53:39.559 --> 00:53:41.320
<v Speaker 2>That is certainly what I think. So if that's the

992
00:53:41.360 --> 00:53:44.119
<v Speaker 2>impression I've given you, that's fantastic. And I think I

993
00:53:44.280 --> 00:53:46.480
<v Speaker 2>just realized I don't think I really addressed the part

994
00:53:46.519 --> 00:53:48.840
<v Speaker 2>of your question earlier where you said why are people

995
00:53:48.880 --> 00:53:50.880
<v Speaker 2>so put off it and afraid of it? And this

996
00:53:51.000 --> 00:53:53.199
<v Speaker 2>is what makes me sad, because I think it's there

997
00:53:53.239 --> 00:53:55.800
<v Speaker 2>to help us, and I think that it's not presented

998
00:53:55.880 --> 00:53:57.039
<v Speaker 2>like that enough.

999
00:53:57.159 --> 00:53:59.480
<v Speaker 1>Mm hmm, okay, I have some questions from listeners. They

1000
00:53:59.480 --> 00:54:02.119
<v Speaker 1>know that you secifically are coming on. But first let's

1001
00:54:02.199 --> 00:54:05.000
<v Speaker 1>raise the bottom line of a cause of the ologist choosing.

1002
00:54:05.000 --> 00:54:09.360
<v Speaker 1>And Eugenia pointed us toward Math Circles of Chicago dot org,

1003
00:54:09.519 --> 00:54:13.400
<v Speaker 1>whose mission statement says, we offer engaging, flexible and free

1004
00:54:13.440 --> 00:54:16.519
<v Speaker 1>math programs to students in grades three through twelve and

1005
00:54:16.559 --> 00:54:20.199
<v Speaker 1>focus on reaching black and Latino communities and other communities

1006
00:54:20.199 --> 00:54:22.960
<v Speaker 1>where most children live in low income households. You can

1007
00:54:23.000 --> 00:54:25.760
<v Speaker 1>find out more at Math Circles of Chicago dot org

1008
00:54:25.840 --> 00:54:27.760
<v Speaker 1>and that will be linked in the show notes. And

1009
00:54:27.800 --> 00:54:31.840
<v Speaker 1>that donation was made possible by sponsors of ologies. All right,

1010
00:54:32.000 --> 00:54:36.440
<v Speaker 1>let's divide and conquer your queries. One wonderful one that

1011
00:54:36.559 --> 00:54:39.199
<v Speaker 1>was asked by Mallory Skinner at doug Pace. Matty s,

1012
00:54:39.679 --> 00:54:45.159
<v Speaker 1>Talia Dunyak, Emily Stauffer, Devin Naples, Devin s As separately

1013
00:54:45.880 --> 00:54:49.400
<v Speaker 1>all asked this similar question. Oh wow, I want to know,

1014
00:54:49.599 --> 00:54:52.480
<v Speaker 1>please explain infinity in a way that my brain can

1015
00:54:52.599 --> 00:54:54.679
<v Speaker 1>really comprehend.

1016
00:54:55.920 --> 00:54:59.480
<v Speaker 2>Well, you know, infinity is really difficult, and so if

1017
00:54:59.480 --> 00:55:02.599
<v Speaker 2>you're bra if you feel like your brain isn't comprehending it,

1018
00:55:02.679 --> 00:55:07.679
<v Speaker 2>then maybe it is well wown. It's supposed to be

1019
00:55:07.800 --> 00:55:11.400
<v Speaker 2>mind blowing. If people who think they understand infinity are

1020
00:55:11.480 --> 00:55:15.599
<v Speaker 2>kind of just deluded, so and so I think that

1021
00:55:16.000 --> 00:55:19.800
<v Speaker 2>the correct feeling is to feel like it's too mind

1022
00:55:19.880 --> 00:55:21.880
<v Speaker 2>boggling to get your head around. That's the whole point

1023
00:55:21.920 --> 00:55:24.000
<v Speaker 2>of it. It's bigger than anything that we can think of.

1024
00:55:24.079 --> 00:55:27.719
<v Speaker 2>It behaves in really weird ways. And I think what

1025
00:55:27.960 --> 00:55:33.239
<v Speaker 2>often makes some people mathematicians and some people mathphobic is

1026
00:55:33.719 --> 00:55:38.239
<v Speaker 2>embracing the feeling of not understanding something, rather than taking

1027
00:55:38.239 --> 00:55:40.840
<v Speaker 2>it as a sign you're bad, taking it as a

1028
00:55:40.880 --> 00:55:43.880
<v Speaker 2>sign that there's something really interesting going on. If you

1029
00:55:43.960 --> 00:55:46.519
<v Speaker 2>go to the edge of a cliff. I don't like

1030
00:55:46.599 --> 00:55:48.719
<v Speaker 2>looking over the edge of a cliff because I'm worried

1031
00:55:48.760 --> 00:55:51.519
<v Speaker 2>I will fall and die. And I think that there's

1032
00:55:51.559 --> 00:55:53.960
<v Speaker 2>a similar kind of vertigo that sometimes people get when

1033
00:55:54.000 --> 00:55:57.920
<v Speaker 2>thinking about math concepts. And people have been so humiliated

1034
00:55:57.960 --> 00:56:01.480
<v Speaker 2>and traumatized by their past math experience that it feels

1035
00:56:01.599 --> 00:56:04.440
<v Speaker 2>like it's they're going to get hurt if they look

1036
00:56:04.519 --> 00:56:07.199
<v Speaker 2>over that cliff. And what I want to say is

1037
00:56:07.199 --> 00:56:10.320
<v Speaker 2>that you're not going to die anyway. By looking over

1038
00:56:10.360 --> 00:56:14.679
<v Speaker 2>the mathematical cliff, you might get some emotions dug up

1039
00:56:14.800 --> 00:56:18.719
<v Speaker 2>from some past negative experiences. But the good thing is

1040
00:56:18.760 --> 00:56:21.639
<v Speaker 2>that you won't physically die by looking over the math cliff.

1041
00:56:21.920 --> 00:56:24.400
<v Speaker 2>And the thing that's over the math cliff is something

1042
00:56:24.400 --> 00:56:29.239
<v Speaker 2>that maybe kind of gives you intellectual vertigo. I don't

1043
00:56:29.320 --> 00:56:32.360
<v Speaker 2>run away from those things, and I think that's the

1044
00:56:32.440 --> 00:56:34.840
<v Speaker 2>only difference. It's not that I'm better at it or something.

1045
00:56:34.880 --> 00:56:38.960
<v Speaker 2>It's just that I have decided that I'm interested in it,

1046
00:56:39.239 --> 00:56:40.880
<v Speaker 2>and that it's not a sign that I'm bad at it.

