Speaker 1: Oh hey, it's quite frankly in the episode that you
Speaker 1: never thought you'd click on, And it's the one that
Speaker 1: I never thought I would do because mathematics it's an
Speaker 1: X it's not an ology. But over the years y'all
Speaker 1: have begged me to cover this, I swear and I
Speaker 1: found an ology suitable and an ologist who's going to
Speaker 1: get us emotional about numbers, believe it, and also non numbers.
Speaker 1: Come on a journey, take this VIP pass, Come slip
Speaker 1: behind the curtain backstage for a more intimate chill hang
Speaker 1: with a topic that maybe has seemed to all low to
Speaker 1: reach a little intimidating. You're about to meet the really
Speaker 1: charming and artsy side of math. So this ologist, of course,
Speaker 1: is a professional mather, an author and a speaker who
Speaker 1: holds a PhD in Pure mathematics from the University of
Speaker 1: Cambridge and taught at the University of Cambridge, Chicago and Niece.
Speaker 1: She won tenure and pure mathematics at the University of
Speaker 1: Sheffield in the UK. Has appeared on late night shows
Speaker 1: hyping people up about math, has given ted talks and
Speaker 1: written several books on topic, such as how to Bake
Speaker 1: Pie and her latest one is is math real How
Speaker 1: simple questions lead us to mathematics deepest truths. She's one
Speaker 1: of us and the best person possible to cover this topic,
Speaker 1: so she jumped on a mic from the Midwest, where
Speaker 1: she's currently the Scientist in Residence at the School of
Speaker 1: the Art Institute of Chicago, and she's also a concert pianist.
Speaker 1: You're just gonna love her. But first, thank you to
Speaker 1: patrons at patreon dot com slash ologies for submitting your questions.
Speaker 1: You can join for a bug a month. And thank
Speaker 1: you to everyone wearing ologies merch from ologiesmerch dot com.
Speaker 1: Heads up if you are hoping to play this episode
Speaker 1: for your kids. This is not an all ages episode,
Speaker 1: but we do have many of those. They're called smologies
Speaker 1: and you'll find them at the link in the show notes.
Speaker 1: Thank you also to everyone who leaves a review, because
Speaker 1: you know I look at them with my eyes, so
Speaker 1: I can say one with my mouth. And this one
Speaker 1: was left this week by minecraft Girl twenty one fifty
Speaker 1: eight thirty seven, who wrote, I listen to you every
Speaker 1: day and you are so good, but can you make
Speaker 1: a cookie one? Minecraft Girl twenty one fifty eight thirty seven.
Speaker 1: First off, that's an appropriate number of numbers in your name.
Speaker 1: And also we do discuss cookies, so you have no
Speaker 1: idea how appropriate that is. So let's get into it. Mathematology.
Speaker 1: Nobody write me and balk at this. Okay, so many
Speaker 1: people have used this word. It's just it's in the air,
Speaker 1: in the universe. We're going for it. Also fun that
Speaker 1: the word math stems from a root meaning simply to learn.
Speaker 1: So come along with me. Let me hold your hand
Speaker 1: and guide you to the wings of academia, the behind
Speaker 1: the scenes of a topic you did not know you
Speaker 1: could adore, like this as I hear about Fibonacci sequences,
Speaker 1: golden ratios, common core, loving my neighbor, slide rules versus calculators,
Speaker 1: imaginary numbers, the nature of zero infinite cookies, fingers toes, knuckles,
Speaker 1: How math will change your relationships, How math is not
Speaker 1: just numbers, but dare I say a lifestyle? And how
Speaker 1: math is weirder and more artsy than you think, and more.
Speaker 1: With author and mathematician and mathematologist doctor Eugenia.
Speaker 2: Chang, I'm Eugenia Chen and I use sheha.
Speaker 1: And you are a pure mathematician, that's right, and an
Speaker 1: abstract mathematician.
Speaker 2: Yes, it's kind of the same thing. I mean, maybe
Speaker 2: one is more specific than the other.
Speaker 1: Which one is more specific?
Speaker 3: That's a great question, do you know, I haven't thought
Speaker 3: about I think that I think that pure mathematics is
Speaker 3: more the name that it gets given to distinguish it
Speaker 3: from applied mathematics in formal context like in university departments
Speaker 3: and in funding bodies.
Speaker 2: I call it abstract mathematics because I think pure sounds
Speaker 2: a bit judgmental.
Speaker 1: Pure it kind of does. It kind of implies that
Speaker 1: there's an impure mathematic exactly. It seems like illogical, right exactly.
Speaker 2: And I think that there's been enough people looking down
Speaker 2: their noses at other people over mathematics that we can
Speaker 2: do with getting rid of any of those things wherever
Speaker 2: we can.
Speaker 1: Yeah, it does seem anathetical to your whole mission, which
Speaker 1: is to make people appreciate and get over their mathmobia, right.
Speaker 2: Or invite them to invite them.
Speaker 1: Yes, it's a good distinction. Okay, quick aside, What is
Speaker 1: the difference between the types of math? What makes one
Speaker 1: kind of math abstract versus applied? If you apply abstract
Speaker 1: to applied math, how abstract is abstract?
Speaker 2: It's one of those things where the boundary isn't very
Speaker 2: clear cut. But the general idea is that abstract mathematics
Speaker 2: is trying to understand things from the point of view
Speaker 2: of uncovering logical structures and just exploring how things fit
Speaker 2: together for their own sake, whereas applied mathematics is much
Speaker 2: more about looking at problems in the concrete world around
Speaker 2: us and coming up with theories to help us understand
Speaker 2: those specific problems. So applied mathematics is closer to physics,
Speaker 2: because physics is really about understanding the physical world around us,
Speaker 2: but applied mathematics uses the techniques that pure mathematicians come
Speaker 2: up with often, but they are really specifically trying to
Speaker 2: solve things in the concrete world. Sometimes people say real world,
Speaker 2: but I don't like that either, because you know what's
Speaker 2: real anyway? Are we real? Is anything real? And I
Speaker 2: suppose that's what the tide love my book is.
Speaker 3: I who know?
Speaker 1: Is math real? Is math real?
Speaker 3: Am I real?
Speaker 1: Nobody knows, And so one thing that I love about
Speaker 1: your book is just that it's one of those questions
Speaker 1: that we're all afraid to ask. I think some very
Speaker 1: intrepid TikToker was doing a get Ready with Me video
Speaker 1: and just like, how do we even know math is real?
Speaker 1: And I feel like like a year or two ago
Speaker 1: it shook the world.
Speaker 4: I was just doing my makeup for work and I
Speaker 4: just wanted to tell you guys about how I don't
Speaker 4: think math is real. And I know that like it's
Speaker 4: real because we all like learned in school or whatever.
Speaker 4: But who came up with this concept?
Speaker 1: And you're like the farious?
Speaker 4: But how like he didn't even have plumbing and he
Speaker 4: was like, let me worry about why EQ was MX
Speaker 4: plus B, which first of all, how would you even
Speaker 4: figure that out? How would you like start on the
Speaker 4: concept of algebra? Like what did you need it for?
Speaker 1: Do you remember that video? Yeah?
Speaker 2: And you know that did what? That was one of
Speaker 2: the things that inspired me to write this book because
Speaker 2: I replied to her. I wrote a document and I
Speaker 2: just stuck it on my web page and I just
Speaker 2: replied to each of her questions. And then I did
Speaker 2: a few radio interviews and people because people picked up
Speaker 2: on the fact that I replied to all her questions,
Speaker 2: and people emailed me from all over the world saying, oh.
Speaker 5: My goodness, I've wanted to ask those questions from my life.
Speaker 5: I was stupid and this last time I thought, maybe
Speaker 5: I'm not stupid, or I thought I was intelligent and
Speaker 5: every other way except this.
Speaker 2: And I'm sitting.
Speaker 3: In my car crying because you finally validated me after
Speaker 3: all these us.
Speaker 2: And I thought, Wow, this is really really tapped into
Speaker 2: something that has hit people all around the world, and
Speaker 2: it's really effective. All these grown adults, including grown men,
Speaker 2: emailing me to say that they were weeping in their
Speaker 2: cars because because I had finally validated their questions after
Speaker 2: all these years, people who thought of themselves as otherwise intelligent.
Speaker 2: And so I thought, Okay, maybe I'll write a whole
Speaker 2: book about this.
Speaker 1: And so did that spark the book? Did you email
Speaker 1: your book agent? And so listen, I already started on
Speaker 1: a doc.
Speaker 2: Here.
Speaker 1: We got something here.
Speaker 2: Yeah, I mean I already had thoughts about the questions
Speaker 2: that people have always wanted to ask, because I've been
Speaker 2: teaching art students at the School of the Art Institute
Speaker 2: for some years now, and they quite often, quite often
Speaker 2: what we do is like therapy for their past matatural
Speaker 2: and they tell me that all the things that went
Speaker 2: wrong and all the ways in which they were made
Speaker 2: to feel stupid and the question the burning questions they
Speaker 2: had that never got answered because they were told though,
Speaker 2: that's a stupid question, or no, you're not supposed to
Speaker 2: ask that question here, You're just supposed to answer the
Speaker 2: questions that I tell you. And so I'd already been
Speaker 2: building up a kind of catalog of questions that people
Speaker 2: have really wanted to ask and that they never get answered.
Speaker 2: And then when Mattam, I thought, Okay, maybe there is
Speaker 2: scope for this as a whole book.
Speaker 1: Was part of that math Trauma Math Barbie. Do you
Speaker 1: remember math? Do you remember that one?
Speaker 5: Oh?
Speaker 2: No, I mean it's very topical at the moment. I know.
Speaker 5: Anyone boy?
Speaker 3: Howdy?
Speaker 1: Okay? So this team Talk Barbie came out in nineteen
Speaker 1: ninety three and rightly enraged female scientists and mathematicians and
Speaker 1: really any human with a brain who thought sexism was
Speaker 1: weird and that children get brainwashed into gender stereotypes. So
Speaker 1: there's one gorilla group themselves, the Barbie Liberation Organization, and
Speaker 1: they bought a bunch of teen talk Barbies and talking
Speaker 1: Gijo dolls, and they swapped through voice boxes so that
Speaker 1: Barbie said things like troops attack and made machine gun noises,
Speaker 1: and then Gi Joe said, let's go shopping. They did
Speaker 1: this in December of that year, and a lot of
Speaker 1: kids and parents were surprised ad on Christmas morning to
Speaker 1: have a tiny man in combat fatigues lamenting that.
Speaker 2: I do not remember that one, but there was a
Speaker 2: spoof that appeared a few years ago in my research field.
