Speaker 1: There's this infinite series of actions you have to complete
Speaker 1: just to high five somebody. And this is true of
Speaker 1: all motion. It feels like all change, anything that you
Speaker 1: want to happen, you can decompose it into an infinite
Speaker 1: series of steps, which, certainly from a perspective making change
Speaker 1: in your life is very daunting thought that somehow any
Speaker 1: change is infinite in scope.
Speaker 2: Welcome to the one you feed throughout time. Great thinkers
Speaker 2: have recognized the importance of the thoughts we have. Quotes
Speaker 2: like garbage in, garbage out, or you are what you think,
Speaker 2: ring true. And yet for many of us, our thoughts
Speaker 2: don't strengthen or empower us. We tend toward negativity, self pity, jealousy,
Speaker 2: or fear. We see what we don't have instead of
Speaker 2: what we do. We think things that hold us back
Speaker 2: and dampen our spirit. But it's not just about thinking.
Speaker 2: Our actions matter. It takes conscious, consistent and creative effort
Speaker 2: to make a life worth life. It This podcast is
Speaker 2: about how other people keep themselves moving in the right direction,
Speaker 2: how they feed their good wolf.
Speaker 3: Math has always been a challenge for me, so naturally,
Speaker 3: I figured why not have a math expert on the podcast?
Speaker 3: Really as a way to explore how we handle challenges
Speaker 3: in general. Today, I'm talking with Ben Orlan, who's a
Speaker 3: math teacher and author who makes problem solving feel surprisingly human.
Speaker 3: We'll explore why struggling is actually a good sign, how
Speaker 3: humor helps us push through tough moments, and even what
Speaker 3: a dog retrieving a ball can teach us about calculus.
Speaker 3: I've spent most of my life intimidated by complex math,
Speaker 3: but as I talked with Ben, I realize that how
Speaker 3: we approach math mirrors how we approach any challenge, whether
Speaker 3: it's breaking a habit, learning something new, or facing uncertainty.
Speaker 3: By the end of this episode, you might not just
Speaker 3: rethink math, you might rethink how you take on hard things.
Speaker 3: I'm Yeric's and this is the one you feed. Hi Ben,
Speaker 3: Welcome to the show.
Speaker 4: Yeah, hi Erk, thanks so much for having me.
Speaker 3: I'm excited to have you on. You are a little
Speaker 3: bit of an odd guest for us. I don't mean
Speaker 3: that you're odd as a person, although perhaps you are.
Speaker 3: I think that's a good thing.
Speaker 1: But yeah, I get that at dinner parties want to
Speaker 1: show up. You're odd guest for us.
Speaker 3: Yeah, you're writing books about mathematics, which is a topic
Speaker 3: we have literally never covered except me trotting out some
Speaker 3: sort of cliched like happiness equations or something. But I
Speaker 3: was really taken by first the title of your book,
Speaker 3: and then as I look deeper into your work, some
Speaker 3: of the other titles and some of the ideas that
Speaker 3: you're playing with. And your new book is called Math
Speaker 3: for English Majors, a human take on the universal language.
Speaker 3: So I think there's a lot that we can cover that. Listeners,
Speaker 3: I think you're going to be surprised at how interesting
Speaker 3: this is, particularly if you don't like math or you're
Speaker 3: afraid of math. This is a great conversation. So we're
Speaker 3: going to start, however, like we always do with the parable.
Speaker 3: And in the Parable, there's a grandparent who's talking with
Speaker 3: their grandchild and they say, in life, there are two
Speaker 3: wolves inside of us that are always at battle. One
Speaker 3: is a good wolf, which represents things like kindness and
Speaker 3: bravery and love, and the other's a bad wolf, which
Speaker 3: represents things like greed and hatred and fear. And the
Speaker 3: grandchild stops and they think about it for a second.
Speaker 3: They look up at their grandparent and they say, well,
Speaker 3: which one wins? And the grandparents says the one you feed.
Speaker 3: So I'd like to start off by asking you what
Speaker 3: that parable means to you in your life and in
Speaker 3: the work that you do.
Speaker 1: Yeah, I think of the feeding as the what you
Speaker 1: do every day. I think sometimes I give into the
Speaker 1: temptation to want to imagine I have this self which
Speaker 1: is somehow separate from the way I spend my time.
Speaker 1: There's this me and I have this high opinion of myself. Maybe,
Speaker 1: but if you look at what I'm doing day by
Speaker 1: day and week by week, it's like, well, am I
Speaker 1: doing those things that I claim to value?
Speaker 4: And so as a teacher, I think about this.
Speaker 1: As a teacher, you're sort of always on the clock
Speaker 1: in some sense, you know, when the students are in
Speaker 1: the classroom with you. Yeah, they're taking the lesson from
Speaker 1: whatever it is you're doing that day. They're not taking
Speaker 1: some lesson you've imagined in your head. And so to me,
Speaker 1: that's what the feeding is, as how are you spending
Speaker 1: every minute, every hour.
Speaker 3: I love that idea. There's a concept out there that
Speaker 3: I know has a name, but I don't know what
Speaker 3: the name is. It's a concept in the mental health
Speaker 3: world a little bit and it basically says that if
Speaker 3: you want to know what somebody values, look at what
Speaker 3: they do actually do, not what they say. I think
Speaker 3: that's a little reductive. I get it because I do
Speaker 3: think it's true that that does show at least what
Speaker 3: our operating values are at the time. But I also
Speaker 3: think that there are ways in which we can get
Speaker 3: better at bridging the gap between that idealized self that
Speaker 3: you talked about in your head and the actual self
Speaker 3: that shows up day to day. Because there's a lot
Speaker 3: of time in my life if you took who I
Speaker 3: was only measured by what I did, you'd be like,
Speaker 3: that guy is a piece of shit, right, Like that
Speaker 3: guy is a real asshole, because I mean I was
Speaker 3: a heroin addict. I mean I was not behaving well,
Speaker 3: and I like to think that wasn't all that was
Speaker 3: true in those moments.
Speaker 4: No, I think that's fair.
Speaker 1: Maybe that's why I think having the multiple wolves and
Speaker 1: the stories is an apt metaphor, because we're not these unified,
Speaker 1: coherent people. Yeah, you can't look at someone and say, ah, yes,
Speaker 1: this is the explanation for their behavior and who they
Speaker 1: are and what they do. It's like, we're not that tidy.
Speaker 1: We're not characters in a fable. We're something much more
Speaker 1: complex than that.
Speaker 3: So let's take that idea there that we're something much
Speaker 3: more complex than that, because we really are. And if
Speaker 3: there's one thing that I sort of push against in
Speaker 3: the space that I'm in is the idea of easy answers,
Speaker 3: the idea that like there's this one size fits all formula,
Speaker 3: or there's these five easy tricks or all of that.
Speaker 3: And I heard you say on a different show. I'm
Speaker 3: not going to get this exact, but you basically said
Speaker 3: that one of the things to be a good problem
Speaker 3: solver is, instead of trying to immediately solve the problem,
Speaker 3: is to relax a little bit into what the problem
Speaker 3: is and explore it a little bit more before you
Speaker 3: move on to solutions. Say a little bit more about that.
Speaker 1: Yeah, Yeah, I've talked about this with students and in
Speaker 1: my writing a little bit. I think if there's certainly
Speaker 1: these four stages of solving a problem, and mathematics is
Speaker 1: a really good place actually for learning these stages, because
Speaker 1: mathematics is a series of challenges of problems that you
Speaker 1: run into, and some of them are routine, you know,
Speaker 1: sort of exercises. It's like doing your weightlifting for the day,
Speaker 1: and you don't get stuck on those. You can just
Speaker 1: kind of move through them. But sometimes you run into
Speaker 1: a problem and you don't know what to do. The
Speaker 1: first thing you try it doesn't work, and then there's
Speaker 1: a temptation to just bounce off that problem and go
Speaker 1: do something else with your day. Especially in math, there's
Speaker 1: a lot of ways to spend a day other than
Speaker 1: doing mathematics. So I know this with my students, like
Speaker 1: there's other ways to spend their time. So when a
Speaker 1: student runs into a problem that they're stuck with, my
Speaker 1: first piece of advice is to stop trying to guess
Speaker 1: the answer or stop trying to solve it right away.