1047
00:56:40.920 --> 00:56:43.360
<v Speaker 2>If I don't understand it, I don't understand anything. If

1048
00:56:43.400 --> 00:56:45.960
<v Speaker 2>I think about it hard enough. The number one? What

1049
00:56:46.159 --> 00:56:49.639
<v Speaker 2>even is that I can't understand the number one. If

1050
00:56:49.639 --> 00:56:51.639
<v Speaker 2>I don't understand the number one, how am I going

1051
00:56:51.719 --> 00:56:54.840
<v Speaker 2>to understand infinity? But that's what drives us to do

1052
00:56:54.920 --> 00:56:58.000
<v Speaker 2>more research. It's the feeling that there is always more

1053
00:56:58.079 --> 00:57:01.119
<v Speaker 2>there to understand, and we want to understand it. We

1054
00:57:01.159 --> 00:57:03.280
<v Speaker 2>don't go, oh, I can't understand this. We go, oh,

1055
00:57:03.360 --> 00:57:06.840
<v Speaker 2>I want to understand more. I'm never going to understand

1056
00:57:06.880 --> 00:57:08.599
<v Speaker 2>all of it, but that doesn't mean I'm going to

1057
00:57:08.599 --> 00:57:11.000
<v Speaker 2>give up. I'm just going to keep trying to understand

1058
00:57:11.000 --> 00:57:12.239
<v Speaker 2>more all the time I can.

1059
00:57:12.519 --> 00:57:15.639
<v Speaker 1>Some people call this a growth versus a fixed mindset,

1060
00:57:15.719 --> 00:57:19.320
<v Speaker 1>and fixed mindsets tend to be afraid to try and fail.

1061
00:57:19.800 --> 00:57:22.960
<v Speaker 1>The growth is like, you know, whatever happens. I learned

1062
00:57:22.960 --> 00:57:27.119
<v Speaker 1>some and from personal experience. Two of the smartest people

1063
00:57:27.159 --> 00:57:31.719
<v Speaker 1>I've ever encountered, my friends, doctors Casey Handmer and Christine Corbett,

1064
00:57:31.920 --> 00:57:36.320
<v Speaker 1>have worked at NASA. Casey now heads Terraform Industries, working

1065
00:57:36.360 --> 00:57:39.280
<v Speaker 1>on these new ways to capture atmospheric carbon and turn

1066
00:57:39.360 --> 00:57:42.239
<v Speaker 1>it into natural gas. Then one thing about the two

1067
00:57:42.280 --> 00:57:44.679
<v Speaker 1>of them, and they're merrit, is that they just try stuff.

1068
00:57:44.840 --> 00:57:47.239
<v Speaker 1>They want to learn something, they just dive right in.

1069
00:57:47.599 --> 00:57:51.119
<v Speaker 1>As a result, doctor Corbett has an extra master's in

1070
00:57:51.239 --> 00:57:54.159
<v Speaker 1>creative writing and just got a black belt in kung fu.

1071
00:57:54.599 --> 00:57:58.639
<v Speaker 1>They are smart people who ask smart people sometimes basic questions.

1072
00:57:58.719 --> 00:58:01.199
<v Speaker 1>And Casey once told me the key to how much

1073
00:58:01.239 --> 00:58:03.880
<v Speaker 1>they get done is that they just learn shamelessly from

1074
00:58:03.920 --> 00:58:06.280
<v Speaker 1>any failure they get it, they keep moving. So they

1075
00:58:06.320 --> 00:58:09.199
<v Speaker 1>are heroes. They are not zeros. Oh, which reminds me

1076
00:58:09.320 --> 00:58:12.400
<v Speaker 1>that Brennett had a question on that note. Jenny Lowl Rhodes,

1077
00:58:12.519 --> 00:58:17.320
<v Speaker 1>Maggie Morgan, Star, Lilian Right, Christine Fixteine, Megsi, Lily Hagadon,

1078
00:58:17.519 --> 00:58:21.159
<v Speaker 1>and Brenna Pixley. I'll have questions about zero. Jenny wants

1079
00:58:21.239 --> 00:58:24.719
<v Speaker 1>to know how long has zero been a thing? Maggie's like,

1080
00:58:24.920 --> 00:58:26.000
<v Speaker 1>is zero a number?

1081
00:58:26.360 --> 00:58:29.440
<v Speaker 2>Great questions. I do know that it has troubled people

1082
00:58:30.000 --> 00:58:32.400
<v Speaker 2>for thousands of years about whether it really ought to

1083
00:58:32.400 --> 00:58:35.199
<v Speaker 2>count as a number or not. My recollection is that

1084
00:58:35.559 --> 00:58:39.480
<v Speaker 2>maybe the Greeks or the Romans one or the other,

1085
00:58:39.719 --> 00:58:43.840
<v Speaker 2>or maybe both that were really unconvinced that zero should

1086
00:58:43.840 --> 00:58:46.880
<v Speaker 2>count as the number philosophically, it really bothers them, and

1087
00:58:46.920 --> 00:58:50.639
<v Speaker 2>that really helped them back, because here's the thing. You

1088
00:58:50.679 --> 00:58:53.360
<v Speaker 2>can decide whether you want zero to count as a

1089
00:58:53.440 --> 00:58:56.519
<v Speaker 2>number or not, but the question is how does it

1090
00:58:56.599 --> 00:58:58.920
<v Speaker 2>help us? There are often no right and wrong answers

1091
00:58:58.920 --> 00:59:01.760
<v Speaker 2>to these things. Meticians say, Okay, here's a world in

1092
00:59:01.800 --> 00:59:03.679
<v Speaker 2>which this thing is true, and here's a different world

1093
00:59:03.760 --> 00:59:05.800
<v Speaker 2>in which something else is true. Which one is going

1094
00:59:05.800 --> 00:59:08.000
<v Speaker 2>to help us? So we can make a world in

1095
00:59:08.039 --> 00:59:10.639
<v Speaker 2>which zero isn't a number, We're not going to be

1096
00:59:10.679 --> 00:59:13.360
<v Speaker 2>able to do very much there. Zero is a really

1097
00:59:13.400 --> 00:59:17.159
<v Speaker 2>helpful number to have around because if we're going to

1098
00:59:17.320 --> 00:59:20.320
<v Speaker 2>represent nothing, what are we going to represent it with

1099
00:59:20.400 --> 00:59:23.559
<v Speaker 2>if we subtract five from five, what do we get

1100
00:59:23.840 --> 00:59:25.840
<v Speaker 2>If we don't have a number called zero, we can't

1101
00:59:25.880 --> 00:59:29.119
<v Speaker 2>do that, and then we can't really make negative numbers either.