Speaker 2: So my research field is category theory, which is considered
Speaker 2: to be one of the most abstract parts of mathematics,
Speaker 2: and even abstract mathematicians sometimes think it's too abstract. And
Speaker 2: so there was this whole series of Barbie cartoons where
Speaker 2: Ken would say things like, oh, my goodness, what even
Speaker 2: is a mona? And then Barbie would just go, well, obviously,
Speaker 2: it's just a monoid in the category of endose.
Speaker 1: Bunxes ps context. This comic was part of a meme
Speaker 1: known as feminist hacker Barbie, which arose in twenty fourteen
Speaker 1: like a phoenix from the firebombed ashes of a matel
Speaker 1: book called Barbie I Can Be a Computer Engineer, which
Speaker 1: was marketed toward children and featured a teen Barbie learning
Speaker 1: to computer and it involved illustrations of Barbie at a
Speaker 1: laptop in class, and it was captioned with passages such
Speaker 1: as I'm only creating the design ideas, Barbie says, laughing,
Speaker 1: I'll need Stevens and Ryan's help to turn it into
Speaker 1: a real game. Naturally, computer people, some of whom were
Speaker 1: known as women, did not enjoy the existence of this book,
Speaker 1: and so one of them, Kathleen Tweet, created a meme
Speaker 1: generator that spawned so many realistic and really sardonic takes
Speaker 1: on feminist hacker Barbie, and you can read more about
Speaker 1: it in an article titled Barbie Fucks it Up Again. So,
Speaker 1: when Barbie explains to her male classmates that a monad
Speaker 1: is just a monoid in the category of endofunctors, it's
Speaker 1: a definition so legendarily opaque that it's become like a
Speaker 1: math and programming joke itself. But if you'd like to know,
Speaker 1: a monad in math is an algebraic structure, and in
Speaker 1: programming it's used to structure computations as a sequence of steps.
Speaker 1: And a monad can be a thing that describes how
Speaker 1: something is supposed to be modified, but it isn't really
Speaker 1: a thing, and the etymology of monad even means everything
Speaker 1: or nothing at all. So if it's confusing. That's the joke.
Speaker 1: And so now we get the joke. If you're seated
Speaker 1: next to someone at a dinner party and they were
Speaker 1: to turn to you and say, is math real? Who
Speaker 1: invented it? And how do we trust it? How do
Speaker 1: you begin in a short interaction to get them to
Speaker 1: trust that math is real or at least look at
Speaker 1: it in a different way.
Speaker 2: Well, first, I would validate that question, because often when
Speaker 2: they're asking those questions, they're already full of doubt, skepticism,
Speaker 2: and past trauma. Sometimes they're trying to say, none of
Speaker 2: this is real, it's all a load of oops, can't
Speaker 2: say any of those words out loud.
Speaker 6: It's all a load of codswallop. It's all a load
Speaker 6: of codswallopd wlop. Okay, that's often the subtext of their question.
Speaker 6: And sometimes it's because, especially in a dinner party situation,
Speaker 6: they may feel intimidated by finding that I'm a mathematician.
Speaker 6: And unfortunately that happens a lot, especially because I'm not
Speaker 6: a male person, I'm not a white person, and I'm.
Speaker 2: Not necessarily how people expect a mathematician to be whatever
Speaker 2: that is. So quite often people feel intimidated and so
Speaker 2: it depends where those questions are coming from. I also say, well,
Speaker 2: what does really even mean? And spoiler alert from my book,
Speaker 2: I don't actually say math is real, nor do I
Speaker 2: say math is not real. What's really more? The point
Speaker 2: is how does it help us? It doesn't matter whether
Speaker 2: something is real or not really if it helps us
Speaker 2: in some way, that's what I think in the end.
Speaker 2: So then the question is does math help us? And
Speaker 2: does it help us in some way that you the
Speaker 2: person asks me the question cares about because people might say, oh, well,
Speaker 2: sure if people can use master wieplanes and to make
Speaker 2: computers work, But that doesn't mean that I have to
Speaker 2: care about it. And so then I say, try and
Speaker 2: find out what they care about themselves, and whether they
Speaker 2: care about thinking clearly about the world around them.
Speaker 1: Do you surf or eat or paint or eat paint
Speaker 1: or golf or wear clothes. Math is in the tides,
Speaker 1: It's in the temperature gauges in your oven, putting angles,
Speaker 1: Rubik's cubes, hair braids, fabric knits, and lasagna gields. So
Speaker 1: we all have stuff. Take kibs with butterflies, just nauseated
Speaker 1: with happiness, and there is a shitload of friendly and
Speaker 1: helpful and benign and dazzling math involved.
Speaker 2: And sometimes depending on where the person is coming from.
Speaker 2: When I say that math helps me empathize with other people,
Speaker 2: that can be really mind blowing because that is not
Speaker 2: something that is often presented in math class.
Speaker 1: I think, Yeah, how does it help you empathize?
Speaker 2: There's two ways, I think. First of all, it's a
Speaker 2: technique for understanding how arguments are structured. If I want
Speaker 2: to try and understand somebody who has a completely opposed
Speaker 2: point of view from mind, then I can do it
Speaker 2: by understanding where their argument is coming from, because it's
Speaker 2: always coming from somewhere, and it's never going to help
Speaker 2: if we just sit there and go, oh, that person
Speaker 2: is just not being logical. Their point of view has
Speaker 2: come from somewhere, and one way to empathize with other
Speaker 2: people is to understand where their point of view has
Speaker 2: come from.
Speaker 1: So being in a math mindset primes your brain for
Speaker 1: taking something complex and going a step back and breaking
Speaker 1: it down through logic. How does one get from there
Speaker 1: to hear?
Speaker 2: It doesn't mean that we're supporting it, and it doesn't
Speaker 2: mean that we are claiming it's good, but we are
Speaker 2: just understanding where it came from from their point of view.
Speaker 2: Abstract mathematics also helps because it's a process of seeing
Speaker 2: patterns and making analogies between different situations. And so at
Speaker 2: the basic level, if you say two plus three equals five,
Speaker 2: what you're really saying is that anytime you take two
Speaker 2: objects and another three objects, as long as they don't
Speaker 2: kind of spontaneously combust or coalesce, you will end up
Speaker 2: with five objects. And that's a pattern that when we
Speaker 2: teach arithmetic to small children, we show them doing that
Speaker 2: with objects, physical objects, over and over again until they
Speaker 2: see the pattern forming in front of their eyes. And
Speaker 2: that's really a way I think to access empathy with
Speaker 2: people who have different opinions from us, because it's about
Speaker 2: finding an analogy between our situation and theirs.
Speaker 1: So between you and the guy who just flipped you
Speaker 1: off in the traders just parking lot, there must be
Speaker 1: a common denominator.
Speaker 2: And so it can be quite a far fetched analogy.
Speaker 2: But because abstract mathematics is really about seeing deep patterns
Speaker 2: where the surface looks completely different, but if you strip
Speaker 2: away enough details you get down to something that's the
Speaker 2: same underneath. I can do that with people who I
Speaker 2: really disagree with by just stripping away so many details
Speaker 2: and finding some kind of some kind of analogy, even
Speaker 2: if the topic is completely different, thinking about some situation
Speaker 2: in which I have experienced something that is even remotely
Speaker 2: abstractly similar. So perhaps where everybody is disagreeing with me
Speaker 2: about something and getting angry with me for thinking something,
Speaker 2: and it's not going to help me change my mind. So,
Speaker 2: for example, if we think about people who don't believe
Speaker 2: in vaccines in all the ways that people kind of
Speaker 2: get angry with them to try and get them to
Speaker 2: believe in vaccines, and then if I think about a
Speaker 2: situation where a lot of people are getting anger with
Speaker 2: me and want me to believe something, then I can
Speaker 2: see that that isn't going to help me change my mind.
Speaker 2: And so that kind of that kind of abstraction and
Speaker 2: analogy helps me understand why people take the positions that
Speaker 2: they take.
Speaker 1: On that note and stay with me. There was something
Speaker 1: about this chat in eugenius book that reminded me of therapy,
Speaker 1: of cognitive behavioral therapy. Here's funny, because I was reading
Speaker 1: your book thinking about how much math must give you
Speaker 1: kind of an edge into understanding your own brain and
Speaker 1: other people's brains by saying, Okay, everybody hates me. No
Speaker 1: one's texted me back today. Is that true? Does everyone
Speaker 1: hate you? What's the logic?
Speaker 2: What is my reason for thinking this exactly? And the
Speaker 2: thing is that I absolutely don't always use logic over feelings.
Speaker 2: I actually do the opposite. I always observe that feelings
Speaker 2: are correct. That's it. Feelings are always true as a
Speaker 2: basic starting point. But sometimes there are other things going
Speaker 2: on as well, and so I've noticed for myself. For example,
Speaker 2: sometimes when I'm feeling terrible because some bad things have
Speaker 2: happened to me, and then they I think about them
Speaker 2: too much. They go around my head and then I
Speaker 2: feel terrible. And sometimes I think to myself, I know intellectually,
Speaker 2: because I have done Callino behavioral therapy, I know that
Speaker 2: if I just go to bed, I will feel better
Speaker 2: in the morning. And what happens after that is that
Speaker 2: I don't want to do it because I don't want
Speaker 2: to just go to sleep and feel better in the morning.
Speaker 2: So then I might say, well, that's not logical, But
Speaker 2: now I think, though that is a true feeling. I
Speaker 2: truly feel this. Okay, Now why am I feeling this,
Speaker 2: and then I realize it's because it seems like cheating.
Speaker 2: I don't want to Then it will feel like it
Speaker 2: will feel like my feelings aren't being validated. If if
Speaker 2: I can just go to sleep and they'll go away.
Speaker 2: So true.
Speaker 1: You're also a musician too. I think we know that
Speaker 1: there's a lot of math in music, but is there
Speaker 1: a lot of emotion in math?
Speaker 2: There's tons of emotion in math. That's such an interesting question.
Speaker 2: I feel things so deeply when I'm doing and seeing
Speaker 2: and experiencing math, and I try to write that into
Speaker 2: my books because on the one hand, the power and
Speaker 2: the strength of math comes from the fact that it
Speaker 2: is it doesn't have emotions in the actual argument of it,
Speaker 2: so it doesn't depend on emotions. It shouldn't depend on
Speaker 2: emotions at all to build the arguments. But humans are
Speaker 2: emotional creatures, and so when we're communicating math, if we
Speaker 2: don't communicate it with emotions, then I don't think anything
Speaker 2: gets through, or at least much less gets through. And
Speaker 2: I think that's one of the big problems with teaching
Speaker 2: and learning math, is that there's the idea that math
Speaker 2: shouldn't have any emotions in it. Which is true. But
Speaker 2: at the same time, all human experiences have emotions in
Speaker 2: and if we try and teach someone something without showing
Speaker 2: the emotional side, or without giving them an emotional connection
Speaker 2: to it, then I just don't think it goes in
Speaker 2: as deeply.