Speaker 1: I remember one time, this is a class of seventh
Speaker 1: grader as I was teaching, and it gave them a
Speaker 1: problem that I thought was going to take the whole
Speaker 1: lesson to solve, but they weren't accustomed to problems like that,
Speaker 1: so some of them just started shouting out guesses, right,
Speaker 1: is it twelve?
Speaker 4: Is it fourteen?
Speaker 1: And it was like, you're probably not going to guess
Speaker 1: the answer in the first thirty seconds. So my advice
Speaker 1: in those situations and beyond math too. Is two explore
Speaker 1: the problem, to make the goal for that next ten minutes,
Speaker 1: for that next half hour, not to solve the problem,
Speaker 1: but to figure out what would a solution look like.
Speaker 1: What are the obstacles here, what's the tension in this problem?
Speaker 1: Why isn't there an easy answer? What other things that
Speaker 1: people have tried maybe for this problem? You know, to
Speaker 1: view it as you're researching and playing with the problem
Speaker 1: rather than trying to solve it. This is something that
Speaker 1: research mathematicians, the people who are trying to solve new
Speaker 1: math problems, tend to be very very good at because
Speaker 1: those problems can take years to solve. I mean some
Speaker 1: of them can take centuries. They're sort of passed on
Speaker 1: generation to generation, and so you have to be patient.
Speaker 1: And sometimes progress on a problem doesn't look like a solution.
Speaker 1: It looks like an idea of what the solution would
Speaker 1: have to look like, or ruling out possible solutions.
Speaker 3: I love that, and I do think that that really
Speaker 3: does apply to challenges in our life. Changes we want
Speaker 3: to make or problems that we're having. Is that if
Speaker 3: we can spend time really looking at the problem or
Speaker 3: the change that we want to make without immediately jumping
Speaker 3: to a conclusion of what we should do. It really helps.
Speaker 3: And you mentioned like there's contradictions and there's opposing tensions,
Speaker 3: and it's like, you know, let's say I suddenly am like, well,
Speaker 3: I want to begin reading for thirty minutes a day.
Speaker 3: I'm just making something out. If you don't spend some
Speaker 3: time to acknowledge like what's been blocking me from doing that,
Speaker 3: you know what other tensions are pulling on me in
Speaker 3: those moments like that sort of exploration can be really
Speaker 3: really valuable. We tend to jump right to action, and
Speaker 3: it's interesting I think a lot about like one of
Speaker 3: the most accepted models for behavior changes called the trans
Speaker 3: theoretical model of behavior change, most commonly known as the
Speaker 3: stages of change model, and there are three stages before
Speaker 3: you even ever get to action, and if you don't
Speaker 3: do some of the work in those stages, very often
Speaker 3: your action just isn't going to go anywhere. It's going
Speaker 3: to just peter out really quickly. And sounds a lot
Speaker 3: like what you're saying, which is like I'm just going
Speaker 3: to start shouting out answers hoping that this problem is
Speaker 3: solved in three minutes and I'm onto the next thing.
Speaker 4: Yeah.
Speaker 1: I like the preparation before the solution seems important. And
Speaker 1: I think another thing that I learned from mathematics is
Speaker 1: the hardest problems don't always look hard, and the easy
Speaker 1: problems don't always look easy. There's a very famous one.
Speaker 1: This is a problem that was first just kind of
Speaker 1: jotted down in the margins of a book four hundred
Speaker 1: years ago, and it was someone who was reading an
Speaker 1: old geometry book Skypierre, and he jotted it down and
Speaker 1: he's like, oh, I've got an idea for another equation here,
Speaker 1: but there's a certain kind of equation that I think
Speaker 1: doesn't have a solution, and he jotted it down in
Speaker 1: the margint He says, oh, and I can actually I
Speaker 1: know the solution to this. I could prove this to you,
Speaker 1: but I don't have quite enough space in this margin
Speaker 1: of the book. And then it just sort of sat
Speaker 1: there in the margin of his book for a few years.
Speaker 1: His son discovered it a few decades later and published
Speaker 1: it with his writings, and people started looking, what was
Speaker 1: this proof that he had come up with that he
Speaker 1: didn't quite have space for. And it took three to
Speaker 1: fifty years. He probably had it wrong, right, His proof
Speaker 1: was probably false. But the thing he was trying to
Speaker 1: prove that this kind of equation didn't have a solution.
Speaker 1: It's a very simple equation. I've showed it to eighth
Speaker 1: graders and it's true what he said. But it was
Speaker 1: one of the hardest problems anyone had ever uttered in
Speaker 1: mathematics up to that moment. You know, it wasn't solvable
Speaker 1: with the mathematics at the time. You needed three hundred
Speaker 1: and fifty more years of mathematical developments for that to
Speaker 1: be solvable. So it looks really simple, and you know
Speaker 1: sometimes in LEO, I want to read for thirty minutes
Speaker 1: a day. It sounds so simple. It's like I got
Speaker 1: books on the shelf, I've got thirty minutes in the calendar.
Speaker 4: This seems very.
Speaker 1: Easy, right, right, But maybe that's tapping into issues of
Speaker 1: attention and patience and anxious worries that keep you from focusing,
Speaker 1: like it can happen into so many.
Speaker 4: Difficult issues exactly. And so yeah, I.
Speaker 1: Find mathematics is a very crisp model of those things.
Speaker 1: Often because in math it seems like, of all places
Speaker 1: it should be easy to tell what's an easy problem.
Speaker 1: What's a hard problem? But things can be simple and
Speaker 1: very hard or complex and actually not so hard. You
Speaker 1: know a lot of surface complication, but if you just
Speaker 1: understand what the terms are, it's actually a straightforward problem.
Speaker 3: This is a question about problems like that, like how
Speaker 3: does someone know that they're proposing a mathematical problem or
Speaker 3: proof or quandary versus just writing down a bunch of nons?
Speaker 3: Like are there points where people are like, we're trying
Speaker 3: to prove something that should not be proved because it's
Speaker 3: not true or real, or like, I know this isn't
Speaker 3: a question that probably is like three podcast interviews, but
Speaker 3: I'm just curious because I often think about that.
Speaker 1: Yeah, that's a nothing more. I think it's interesting to
Speaker 1: hear what mathematicians say about this. I'm a math teacher, right,
Speaker 1: I don't do my own mathematical research, but knowing lots
Speaker 1: of people who do, often they'll run into a question
Speaker 1: where you're trying to decide, Okay, it's this statement true
Speaker 1: or false, And actually if you sit there wondering whether
Speaker 1: it's true or false, you never get anywhere. What they
Speaker 1: have to do is they have to commit to the thought. Okay, today,
Speaker 1: I'm going to try to prove it's true. I think
Speaker 1: it's true.
Speaker 4: I'm going to try to.
Speaker 1: Prove it, and they'll work to prove it, and maybe
Speaker 1: in the process of trying to prove it, they'll find
Speaker 1: out that it's false, or maybe they just don't get anywhere,
Speaker 1: and the next day they go, Okay, given I couldn't
Speaker 1: find a proof yesterday, I think this is false, I'm
Speaker 1: going to look for an example that shows this is false,
Speaker 1: something that breaks the purported rule, and then they'll do that.
Speaker 1: But what I've heard from a lot of Matheaticians is
Speaker 1: you can't occupy both states at once. You have to
Speaker 1: at least temporarily commit yourself to one side of the ledger.
Speaker 1: You know, I'm going to push in this direction today,
Speaker 1: And even if you don't know which direction to go,
Speaker 1: you learn a lot by picking a direction and trying that.