1102
00:59:29.199 --> 00:59:31.159
<v Speaker 2>If we can't make negative numbers, there are all sorts

1103
00:59:31.159 --> 00:59:33.719
<v Speaker 2>of things we can't do. And so if we do

1104
00:59:33.840 --> 00:59:36.320
<v Speaker 2>call zero a number, then we do get to do

1105
00:59:36.400 --> 00:59:39.719
<v Speaker 2>all these things. And so that's why mathematicians generally have

1106
00:59:39.840 --> 00:59:42.400
<v Speaker 2>decided that zero should get to count as a number,

1107
00:59:42.679 --> 00:59:44.639
<v Speaker 2>just so that we can do all of those things.

1108
00:59:44.920 --> 00:59:48.840
<v Speaker 2>It's just language. So as long as we can manipulate

1109
00:59:48.960 --> 00:59:51.920
<v Speaker 2>zero in some way, we can get to do those things.

1110
00:59:52.280 --> 00:59:54.360
<v Speaker 2>If you feel like you don't want to call it

1111
00:59:54.400 --> 00:59:57.559
<v Speaker 2>a number, then that's fine, don't call it a number,

1112
00:59:57.639 --> 00:59:59.800
<v Speaker 2>as long as you can still manipulate it in those ways,

1113
01:00:00.039 --> 01:00:01.800
<v Speaker 2>because it's really helpful to do it.

1114
01:00:02.199 --> 01:00:05.039
<v Speaker 1>So zero we can wrap our brains around that. Some

1115
01:00:05.079 --> 01:00:08.000
<v Speaker 1>of you had a weirder concept plaguing you, such as

1116
01:00:08.000 --> 01:00:11.920
<v Speaker 1>Anna Thompson, Jennifer Lemon, Ariel van Sand, Christina kuns, Eleanora

1117
01:00:12.039 --> 01:00:15.639
<v Speaker 1>Renaud Vanville, c J. Wyatt, Tony Vessels, Sarah val McKelvey,

1118
01:00:15.760 --> 01:00:18.639
<v Speaker 1>Felicia Chandler, Valerie Bertha and first time question asker build

1119
01:00:18.679 --> 01:00:22.920
<v Speaker 1>a branch, and Christina Kuhns asks imaginary numbers? What the fuck?

1120
01:00:23.360 --> 01:00:26.559
<v Speaker 1>What is the imaginar number? What's going on?

1121
01:00:26.719 --> 01:00:28.639
<v Speaker 2>Yeah, this is great and this is a great thing

1122
01:00:28.719 --> 01:00:31.159
<v Speaker 2>to say after is zero a number? Because sometimes people

1123
01:00:31.199 --> 01:00:35.039
<v Speaker 2>go are imagining numbers and number So magnaticians really don't

1124
01:00:35.119 --> 01:00:38.119
<v Speaker 2>like having rules impose on them. And it makes me

1125
01:00:38.199 --> 01:00:39.960
<v Speaker 2>sad that one of the things that puts people off

1126
01:00:40.039 --> 01:00:41.840
<v Speaker 2>math is that there seems to be all of these

1127
01:00:41.880 --> 01:00:44.920
<v Speaker 2>rules that you have to follow, whereas math magicians go, wait, okay,

1128
01:00:45.159 --> 01:00:48.400
<v Speaker 2>those rules. We had to follow those rules in this world,

1129
01:00:48.400 --> 01:00:50.159
<v Speaker 2>but I don't want to follow them anymore. Can I

1130
01:00:50.239 --> 01:00:52.480
<v Speaker 2>build a different world in which I don't have to

1131
01:00:52.480 --> 01:00:55.400
<v Speaker 2>follow those rules? And so one of the rules mathematicians

1132
01:00:55.400 --> 01:00:57.119
<v Speaker 2>don't like having to follow, and I do talk about

1133
01:00:57.119 --> 01:00:59.719
<v Speaker 2>this in the book, is you can't take the square

1134
01:00:59.800 --> 01:01:02.480
<v Speaker 2>root of a negative number. Well, why can't you take

1135
01:01:02.519 --> 01:01:05.440
<v Speaker 2>the square to a negative number, because if you try

1136
01:01:05.480 --> 01:01:09.079
<v Speaker 2>squaring numbers, square routing is sort of the opposite of squaring, right,

1137
01:01:09.119 --> 01:01:11.559
<v Speaker 2>So you're saying, is there any number such that when

1138
01:01:11.599 --> 01:01:14.320
<v Speaker 2>I multiply it by itself, I get negative one? Well,

1139
01:01:14.400 --> 01:01:17.039
<v Speaker 2>let's think about that. If I multiply a positive number

1140
01:01:17.039 --> 01:01:20.199
<v Speaker 2>by itself, I get a positive number. If I multiply

1141
01:01:20.280 --> 01:01:23.760
<v Speaker 2>a negative number by itself, I also get a positive number.

1142
01:01:23.960 --> 01:01:25.719
<v Speaker 3>You are employing a double negative.

1143
01:01:25.920 --> 01:01:28.280
<v Speaker 2>So we seem to be out of options for things.

1144
01:01:28.280 --> 01:01:31.280
<v Speaker 2>We could multiply by themselves and get a negative number,

1145
01:01:31.639 --> 01:01:35.280
<v Speaker 2>but mathematicians go, never mind, I'll just make something up

1146
01:01:35.360 --> 01:01:39.400
<v Speaker 2>and someone else. And so it's called an imaginary number

1147
01:01:39.400 --> 01:01:42.199
<v Speaker 2>because we sort of just imagined it. And the wonderful

1148
01:01:42.199 --> 01:01:45.400
<v Speaker 2>thing about abstract concepts is as soon as you imagine them,

1149
01:01:46.079 --> 01:01:50.119
<v Speaker 2>they become something that exists because it's an abstract concept.

1150
01:01:50.440 --> 01:01:53.239
<v Speaker 2>And so I would love to imagine my dinner and

1151
01:01:53.320 --> 01:01:55.679
<v Speaker 2>for it just to exist. That doesn't work like that.

1152
01:01:55.800 --> 01:01:58.159
<v Speaker 2>Or you imagine some dollars in my bank account, Oh,

1153
01:01:58.199 --> 01:02:00.480
<v Speaker 2>there they are, But I love that at that mouth

1154
01:02:00.519 --> 01:02:02.760
<v Speaker 2>you can just imagine something into existence. So you just

1155
01:02:02.880 --> 01:02:05.719
<v Speaker 2>imagine that there is something, and you take it square

1156
01:02:05.800 --> 01:02:08.519
<v Speaker 2>and it is negative one. So what is it? Well,

1157
01:02:08.559 --> 01:02:11.639
<v Speaker 2>it doesn't really matter, because in mouth, it doesn't matter

1158
01:02:11.679 --> 01:02:15.760
<v Speaker 2>what something is. It only matters what it does. And

1159
01:02:15.880 --> 01:02:17.719
<v Speaker 2>I think this is a wonderful thing to think about

1160
01:02:17.800 --> 01:02:20.679
<v Speaker 2>in life as well, because really it shouldn't matter what

1161
01:02:20.840 --> 01:02:24.199
<v Speaker 2>somebody is. No, it shouldn't matter what the color of

1162
01:02:24.199 --> 01:02:27.199
<v Speaker 2>their skin is, or what they look like, or how

1163
01:02:27.280 --> 01:02:30.360
<v Speaker 2>large they are, or or what gender they are anything

1164
01:02:30.440 --> 01:02:32.519
<v Speaker 2>that it should only really matter what they do. Are

1165
01:02:32.519 --> 01:02:35.000
<v Speaker 2>they a nice person? Are they helpful? Are they kind?