Speaker 1: So there are many papers on this, but a fresh
Speaker 1: twenty twenty three study called Emotions and Motivation in Mathematics Education,
Speaker 1: Where we Are Today and Where we Need to Go,
Speaker 1: stated that female students enjoyment of and interest in fashion
Speaker 1: was found to result in lower engagement in mathematics and
Speaker 1: prevent them from solving word problems. And I was like,
Speaker 1: hold up, what that seems weird? So I checked out
Speaker 1: the nineteen ninety four study they cited titled When Do
Speaker 1: Girls Prefer Football to Fashion? An Analysis of Female underachievement
Speaker 1: in relation to realistic mathematic contexts, And what that study
Speaker 1: was actually looking at was the tendency for contextual problems
Speaker 1: in math lessons to make no fucking practical sense at all,
Speaker 1: Like you're given this long fictional scenario which you'd approach
Speaker 1: from an entirely different perspective in real life, like the
Speaker 1: fashion problem in the actual nineteen ninety four study was
Speaker 1: that girls scored lower on the fashion design math calculation
Speaker 1: than one about football or just an abstract question because
Speaker 1: the fashion problem made no sense, like, in order to
Speaker 1: divide hours of labor in a mathematically sound way, which
Speaker 1: is what the problem was about, you'd have to deliver
Speaker 1: the finished dresses before you sowed them. And this nineteen
Speaker 1: ninety four study concluded that two thirds of girls used
Speaker 1: their common sense as well as their mathematical knowledge and
Speaker 1: then were penalized for doing so. Anyway, there was actually
Speaker 1: more engagement in the problem, but the problem only made
Speaker 1: sense on a math test, not in the real world.
Speaker 1: And research has also shown that figuring out solutions to
Speaker 1: hands on actual scenarios gets us more engaged in finding
Speaker 1: this solution. So it's actually a two pronged approach to
Speaker 1: make people actually care. And yes, folks are quick to
Speaker 1: penalize others without realizing that, hey, they're actually asking really good,
Speaker 1: important questions and the problem is more complex and that
Speaker 1: the emperor wait a second, is very naked. Why am
Speaker 1: I seeing his parabot X.
Speaker 2: Let me put it this way, if you do have
Speaker 2: an emotional experience when you're doing something, you will remember
Speaker 2: it more deeply, and so I try to talk about things.
Speaker 2: First of all, talk about how I feel about mathematics,
Speaker 2: and secondly, I encourage my students and my readers to
Speaker 2: have feelings about it, and I try to link it
Speaker 2: to topics that they already have feelings about, because if
Speaker 2: I'm talking about why one first one equals to someone
Speaker 2: may have no feelings about that, apart from horror when
Speaker 2: they remember their math lessons in school, all right down.
Speaker 2: But then if I can find something else, like my
Speaker 2: wonderful students who came up with thinking about when you
Speaker 2: mix paints together, when you mix one color of paint
Speaker 2: with one color of paint, you actually don't get to
Speaker 2: because you get a new color of paint. And maybe
Speaker 2: mixing paint is something that some people have much more
Speaker 2: feeling about. Or if you're making cookies and you've got
Speaker 2: balls of dough and you decide you're going to make
Speaker 2: one bigger one instead of two small, and you take
Speaker 2: two bits of dough and you stick them together and
Speaker 2: you make a bigger cookie, that may be something that
Speaker 2: someone can have a feeling about rather than just it
Speaker 2: being some abstract concept. And so the power of abstract
Speaker 2: mathematics is that it does not involve emotions, but that
Speaker 2: also makes it difficult to learn and understand.
Speaker 1: Well, how does an abstract mathematician deal with those bars
Speaker 1: of cookie dough. What's the answer that's going to trouble
Speaker 1: me my whole life.
Speaker 2: Well, it depends because if you in one way, if
Speaker 2: you take two balls of cookie dough, you get two
Speaker 2: balls of cookie dough. So you take one boy and
Speaker 2: you take one ball, and that's two. But there's another
Speaker 2: thing you can do, which is smash them together and
Speaker 2: get one bigger one, in which case you've kind of done.
Speaker 2: One plus one equals one bigger one. And those are
Speaker 2: two scenarios that are both real and so it's not
Speaker 2: that one plus one always equals too, it's under what
Speaker 2: circumstances does one plus one equal to And that's where
Speaker 2: we get to the whole. Oh, as long as we
Speaker 2: don't smash things together, we don't eat the cookie dough
Speaker 2: because cookie dough is delicious.
Speaker 1: So in her book Beyond Infinity, An Expedition to the
Speaker 1: Outer Limits of Mathematics, Eugenia also just steers infinity right
Speaker 1: the mouth while discussing dividing cookies for all eternity. So
Speaker 1: many cookies, man, Hell yeah, yeah, maam, yam right on
Speaker 1: where in the brain is math coming from? And why
Speaker 1: when I am stoned? Do I think I understand math better?
Speaker 2: I cannot possibly address that last question. I have absolutely
Speaker 2: no experience about whatsoever, and that is for real. However,
Speaker 2: there's a popular idea that math is on one side
Speaker 2: of the brain. I'm a whole left right brain thing
Speaker 2: I think has been mostly completely debunked. But I remember
Speaker 2: it was actually my piano teacher who introduced me to
Speaker 2: the book drawing with the right side of the brain,
Speaker 2: and so I think, of my head, the idea is
Speaker 2: that the right side is the logical side and the
Speaker 2: left side is the creative side. Is that is that
Speaker 2: I think the myth was right. So I'd just like
Speaker 2: to stress that I'm pretty sure it's all being debunked
Speaker 2: and that both sides of the brain work together and
Speaker 2: are very highly connected.
Speaker 1: So while the hypothesis was flipped and the left side
Speaker 1: of the brain is supposedly logical, the right is supposedly creative.
Speaker 1: It's been flim flammed by medicine itself. And for more
Speaker 1: on this, you can read an evaluation of the left
Speaker 1: brain versus right brain hypothesis. With resting state, functional connectivity,
Speaker 1: magnetic resonance imaging, and you got to use your whole
Speaker 1: brain for that study, because it concluded from over a
Speaker 1: thousand scans that there's no evidence that the people nestled
Speaker 1: into their brain imaging chambers use one side other punkin
Speaker 1: more than the other. Rather, your whole shebang is interconnected
Speaker 1: and quote, the two hemispheres support each other in its
Speaker 1: processes and functions, which is tender and kind. So if
Speaker 1: you feel like you need to get it together, don't worry.
Speaker 1: You have you are together.
Speaker 2: And there are people who have either never had one
Speaker 2: side of their brain or lose the use of it,
Speaker 2: and then the other side is able to compensate. And
Speaker 2: of course there's tons of stuff about the plasticity of
Speaker 2: the brain learning to do things. But even if one
Speaker 2: side of the brain were logical on the other side's creative,
Speaker 2: that just panders to the idea that math is only
Speaker 2: logical and not creative, and it's really both together. It's
Speaker 2: just that when you're doing arithmetic in elementary school or
Speaker 2: wherever you first do it, that might not be extremely creative.
Speaker 2: But amo the people who came up with arithmetic in
Speaker 2: the first place, that's creative.
Speaker 1: I have questions. Yeah, I have so many questions. And
Speaker 1: I don't remember how old I was when I realized, oh,
Speaker 1: everything's multiplied by ten because of our fingers. Yeah, like
Speaker 1: it didn't. It didn't occur to me. The base ten
Speaker 1: thing didn't occur to me for so long. But where
Speaker 1: did math come from? And how many generations has been
Speaker 1: passed down? And if we didn't learn it from someone
Speaker 1: older than us who raised us, would we even have
Speaker 1: any capacity to just come up with, you know, theorems
Speaker 1: and proofs and calculus and everything out of thin air
Speaker 1: or does it really just keep building on itself.
Speaker 2: That Those are fascinating questions, and I think those are
Speaker 2: really great questions. And so humans did come up with
Speaker 2: those things, but it took them thousands of years. I mean,
Speaker 2: people came up with the idea of numbers thousands of
Speaker 2: years ago, but it was ancient cultures. While the numbers
Speaker 2: that we use today are mostly based on ten fingers,
Speaker 2: different cultures based things on different things. And so there
Speaker 2: are some cultures that base things on eight because of knuckles,
Speaker 2: and then there are some people who use the spaces
Speaker 2: in between their fingers as well. And there are some
Speaker 2: cultures who based on twenty.
Speaker 4: Twenty fingers and twenty.
Speaker 2: Twos, and the number system in French has traces of that,
Speaker 2: where eighty is catravan with four twenties. Ninety isn't ninety,
Speaker 2: it's four twenties plus ten because it's as if you're
Speaker 2: counting up in twenties. So there are different things. But
Speaker 2: then this base ten thing has really taken over.
Speaker 1: So base ten systems have been used for probably as
Speaker 1: long as we've had ten fingers, And though the written
Speaker 1: records go back to three thousand BCE in Egypt, it
Speaker 1: wasn't until between one hundred and four hundred years into
Speaker 1: the Common era that the Hindu Arabic numeral system of
Speaker 1: zero to ten kind of won out. And this number
Speaker 1: system has only been in use in Europe for like
Speaker 1: the last one thousand years. But yeah, it goes far
Speaker 1: far beyond that in different forms. But staring at your
Speaker 1: hands for a while, that's math, people.
Speaker 2: And there were some ancient cultures I think it might
Speaker 2: have been Mayan culture that used base sixty, which is
Speaker 2: why there are sixty minutes in an hour and sixty
Speaker 2: seconds in a minute. No, right, So many of our
Speaker 2: things are in tens. The lovely American system still uses fahrenheit.
Speaker 2: That doesn't fit well with hundreds.
Speaker 5: You, no, it does not.