Speaker 3: I find that ability to sit with a problem like
Speaker 3: that for years astounding. I recently, very recently figured out
Speaker 3: that I can solve crossword puzzles. Now, as a fifty
Speaker 3: year old man of fifty plus years who loves words,
Speaker 3: I should have known that sooner, but I didn't because
Speaker 3: I would get stumped early on and be like, Eh,
Speaker 3: I can't do this. Now I realize like, oh, I
Speaker 3: can do this. I love doing this. This is fun,
Speaker 3: this is enjoyable. There is some switch in me, And
Speaker 3: I don't know if that switch was that I suddenly
Speaker 3: started to believe that I could do it, and then
Speaker 3: that enabled me to stick with it. But I think
Speaker 3: that we could extrapolate this idea a little bit to
Speaker 3: how do we stick with things that we feel like
Speaker 3: we can't do. Now. You must face this all the
Speaker 3: time as a math teacher, right because one of the
Speaker 3: most common things you'll hear people say is I'm not
Speaker 3: good at math. You know, if you ask people what
Speaker 3: they're good at or it comes up, you're gonna hear
Speaker 3: I'm not good at math a lot. So I think
Speaker 3: there's a similarity here to me and my crossword puzzles.
Speaker 3: So let's talk a little bit about that process, maybe
Speaker 3: in how you teach it for math, and then maybe
Speaker 3: we can broaden it out to how we apply it
Speaker 3: to other areas of our lives that may be more
Speaker 3: impactful than a crossword puzzle.
Speaker 4: Yeah, yea, Although I love crossword puzzle, that's pretty high impact.
Speaker 1: You know, you can spend a fifteen minutes a day
Speaker 1: sort of enjoying the New York Times puzzle.
Speaker 4: That's a nice way to spend the time.
Speaker 3: It is. It is.
Speaker 1: Yeah, it's definitely true what you say about people identifying
Speaker 1: as not a math person. It's sort of funny because
Speaker 1: everyone when they present it, they present it as sort
Speaker 1: of this idiosyncratic fact about them personally. It's like, oh,
Speaker 1: you know, it's just me. I'm just this funny person
Speaker 1: who's like, ah, I didn't really math didn't really click
Speaker 1: with me. It's like, yeah, there's hundreds of millions of people.
Speaker 4: Like that in the United States.
Speaker 1: Like this is a solid majority of the country. I
Speaker 1: would say, so it's obviously not and maybe that's I
Speaker 1: think the first step for people. And it's not some
Speaker 1: personal failing of yours. And I try not to blame you.
Speaker 4: I'm a teacher. I love lots of other teachers.
Speaker 1: I try not to blame. It's not the teachers have failed.
Speaker 1: It's a weird thing we're trying to accomplish in math education.
Speaker 1: We're taking these five year olds and setting them down
Speaker 1: on this ten year journey where they're supposed to come
Speaker 1: out the other side having learned sort of like centuries
Speaker 1: worth of mathematical ideas, becoming expert in stuff that really
Speaker 1: only a very small elite would have ever had to
Speaker 1: learn in a lot of past generations. You know, these
Speaker 1: very abstract ideas that come with their own language that's
Speaker 1: presented in a pithy, very sometimes too short to brief
Speaker 1: the glimpse you get of these ideas. To me, there's
Speaker 1: no shock when someone struggles with mathematics or with mathematics education.
Speaker 1: That's sort of the default state. And I think for
Speaker 1: me that's a first step when there's something that I'm
Speaker 1: struggling with mathematical or something else, or when I see
Speaker 1: a student struggling, is to depersonalize it a little bit.
Speaker 1: It's not some shortcoming, some gap within you. You know,
Speaker 1: there's some missing jigsaw piece in your brain that you're
Speaker 1: never going to be able to get this. It's like
Speaker 1: not things are hard to learn. It takes time, it
Speaker 1: takes effort to take the teacher to walk you through it.
Speaker 1: So that's the first step for me. The second step
Speaker 1: is often motivational, why would I want to learn it?
Speaker 1: For a lot of students, the benefit to learning math
Speaker 1: is you can pass math classes and then stop taking
Speaker 1: them like that that's really it's a thing you want
Speaker 1: to learn so you can cease ever having to think
Speaker 1: about it. And so this varies a lot from person
Speaker 1: to person, but I try to find something that that
Speaker 1: feels meaningful to them, that will open something up for
Speaker 1: them in their life. Just a student the other day
Speaker 1: actually is their first day coming to my class. They
Speaker 1: enrolled late and missed the first week. And we were
Speaker 1: doing a little bit of work in spreadsheet programs, just
Speaker 1: in Microsoft Excel, and the student was saying it was
Speaker 1: just sort of like mouth open. They're like, my mom's
Speaker 1: been running a small business for years and doing the
Speaker 1: accounting with literal spreadsheets, like sheets of paper spread out
Speaker 1: and a hand calculator and adding up the numbers, you know,
Speaker 1: hours every month to get that to work. And I
Speaker 1: was like, oh, yeah, no, take this home. By the
Speaker 1: end of the semester, you'll be able to do that
Speaker 1: hours of work in five to ten minutes of updating
Speaker 1: the spreadsheet of people. I think it's's personal finance. You
Speaker 1: can give you a grasp on money and where you're
Speaker 1: putting it and how it's flowing and where it goes.
Speaker 1: You know, when the money's gone from the bank account.
Speaker 4: Where did it go?
Speaker 1: Just a little bit of extra grasp on mathematics and
Speaker 1: mathematical tools can really help with personal finance. So, especially
Speaker 1: for a lot of the adults I teach at community college,
Speaker 1: that's a very relevant one. And then especially for younger students,
Speaker 1: but for some adults too, mathematics is just this kind
Speaker 1: of beautiful set of ideas. It's connected to everything a
Speaker 1: little bit. It's kind of like this underground water source
Speaker 1: or something underground river that sort of connects all these
Speaker 1: different parts of the landscape that you wouldn't have thought
Speaker 1: were connected. And so, you know, one of the things
Speaker 1: I love to do is kind of collect great thinkers
Speaker 1: who are fascinated by mathematics. And you know, Abraham Lincoln
Speaker 1: loved mathematics, right, He read a lot of Euclid the geometry.
Speaker 1: He in fact memorized the whole geometry book. While he
Speaker 1: was in law school he was sort of working on
Speaker 1: his legal studies. He goes, oh, I'm never going to
Speaker 1: be a good lawyer unless I really understand argument, logic
Speaker 1: and proof. So okay, so I guess I've got to
Speaker 1: go read ancient geometry texts and learn it that way.
Speaker 3: And memorize them.
Speaker 4: Is there, Oh yeah, he memorized the arguments.
Speaker 3: Yeah, I guess you can just get a lot done
Speaker 3: if you don't have TVs or cell phones or you know.
Speaker 4: Right right, all you had to do back then was
Speaker 4: chop chop.
Speaker 3: Electric lights.
Speaker 1: I mean, that's what I've been saying for you is
Speaker 1: electric lights are a huge distraction for us. It's really
Speaker 1: you know, it's shortening our attention span. It's we really
Speaker 1: got to got to go back to candles. Is rambling
Speaker 1: here in this answer, but yeah, I think the reason
Speaker 1: I ramble a little bit is because every person needs
Speaker 1: to find their own connection here. You know, for it
Speaker 1: was logic, it was mathematics as a model of logic,
Speaker 1: and for people who love Sudoku puzzles, that's a little
Speaker 1: bit the same thing. That's that's all, you know, air
Speaker 1: tight logical reasoning. And for some people it's you know,
Speaker 1: mathematics being connected to the arts and sort of the
Speaker 1: ways geometry plays into different artistic traditions. Cosmology is a
Speaker 1: topic that I'm always fascinated by, like what is this universe?
Speaker 1: And how does it work? And what on Earth is
Speaker 1: going on here? How did we get here, and mathematics
Speaker 1: really central to answering some of those questions. So for
Speaker 1: some people they sort of you get excited about science
Speaker 1: and maybe learning a little bit of mathematics will help
Speaker 1: open doors there.
Speaker 3: That is a quandary I run into often, which is
Speaker 3: the last time I took math would have been a
Speaker 3: long time ago. My main attempt in most of high
Speaker 3: school was simply how do I not go to school?