1166
01:02:35.039 --> 01:02:37.400
<v Speaker 2>Are they generous? Those kinds of things. And so in

1167
01:02:37.480 --> 01:02:40.639
<v Speaker 2>math we kind of put aside the question of what

1168
01:02:40.639 --> 01:02:42.800
<v Speaker 2>that imagining of it is. We just say what does

1169
01:02:42.840 --> 01:02:45.800
<v Speaker 2>it do? And it's like when children make up a game,

1170
01:02:46.199 --> 01:02:48.199
<v Speaker 2>they will make up a whole world and they will

1171
01:02:48.239 --> 01:02:51.639
<v Speaker 2>play that game. And that's what math is. But then

1172
01:02:51.679 --> 01:02:56.440
<v Speaker 2>it goes work further because it goes, oh is this helpful? Crikey?

1173
01:02:56.719 --> 01:03:00.519
<v Speaker 2>It actually is. It starts off as being just kind

1174
01:03:00.519 --> 01:03:02.880
<v Speaker 2>of ludicrous game that we're playing in our heads, beople

1175
01:03:02.920 --> 01:03:05.880
<v Speaker 2>turned out to be really helpful for solving problems in physics.

1176
01:03:06.320 --> 01:03:09.639
<v Speaker 2>It's not extraordinary, And I just think it's extraordinary that

1177
01:03:09.679 --> 01:03:11.719
<v Speaker 2>this thing that we made up that doesn't have any

1178
01:03:11.719 --> 01:03:15.320
<v Speaker 2>physical reality to it is helpful in physics. Because what

1179
01:03:15.440 --> 01:03:18.679
<v Speaker 2>happens is that you draw pictures of it, and when

1180
01:03:18.719 --> 01:03:21.239
<v Speaker 2>you have ordinary numbers, you draw them on a number line. Right,

1181
01:03:21.280 --> 01:03:23.559
<v Speaker 2>We put numbers on a line, and it's one line.

1182
01:03:23.639 --> 01:03:26.559
<v Speaker 2>A line is very flat, it's one dimensional. But if

1183
01:03:26.559 --> 01:03:29.840
<v Speaker 2>you don't add imaginary numbers into that mix, where do

1184
01:03:29.920 --> 01:03:32.719
<v Speaker 2>you imaginary numbers go, Well, they're not on the line,

1185
01:03:32.840 --> 01:03:34.480
<v Speaker 2>so they just have to go in a different direction,

1186
01:03:34.760 --> 01:03:36.480
<v Speaker 2>so you can just make them sort of go up

1187
01:03:36.760 --> 01:03:39.119
<v Speaker 2>the pain. And then when you mix all those things up,

1188
01:03:39.159 --> 01:03:41.679
<v Speaker 2>you get a two dimensional space instead of a one

1189
01:03:41.719 --> 01:03:45.079
<v Speaker 2>dimensional space. And you know, in two dimensional space you

1190
01:03:45.159 --> 01:03:48.239
<v Speaker 2>can see beautiful patterns that you can't see in one

1191
01:03:48.280 --> 01:03:51.880
<v Speaker 2>dimensional space because it's so incredibly thin. A line is

1192
01:03:51.920 --> 01:03:54.000
<v Speaker 2>just too thin. You can't see patterns, whereas in the

1193
01:03:54.039 --> 01:03:58.400
<v Speaker 2>two dimensional space you can see gorgeous patterns. And that's

1194
01:03:58.480 --> 01:04:02.480
<v Speaker 2>how it's helpful in things like physics, because you see

1195
01:04:02.599 --> 01:04:05.119
<v Speaker 2>you work out the patterns using the two dimensional space,

1196
01:04:05.159 --> 01:04:07.320
<v Speaker 2>and then once you apply it to the real world

1197
01:04:07.400 --> 01:04:09.519
<v Speaker 2>again you just take the part that's on the line.

1198
01:04:09.679 --> 01:04:12.079
<v Speaker 2>But it's just that you can recognize what the patterns

1199
01:04:12.079 --> 01:04:15.000
<v Speaker 2>are because you are exploring them in two dimensional space.

1200
01:04:15.320 --> 01:04:17.639
<v Speaker 2>It's kind of like if you're clearing out your closet,

1201
01:04:17.679 --> 01:04:19.320
<v Speaker 2>you kind of need to take everything off the rail

1202
01:04:19.360 --> 01:04:21.800
<v Speaker 2>and spread it out on your bed before you put

1203
01:04:21.840 --> 01:04:22.679
<v Speaker 2>it back on the rail again.

1204
01:04:22.920 --> 01:04:26.360
<v Speaker 1>So behind every perfectly, Marie condoed closet is the chaos

1205
01:04:26.360 --> 01:04:29.480
<v Speaker 1>and the pain and the discovery and the beauty of

1206
01:04:29.679 --> 01:04:34.360
<v Speaker 1>purging and whittling what's hiding in the universe's little crevices

1207
01:04:34.360 --> 01:04:37.480
<v Speaker 1>and corners. Well, kind of on that note too, Felicia

1208
01:04:37.519 --> 01:04:40.920
<v Speaker 1>Chandler and James Dean Cotton want to know about the

1209
01:04:40.960 --> 01:04:44.639
<v Speaker 1>Fibonacci sequence, and Felicia asks, why do we see it

1210
01:04:44.639 --> 01:04:48.039
<v Speaker 1>so much of nature? I imagine that Dan Brown's the

1211
01:04:48.079 --> 01:04:53.360
<v Speaker 1>Da Vinci code really put the Fibonacci sequence on the map.

1212
01:04:53.599 --> 01:04:56.000
<v Speaker 4>I'm into somebody here that I cannot understand.

1213
01:04:55.880 --> 01:04:59.400
<v Speaker 1>What does math have to say about that particular equation

1214
01:04:59.599 --> 01:05:00.000
<v Speaker 1>in nati.

1215
01:05:00.320 --> 01:05:03.400
<v Speaker 2>So perhaps I should remind everyone that the Fibonacci sequence

1216
01:05:03.400 --> 01:05:06.000
<v Speaker 2>starts one one, and then you add up the two

1217
01:05:06.039 --> 01:05:09.360
<v Speaker 2>previous numbers to produce the next number. So you get one,

1218
01:05:09.360 --> 01:05:11.360
<v Speaker 2>add one, which is two, and then you add that

1219
01:05:11.440 --> 01:05:13.920
<v Speaker 2>to the previous number one a two, which is three.