Speaker 2: But we have this thing with sixty seconds in a
Speaker 2: minute and sixty minutes in an hour, and sixties are
Speaker 2: great number to use because it has a lot of
Speaker 2: factors and so you can divide an hour into a
Speaker 2: lot of really nice chunks. Whereas if we went decimal
Speaker 2: on time. I think there's some fantastic society somewhere that
Speaker 2: thinks we should go a metric on time and have
Speaker 2: one hundred minutes in an hour, we would actually not
Speaker 2: be able to divide it up into quite so many
Speaker 2: handy units, because we wouldn't be able to do a
Speaker 2: third in quite a handy way. So we can do
Speaker 2: we can divide an hour into half thirds, quarters, fifths, tenths, twelfth,
Speaker 2: I mean, we can do all sorts of things, and
Speaker 2: so sixties sixties are pretty good number for that. But
Speaker 2: the whole ten finger thing eventually took over. And to
Speaker 2: answer your question about if we grew up and nobody
Speaker 2: older than us taught us enough, would we be able
Speaker 2: to come up with all of it? Well, I here's
Speaker 2: what I think, and this is just pure speculation. I
Speaker 2: think it would be hard to do that in a
Speaker 2: single lifetime. It did take humans thousands of years to
Speaker 2: get to the point we are, and I think it's
Speaker 2: amazing how fast an individual human is now able to
Speaker 2: learn all of those things that it took humans thousands
Speaker 2: of years to learn. And it's because we communicate with
Speaker 2: each other, and so it's really dependent on people who
Speaker 2: already know it passing it down to the next generation.
Speaker 2: If we each had to develop it from scratch, it
Speaker 2: would take a really long time, and I don't know
Speaker 2: how far an individual would get.
Speaker 1: Well, do you think there's any maths systems that have
Speaker 1: been completely forgotten that some people cultivated for a couple
Speaker 1: thousand years and then just wasn't a record of it,
Speaker 1: And we just have no idea that there's a whole
Speaker 1: math system based on pie or the Fibonacci sequence or
Speaker 1: like seven or something.
Speaker 2: Almost certainly, especially because so many cultures passed things down
Speaker 2: from generation to generation and then maybe died out or
Speaker 2: got killed off by white European people or are living
Speaker 2: uncontacted somewhere. And I think that there are certainly pieces
Speaker 2: of math that are obsolete now because we've developed more technology. So,
Speaker 2: for example, there's the whole math of the slide rule.
Speaker 2: For my parents' generation had to learn how to use
Speaker 2: a slide rule, which is a really clever device for
Speaker 2: multiplying large numbers together using logarithms. And the thing is,
Speaker 2: we just really don't need that anymore because we've got calculators.
Speaker 1: So that slide roll system was invented by a dude
Speaker 1: named Edmundculter in sixteen twenty, and that was the same
Speaker 1: year that the Mayflower crashed the party that's now known
Speaker 1: as North America. Slide rule was technically an analog computer,
Speaker 1: and it had this ability to glide to different positions
Speaker 1: to reveal these complex math solutions. And this is how
Speaker 1: folks conquered big multiplication and division of numbers until about
Speaker 1: the nineteen seventies, when electronic calculators just be booped their
Speaker 1: way onto office desks next to ashtrays and diepepsi and
Speaker 1: became accessible and commonplace. Now, as for this so called slipstick,
Speaker 1: it became obsolete partly because you could not write boobies
Speaker 1: upside down with it.
Speaker 2: And so the slide rule has become obsolete. I don't
Speaker 2: know how to use one myself. I expect my parents
Speaker 2: had it drummed into them so hard that they could
Speaker 2: still do it with a slide rule. I'm sure there's
Speaker 2: somebody out there who still loves using this slide rule.
Speaker 1: I mean, I remember the anxiety of how to afford
Speaker 1: Texas instruments TI eighty.
Speaker 2: Seven graphical calculator.
Speaker 1: Yeah, like meeting one of those in high school, being
Speaker 1: like I need one hundred and nine dollars for a
Speaker 1: calculator size of a brick, you know, like how much
Speaker 1: it's maybe that's not used aaymore, but maybe it is
Speaker 1: in testing situations. But I know, I know you get
Speaker 1: assets all the time, but who is good at math?
Speaker 1: How much is it aptitude? How much is it attitude?
Speaker 1: How much is it access? And why are we so
Speaker 1: afraid of it? Why do so many people just throw
Speaker 1: their hands up and say nope, a sack by like
Speaker 1: you split the bill I'm not dealing with.
Speaker 2: So, first of all, I think it's mostly access and
Speaker 2: how much help you've had and how much that help
Speaker 2: was specifically helpful to you. All the scientific research at
Speaker 2: the moment points to brains being spectacularly plastic. Neuroplasticity, it's
Speaker 2: extraordinary how much brains can change according to how they
Speaker 2: are used and how they are stimulated, so.
Speaker 1: You can coax your brain toward a better life, which
Speaker 1: means maybe one day I will be good at dancing.
Speaker 2: And so there is almost no evidence, there's basically no
Speaker 2: evidence to show that there's some kind of hard wiring
Speaker 2: at birth that means that some people are destined to
Speaker 2: be better at math than others. And in my previous
Speaker 2: book X plus Y and Mathematicians Manifesto for Rethinking Gender,
Speaker 2: I talked about this a bit because there are still
Speaker 2: some people who think that maybe there's just some biological
Speaker 2: reason that for men to be better than women at math,
Speaker 2: and there's therefore there's nothing we can do about it.
Speaker 2: And the evidence, the scientific evidence of that is just
Speaker 2: so thin that it's actually laughable. I mean I laugh
Speaker 2: at it. That means it's laughable, right.
Speaker 1: And.
Speaker 2: So, because how can you even tell that something is
Speaker 2: hardwired at birth except by testing newborn babies? But how
Speaker 2: do you even test newborn babies? They don't do anything,
Speaker 2: you can't you can't get them to do anything. And
Speaker 2: so the idea that anything you can get a newborn
Speaker 2: baby to do is going to be indicative of their
Speaker 2: future mathability. It's just ludicrous to me because mathability is
Speaker 2: a really complicated combination of things. It's not just about
Speaker 2: being how fast you can do arithmetic. And so I
Speaker 2: always say that the things that you can test in
Speaker 2: lab controlled situations are necessarily very restrictive, just like you
Speaker 2: can test how far people can sprint the one hundred meters.
Speaker 2: And I don't think anybody really argues with the fact
Speaker 2: that men can the fastest men can run one hundred
Speaker 2: meters faster than the fastest women. It's to do with
Speaker 2: body strength and stuff like that. But ultra marathons. Women
Speaker 2: have been beating men at ultra marathons. I can't remember
Speaker 2: how long it counts as an ultramathm, but it might
Speaker 2: be two hundred and fifty miles or something.
Speaker 1: Okay, so technically everything over twenty six point two is
Speaker 1: an ultra marathon. But the longest and the most grueling
Speaker 1: is the Hong Kong two hundred and ninety eight k
Speaker 1: with no stopping or sleep or support on the trails,
Speaker 1: just two to three days of continuous running. Why why
Speaker 1: why why why? But take a gander at this one
Speaker 1: article from twenty twenty one titled why women are faster
Speaker 1: than men in long runs, and you'll learn that the
Speaker 1: men among us tend to have larger hearts to pump
Speaker 1: oxygen for powerful sprints and more muscle mass to power
Speaker 1: those bursts of energy. However, that's the ganders the geese
Speaker 1: in this situation. Lady athletes excel at endurance due to
Speaker 1: a multitude effectors, such as a higher body fat percentage
Speaker 1: that helps when they hit a wall figuratively, more slow
Speaker 1: twitch muscle fibers, and yes, emotional resilience in general, because
Speaker 1: some of these bodies have thrust a whole person out
Speaker 1: of their more sensitive aperture. So maybe an ultra marathon
Speaker 1: is like a walk in the park, but just without
Speaker 1: ever stopping until you've collapsed at the end.
Speaker 2: And that's a really complicated combination of skill, much more
Speaker 2: complicated than running one hundred meters, which you have to say,
Speaker 2: unne hundred meters and hard. It's just a much more
Speaker 2: focused thing, Whereas an ultra mouth involves planning, strategy, self knowledge, pacing,
Speaker 2: and math is like that because math isn't just about
Speaker 2: memorizing things or manipulating large numbers. Math is about spotting
Speaker 2: patterns and being able to perform abstractions in order to
Speaker 2: see patterns that previously weren't visible, and having ideas for
Speaker 2: how to group objects together to make structures that will
Speaker 2: be useful to us. It's a bit like designing a
Speaker 2: useful tool for building a house, except that it's an
Speaker 2: abstract tool for building ideas.
Speaker 1: Okay, so it's like a hammer to drive nails versus
Speaker 1: the idea of a hammer to drive the idea of
Speaker 1: a nail, which can be applied to the mathematics of
Speaker 1: the physics of the fabrication of the tool to drive
Speaker 1: the nails, which becomes the real hammer. Woodworkers, You love math, So.
Speaker 2: How on earth do you measure a biological predisposition for
Speaker 2: doing that? They're not skills that are just something that
Speaker 2: you can be born with. How are we going to
Speaker 2: test whether a newborn baby can do that? We can't.
Speaker 1: Well, what do you think about common core? Because I
Speaker 1: don't have kids, but all I know is that my
Speaker 1: friends with kids seem horrified or confused by common Core.
Speaker 1: I don't quite understand what it is. But why has
Speaker 1: there been this shift in the way that we're teaching math?
Speaker 1: And I guess like the last ten or so years.
Speaker 2: The reason there's been a shift in the way we're
Speaker 2: teaching math is because most people have acknowledged that it
Speaker 2: wasn't going very well. It's just people haven't really agreed
Speaker 2: on what to do about it. And I think one
Speaker 2: of the problems with changing the system is that a
Speaker 2: lot of teachers don't get autonomy over what they're allowed
Speaker 2: to teach. They get it planked on them and say,
Speaker 2: now you have to teach like this and that's that,
Speaker 2: and then you have to prepare people for standardized tests,
Speaker 2: and then you get judged on how they do in
Speaker 2: those standardized tests. And I think that that any time
Speaker 2: that we're aiming to teach people content like can you
Speaker 2: do this thing at the end of it, then that
Speaker 2: is going to be less successful than teaching them basically
Speaker 2: the appreciation and allowing teachers more autonomy to teach the
Speaker 2: things that they care about in the way that they
Speaker 2: care about. And as the world changes, some basic things
Speaker 2: become less important, just like the slide rule is not
Speaker 2: important anymore and controversial idea, but I don't think that
Speaker 2: long multiplication is important anymore. They've got calculators and it's
Speaker 2: just like learning to ride a horse. Isn't important anymore,
Speaker 2: which doesn't mean no one should learn to ride a horse.
Speaker 2: If someone learns riding a horse, great, but it's not
Speaker 2: an important it's not a crucial skill for most people's
Speaker 2: daily lives. And I think that sometimes parents get really
Speaker 2: upset if they don't understand the work that their children
Speaker 2: are being asked to do. And I've talked to many
Speaker 2: math teachers who say that the parents complain to them
Speaker 2: that it's not like it was when they were young.