Speaker 3: How can I get out of going? So if I
Speaker 3: could have used mathematics to help with that, I probably
Speaker 3: would have. But I love popular science, but a lot
Speaker 3: of it. I'm reading the introduction and I'm like, okay,
Speaker 3: I'm cruising along here, and then start the equations, and
Speaker 3: all of a sudden, I'm like, you know what, to
Speaker 3: understand this, I'm going to have to go back a
Speaker 3: little ways. And I just never quite take the time
Speaker 3: then to go back and go you know what, some
Speaker 3: basic algebra W has served me really well in getting
Speaker 3: into all of these ideas.
Speaker 1: Yeah, yeah, I think of algebra especially it opens a
Speaker 1: lot of doors.
Speaker 4: It's a key.
Speaker 1: It's a key that's very hard to acquire, right. It
Speaker 1: takes a few years of education, and you know, in
Speaker 1: the USB teach course called algebra to you know, usually
Speaker 1: fourteen year olds or so. And I've taught that course
Speaker 1: and students don't really internalize it, don't really learn it
Speaker 1: until usually three four years later at the earliest, when
Speaker 1: they're when they're taking calculus or something like that. It's
Speaker 1: having to use those algebra skills later on that really
Speaker 1: forces you to absorb them. So it's not easy to
Speaker 1: learn algebra, but it just opens up so many doors
Speaker 1: down the road that you wouldn't have guessed. Yeah, especially
Speaker 1: in the sciences, but well, I don't know. Sciences touch everything,
Speaker 1: So you know, if you want to learn about economics
Speaker 1: or finance, or astronomy or or population biology or epidemiology
Speaker 1: and think about predicting the next pandemic, any of that, Yeah,
Speaker 1: just having the language of algebra really pays off.
Speaker 3: I'm trying to balance the desire to keep this conversation
Speaker 3: somewhat about what the one you feed talks about versus
Speaker 3: chasing it down mathematical rabbit holes. So I'm going to
Speaker 3: pull back up here for a second and say, like,
Speaker 3: let's keep going with this question of Okay, there's something
Speaker 3: in life that I can't seem to do or I'm
Speaker 3: intimidating by how do I work through it? And we've
Speaker 3: talked about how recognizing you're not alone in doing it
Speaker 3: is really important, right, recognizing that there is a problem
Speaker 3: lots of people share, humanizing it. We've moved on to
Speaker 3: trying to connect it to why it matters, and I
Speaker 3: think that's really important too. Same thing with like reading
Speaker 3: a book for thirty minutes, Like, Okay, why why does
Speaker 3: that actually matter to you? If we're unable to articulate that, well,
Speaker 3: we're not going to have sufficient motivation to stick with it,
Speaker 3: which I think is what you're saying about math. You've
Speaker 3: got to get the student interested somehow. So okay, now
Speaker 3: you've got the student recognizing I'm not alone and not
Speaker 3: liking math. Okay, I can see why this might be
Speaker 3: valid to me. You know, I have always wanted to
Speaker 3: read Brief History of Time by Stephen Hawking and I can't.
Speaker 3: And so, okay, algebra, where do we go next?
Speaker 4: Yeah?
Speaker 1: Yeah, for solving any particular problem. What I like to say,
Speaker 1: sort of the next step, once we've kind of walked
Speaker 1: around the outside of the problem and we're motivated to
Speaker 1: solve it, is getting a wrong answer down on the
Speaker 1: page deliberately wrong, right, Like you're not trying to answer
Speaker 1: it correctly, yet you're trying to get sort of maybe
Speaker 1: an obvious wrong answer, and then that gives you something
Speaker 1: to work on that sort of solves that blank page problem.
Speaker 2: Right.
Speaker 1: Anyone who's written knows that it really helps to have
Speaker 1: a draft in front of you, right. Getting that first
Speaker 1: draft down is pulling teeth. That's that's the hard part
Speaker 1: when solving a problem, just getting an answer down. In math,
Speaker 1: one of the questions I like to test students is,
Speaker 1: you know, what's an answer you know is much too big?
Speaker 1: And what's an answer you know is much too small?
Speaker 1: If we're trying to solve for some number, and that
Speaker 1: can start to build some intuition. It sort of says, okay,
Speaker 1: this is the sort of thing we're looking for. Or
Speaker 1: you know, if you're looking for some problem solving method,
Speaker 1: you say, okay, well, why wouldn't this work. It's another
Speaker 1: way of teaching yourself about the problem, introducing something that
Speaker 1: you know isn't quite the right solution. Yeah, it gives
Speaker 1: you a first draft to build on.
Speaker 4: Excellent.
Speaker 3: I want to jump back to a loop I didn't
Speaker 3: close earlier, which is you talked about, like, I think
Speaker 3: you talked about four steps of solving a problem, or
Speaker 3: four stages, and I think we got through about half
Speaker 3: of them. So maybe we can pause right now and
Speaker 3: close that because I think it's relevant to where we
Speaker 3: are in the conversation.
Speaker 1: Yeah, yeah, this doubles I think making mistakes sort of
Speaker 1: like getting a wrong answer down. I would call that, yeah,
Speaker 1: sort of my second step there. Once you've explored the problem,
Speaker 1: once you've explored it further and you've worked for a while,
Speaker 1: one very important step I think is to step away
Speaker 1: from it, to not have a false sense of urgency
Speaker 1: that you have to solve it in the next ten minutes,
Speaker 1: and just give it some time, especially once it's kind
Speaker 1: of circulating.
Speaker 4: Around your mind.
Speaker 1: The back of your brain can do incredible things given
Speaker 1: a little space to breathe. So for me, it's you know,
Speaker 1: putting on headphones and going for a walk or going
Speaker 1: for a run, although I have to be careful when
Speaker 1: I'm on a run off and I'll have ideas that
Speaker 1: I think are brilliant at the time, and then I
Speaker 1: get home and look at like the little note I
Speaker 1: took on my phone. It's like waking up after a
Speaker 1: dream like, oh that that wasn't wasn't the idea I
Speaker 1: thought it was.
Speaker 3: Yeah. What's interesting about that is I do think it
Speaker 3: mirrors an experience I used to have when I was
Speaker 3: a heavy substance users. I would write some part of
Speaker 3: a song or something and be like this is incredible
Speaker 3: and wake up in the morning and be like not
Speaker 3: so much. And for some reason, walk seem to do
Speaker 3: a little of the same thing. Some of the ideas
Speaker 3: are great, but I'm a little bit of stick by
Speaker 3: how some of them. I'm like, there must be something
Speaker 3: about the state of flow or it is what you
Speaker 3: want to have happen when you're initially brainstorming, which is
Speaker 3: the critic takes a vacation for a little bit like
Speaker 3: go away, critic, and walking seems to do that for me.
Speaker 1: Yeah, yeah, I think it puts me a little more
Speaker 1: at ease. And it's a good reminder to someone who
Speaker 1: very much lives in my head, you know. I think
Speaker 1: math induces this, and people who sort of like you
Speaker 1: spend a lot of time with your thoughts and looking
Speaker 1: at screens, looking at paper. But it's good to remember
Speaker 1: I'm a body, you know, That's what I am. That's
Speaker 1: what I have, and then it moves around the world.
Speaker 1: I'm not just a computer where you can predictably feed
Speaker 1: me inputs and get the right outputs. You know, I
Speaker 1: need I need a little bit of serendipity. I need
Speaker 1: some surprises and things in front of my eyes that
Speaker 1: I didn't expect to see. I think stepping away and
Speaker 1: going for a walk, or cooking a meal or whatever
Speaker 1: it is that gives you something to keep your hands
Speaker 1: or your feet busy, and then your brain can keep
Speaker 1: working in the background. And then the final step is
Speaker 1: sort of the counterpoint to that, which is then you've
Speaker 1: got to go back to work. Yeah, you can hope
Speaker 1: that some inspiration will come, But this is true even
Speaker 1: of artists, right. A lot of the artists I admire,
Speaker 1: they have a very strict writing regimen, right. I mean
Speaker 1: Paul Simon when he was writing albums, he would just
Speaker 1: be writing a certain number of hours every day and
Speaker 1: that's how he generated it. Stephen King wrote, you know,
Speaker 1: three thousand words a day or some completely superhuman number
Speaker 1: of words.