1220
01:05:14.119 --> 01:05:15.920
<v Speaker 2>Then you get five, and then you get eight, and

1221
01:05:15.960 --> 01:05:17.559
<v Speaker 2>then get thirteen and so on.

1222
01:05:17.800 --> 01:05:21.320
<v Speaker 1>Okay, so just a quick primer Fibonacci. Leonardo Pizzano was

1223
01:05:21.320 --> 01:05:25.000
<v Speaker 1>an Italian guy who around the year twelve hundred wrote

1224
01:05:25.039 --> 01:05:29.239
<v Speaker 1>a book about math and popularized the standard Hindu Arabic

1225
01:05:29.440 --> 01:05:32.159
<v Speaker 1>numerals in Europe. Everyone loved him for it, thought he

1226
01:05:32.239 --> 01:05:34.519
<v Speaker 1>was dope at math, and then he died and everyone

1227
01:05:34.519 --> 01:05:36.519
<v Speaker 1>forgot about him for like four hundred years until the

1228
01:05:36.519 --> 01:05:39.679
<v Speaker 1>eighteen hundreds. Two things, he didn't actually invent or discover

1229
01:05:39.719 --> 01:05:43.159
<v Speaker 1>the Fibonacci sequence that dates back to at least three

1230
01:05:43.239 --> 01:05:47.320
<v Speaker 1>hundred BCE, when this Indian poet Bengala was already down

1231
01:05:47.360 --> 01:05:50.719
<v Speaker 1>with it. Not Fibonacci's fault that we named the sequence

1232
01:05:50.719 --> 01:05:53.480
<v Speaker 1>after him. Another thing is that Fibonacci was from Pisa,

1233
01:05:53.679 --> 01:05:56.480
<v Speaker 1>which is where the Leaning Tower of Pisa is and

1234
01:05:56.559 --> 01:05:59.840
<v Speaker 1>it was built around twelve hundred during his life span.

1235
01:06:00.159 --> 01:06:04.280
<v Speaker 1>So where was he when it came to applied mathematics. Yeah,

1236
01:06:04.599 --> 01:06:09.159
<v Speaker 1>I'm super busy these days. Also, I didn't intend this,

1237
01:06:09.440 --> 01:06:13.480
<v Speaker 1>but worldwide Fibonacci Day is this week, occurring on the

1238
01:06:13.519 --> 01:06:17.079
<v Speaker 1>same day as the dog holiday, Wolfanut and American Thanksgiving.

1239
01:06:17.199 --> 01:06:21.280
<v Speaker 1>But every year you can celebrate Fibonacci by eating artichokes

1240
01:06:21.639 --> 01:06:27.480
<v Speaker 1>and romanescuco and pineapple because eleven twenty three is Fibonacci esque,

1241
01:06:27.599 --> 01:06:30.199
<v Speaker 1>even though again it wasn't him to discover the sequence. Also,

1242
01:06:30.280 --> 01:06:32.280
<v Speaker 1>I need you to note that I only found out

1243
01:06:32.440 --> 01:06:36.039
<v Speaker 1>about Fibonacci day because I googled was Fibonacci hot? And

1244
01:06:36.079 --> 01:06:39.000
<v Speaker 1>I happened upon a blog that mentioned one, one, two, three,

1245
01:06:39.280 --> 01:06:42.000
<v Speaker 1>and that there is little known of his physical appearance.

1246
01:06:42.159 --> 01:06:43.519
<v Speaker 1>I don't know. I just have a hunch. I bet

1247
01:06:43.559 --> 01:06:45.039
<v Speaker 1>he was hot, maybe like a ten.

1248
01:06:45.480 --> 01:06:47.760
<v Speaker 2>I think the first thing to say is that it

1249
01:06:47.880 --> 01:06:52.400
<v Speaker 2>is not quite as prevalent as its popularity may suggest.

1250
01:06:52.440 --> 01:06:55.280
<v Speaker 1>Okay, that's good to know.

1251
01:06:55.920 --> 01:06:58.480
<v Speaker 2>It's point the golden ratio, which isn't nearly as prevalent

1252
01:06:58.519 --> 01:07:02.199
<v Speaker 2>as its popularity would would indicate either. But I think

1253
01:07:02.239 --> 01:07:07.840
<v Speaker 2>the reason is that nature. I don't want to anthropopomorphized

1254
01:07:07.920 --> 01:07:10.960
<v Speaker 2>nature too much, but nature is trying to do as

1255
01:07:11.039 --> 01:07:14.159
<v Speaker 2>much as it can with the smallest starting point as possible,

1256
01:07:15.199 --> 01:07:19.840
<v Speaker 2>because that's kind of efficient. And why that is the

1257
01:07:19.840 --> 01:07:23.079
<v Speaker 2>case is a whole deep philosophical or possibly biological question,

1258
01:07:23.519 --> 01:07:27.199
<v Speaker 2>but it may be to do with survival of the

1259
01:07:27.239 --> 01:07:30.199
<v Speaker 2>fittest and evolution. The things that survived are the ones

1260
01:07:30.239 --> 01:07:32.760
<v Speaker 2>which did the most possible stuff with the smallest possible

1261
01:07:32.760 --> 01:07:37.119
<v Speaker 2>amount of information, and so sometimes it really is a

1262
01:07:37.159 --> 01:07:40.440
<v Speaker 2>sheer mathematical situation. So, for example, the spirals on a

1263
01:07:40.480 --> 01:07:47.199
<v Speaker 2>pineapple are typically Febonanci numbers, and so if you count

1264
01:07:47.239 --> 01:07:51.400
<v Speaker 2>how many spirals there are in each of the different directions,

1265
01:07:51.440 --> 01:07:53.840
<v Speaker 2>there are three different directions that spirals on a pineapple

1266
01:07:53.840 --> 01:07:56.400
<v Speaker 2>can take. There's the kind of really vertical direction, there's

1267
01:07:56.400 --> 01:07:59.039
<v Speaker 2>the more obvious slanty direction, and then there's the really

1268
01:07:59.159 --> 01:08:03.159
<v Speaker 2>really really that's less obvious. And the thing is that

1269
01:08:03.239 --> 01:08:06.000
<v Speaker 2>geometrically the two smaller numbers have to add up to

1270
01:08:06.039 --> 01:08:08.119
<v Speaker 2>the bigger one that you can work that out on

1271
01:08:08.199 --> 01:08:10.639
<v Speaker 2>any shape at all. Why they typically turn out to

1272
01:08:10.639 --> 01:08:14.119
<v Speaker 2>be feb Naci numbers may be something to do with