Speaker 2: But then the teachers say to them, well, did you
Speaker 2: like math, and they go, no, I hated it. They go, well,
Speaker 2: why do you want me to do that to your children?
Speaker 1: Oh, it's sympathetic.
Speaker 2: And sometimes people say, oh, it's terrible, I can't help
Speaker 2: my children with their homework. And sometimes I want to go, well,
Speaker 2: don't help them with their homework, then it's their homework.
Speaker 1: Okay, this just didn't It turns out that I had
Speaker 1: no idea what common core really meant because I don't
Speaker 1: have kids and I don't listen.
Speaker 2: Well.
Speaker 1: So common Core was adopted in US states around twenty ten,
Speaker 1: and it's actually the set of standardized assessments measuring where
Speaker 1: kids should be for every school year. But that term
Speaker 1: common core, often mistakenly is applied to just this new
Speaker 1: way of teaching math that's more intuitive and is actually
Speaker 1: a very old way of doing math. So instead of
Speaker 1: going and fetching a piece of paper to figure out
Speaker 1: what's sixty three minus forty two and then borrowing some
Speaker 1: numbers and stacking figures on top of each other, kids learn, well,
Speaker 1: if you add one to forty two, than sixty three
Speaker 1: minus forty three would be twenty. So it's twenty plus one,
Speaker 1: which is twenty one. Because we all have pocket computers
Speaker 1: for the bigger arithmetic issues, teaching these quicker and less
Speaker 1: fussy ways of handling numerical concepts is more valuable and
Speaker 1: future generations will probably thank us when it comes to
Speaker 1: adding tips to dinner bills, that is, if American restaurant
Speaker 1: workers are still making minimum wage and at the mercy
Speaker 1: of groutsey customers to actually pay for the rent. We
Speaker 1: thought we'd have flying cars, but really just one healthcare Well,
Speaker 1: I wonder how do you think the world will change
Speaker 1: with a new generation learning math in a different way.
Speaker 1: Do you think we'll have more mathematicians, more statisticians, more scientists,
Speaker 1: or do you think will progress even faster through mathematics.
Speaker 2: Is that a good thing. I'm much more worried about
Speaker 2: the people who fall off and get put off and
Speaker 2: get traumatized by it. What I would like to see
Speaker 2: is not more mathematicians and more scientists. It's fewer people
Speaker 2: who hate it. That's what I really want to see.
Speaker 2: And partly because when there's half or more of adult
Speaker 2: humans who either hate math, are traumatized by it, or
Speaker 2: who are actively hostile towards math and science, we've got
Speaker 2: problems with persuading people that things like vaccines are real,
Speaker 2: that the pandemic is real, and that we need to
Speaker 2: do something about it, that climate change is definitely something
Speaker 2: that we need to worry about. I think that that's
Speaker 2: a big problem for the way that society is going,
Speaker 2: if people are ready to just believe those kind of lives.
Speaker 2: And I do think that my background and training in
Speaker 2: abstract mathematics really helps me to not be manipulated by
Speaker 2: people who are lying to me, and it helps me
Speaker 2: always to be aware of the frameworks for finding out
Speaker 2: whether information is good or not and deciding whether something
Speaker 2: that someone is saying is probably true or not. And
Speaker 2: I think that that is all part of what I
Speaker 2: think education should be aiming for. Not can you multiply
Speaker 2: these large numbers together, and can you calculate this thing
Speaker 2: and get the right tanswer? And can you solve this equation?
Speaker 2: But can you think clearly about the world around you.
Speaker 2: Can you make sure that people don't manipulate you and
Speaker 2: can't lie to you about things just so that they
Speaker 2: can get your vote or your money. And can we
Speaker 2: make a contribution to the world that benefits more people
Speaker 2: and not just ourselves.
Speaker 1: The way that social media is, I feel like we're
Speaker 1: going toward kind of a quantitative rather than a qualitative
Speaker 1: assessment of our lives. And maybe there creates a little
Speaker 1: bit of an anxiety around math there too. And we
Speaker 1: look at how many followers, how many likes something has
Speaker 1: we've really started to introduce numbers to things that are
Speaker 1: much more qualitative.
Speaker 2: Oh that's a really interesting point. Yeah, right. I think
Speaker 2: it's because society is trying to rank everything all the time.
Speaker 1: Yeah.
Speaker 2: And it starts in school because the system tries to
Speaker 2: rank students. But then we get into this this frame
Speaker 2: of mind where everything has to be ranked by a number.
Speaker 2: And it might sound funny because I'm a mathematician. I'm
Speaker 2: saying shouldn't rank things point number anymore, but tays in
Speaker 2: point is that at the School of the Art Institute
Speaker 2: where I teach, we don't have grades, and so there
Speaker 2: is an understanding that we are not trying to rank
Speaker 2: everybody by a gping because there are no grades, and
Speaker 2: I just think that's wonderful, so we can focus on
Speaker 2: educating rather than ranking.
Speaker 1: For more in this you can see the twenty twenty
Speaker 1: one paper grade Less Learning, The Effect of Eliminating Traditional
Speaker 1: grading practices on Student Engagement and Learning, which notes that
Speaker 1: throughout their study, it became clear that students want to learn.
Speaker 1: Accurate feedback is a vital part of the learning process,
Speaker 1: it says, but grades are not. The traditional grading system
Speaker 1: pits students and teachers against one another, often leading to
Speaker 1: either side bickering over fractions of percentage points, which I
Speaker 1: guess is applied mathematics. But I don't think that's the
Speaker 1: lesson here, and I wanted to ask a little bit
Speaker 1: about some basics for people who maybe are not math majors.
Speaker 1: But when things go from numerical to letters, we're in
Speaker 1: the learning process of math, from like arithmetic to pre
Speaker 1: algebra to algebra to precalculus to calculus, Like where do
Speaker 1: things start turning from numbers into letters? Why does that happen? Oh?
Speaker 2: Thank you? That is one of the questions that I
Speaker 2: address in the book because it is something people say
Speaker 2: to me a lot like. And so we're not with
Speaker 2: kind into letters exactly, and so we're thinking about the
Speaker 2: idea of a person, and so we don't name them
Speaker 2: because we don't know who they are, and so that's
Speaker 2: why we do that with numbers as well. It's possible.
Speaker 2: But I also introduced it like a murder mystery where
Speaker 2: someone is a murderer and you're trying to find out
Speaker 2: who they are, but you can't refer to them by
Speaker 2: naming it because you don't know who they are, a
Speaker 2: whole load of evidence about them and then you pin
Speaker 2: them down and go ah ah. It was actually changed
Speaker 2: or often in math, we're trying to find out what
Speaker 2: something is, but we don't know what it is yet,
Speaker 2: so how can we refer to it? So we use
Speaker 2: something like a pronoun, but it's a letter because that's
Speaker 2: what we do in math instead of a pronoun, And
Speaker 2: then we gather evidence about it and so we say, oh, well,
Speaker 2: it's related to this other thing like this, and when
Speaker 2: we do this to it, it behaves like that, and
Speaker 2: when we do this to it. So it's like twenty questions.
Speaker 2: You say, what happens when you do this? What happens
Speaker 2: when you do this to it? And then you find
Speaker 2: all these relationships. And so that's what solving equations is about.
Speaker 2: It's about putting that thing, you don't know what it
Speaker 2: is yet, into a relationship where you found out various
Speaker 2: aspects of its behavior. And now you find out now
Speaker 2: you can pin down what that thing actually is. And
Speaker 2: that is the point of using letters, and that is
Speaker 2: the point of solving equations. It really is like a
Speaker 2: murder and mystery. So anyone who enjoys any kind of
Speaker 2: murder mystery, I think that that's I think it's math.
Speaker 1: One thing that does not embarrass me is asking really
Speaker 1: basic questions for me and for the good of all
Speaker 1: of us, such as, what is the difference between a
Speaker 1: logarithm and an algorithm? They sound alike, are they friends?
Speaker 2: A logarithm is very different from an algorithm. Okay, A
Speaker 2: logarithm is a particular function, and it I'm now doing
Speaker 2: hand motions that doesn't help on an audio. So the
Speaker 2: graph of a logarithm, it starts down at infinity and
Speaker 2: it goes up really fast, and then it tails off.
Speaker 2: So it's kind of like the opposite of an exponential
Speaker 2: so much so that it actually is the opposite of
Speaker 2: an exponential, So it's the inverse of an exponential function,
Speaker 2: and so that tails off as it goes along. That's
Speaker 2: completely different from an algorithm. So an algorithm is a
Speaker 2: method for doing something, and it's a particular form of method,
Speaker 2: like a really really step by step recipe, the step
Speaker 2: by step process that you could tell a computer to do. So,
Speaker 2: for example, the dreaded long multiplication is an algorithm. It's
Speaker 2: a step by step process whereby you can follow these
Speaker 2: steps and multiply large numbers together by following the steps
Speaker 2: all the way through. But the algorithm says, if this happens,
Speaker 2: to do that, now, if this happens to do that now,
Speaker 2: it's like flow chart. And so that's not really math.
Speaker 2: And that's why I say that we don't really need
Speaker 2: long malved creation anymore, because it's an algorithm. It's a
Speaker 2: handy algorithm for doing something, but it's not really math.
Speaker 2: And when people say, the algorithm. Are you're talking about
Speaker 2: the Internet.
Speaker 1: Yeah, the algorithm is showing my videos, or the algorithm
Speaker 1: wants me to listen to the new Yes.
Speaker 2: Right, So that's a particular Really, it's a particular algorithm
Speaker 2: that the Internet, or most places we interact with it
Speaker 2: on the Internet, use some process for deciding how to
Speaker 2: show you something next. And it's a bit murky exactly
Speaker 2: what their process is, and that many people think that
Speaker 2: there's something nefarious going on behind it, which there probably is,
Speaker 2: and it's probably based on money. So they have applied
Speaker 2: some step by step algorithm, and that one really is
Speaker 2: implemented by computer to say, based on this person's previous activity,
Speaker 2: follow these steps and show them this next thing. That's
Speaker 2: kind of capital T capital a the algorithm.
Speaker 1: So this is the math that expertly hooks us with
Speaker 1: engaging but ultimately never satisfying, and infinity like scroll of content,
Speaker 1: just harvesting our tastes and churning out more like it
Speaker 1: back with this boggling speed. Now Twitter looks at half
Speaker 1: a billion tweets every day and then decides exactly what
Speaker 1: to show you. And one article titled the TikTok Algorithm
Speaker 1: knew my sexuality better than I did. Pretty much says
Speaker 1: it all. So we cover more of this in Yes,
Speaker 1: the tic Tocology episode with your favorite sycomer on there,
Speaker 1: mister Hank Green, and yeah, we will link that in
Speaker 1: the show notes.