Speaker 4: And I think, you know, most working artists, I should say,
Speaker 4: they do.
Speaker 1: They have to write, otherwise you don't create what you
Speaker 1: need to create, Otherwise you don't solve the problems you're
Speaker 1: trying to solve within each work. Even if you feel uninspired,
Speaker 1: you've got to go back to it.
Speaker 3: Let's shift direction just a little bit here. We're still
Speaker 3: talking about sort of overcoming fear or overcoming being stuck.
Speaker 3: I want to talk a little bit about the role
Speaker 3: of play in that, the role of humor, because you know,
Speaker 3: your first book was I think called Math with Bad Drawings.
Speaker 1: Yeah, that's right, Yeah, yeah, you it's its fund seeing
Speaker 1: how translators handle that. There's one one where it just
Speaker 1: translates Math with the Worst Drawings.
Speaker 4: Got I've got demoted here.
Speaker 3: So yeah, you draw humorous little drawings that are intended
Speaker 3: to illustrate the concept, but also oftentimes just have fun. Right.
Speaker 3: There are times I see they help me figure out
Speaker 3: the concept, and there are other times I think they
Speaker 3: just sort of make light of the whole thing a
Speaker 3: little bit, which I think causes a reduction in the
Speaker 3: strain around trying to figure it out. So talk to
Speaker 3: me about play and humor and why that is the
Speaker 3: direction you've chosen to go.
Speaker 4: Yeah.
Speaker 1: Yeah, for me, the bad drawings, there's a few things
Speaker 1: that led me to them, and one is my inability
Speaker 1: to draw or I just can't do it. And math
Speaker 1: is very visual, so you need you need pictures to
Speaker 1: explain things, and you need pictures to kind of punctuate,
Speaker 1: you know, the end of a thought. So I needed
Speaker 1: to draw, and I've never doodled as a kid. I
Speaker 1: really I should have practiced more. Yeah, But anyway, so
Speaker 1: I arrived in a and wanted to write these books
Speaker 1: about math and wasn't able to draw.
Speaker 4: So okay, we're going to do stick figures.
Speaker 3: We're going to do you embraced your limitation.
Speaker 4: Yeah, exactly.
Speaker 1: Yeah, And I think it wasn't a calculation on my part.
Speaker 1: It was sort of a shrugger of the shoulders and like, Okay,
Speaker 1: I guess that's the best I can do. But I
Speaker 1: think it creates a different tone or a different kind
Speaker 1: of space for people coming to mathematics, maybe not super
Speaker 1: enamored with the subject, because you come thinking, oh, I'm
Speaker 1: not really a math person. And it sort of activates
Speaker 1: people's defenses around being good at things being bad at things.
Speaker 1: And so to have the person you're learning this stuff
Speaker 1: from be very self evidently leading with something they're bad at,
Speaker 1: right kind of putting their worst foot forward. Yeah, yeah,
Speaker 1: I think it kind of demystifies a little bit. Or
Speaker 1: we're coming here as fellow human beings, with our strengths
Speaker 1: and our weaknesses and our gaps and our knowledge sets.
Speaker 1: We're here to share things. I'm not here to stand
Speaker 1: on a mountaintop and pronounce the truths of mathematics.
Speaker 3: One of your earlier books is called Change is the
Speaker 3: Only Constant. It's about calculus. I may not have that
Speaker 3: title exactly right, but as a person who studied a
Speaker 3: lot of Buddhist and Eastern thought, this idea of impermanency
Speaker 3: is central to the whole game. Talk to me about
Speaker 3: the role that change plays in mathematics. Yeah, and maybe
Speaker 3: how math brings that concept alive. And I'll say one
Speaker 3: last thing and then I'm to turn it over to you.
Speaker 3: There's a phrase from the Japanese poet bas Show, who says,
Speaker 3: I'm not going to get it exactly right. You learn
Speaker 3: more about impermanence from a falling leaf than like a
Speaker 3: thousand words about it. So, but math probably shines a
Speaker 3: different light on that same idea. Right, there's another way
Speaker 3: of learning more about impermanence. Talk to me about it mathematically.
Speaker 1: Yeah, change was something that mathematics always struggled with. I
Speaker 1: think it's one way to put it. That's somehow. A
Speaker 1: lot of mathematics that was developed by brilliant mathematicians dealt
Speaker 1: with static situations, and it was actually change in motion
Speaker 1: that presented some of the most vexing mysteries, and of
Speaker 1: course one of the most ancient ones. And this comes
Speaker 1: up in the Western tradition, comes up in the Chinese
Speaker 1: school of Nams was a philosophical school, is what we
Speaker 1: call Zeno's paradox. So the idea that you know, if
Speaker 1: you and I are going to high five each other,
Speaker 1: you know, would phrase it a little differently. But if
Speaker 1: we're going to do a high five, like to complete
Speaker 1: that high five, we need to get halfway there, right,
Speaker 1: Like our hands start three feet apart, we got to
Speaker 1: get to a foot and a half apart, and then okay,
Speaker 1: that takes some amount of time. But then to complete
Speaker 1: the high five, now we need to go halfway again
Speaker 1: and get to you know, three quarters of befoot apart
Speaker 1: or nine inches apart now, but we're still not there yet.
Speaker 1: There's another step. We got to go halfway again, and
Speaker 1: now our hands are really close, but there's still another step.
Speaker 1: You got to go halfway again and halfway again, and
Speaker 1: so there's this infinite series of actions you have to
Speaker 1: complete just to high five somebody.
Speaker 4: And this is sort of true of all motion. It
Speaker 4: feels like all.
Speaker 1: Change, anything that you want to happen, you can decompose
Speaker 1: it into an infinite series of steps, which, certainly from
Speaker 1: a perspective making change in your life is very daunting
Speaker 1: thought that somehow any change is infinite in scope.
Speaker 3: It often is. I think there is change that is
Speaker 3: goal oriented, as in I'm going to run a five k,
Speaker 3: But if your bigger goal, the reason you want to
Speaker 3: run a five k, is that you value your physical health,
Speaker 3: then change is infinite because there's never a day that
Speaker 3: your physical health is like, Okay, I have established it.
Speaker 3: Now it is set. I will go about all my
Speaker 3: other business and it will remain in place. It's the
Speaker 3: same thing with like we can't just eat once.
Speaker 1: I've locked in healthy eating. I had a salad for
Speaker 1: lunch yesterday. It was delicious, that was it, and now
Speaker 1: I'm done. Now I can have cinnamon buns.
Speaker 3: Every day and yeah, yeah, exactly.
Speaker 1: Yeah, So maybe that's right, though, Yeah, Zeno was onto something.
Speaker 1: I think, as you know, was certainly onto something. Obviously,
Speaker 1: as Zino understood, you can complete an action, right, we
Speaker 1: see people walk across a room and they get all
Speaker 1: the way to the end. So clearly there's something a
Speaker 1: little tricky about his logic. But Bertrand Russell, the twentieth
Speaker 1: century philosopher, said that sort of every generation since Zeno
Speaker 1: has had to reckon with that paradox. Right, on the
Speaker 1: one hand, we do complete actions. On the other hand,
Speaker 1: there's this sort of compelling argument that it's impossible, that
Speaker 1: it's infinite, that we'll never get there, and so every
Speaker 1: generation has sort of had a different answer to that question.
Speaker 3: What does your generation? I think we're probably sort of
Speaker 3: a generation apart, not quite so, what would Russell say,
Speaker 3: your generations wrangling with Zeno's paradoxes?
Speaker 1: Oh, that's interesting, right, I guess I'm sort of a
Speaker 1: squarely in the millennial generation.
Speaker 4: Yeah, yeah, I don't know.