1273
01:08:14.920 --> 01:08:17.199
<v Speaker 2>the way that the little fruitlets grow, and it's the

1274
01:08:17.239 --> 01:08:20.000
<v Speaker 2>same with the leaves on the stem of a plant,

1275
01:08:20.359 --> 01:08:23.399
<v Speaker 2>that they grow at different angles, spiraling around the plant,

1276
01:08:23.600 --> 01:08:30.119
<v Speaker 2>possibly to get as much sunlight as possible, and the angles,

1277
01:08:30.520 --> 01:08:33.520
<v Speaker 2>the way that the angles work in a feber Narchi

1278
01:08:33.560 --> 01:08:36.039
<v Speaker 2>sequence is sort of to try and make sure the

1279
01:08:36.079 --> 01:08:38.760
<v Speaker 2>next time a leaf lines up with the one beneath it,

1280
01:08:38.760 --> 01:08:41.680
<v Speaker 2>it's as far away as possible. But it's often only

1281
01:08:41.720 --> 01:08:44.920
<v Speaker 2>a very small part of the feber Narci sequence, so

1282
01:08:45.119 --> 01:08:47.960
<v Speaker 2>it's just like two consecutive numbers or something, and so

1283
01:08:48.039 --> 01:08:50.920
<v Speaker 2>that's why I think it's not quite so prevalent. If

1284
01:08:50.960 --> 01:08:54.079
<v Speaker 2>you have if you have leaves spiraling around and it

1285
01:08:54.079 --> 01:08:57.479
<v Speaker 2>happens to be in a pattern three and five, that's

1286
01:08:57.520 --> 01:08:59.560
<v Speaker 2>only two numbers out of the feber Archi sequence, So

1287
01:08:59.600 --> 01:09:03.199
<v Speaker 2>I wouldn't oh, wow, it's a Febonachi sequet. And maybe

1288
01:09:03.239 --> 01:09:04.920
<v Speaker 2>it's just three and five and it's nothing to do

1289
01:09:04.960 --> 01:09:09.439
<v Speaker 2>with the Fibonacci sequence at all. And sometimes the reason

1290
01:09:09.520 --> 01:09:13.199
<v Speaker 2>that something that's constructed very simply in mouth pops up

1291
01:09:13.520 --> 01:09:16.840
<v Speaker 2>all over the place is a beautiful and maybe slightly

1292
01:09:16.880 --> 01:09:20.399
<v Speaker 2>mysterious thing, and that's one of the things that's wonderful

1293
01:09:20.399 --> 01:09:23.159
<v Speaker 2>about it. And that is maybe not an answerable question.

1294
01:09:23.720 --> 01:09:28.279
<v Speaker 2>And this is why sometimes people believe in a higher being,

1295
01:09:28.359 --> 01:09:31.560
<v Speaker 2>because it seems like some higher being created now. But

1296
01:09:31.920 --> 01:09:34.960
<v Speaker 2>I personally don't feel the need to say that it

1297
01:09:35.079 --> 01:09:39.159
<v Speaker 2>was a higher being, a specific kind of delineated higher being.

1298
01:09:39.479 --> 01:09:41.439
<v Speaker 2>I just think that Math is a higher being.

1299
01:09:41.680 --> 01:09:43.079
<v Speaker 3>Math is my co pilot.

1300
01:09:43.279 --> 01:09:46.119
<v Speaker 1>This one was on the minds of Chimpumpeo, Milan Il

1301
01:09:46.199 --> 01:09:49.600
<v Speaker 1>Niki Mushroom, Morgan, Rachel Gardner, Taylor, the ren you know,

1302
01:09:49.880 --> 01:09:54.239
<v Speaker 1>Karina Reagan, Felix, Osel klarenerk and listener Victoria Sauder, who

1303
01:09:54.239 --> 01:09:57.479
<v Speaker 1>wrote be a Patreon our karmsashologies. I'm so excited you're

1304
01:09:57.520 --> 01:09:59.920
<v Speaker 1>talking to Eugenia Chang. I have huge math crash on her.

1305
01:10:00.279 --> 01:10:02.600
<v Speaker 1>I have two of her books, Victoria Rights. As a teacher,

1306
01:10:02.640 --> 01:10:04.399
<v Speaker 1>I believe math is for everybody, and I try to

1307
01:10:04.439 --> 01:10:07.520
<v Speaker 1>make clearer that math isn't an isolated subject when we

1308
01:10:07.640 --> 01:10:10.800
<v Speaker 1>use it to understand all parts of the world. Suggestions

1309
01:10:10.800 --> 01:10:13.319
<v Speaker 1>to bring maths into the living room, so to speak,

1310
01:10:13.560 --> 01:10:18.039
<v Speaker 1>that's a little juicier, Victoria Rights. Last question from listeners,

1311
01:10:19.279 --> 01:10:24.479
<v Speaker 1>So many people wanted your expert advice, and Elsa Sparks

1312
01:10:24.760 --> 01:10:28.000
<v Speaker 1>wanted to know any recommendations for teaching number sense to

1313
01:10:28.159 --> 01:10:32.720
<v Speaker 1>very young students. Blessed are the cheesemakers, I asked math

1314
01:10:32.760 --> 01:10:35.720
<v Speaker 1>professor here, do you have any advice for college professors

1315
01:10:35.840 --> 01:10:38.880
<v Speaker 1>or any teachers who want to improve their teaching? So

1316
01:10:39.159 --> 01:10:43.960
<v Speaker 1>any advice to people teaching or learning math that you

1317
01:10:44.039 --> 01:10:47.199
<v Speaker 1>feel like has been empowering to people, well, see her book.

1318
01:10:47.439 --> 01:10:49.000
<v Speaker 2>This is why I write all my books to try

1319
01:10:49.039 --> 01:10:51.119
<v Speaker 2>and give people ideas and help people get over their

1320
01:10:51.159 --> 01:10:54.199
<v Speaker 2>past forumas I think that one of the messages that

1321
01:10:54.279 --> 01:10:57.319
<v Speaker 2>I most want to say to everyone who's learning math,

1322
01:10:57.399 --> 01:11:00.199
<v Speaker 2>and therefore I want everyone who's teaching it so also us.

1323
01:11:00.239 --> 01:11:02.840
<v Speaker 2>That on is that if you find it hard, that

1324
01:11:02.880 --> 01:11:06.079
<v Speaker 2>doesn't mean you're bad at it. You're probably just right.