Speaker 2: There are many other algorithms algorithms, and sometimes algorithms are
Speaker 2: great because they help us conserve our brain energy. And
Speaker 2: I think that's really important because our brains are finite
Speaker 2: and very puny, and so if we can concert that
Speaker 2: as much as possible, that's really helpful. So I personally
Speaker 2: have all sorts of algorithms for helping me run my life.
Speaker 2: And this may be me as a math magician speaking,
Speaker 2: but it's because I don't want to use up my
Speaker 2: brain energy on something that's kind of irrelevant.
Speaker 1: What do you have? Yeah, tell me, tell me? Tell me?
Speaker 2: For example, I have algorithms for where I buy more coffee.
Speaker 2: For example, Okay, tell me everything. So I buy five
Speaker 2: pound bags of beans, but then I keep a pot
Speaker 2: of them on the counter, So I refill the pot
Speaker 2: on the counter from the bag of beans, and then
Speaker 2: once the last bit of the bag of beans has
Speaker 2: filled the pot, then I immediately buy another bag of beans.
Speaker 2: So that it's ready by the time I get to
Speaker 2: the end of the pot, and I don't have to
Speaker 2: think about that. Now, maybe one day I can have
Speaker 2: a smart coffee bean pot which will automatically order it
Speaker 2: for me. But that is my algorithm for coffee beans.
Speaker 1: I love that those are algorithms. Can you tell me
Speaker 1: some other places where we don't realize there's math just
Speaker 1: everywhere I know a video going viral. I know you've
Speaker 1: seen sine waves in your wraps and rado. There's math
Speaker 1: in braids and halla. Where are some of the unexpected
Speaker 1: places where math is like really making our lives amazing.
Speaker 2: Well, one thing that I do when I'm walking across Chicago,
Speaker 2: which is on a grid, is that thing where I
Speaker 2: walk in one direction until I hit a stop sign,
Speaker 2: and so if I don't get a crosswalk the light
Speaker 2: on the crosswalk, then I turn and take the crosswalk
Speaker 2: going the other way, and then I keep going in
Speaker 2: that direction until So that's my algorithm for walking across Chicago,
Speaker 2: And there's some math in there that's telling us that
Speaker 2: wherever we turn it doesn't matter. So if I need
Speaker 2: to go five blocks east and ten blocks north, then
Speaker 2: it doesn't matter where I turn, it will still be
Speaker 2: the same distance of walking, as long as I consider
Speaker 2: that turning doesn't exhaust me. And that's actually a part
Speaker 2: of metrics spaces, and so a metric is a more
Speaker 2: general form of distance. And we think about distance usually
Speaker 2: as distance as the crow flies, but you don't fly
Speaker 2: like a crow when you're walking across Chicago. There are
Speaker 2: buildings in the way, and so the distance we actually
Speaker 2: need to go to get somewhere is not the distance
Speaker 2: of the crow flies. It's the distance along in this grid.
Speaker 2: And so we need to know that it doesn't matter,
Speaker 2: it doesn't matter where we turn, and that's intuitively kind
Speaker 2: of clear, right, And then you can do things like say,
Speaker 2: what's a circle if we're using this form of distance,
Speaker 2: because a circle doesn't quite look like a circle anymore.
Speaker 2: It looks more like a diamond shape. But that counts
Speaker 2: as a circle because it's all the points that are
Speaker 2: four blocks away from you. And I think that's kind
Speaker 2: of hilarious because I like things that challenge the received wisdom,
Speaker 2: which makes me sound like a pointless rebel, but I
Speaker 2: like to a point full rebel because maths about not
Speaker 2: making assumptions that you don't need to make, and I
Speaker 2: think that that's really important life as well, because a
Speaker 2: lot of the problems with society come from people making
Speaker 2: assumptions about other people that you don't need to make.
Speaker 2: Which doesn't mean we shouldn't make any assumptions about people,
Speaker 2: because actually that's impossible. As soon as we meet someone,
Speaker 2: we have to start somewhere, and so we have to
Speaker 2: have an instinctive, intuitive, gut response to them. But the
Speaker 2: really important thing is to be ready to change it
Speaker 2: when we get new information, and math is really about that.
Speaker 2: You can be aware you made them so that if
Speaker 2: they turn out not to be right, you can change
Speaker 2: them and then get a different result.
Speaker 1: It seems like once you embrace math, you understand that
Speaker 1: it can be very empowering and that could offer a
Speaker 1: lot of clarity.
Speaker 2: That is certainly what I think. So if that's the
Speaker 2: impression I've given you, that's fantastic. And I think I
Speaker 2: just realized I don't think I really addressed the part
Speaker 2: of your question earlier where you said why are people
Speaker 2: so put off it and afraid of it? And this
Speaker 2: is what makes me sad, because I think it's there
Speaker 2: to help us, and I think that it's not presented
Speaker 2: like that enough.
Speaker 1: Mm hmm, okay, I have some questions from listeners. They
Speaker 1: know that you secifically are coming on. But first let's
Speaker 1: raise the bottom line of a cause of the ologist choosing.
Speaker 1: And Eugenia pointed us toward Math Circles of Chicago dot org,
Speaker 1: whose mission statement says, we offer engaging, flexible and free
Speaker 1: math programs to students in grades three through twelve and
Speaker 1: focus on reaching black and Latino communities and other communities
Speaker 1: where most children live in low income households. You can
Speaker 1: find out more at Math Circles of Chicago dot org
Speaker 1: and that will be linked in the show notes. And
Speaker 1: that donation was made possible by sponsors of ologies. All right,
Speaker 1: let's divide and conquer your queries. One wonderful one that
Speaker 1: was asked by Mallory Skinner at doug Pace. Matty s,
Speaker 1: Talia Dunyak, Emily Stauffer, Devin Naples, Devin s As separately
Speaker 1: all asked this similar question. Oh wow, I want to know,
Speaker 1: please explain infinity in a way that my brain can
Speaker 1: really comprehend.
Speaker 2: Well, you know, infinity is really difficult, and so if
Speaker 2: you're bra if you feel like your brain isn't comprehending it,
Speaker 2: then maybe it is well wown. It's supposed to be
Speaker 2: mind blowing. If people who think they understand infinity are
Speaker 2: kind of just deluded, so and so I think that
Speaker 2: the correct feeling is to feel like it's too mind
Speaker 2: boggling to get your head around. That's the whole point
Speaker 2: of it. It's bigger than anything that we can think of.
Speaker 2: It behaves in really weird ways. And I think what
Speaker 2: often makes some people mathematicians and some people mathphobic is
Speaker 2: embracing the feeling of not understanding something, rather than taking
Speaker 2: it as a sign you're bad, taking it as a
Speaker 2: sign that there's something really interesting going on. If you
Speaker 2: go to the edge of a cliff. I don't like
Speaker 2: looking over the edge of a cliff because I'm worried
Speaker 2: I will fall and die. And I think that there's
Speaker 2: a similar kind of vertigo that sometimes people get when
Speaker 2: thinking about math concepts. And people have been so humiliated
Speaker 2: and traumatized by their past math experience that it feels
Speaker 2: like it's they're going to get hurt if they look
Speaker 2: over that cliff. And what I want to say is
Speaker 2: that you're not going to die anyway. By looking over
Speaker 2: the mathematical cliff, you might get some emotions dug up
Speaker 2: from some past negative experiences. But the good thing is
Speaker 2: that you won't physically die by looking over the math cliff.
Speaker 2: And the thing that's over the math cliff is something
Speaker 2: that maybe kind of gives you intellectual vertigo. I don't
Speaker 2: run away from those things, and I think that's the
Speaker 2: only difference. It's not that I'm better at it or something.
Speaker 2: It's just that I have decided that I'm interested in it,
Speaker 2: and that it's not a sign that I'm bad at it.
Speaker 2: If I don't understand it, I don't understand anything. If
Speaker 2: I think about it hard enough. The number one? What
Speaker 2: even is that I can't understand the number one. If
Speaker 2: I don't understand the number one, how am I going
Speaker 2: to understand infinity? But that's what drives us to do
Speaker 2: more research. It's the feeling that there is always more
Speaker 2: there to understand, and we want to understand it. We
Speaker 2: don't go, oh, I can't understand this. We go, oh,
Speaker 2: I want to understand more. I'm never going to understand
Speaker 2: all of it, but that doesn't mean I'm going to
Speaker 2: give up. I'm just going to keep trying to understand
Speaker 2: more all the time I can.
Speaker 1: Some people call this a growth versus a fixed mindset,
Speaker 1: and fixed mindsets tend to be afraid to try and fail.
Speaker 1: The growth is like, you know, whatever happens. I learned
Speaker 1: some and from personal experience. Two of the smartest people
Speaker 1: I've ever encountered, my friends, doctors Casey Handmer and Christine Corbett,
Speaker 1: have worked at NASA. Casey now heads Terraform Industries, working
Speaker 1: on these new ways to capture atmospheric carbon and turn
Speaker 1: it into natural gas. Then one thing about the two
Speaker 1: of them, and they're merrit, is that they just try stuff.
Speaker 1: They want to learn something, they just dive right in.
Speaker 1: As a result, doctor Corbett has an extra master's in
Speaker 1: creative writing and just got a black belt in kung fu.
Speaker 1: They are smart people who ask smart people sometimes basic questions.
Speaker 1: And Casey once told me the key to how much
Speaker 1: they get done is that they just learn shamelessly from
Speaker 1: any failure they get it, they keep moving. So they
Speaker 1: are heroes. They are not zeros. Oh, which reminds me
Speaker 1: that Brennett had a question on that note. Jenny Lowl Rhodes,
Speaker 1: Maggie Morgan, Star, Lilian Right, Christine Fixteine, Megsi, Lily Hagadon,
Speaker 1: and Brenna Pixley. I'll have questions about zero. Jenny wants
Speaker 1: to know how long has zero been a thing? Maggie's like,
Speaker 1: is zero a number?