Speaker 1: I think the millennials that looking at us from the outside,
Speaker 1: I think we have a reputation for being a little square,
Speaker 1: a little earnest, you know, compared to Gen X, which
Speaker 1: was always steeped in irony and gen Z, which sort
Speaker 1: of finds millennials hopelessly straightforward in earnest. I think there's
Speaker 1: something about millennials maybe that just want to be like, no, no,
Speaker 1: I'm gonna I'm gonna get there, I'm gonna I'm gonna
Speaker 1: go halfway and halfway again. I'm going to complete that
Speaker 1: sequence of actions.
Speaker 3: Yeah.
Speaker 1: So maybe, yeah, maybe the lesson for millennials would be
Speaker 1: to embrace a little more, a little more mystery in that,
Speaker 1: a little more accepting it as a paradox.
Speaker 3: So listener, consider this. You're halfway through the episode. Integration reminder.
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Speaker 3: are good Wolves together. So there's a recent post on
Speaker 3: your blog about the poet Adrian Rich and really about
Speaker 3: this idea of change. Can you share a little bit
Speaker 3: more of what you wrote there?
Speaker 1: Yeah, yeah, I came case you're in Rich very sideways.
Speaker 1: It was just through I came across a quotation of hers,
Speaker 1: totally out of context, that the moment of change is
Speaker 1: the only poem, and I thought that was lovely. Didn't
Speaker 1: know anything about Adrian Rich because I'm not particularly noulptible
Speaker 1: about poetry. And so this is actually while I was
Speaker 1: working on that Calculus book, I went and read, you know,
Speaker 1: a few of her collections and essays she'd written, and
Speaker 1: found her a fascinating figure and really someone who embodied
Speaker 1: change in her life because she had, say she was
Speaker 1: living in doing her best work in the sixties, seventies, eighties,
Speaker 1: and so as of the late fifties into the early sixties,
Speaker 1: she was living a very sort of conventional looking life.
Speaker 1: You know, she was, I think mostly a homemaker, housewife.
Speaker 1: She had a few kids, her husband was a professor
Speaker 1: at Harvard, and she wrote very careful and sort of
Speaker 1: immaculate but fairly traditional poetry. And anyone who knows Adrian
Speaker 1: Rich knows her as a radical feminist, lesbian, you know,
Speaker 1: who had female lovers and wrote about sort of breaking
Speaker 1: loose from societal constraints and completely reimagining out of the
Speaker 1: world around us. And so how did she get from
Speaker 1: the one spot to the other? And it was sort
Speaker 1: of this gradual process. One of the things she started
Speaker 1: doing was putting the date the year in parentheses at
Speaker 1: the end of each of her poems. You know, I'm
Speaker 1: sure it was just a sort of artistic intuition, but
Speaker 1: later when she reflected on it, she said they were
Speaker 1: starting to feel more like snapshots, less like completed works,
Speaker 1: and more like, yeah, moments.
Speaker 3: Of an ongoing dialogue.
Speaker 1: Exactly, Yeah, yeah, something ongoing and evolving. And that poem
Speaker 1: that has the line the moment of change is the
Speaker 1: only poem. It's dedicated to the French film director Godard,
Speaker 1: and so yeah, it begins the opening line is driving
Speaker 1: to the limit of the city of Words, which I
Speaker 1: love as a line. The word the limit happens to
Speaker 1: be a very important word in mathematics and calculus. She's
Speaker 1: coming out the kind of the same idea from a
Speaker 1: different direction. She's saying, what are you trying to do
Speaker 1: in film or in poetry? You're trying to go right
Speaker 1: to the edge of what words can tell us and
Speaker 1: let those words gesture at something beyond themselves. And then
Speaker 1: towards the end of the poem she kind of circles
Speaker 1: around this thought or uses this thought to propel herself forward.
Speaker 1: She says, the notes for the poem are the only poem,
Speaker 1: which I sort of like that.
Speaker 4: You know.
Speaker 1: The idea is that the poem itself is too polish,
Speaker 1: too final, and like, really, the magic the poetry is
Speaker 1: in those notes, is in that first impression. And then
Speaker 1: a few lines later she comes back, she just know
Speaker 1: the mind of the poet is the only poem. Now,
Speaker 1: even the notes there's something, there's something recorded and documentary
Speaker 1: about that, and really it's just what's happening in the airspace.
Speaker 1: And then the very final line of the poem is
Speaker 1: the moment of change is the only poem. It's like, no, no,
Speaker 1: it's not even really the mind. It's something I don't know, like,
Speaker 1: can't I can't explain in words because she's gesturing beyond words.
Speaker 1: I wrote a whole chapter that I wound up cutting
Speaker 1: from the Calculus book because it was more about poetry
Speaker 1: than it was about calculus. But it really shaped my
Speaker 1: thinking about when I was writing that book about calculus.
Speaker 1: I suspect I'm the first author of a calculus book
Speaker 1: to really have my thoughts on the subject shaped by
Speaker 1: Adrian Rich and her radical poetry. But it really it
Speaker 1: felt very true to the insights of the math to
Speaker 1: me that there's something about trying to reach towards something
Speaker 1: infinite that you can't ever quite attain, but there's a
Speaker 1: lot of meaning and purpose in that reaching.
Speaker 3: Yeah, that whole thing is such a Zen idea. I mean,
Speaker 3: Zen is a form of Buddhism that really talks a
Speaker 3: lot about how, yeah, words, you need them because they're
Speaker 3: the main thing we have. And yet they're only pointing
Speaker 3: at something, you know, they're only trying to get you
Speaker 3: to look in a certain direction, in a certain way.
Speaker 3: And then that same idea of we tend to think
Speaker 3: that the end output is the thing, and Zen would
Speaker 3: say no, no, no, it's much more the doing, the
Speaker 3: being one with the doing. And then ultimately it would
Speaker 3: go on to say, sort of that last level is
Speaker 3: that even the mind itself is in change. You can't
Speaker 3: pin it down to anything. You know. What you think
Speaker 3: is your mind is this constellation of conditions that have
Speaker 3: come together extraordinarily temporarily right, and that you're freezing. And
Speaker 3: so change is the only poem resonated so much with me.
Speaker 3: I thought the way you wrote that up and her
Speaker 3: lines are really beautiful.
Speaker 1: Yeah, and I think you no, I really do. I
Speaker 1: love that poem. It's a fun wonder revisit.
Speaker 3: On the subject of your calculus book, I read your
Speaker 3: latest book, which is the Math for English majors a
Speaker 3: human take on the universal language, and really enjoyed it.
Speaker 3: But I sometimes dig a little bit deeper with guests,
Speaker 3: and so I opened up your Calculus book about change
Speaker 3: and the chapter titles. If I wasn't like an hour
Speaker 3: and a half from an interview with you, I would
Speaker 3: have bought that book, and like, I've got to read this,
Speaker 3: and I may go back because the chapter titles are
Speaker 3: so good. But I thought maybe we could talk about
Speaker 3: a couple of them. And the first is when the
Speaker 3: Mississippi ran a million miles long, how Calculus plays a prank.
Speaker 1: Yeah, So there's this fun passage in Mark Twain. One
Speaker 1: of his nonfiction books is The History of the Mississippi,
Speaker 1: and he talks about this funny fact about rivers, which
Speaker 1: is that they create these meanders right over time. They
Speaker 1: sort of have these curves and so you get these wide,
Speaker 1: you know, almost circles, and every so often the river
Speaker 1: will actually complete the circle. So just time going on
Speaker 1: and the water changing course, it'll sort of jump the gap,
Speaker 1: especially during a flood. And so this has happened periodically
Speaker 1: on the Misissippi. We have we have decent records of this,
Speaker 1: and so in the century or two. You know, sort
Speaker 1: of before when Twain was writing this, you could sort
Speaker 1: of chart the decrease in the length of the Mississippi
Speaker 1: as it sort of jumped those gaps, and so a
Speaker 1: long kind of circular meander became straight jump. He's just
Speaker 1: sort of applying arithmeticul learned in school. He said, well,
Speaker 1: here's what you can do. You can say, Okay, if
Speaker 1: the Mississippi River has I'm gonna get the number is wrong,
Speaker 1: but the missip River has gotten one hundred miles shorter
Speaker 1: in the last one hundred years. Well, that means Mississippi
Speaker 1: is shrinking by about a mile a year. So a
Speaker 1: million years ago, the Mississippi River would have been a
Speaker 1: million miles long, right, it would have stretched out four
Speaker 1: times past the moon. It would have been this, you know,
Speaker 1: visible from deep in the solar system, just this extraordinary
Speaker 1: astronomical river or maybe wrapping many times around the Earth.