1325
01:11:06.279 --> 01:11:08.640
<v Speaker 2>It is hard, and that that's not a reason to

1326
01:11:08.640 --> 01:11:10.760
<v Speaker 2>be put off it. And if you look around you

1327
01:11:10.800 --> 01:11:13.159
<v Speaker 2>and it seems that other people are finding it easier,

1328
01:11:13.560 --> 01:11:17.039
<v Speaker 2>they might just be talking out of their arm pits

1329
01:11:18.479 --> 01:11:22.600
<v Speaker 2>in order to intimidate other people. Because most mathematicians, in fact,

1330
01:11:22.680 --> 01:11:25.720
<v Speaker 2>every mathematician I know, thinks they're stupid and finds everything

1331
01:11:25.800 --> 01:11:26.359
<v Speaker 2>very difficult.

1332
01:11:26.680 --> 01:11:27.199
<v Speaker 1>Is that true?

1333
01:11:27.560 --> 01:11:29.880
<v Speaker 2>Yes, that is the I think that is a real

1334
01:11:30.520 --> 01:11:33.239
<v Speaker 2>it's a correct impulse to think it's hard, because it

1335
01:11:33.319 --> 01:11:36.520
<v Speaker 2>is hard. But the point is we can keep understanding

1336
01:11:36.560 --> 01:11:39.039
<v Speaker 2>more of it all the time. And I think that

1337
01:11:39.039 --> 01:11:44.319
<v Speaker 2>that celebrating the questions that children ask and not being

1338
01:11:44.359 --> 01:11:46.640
<v Speaker 2>afraid if it's a question that you don't know how

1339
01:11:46.680 --> 01:11:50.199
<v Speaker 2>to answer, because then you can celebrate them for having

1340
01:11:50.279 --> 01:11:52.119
<v Speaker 2>asked a question you don't know how to answer, and

1341
01:11:52.159 --> 01:11:55.119
<v Speaker 2>then we can all learn about how you discover answers

1342
01:11:55.119 --> 01:11:58.039
<v Speaker 2>to questions. And then if it's a question that nobody

1343
01:11:58.039 --> 01:12:00.279
<v Speaker 2>knows the answer to, like why does the fee the

1344
01:12:00.359 --> 01:12:02.199
<v Speaker 2>Nachi sequence come from nature. Then you can say to

1345
01:12:02.239 --> 01:12:05.239
<v Speaker 2>A twelve, if you become an expert in that field,

1346
01:12:05.359 --> 01:12:08.079
<v Speaker 2>you could be the one who answers it, and then

1347
01:12:08.199 --> 01:12:10.880
<v Speaker 2>you could be the one going on this podcast explaining

1348
01:12:10.880 --> 01:12:11.680
<v Speaker 2>it to other people.

1349
01:12:12.039 --> 01:12:15.560
<v Speaker 1>Please do what about I always have to end with these,

1350
01:12:15.600 --> 01:12:19.520
<v Speaker 1>but what's your least favorite thing about what you do

1351
01:12:19.800 --> 01:12:23.119
<v Speaker 1>as a professional abstract mathematician.

1352
01:12:23.880 --> 01:12:27.399
<v Speaker 2>I think it is overcoming people's misconceptions, and it's the

1353
01:12:27.439 --> 01:12:32.000
<v Speaker 2>fact that the misconceptions are so deeply embedded culturally, and

1354
01:12:32.000 --> 01:12:34.399
<v Speaker 2>that's what I'm trying to overcome. I'm not trying to

1355
01:12:34.439 --> 01:12:36.680
<v Speaker 2>get everybody to love math, because we don't all have

1356
01:12:36.760 --> 01:12:39.319
<v Speaker 2>to love the same things, right, I'm just trying to

1357
01:12:40.039 --> 01:12:42.479
<v Speaker 2>show it for what it really is. If everyone saw

1358
01:12:42.520 --> 01:12:44.840
<v Speaker 2>it for what I think it is and they still

1359
01:12:44.840 --> 01:12:46.800
<v Speaker 2>didn't like it, then you know, fine, we can all

1360
01:12:46.920 --> 01:12:50.600
<v Speaker 2>like different things. It's the fact that people see some

1361
01:12:50.800 --> 01:12:56.880
<v Speaker 2>really really narrow, shallow side of it and then write

1362
01:12:56.880 --> 01:12:59.800
<v Speaker 2>it off from their lives when I think it can

1363
01:13:00.199 --> 01:13:04.720
<v Speaker 2>everybody that I find that frustrating. But that's the challenge.

1364
01:13:04.720 --> 01:13:11.199
<v Speaker 2>It's to overcome those deeply embedded misconceptions. And it's been

1365
01:13:11.239 --> 01:13:13.199
<v Speaker 2>so great talking to you about it, because it doesn't

1366
01:13:13.199 --> 01:13:16.159
<v Speaker 2>sound like you have those things. But sometimes even getting

1367
01:13:16.199 --> 01:13:20.640
<v Speaker 2>something published can be difficult because the people who want

1368
01:13:20.680 --> 01:13:23.479
<v Speaker 2>to publish something have their own misconceptions and go, well,

1369
01:13:23.520 --> 01:13:25.479
<v Speaker 2>I want you to write about math, but this isn't math,

1370
01:13:25.600 --> 01:13:27.399
<v Speaker 2>And so then I have to persuade them that this

1371
01:13:27.560 --> 01:13:27.920
<v Speaker 2>is math.

1372
01:13:28.800 --> 01:13:32.079
<v Speaker 1>What about your favorite thing or your favorite number, your

1373
01:13:32.119 --> 01:13:35.600
<v Speaker 1>favorite theorem, your favorite moment, what has just made your

1374
01:13:35.640 --> 01:13:37.880
<v Speaker 1>heart seeing the most in your career.

1375
01:13:38.640 --> 01:13:42.960
<v Speaker 2>My favorite thing is being able to help people understand

1376
01:13:42.960 --> 01:13:46.520
<v Speaker 2>something they didn't previously understand and seeing their gasps of

1377
01:13:46.560 --> 01:13:51.239
<v Speaker 2>delight when some mathematical thing has got them to be

1378
01:13:51.279 --> 01:13:54.319
<v Speaker 2>as excited as when I see it. That is what

1379
01:13:54.439 --> 01:13:57.680
<v Speaker 2>gives me the most joy in math, I think is

1380
01:13:57.920 --> 01:14:00.920
<v Speaker 2>being able to give them enjoy to other people.

1381
01:14:01.560 --> 01:14:04.079
<v Speaker 1>I wonder if there's a word in any language for

1382
01:14:04.159 --> 01:14:07.319
<v Speaker 1>that moment when something clicks, when you are figuring it out,

1383
01:14:07.319 --> 01:14:10.800
<v Speaker 1>figuring out, figuring out, you don't get it. You don't

1384
01:14:10.800 --> 01:14:13.840
<v Speaker 1>get it. And I've been I've sat in calculus classes before,

1385
01:14:14.000 --> 01:14:17.520
<v Speaker 1>I don't get it, and then suddenly something changes over

1386
01:14:17.600 --> 01:14:19.399
<v Speaker 1>and you're like, I get it, I get it. I

1387
01:14:19.439 --> 01:14:22.279
<v Speaker 1>get it, whether it's a joke, or whether it is

1388
01:14:22.600 --> 01:14:25.960
<v Speaker 1>a theorem or something. I wonder what is happening in

1389
01:14:26.000 --> 01:14:28.880
<v Speaker 1>the brain, because that moment is just unlike anything else

1390
01:14:28.920 --> 01:14:31.680
<v Speaker 1>when you finally get it, and it really.