Speaker 2: Great questions. I do know that it has troubled people
Speaker 2: for thousands of years about whether it really ought to
Speaker 2: count as a number or not. My recollection is that
Speaker 2: maybe the Greeks or the Romans one or the other,
Speaker 2: or maybe both that were really unconvinced that zero should
Speaker 2: count as the number philosophically, it really bothers them, and
Speaker 2: that really helped them back, because here's the thing. You
Speaker 2: can decide whether you want zero to count as a
Speaker 2: number or not, but the question is how does it
Speaker 2: help us? There are often no right and wrong answers
Speaker 2: to these things. Meticians say, Okay, here's a world in
Speaker 2: which this thing is true, and here's a different world
Speaker 2: in which something else is true. Which one is going
Speaker 2: to help us? So we can make a world in
Speaker 2: which zero isn't a number, We're not going to be
Speaker 2: able to do very much there. Zero is a really
Speaker 2: helpful number to have around because if we're going to
Speaker 2: represent nothing, what are we going to represent it with
Speaker 2: if we subtract five from five, what do we get
Speaker 2: If we don't have a number called zero, we can't
Speaker 2: do that, and then we can't really make negative numbers either.
Speaker 2: If we can't make negative numbers, there are all sorts
Speaker 2: of things we can't do. And so if we do
Speaker 2: call zero a number, then we do get to do
Speaker 2: all these things. And so that's why mathematicians generally have
Speaker 2: decided that zero should get to count as a number,
Speaker 2: just so that we can do all of those things.
Speaker 2: It's just language. So as long as we can manipulate
Speaker 2: zero in some way, we can get to do those things.
Speaker 2: If you feel like you don't want to call it
Speaker 2: a number, then that's fine, don't call it a number,
Speaker 2: as long as you can still manipulate it in those ways,
Speaker 2: because it's really helpful to do it.
Speaker 1: So zero we can wrap our brains around that. Some
Speaker 1: of you had a weirder concept plaguing you, such as
Speaker 1: Anna Thompson, Jennifer Lemon, Ariel van Sand, Christina kuns, Eleanora
Speaker 1: Renaud Vanville, c J. Wyatt, Tony Vessels, Sarah val McKelvey,
Speaker 1: Felicia Chandler, Valerie Bertha and first time question asker build
Speaker 1: a branch, and Christina Kuhns asks imaginary numbers? What the fuck?
Speaker 1: What is the imaginar number? What's going on?
Speaker 2: Yeah, this is great and this is a great thing
Speaker 2: to say after is zero a number? Because sometimes people
Speaker 2: go are imagining numbers and number So magnaticians really don't
Speaker 2: like having rules impose on them. And it makes me
Speaker 2: sad that one of the things that puts people off
Speaker 2: math is that there seems to be all of these
Speaker 2: rules that you have to follow, whereas math magicians go, wait, okay,
Speaker 2: those rules. We had to follow those rules in this world,
Speaker 2: but I don't want to follow them anymore. Can I
Speaker 2: build a different world in which I don't have to
Speaker 2: follow those rules? And so one of the rules mathematicians
Speaker 2: don't like having to follow, and I do talk about
Speaker 2: this in the book, is you can't take the square
Speaker 2: root of a negative number. Well, why can't you take
Speaker 2: the square to a negative number, because if you try
Speaker 2: squaring numbers, square routing is sort of the opposite of squaring, right,
Speaker 2: So you're saying, is there any number such that when
Speaker 2: I multiply it by itself, I get negative one? Well,
Speaker 2: let's think about that. If I multiply a positive number
Speaker 2: by itself, I get a positive number. If I multiply
Speaker 2: a negative number by itself, I also get a positive number.
Speaker 3: You are employing a double negative.
Speaker 2: So we seem to be out of options for things.
Speaker 2: We could multiply by themselves and get a negative number,
Speaker 2: but mathematicians go, never mind, I'll just make something up
Speaker 2: and someone else. And so it's called an imaginary number
Speaker 2: because we sort of just imagined it. And the wonderful
Speaker 2: thing about abstract concepts is as soon as you imagine them,
Speaker 2: they become something that exists because it's an abstract concept.
Speaker 2: And so I would love to imagine my dinner and
Speaker 2: for it just to exist. That doesn't work like that.
Speaker 2: Or you imagine some dollars in my bank account, Oh,
Speaker 2: there they are, But I love that at that mouth
Speaker 2: you can just imagine something into existence. So you just
Speaker 2: imagine that there is something, and you take it square
Speaker 2: and it is negative one. So what is it? Well,
Speaker 2: it doesn't really matter, because in mouth, it doesn't matter
Speaker 2: what something is. It only matters what it does. And
Speaker 2: I think this is a wonderful thing to think about
Speaker 2: in life as well, because really it shouldn't matter what
Speaker 2: somebody is. No, it shouldn't matter what the color of
Speaker 2: their skin is, or what they look like, or how
Speaker 2: large they are, or or what gender they are anything
Speaker 2: that it should only really matter what they do. Are
Speaker 2: they a nice person? Are they helpful? Are they kind?
Speaker 2: Are they generous? Those kinds of things. And so in
Speaker 2: math we kind of put aside the question of what
Speaker 2: that imagining of it is. We just say what does
Speaker 2: it do? And it's like when children make up a game,
Speaker 2: they will make up a whole world and they will
Speaker 2: play that game. And that's what math is. But then
Speaker 2: it goes work further because it goes, oh is this helpful? Crikey?
Speaker 2: It actually is. It starts off as being just kind
Speaker 2: of ludicrous game that we're playing in our heads, beople
Speaker 2: turned out to be really helpful for solving problems in physics.
Speaker 2: It's not extraordinary, And I just think it's extraordinary that
Speaker 2: this thing that we made up that doesn't have any
Speaker 2: physical reality to it is helpful in physics. Because what
Speaker 2: happens is that you draw pictures of it, and when
Speaker 2: you have ordinary numbers, you draw them on a number line. Right,
Speaker 2: We put numbers on a line, and it's one line.
Speaker 2: A line is very flat, it's one dimensional. But if
Speaker 2: you don't add imaginary numbers into that mix, where do
Speaker 2: you imaginary numbers go, Well, they're not on the line,
Speaker 2: so they just have to go in a different direction,
Speaker 2: so you can just make them sort of go up
Speaker 2: the pain. And then when you mix all those things up,
Speaker 2: you get a two dimensional space instead of a one
Speaker 2: dimensional space. And you know, in two dimensional space you
Speaker 2: can see beautiful patterns that you can't see in one
Speaker 2: dimensional space because it's so incredibly thin. A line is
Speaker 2: just too thin. You can't see patterns, whereas in the
Speaker 2: two dimensional space you can see gorgeous patterns. And that's
Speaker 2: how it's helpful in things like physics, because you see
Speaker 2: you work out the patterns using the two dimensional space,
Speaker 2: and then once you apply it to the real world
Speaker 2: again you just take the part that's on the line.
Speaker 2: But it's just that you can recognize what the patterns
Speaker 2: are because you are exploring them in two dimensional space.
Speaker 2: It's kind of like if you're clearing out your closet,
Speaker 2: you kind of need to take everything off the rail
Speaker 2: and spread it out on your bed before you put
Speaker 2: it back on the rail again.
Speaker 1: So behind every perfectly, Marie condoed closet is the chaos
Speaker 1: and the pain and the discovery and the beauty of
Speaker 1: purging and whittling what's hiding in the universe's little crevices
Speaker 1: and corners. Well, kind of on that note too, Felicia
Speaker 1: Chandler and James Dean Cotton want to know about the
Speaker 1: Fibonacci sequence, and Felicia asks, why do we see it
Speaker 1: so much of nature? I imagine that Dan Brown's the
Speaker 1: Da Vinci code really put the Fibonacci sequence on the map.
Speaker 4: I'm into somebody here that I cannot understand.
Speaker 1: What does math have to say about that particular equation
Speaker 1: in nati.
Speaker 2: So perhaps I should remind everyone that the Fibonacci sequence
Speaker 2: starts one one, and then you add up the two
Speaker 2: previous numbers to produce the next number. So you get one,
Speaker 2: add one, which is two, and then you add that
Speaker 2: to the previous number one a two, which is three.
Speaker 2: Then you get five, and then you get eight, and
Speaker 2: then get thirteen and so on.
Speaker 1: Okay, so just a quick primer Fibonacci. Leonardo Pizzano was
Speaker 1: an Italian guy who around the year twelve hundred wrote
Speaker 1: a book about math and popularized the standard Hindu Arabic
Speaker 1: numerals in Europe. Everyone loved him for it, thought he
Speaker 1: was dope at math, and then he died and everyone
Speaker 1: forgot about him for like four hundred years until the
Speaker 1: eighteen hundreds. Two things, he didn't actually invent or discover
Speaker 1: the Fibonacci sequence that dates back to at least three
Speaker 1: hundred BCE, when this Indian poet Bengala was already down
Speaker 1: with it. Not Fibonacci's fault that we named the sequence
Speaker 1: after him. Another thing is that Fibonacci was from Pisa,
Speaker 1: which is where the Leaning Tower of Pisa is and
Speaker 1: it was built around twelve hundred during his life span.
Speaker 1: So where was he when it came to applied mathematics. Yeah,
Speaker 1: I'm super busy these days. Also, I didn't intend this,
Speaker 1: but worldwide Fibonacci Day is this week, occurring on the
Speaker 1: same day as the dog holiday, Wolfanut and American Thanksgiving.
Speaker 1: But every year you can celebrate Fibonacci by eating artichokes
Speaker 1: and romanescuco and pineapple because eleven twenty three is Fibonacci esque,
Speaker 1: even though again it wasn't him to discover the sequence. Also,
Speaker 1: I need you to note that I only found out
Speaker 1: about Fibonacci day because I googled was Fibonacci hot? And
Speaker 1: I happened upon a blog that mentioned one, one, two, three,
Speaker 1: and that there is little known of his physical appearance.
Speaker 1: I don't know. I just have a hunch. I bet
Speaker 1: he was hot, maybe like a ten.
Speaker 2: I think the first thing to say is that it
Speaker 2: is not quite as prevalent as its popularity may suggest.
Speaker 1: Okay, that's good to know.