Speaker 1: Who knows how you want to do it. And then
Speaker 1: his line, which I love. Twenty is such a brilliant stylist.
Speaker 1: He says, that's the marvelous thing about science or mathematics, say,
Speaker 1: is nowhere else can you get such a wholesale return
Speaker 1: of conjecture from such a trifling investment of fact, which
Speaker 1: is very astute I think as to what science and
Speaker 1: mathematics can often do. Say that again, a wholesale return
Speaker 1: of conjecture from a trifling investment of fact.
Speaker 3: I would say that might be shaping a lot of
Speaker 3: our online political discourse at this point.
Speaker 4: Also, No, I think it very limited investment effects.
Speaker 3: We've got a whole lot of conjecture, not very fun conjecture,
Speaker 3: to be honest, for a trifling amount of fact.
Speaker 4: No, I think we'd be better off.
Speaker 1: I mean, I spend more time reading social media than
Speaker 1: I do Twain, but I should probably defert that into
Speaker 1: into reading more Twain. The lesson I take away from
Speaker 1: that Twain knows that that's not what happens, right like obvious,
Speaker 1: Thessissippi River did not wrap many times around the earth.
Speaker 1: But it's actually it's quite an important lesson in mathematics
Speaker 1: and I think in life, which is that there's growth
Speaker 1: patterns that mathematicians talk about, and in particular linear growth,
Speaker 1: which is what Twain was talking about, where sort of
Speaker 1: every time period the same thing happens. You know, each
Speaker 1: year it gets one mile shorter, and then there's other
Speaker 1: growth patterns. So we saw this very vividly at COVID,
Speaker 1: for example, where from day to day you would get
Speaker 1: big increases. Right, I'm thinking like March twenty twenty when
Speaker 1: the caseloads were starting to explode. You know, day to
Speaker 1: day wasn't the same change. You know, March second, you
Speaker 1: get one hundred new cases. Mark third, you get three
Speaker 1: hundred new cases. March fourth, it's five hundred new cases.
Speaker 1: So it's the change is not linear, it's accelerating. But
Speaker 1: the funny thing about changes like that is that if
Speaker 1: you zoom in enough, they always look linear. Yes, So
Speaker 1: it's only at a big scale that you see the
Speaker 1: actual pattern of the change, yes, which is almost never
Speaker 1: linear forever. It's sort of analogous to how the Earth
Speaker 1: looks quite flat. You know, every experience I've ever had
Speaker 1: of the Earth, it looks very flat. But I know
Speaker 1: it's a sphere. It's just that I'm very small. The
Speaker 1: Earth is very big, and so if I got up
Speaker 1: in a spaceship, I could see the whole thing and
Speaker 1: see the curvature. But from the zoomed in perspective, it
Speaker 1: just looks linear. Everything looks flat, And so the same
Speaker 1: thing is happening there with Twain. Obviously, over time, the
Speaker 1: Mississippi River has grown and shrunk and changed length in
Speaker 1: a very nonlinear way. It's probably over thousands of years,
Speaker 1: it's gone up and down, you know, extends a little
Speaker 1: bit through those lakes, and it gets cut off and
Speaker 1: you know, some of your tributary joins it. So at
Speaker 1: the big scale, it's very nonlinear. But over a few
Speaker 1: hundred years, that's actually a pretty small scale for a
Speaker 1: geological feature like a river. Yeah, So that's the takeaway
Speaker 1: lesson on that chapter is that if you zoom in
Speaker 1: really close on something, you're going to think it's some
Speaker 1: more predictable kind of change, but over large scales you
Speaker 1: get surprises.
Speaker 3: I love that idea. It really echoes a couple of
Speaker 3: things that I talk about and teach, and one of
Speaker 3: them is that idea of you little by little, little
Speaker 3: becomes a lot right that day to day doing a
Speaker 3: little thing and a little thing and a little thing,
Speaker 3: you don't really see much, but you zoom out far
Speaker 3: enough and you're like, oh, that actually really did add
Speaker 3: up to something substantial. And then the second is that
Speaker 3: idea of zooming out in general as a way of
Speaker 3: having a different perspective, right. I mean, there's that phrase
Speaker 3: that people use, like making a mountain out of a
Speaker 3: mole hill. The way you make a mountain out of
Speaker 3: a molehill is you get really close to a little
Speaker 3: bump on the ground and you stare at it, right,
Speaker 3: it looks really big. Then you stand up and you're like, oh,
Speaker 3: it's just a little bump on the ground. And so
Speaker 3: that same idea of if we can zoom out, if
Speaker 3: we can change our perspective, would be the core thing.
Speaker 3: But zooming out is just a really easy way to
Speaker 3: do it.
Speaker 1: Yeah, yeah, yeah, I think that's right. Not always easy
Speaker 1: to do. It's actually easier on a graphic calculator. And
Speaker 1: then it is like graphic get the minus buttoning of
Speaker 1: mines Zu amount.
Speaker 3: One hundred percent. Okay, what about There's so many great
Speaker 3: titles in here. I'm just going to read a couple.
Speaker 3: We're not even going to talk about them. But that's
Speaker 3: Professor Dog to You, in which Calculus vaults a dog
Speaker 3: to start them. That's a pretty good one. What the
Speaker 3: wind leaves behind when Calculus poses a riddle another great one.
Speaker 3: But the one we're going to talk about is if
Speaker 3: pains must come in which calculus takes the measure of
Speaker 3: your soul.
Speaker 1: Yeah, right, which I don't know. It makes my soul
Speaker 1: shutter a little bit. I'm not sure I want calculus
Speaker 1: taking that.
Speaker 3: Measure precisely, it would come up with an equation I'm
Speaker 3: certain that I wouldn't be able to solve, and I
Speaker 3: would be no further along in understanding soul than I
Speaker 3: am today. But yeah, you might be able to understand.
Speaker 1: It, right, I mean, I think one of the things
Speaker 1: I take from math, and actually there's very much theme
Speaker 1: of this chapter is that math, although it feels complex
Speaker 1: when you're learning it, math is designed to offer us
Speaker 1: simplified answers. And because they're simplified, they're almost never quite right, right.
Speaker 1: They're always capturing some feature of the world but leaving
Speaker 1: something else out. But they can still be useful because
Speaker 1: they're these simple schematics. They're sort of these stick figure
Speaker 1: drawings of reality. So the one there, I think it
Speaker 1: opens with a quote from the economist Jeevans, a nineteenth
Speaker 1: century economist, and he was writing at a time when
Speaker 1: there was sort of a lot of excitement about math
Speaker 1: is doing so much for us, right, Like, look at
Speaker 1: what math did for physics. You know, we went from
Speaker 1: a world where it was kind of hard to explain
Speaker 1: how things move and the basic mechanics of stuff in
Speaker 1: the world too. We've got great equations for this, we
Speaker 1: can predict it with exquisite accuracy, and economists in his
Speaker 1: day we're hoping like, maybe we can do the same
Speaker 1: thing for a lot of human behavior, you know, not
Speaker 1: just for markets, but for for individuals, for sort of
Speaker 1: you know, your your moral sentiments or even your sort
Speaker 1: of sense of happiness in life. What he does, what
Speaker 1: Juveans does, He sort of imagines a graph of your happiness,
Speaker 1: your state of mind, and he says, well, you know,
Speaker 1: imagine overtime sort of we got this line going up
Speaker 1: and down, and if you feel bad, it goes down,
Speaker 1: if you feel good, it goes up. Maybe that's it.