1391
01:14:31.439 --> 01:14:34.840
<v Speaker 2>Feels like pieces falling physically into place, doesn't it.

1392
01:14:34.800 --> 01:14:35.560
<v Speaker 1>Mm hmm it does.

1393
01:14:35.640 --> 01:14:38.279
<v Speaker 2>Yeah, I'm fascinated by the brain. I'd love to try

1394
01:14:38.319 --> 01:14:40.560
<v Speaker 2>and do brain scans while I'm doing things like that

1395
01:14:40.640 --> 01:14:41.800
<v Speaker 2>to try and see what's going on.

1396
01:14:42.840 --> 01:14:44.199
<v Speaker 1>This has just been such a joy.

1397
01:14:44.359 --> 01:14:46.640
<v Speaker 2>Oh, I've been really enjoyed it too. Thank you so much.

1398
01:14:48.239 --> 01:14:50.600
<v Speaker 1>So you have it. Ask the simplest questions and you'll

1399
01:14:50.640 --> 01:14:52.760
<v Speaker 1>learn the deepest truths. And for more on that, you

1400
01:14:52.800 --> 01:14:56.039
<v Speaker 1>can see doctor Eugenia Chang's Frickin' book titled is math

1401
01:14:56.079 --> 01:14:59.960
<v Speaker 1>Reel How Simple Questions lead Us to Mathematics Deepest Truths,

1402
01:15:00.239 --> 01:15:02.319
<v Speaker 1>which is linked in the show notes alongside her website

1403
01:15:02.319 --> 01:15:05.479
<v Speaker 1>and her social media. We are at ologies on Instagram

1404
01:15:05.520 --> 01:15:08.520
<v Speaker 1>and I guess Twitter, but I'm at Aliward with one

1405
01:15:08.760 --> 01:15:11.279
<v Speaker 1>L on both. An Ologies merch is available at ologies

1406
01:15:11.319 --> 01:15:13.880
<v Speaker 1>merch dot com. In case you need holiday gifts, smologies

1407
01:15:13.960 --> 01:15:16.439
<v Speaker 1>are available for free. They are g rated. They're at

1408
01:15:16.479 --> 01:15:19.960
<v Speaker 1>Alleyward dot com. Slash smologies. Those are kid friendly versions

1409
01:15:19.960 --> 01:15:22.960
<v Speaker 1>of classic episodes. To join Patreon and submit your questions

1410
01:15:23.000 --> 01:15:26.760
<v Speaker 1>before recording, head to patreon dot com. Slash Ologies Aaron

1411
01:15:26.840 --> 01:15:29.640
<v Speaker 1>Talbert admin's the Oologies podcast facebook group. Emily White of

1412
01:15:29.680 --> 01:15:33.600
<v Speaker 1>The Wordy makes our professional transcripts. Noel Dilworth is scheduling producer.

1413
01:15:33.640 --> 01:15:36.880
<v Speaker 1>Susan Hale is our major managing director who also assisted

1414
01:15:36.920 --> 01:15:39.560
<v Speaker 1>in research for this episode. Kelly arn Dwyer makes the

1415
01:15:39.600 --> 01:15:42.359
<v Speaker 1>website Seecred Wiguz Thomas and Jerry Slieper of Mindgem Media

1416
01:15:42.399 --> 01:15:45.399
<v Speaker 1>worked on Smologies alongside our lead editor of this episode

1417
01:15:45.399 --> 01:15:49.319
<v Speaker 1>and of Ologies, the infinitely talented Mercedes Maitland of Maitland Audio.

1418
01:15:49.439 --> 01:15:51.520
<v Speaker 1>Nick Thorburn wrote the theme music and if you stick

1419
01:15:51.560 --> 01:15:55.479
<v Speaker 1>around after the show, I tell you a secret. Okay,

1420
01:15:55.560 --> 01:15:57.640
<v Speaker 1>So this week it's that I used to make cocktail

1421
01:15:57.640 --> 01:16:00.319
<v Speaker 1>recipes for cooking sites. I used to write about life

1422
01:16:00.319 --> 01:16:03.760
<v Speaker 1>way back when, so I'm pretty versed in making cocktails.

1423
01:16:03.880 --> 01:16:05.840
<v Speaker 1>Like at a party, people would be like, we got

1424
01:16:05.840 --> 01:16:08.720
<v Speaker 1>some pepperminte schnops and a cantalope and a pixie stick

1425
01:16:08.800 --> 01:16:10.720
<v Speaker 1>and some tabasco makes up out of it, and I

1426
01:16:10.720 --> 01:16:12.920
<v Speaker 1>could usually whip something up. But I'm not much of

1427
01:16:12.960 --> 01:16:15.399
<v Speaker 1>like a make cocktails at home kind of person these days,

1428
01:16:15.520 --> 01:16:18.319
<v Speaker 1>pretty chill. But I just found myself making a beverage

1429
01:16:18.359 --> 01:16:21.439
<v Speaker 1>and I use like some lemon powder and some peach

1430
01:16:21.479 --> 01:16:26.000
<v Speaker 1>emergency and uh keeping scoop of metamucil, and I had

1431
01:16:26.039 --> 01:16:27.880
<v Speaker 1>it an analogene and I was just shaking that thing

1432
01:16:27.960 --> 01:16:30.239
<v Speaker 1>up because you have to. And I realized that the

1433
01:16:30.319 --> 01:16:33.479
<v Speaker 1>muscle memory of the cocktail shaking is still there. It's

1434
01:16:33.520 --> 01:16:37.319
<v Speaker 1>still strong, but just a very different contents and very

1435
01:16:37.319 --> 01:16:41.720
<v Speaker 1>different vibe. But hey, you gotta hydrate, gotta get those electrolytes.

1436
01:16:41.920 --> 01:16:45.960
<v Speaker 1>Colon motility is important, and so is math. Math is real,

1437
01:16:47.159 --> 01:16:50.560
<v Speaker 1>but nothing's real, and life is very beautiful and meta

1438
01:16:50.640 --> 01:16:57.000
<v Speaker 1>mucil can be tasty all right. By Pacaderman Coollege hommeology, cryptozoology,

1439
01:16:57.720 --> 01:17:07.119
<v Speaker 1>lithology and mnology, meteorology, wold fedatology, menthology, seriology, seleology.

1440
01:17:14.800 --> 01:17:17.159
<v Speaker 2>Math is elegant, Math is fun