Speaker 2: It's point the golden ratio, which isn't nearly as prevalent
Speaker 2: as its popularity would would indicate either. But I think
Speaker 2: the reason is that nature. I don't want to anthropopomorphized
Speaker 2: nature too much, but nature is trying to do as
Speaker 2: much as it can with the smallest starting point as possible,
Speaker 2: because that's kind of efficient. And why that is the
Speaker 2: case is a whole deep philosophical or possibly biological question,
Speaker 2: but it may be to do with survival of the
Speaker 2: fittest and evolution. The things that survived are the ones
Speaker 2: which did the most possible stuff with the smallest possible
Speaker 2: amount of information, and so sometimes it really is a
Speaker 2: sheer mathematical situation. So, for example, the spirals on a
Speaker 2: pineapple are typically Febonanci numbers, and so if you count
Speaker 2: how many spirals there are in each of the different directions,
Speaker 2: there are three different directions that spirals on a pineapple
Speaker 2: can take. There's the kind of really vertical direction, there's
Speaker 2: the more obvious slanty direction, and then there's the really
Speaker 2: really really that's less obvious. And the thing is that
Speaker 2: geometrically the two smaller numbers have to add up to
Speaker 2: the bigger one that you can work that out on
Speaker 2: any shape at all. Why they typically turn out to
Speaker 2: be feb Naci numbers may be something to do with
Speaker 2: the way that the little fruitlets grow, and it's the
Speaker 2: same with the leaves on the stem of a plant,
Speaker 2: that they grow at different angles, spiraling around the plant,
Speaker 2: possibly to get as much sunlight as possible, and the angles,
Speaker 2: the way that the angles work in a feber Narchi
Speaker 2: sequence is sort of to try and make sure the
Speaker 2: next time a leaf lines up with the one beneath it,
Speaker 2: it's as far away as possible. But it's often only
Speaker 2: a very small part of the feber Narci sequence, so
Speaker 2: it's just like two consecutive numbers or something, and so
Speaker 2: that's why I think it's not quite so prevalent. If
Speaker 2: you have if you have leaves spiraling around and it
Speaker 2: happens to be in a pattern three and five, that's
Speaker 2: only two numbers out of the feber Archi sequence, So
Speaker 2: I wouldn't oh, wow, it's a Febonachi sequet. And maybe
Speaker 2: it's just three and five and it's nothing to do
Speaker 2: with the Fibonacci sequence at all. And sometimes the reason
Speaker 2: that something that's constructed very simply in mouth pops up
Speaker 2: all over the place is a beautiful and maybe slightly
Speaker 2: mysterious thing, and that's one of the things that's wonderful
Speaker 2: about it. And that is maybe not an answerable question.
Speaker 2: And this is why sometimes people believe in a higher being,
Speaker 2: because it seems like some higher being created now. But
Speaker 2: I personally don't feel the need to say that it
Speaker 2: was a higher being, a specific kind of delineated higher being.
Speaker 2: I just think that Math is a higher being.
Speaker 3: Math is my co pilot.
Speaker 1: This one was on the minds of Chimpumpeo, Milan Il
Speaker 1: Niki Mushroom, Morgan, Rachel Gardner, Taylor, the ren you know,
Speaker 1: Karina Reagan, Felix, Osel klarenerk and listener Victoria Sauder, who
Speaker 1: wrote be a Patreon our karmsashologies. I'm so excited you're
Speaker 1: talking to Eugenia Chang. I have huge math crash on her.
Speaker 1: I have two of her books, Victoria Rights. As a teacher,
Speaker 1: I believe math is for everybody, and I try to
Speaker 1: make clearer that math isn't an isolated subject when we
Speaker 1: use it to understand all parts of the world. Suggestions
Speaker 1: to bring maths into the living room, so to speak,
Speaker 1: that's a little juicier, Victoria Rights. Last question from listeners,
Speaker 1: So many people wanted your expert advice, and Elsa Sparks
Speaker 1: wanted to know any recommendations for teaching number sense to
Speaker 1: very young students. Blessed are the cheesemakers, I asked math
Speaker 1: professor here, do you have any advice for college professors
Speaker 1: or any teachers who want to improve their teaching? So
Speaker 1: any advice to people teaching or learning math that you
Speaker 1: feel like has been empowering to people, well, see her book.
Speaker 2: This is why I write all my books to try
Speaker 2: and give people ideas and help people get over their
Speaker 2: past forumas I think that one of the messages that
Speaker 2: I most want to say to everyone who's learning math,
Speaker 2: and therefore I want everyone who's teaching it so also us.
Speaker 2: That on is that if you find it hard, that
Speaker 2: doesn't mean you're bad at it. You're probably just right.
Speaker 2: It is hard, and that that's not a reason to
Speaker 2: be put off it. And if you look around you
Speaker 2: and it seems that other people are finding it easier,
Speaker 2: they might just be talking out of their arm pits
Speaker 2: in order to intimidate other people. Because most mathematicians, in fact,
Speaker 2: every mathematician I know, thinks they're stupid and finds everything
Speaker 2: very difficult.
Speaker 1: Is that true?
Speaker 2: Yes, that is the I think that is a real
Speaker 2: it's a correct impulse to think it's hard, because it
Speaker 2: is hard. But the point is we can keep understanding
Speaker 2: more of it all the time. And I think that
Speaker 2: that celebrating the questions that children ask and not being
Speaker 2: afraid if it's a question that you don't know how
Speaker 2: to answer, because then you can celebrate them for having
Speaker 2: asked a question you don't know how to answer, and
Speaker 2: then we can all learn about how you discover answers
Speaker 2: to questions. And then if it's a question that nobody
Speaker 2: knows the answer to, like why does the fee the
Speaker 2: Nachi sequence come from nature. Then you can say to
Speaker 2: A twelve, if you become an expert in that field,
Speaker 2: you could be the one who answers it, and then
Speaker 2: you could be the one going on this podcast explaining
Speaker 2: it to other people.
Speaker 1: Please do what about I always have to end with these,
Speaker 1: but what's your least favorite thing about what you do
Speaker 1: as a professional abstract mathematician.
Speaker 2: I think it is overcoming people's misconceptions, and it's the
Speaker 2: fact that the misconceptions are so deeply embedded culturally, and
Speaker 2: that's what I'm trying to overcome. I'm not trying to
Speaker 2: get everybody to love math, because we don't all have
Speaker 2: to love the same things, right, I'm just trying to
Speaker 2: show it for what it really is. If everyone saw
Speaker 2: it for what I think it is and they still
Speaker 2: didn't like it, then you know, fine, we can all
Speaker 2: like different things. It's the fact that people see some
Speaker 2: really really narrow, shallow side of it and then write
Speaker 2: it off from their lives when I think it can
Speaker 2: everybody that I find that frustrating. But that's the challenge.
Speaker 2: It's to overcome those deeply embedded misconceptions. And it's been
Speaker 2: so great talking to you about it, because it doesn't
Speaker 2: sound like you have those things. But sometimes even getting
Speaker 2: something published can be difficult because the people who want
Speaker 2: to publish something have their own misconceptions and go, well,
Speaker 2: I want you to write about math, but this isn't math,
Speaker 2: And so then I have to persuade them that this
Speaker 2: is math.
Speaker 1: What about your favorite thing or your favorite number, your
Speaker 1: favorite theorem, your favorite moment, what has just made your
Speaker 1: heart seeing the most in your career.
Speaker 2: My favorite thing is being able to help people understand
Speaker 2: something they didn't previously understand and seeing their gasps of
Speaker 2: delight when some mathematical thing has got them to be
Speaker 2: as excited as when I see it. That is what
Speaker 2: gives me the most joy in math, I think is
Speaker 2: being able to give them enjoy to other people.
Speaker 1: I wonder if there's a word in any language for
Speaker 1: that moment when something clicks, when you are figuring it out,
Speaker 1: figuring out, figuring out, you don't get it. You don't
Speaker 1: get it. And I've been I've sat in calculus classes before,
Speaker 1: I don't get it, and then suddenly something changes over
Speaker 1: and you're like, I get it, I get it. I
Speaker 1: get it, whether it's a joke, or whether it is
Speaker 1: a theorem or something. I wonder what is happening in
Speaker 1: the brain, because that moment is just unlike anything else
Speaker 1: when you finally get it, and it really.
Speaker 2: Feels like pieces falling physically into place, doesn't it.
Speaker 1: Mm hmm it does.
Speaker 2: Yeah, I'm fascinated by the brain. I'd love to try
Speaker 2: and do brain scans while I'm doing things like that
Speaker 2: to try and see what's going on.
Speaker 1: This has just been such a joy.
Speaker 2: Oh, I've been really enjoyed it too. Thank you so much.
Speaker 1: So you have it. Ask the simplest questions and you'll
Speaker 1: learn the deepest truths. And for more on that, you
Speaker 1: can see doctor Eugenia Chang's Frickin' book titled is math
Speaker 1: Reel How Simple Questions lead Us to Mathematics Deepest Truths,
Speaker 1: which is linked in the show notes alongside her website
Speaker 1: and her social media. We are at ologies on Instagram
Speaker 1: and I guess Twitter, but I'm at Aliward with one
Speaker 1: L on both. An Ologies merch is available at ologies
Speaker 1: merch dot com. In case you need holiday gifts, smologies
Speaker 1: are available for free. They are g rated. They're at
Speaker 1: Alleyward dot com. Slash smologies. Those are kid friendly versions
Speaker 1: of classic episodes. To join Patreon and submit your questions
Speaker 1: before recording, head to patreon dot com. Slash Ologies Aaron
Speaker 1: Talbert admin's the Oologies podcast facebook group. Emily White of
Speaker 1: The Wordy makes our professional transcripts. Noel Dilworth is scheduling producer.
Speaker 1: Susan Hale is our major managing director who also assisted
Speaker 1: in research for this episode. Kelly arn Dwyer makes the
Speaker 1: website Seecred Wiguz Thomas and Jerry Slieper of Mindgem Media
Speaker 1: worked on Smologies alongside our lead editor of this episode
Speaker 1: and of Ologies, the infinitely talented Mercedes Maitland of Maitland Audio.
Speaker 1: Nick Thorburn wrote the theme music and if you stick
Speaker 1: around after the show, I tell you a secret. Okay,
Speaker 1: So this week it's that I used to make cocktail
Speaker 1: recipes for cooking sites. I used to write about life
Speaker 1: way back when, so I'm pretty versed in making cocktails.
Speaker 1: Like at a party, people would be like, we got
Speaker 1: some pepperminte schnops and a cantalope and a pixie stick
Speaker 1: and some tabasco makes up out of it, and I
Speaker 1: could usually whip something up. But I'm not much of
Speaker 1: like a make cocktails at home kind of person these days,
Speaker 1: pretty chill. But I just found myself making a beverage
Speaker 1: and I use like some lemon powder and some peach
Speaker 1: emergency and uh keeping scoop of metamucil, and I had
Speaker 1: it an analogene and I was just shaking that thing
Speaker 1: up because you have to. And I realized that the
Speaker 1: muscle memory of the cocktail shaking is still there. It's
Speaker 1: still strong, but just a very different contents and very
Speaker 1: different vibe. But hey, you gotta hydrate, gotta get those electrolytes.
Speaker 1: Colon motility is important, and so is math. Math is real,
Speaker 1: but nothing's real, and life is very beautiful and meta
Speaker 1: mucil can be tasty all right. By Pacaderman Coollege hommeology, cryptozoology,
Speaker 1: lithology and mnology, meteorology, wold fedatology, menthology, seriology, seleology.
Speaker 2: Math is elegant, Math is fun