Speaker 1: Maybe maybe that's the model of what happiness is. You
Speaker 1: can sort of picture this line going up and down,
Speaker 1: and you get to the end of the day, and
Speaker 1: what you actually want is you want to maximize the
Speaker 1: area under the curve, because if it's very high all
Speaker 1: day long, there'd be a lot of area under there.
Speaker 1: And if it's very low all day long, right, it'd
Speaker 1: sort of be very close to the bottom of the graph,
Speaker 1: and there'd be a very little area under the curve,
Speaker 1: and you can sort of make up for things, right
Speaker 1: if it's kind of low most of the day, but
Speaker 1: then it has a really high spike, then you'll get
Speaker 1: a lot of happiness total. But it's sort of about
Speaker 1: adding up the area under the curve, which is what
Speaker 1: the calpulist teacher would call an integral and what Jeeven's
Speaker 1: calls an.
Speaker 3: Help me understand the curve. I'm not visualized in this.
Speaker 4: Oh sure, sure, I try a picture. Imagine.
Speaker 1: Let's say you've got a big piece of paper on
Speaker 1: your wall and you mark it along the bottom, you know, midnight,
Speaker 1: one am, two am, you know, all the way to
Speaker 1: the next midnight, and every hour or even every minute,
Speaker 1: you go and you sort of extend a line starting
Speaker 1: from the left, and if you're feeling really unhappy, the
Speaker 1: line goes down towards the bottom of the page yep.
Speaker 1: And if you're feeling great, you're feeling really happy, the
Speaker 1: line goes soaring up towards the top yep. And what
Speaker 1: you'd be able to do at the end of the
Speaker 1: day is look at this picture and it would be
Speaker 1: kind of this abstract picture of your experience of that day.
Speaker 1: And you know, maybe you know, if you had a
Speaker 1: great breakfast, it sort of starts out low, but then
Speaker 1: it spikes really high, delicious eggs, and then it maybe
Speaker 1: goes back towards the middle. Is you know, you go
Speaker 1: to work and it's kind of it's hovering around the middle.
Speaker 1: You have a boring meeting, it dips towards the bottom,
Speaker 1: you have a nice afternoon, it kind of rises up.
Speaker 1: You get home and you're for me getting home and
Speaker 1: having my little ones run up to me is like
Speaker 1: that's my happing a spiking way up high. Right, you
Speaker 1: two year old jumps into my arms. I gotta, I
Speaker 1: gotta extend the paper at the top and then she
Speaker 1: throws a tantrum.
Speaker 3: Later you're exhibit yeah, that's right.
Speaker 1: And that network back towards the bottom, and then you know,
Speaker 1: you get this this kind of abstract picture of your day,
Speaker 1: this mountain range. And what Jeevens is suggesting he wasn't
Speaker 1: the first to suggest it. He just he put it
Speaker 1: very nicely. Is why I quote him, is that maybe
Speaker 1: this mountain range, maybe that's your day. Maybe that's it,
Speaker 1: Like that's you know, it's the highs the lows, and
Speaker 1: what you want in a day is you want kind
Speaker 1: of a big mountain range. And there's a few ways
Speaker 1: to have it. It could be a very flat mountain
Speaker 1: range and not a lot of up and down, but
Speaker 1: it's just at a pretty high level. Or maybe it
Speaker 1: has some real lows but also some incredible highs, and
Speaker 1: that would be another way to get a big mountain range.
Speaker 1: Robert Frost has a poem that's titled Happiness makes up
Speaker 1: in height what it lacks in length.
Speaker 4: Wow.
Speaker 1: Yeah, maybe getting the phrasing slightly wrong there, but anyway,
Speaker 1: but the same idea, right, Happiness can be kind of
Speaker 1: an intense, exultant happiness can make up for its brevity.
Speaker 3: Say that again, happiness.
Speaker 1: Yeah, happiness makes up in height what it lacks in length.
Speaker 4: I think that's it. I see something along those lines.
Speaker 3: Love that. So that makes me think about these sort
Speaker 3: of half baked equations I occasionally hear for happiness or
Speaker 3: for well being. There's two that I really like. There's
Speaker 3: one that I love, and it's suffering equals pain times resistance,
Speaker 3: And I like the mathematical precision of this one. Actually,
Speaker 3: if you assume suffering is to the total amount of
Speaker 3: overall suffering that you have in relation to something. You
Speaker 3: can break that down and say, well, some of that
Speaker 3: is pain. So let's just take like, my back hurts.
Speaker 3: There's a physical sensation of pain, and then there is
Speaker 3: all the things I'm thinking about that pain. Oh God,
Speaker 3: it shouldn't be happening. Oh if I feel like this
Speaker 3: at fifty, what am I going to feel like at eighty?
Speaker 3: My mom has all that And so a lot of
Speaker 3: that is we could call sort of resistance to the pain.
Speaker 3: And so if you were to make this mathematical, and
Speaker 3: let's say you might say that your pain is a
Speaker 3: five and your resistance is a five, you've got twenty
Speaker 3: five total units of suffering. What I love about this
Speaker 3: is oftentimes I can't change the pain, right, a lot
Speaker 3: of situations in life, you can't change the thing that's wrong.
Speaker 3: So I'm going to have five units of pain no
Speaker 3: matter what I do. But if I can lessen that
Speaker 3: resistance from a five to a three, well now I
Speaker 3: have fifteen total units of suffering, which is way better
Speaker 3: without changing the underlying problem. And I'm not a believer
Speaker 3: that resistance ever goes to zero. Maybe that's what enlightenment
Speaker 3: is when resistance go to zero. But for most of us,
Speaker 3: we're not going to get there. But if we can
Speaker 3: turn down the what would be the way to say it,
Speaker 3: turn the dial, all of a sudden, you have less
Speaker 3: units of suffering. So that's one that I've always really loved,
Speaker 3: and I've understood the math of oh.
Speaker 4: Yeah, to jump in.
Speaker 3: No.
Speaker 1: I like your thought on zero, the unattainability of zero there,
Speaker 1: because that was my first thought. When you when you
Speaker 1: multiply two things, if one of them is zero, then
Speaker 1: it's gone, you know. So if you can get the
Speaker 1: resistance down to nothing, then somehow you could have pain
Speaker 1: without suffering. Yeah, and maybe that maybe when I think
Speaker 1: about I'm a very amateur student of Buddhism, but when
Speaker 1: I think about the Buddha like that sort of seems
Speaker 1: to be the image that that's conjured for me, that somehow,
Speaker 1: I for the resistance vanishes entirely, then there can be pain.
Speaker 1: But maybe it's not pain that really matters. Maybe it
Speaker 1: is suffering.
Speaker 3: Yeah, yeah, I mean that is a core Buddhist idea
Speaker 3: and core Buddhist message. I've had big enlightenment like experiences.
Speaker 3: You know that were like everything you read about in
Speaker 3: the book, and I would say, yeah, resistance was near zero,
Speaker 3: but boy, it just doesn't want to stay there, because
Speaker 3: it does seem to me that if you look at
Speaker 3: things from an organism perspective, we move away from what
Speaker 3: causes pain and we move towards what is nourishing or
Speaker 3: causes pleasure. You can see this in an amoeba, right,
Speaker 3: put something that's toxic to it on one side and
Speaker 3: put something that's nutritive to it on the other side.
Speaker 3: You know which side is going to go to, and
Speaker 3: so if you try and push it towards the toxic side,
Speaker 3: it's probably going to be like, no, thank you. And
Speaker 3: so it almost feels like some degree of resistance to
Speaker 3: me seems built into being an organism. Yeah, you know,
Speaker 3: it's so deep that hoping to make it go away
Speaker 3: on any kind of permanent basis is to hope to
Speaker 3: be something that as a living creature. I don't know
Speaker 3: that will ever be, but I do think you can
Speaker 3: turn that resistance down in a truly meaningful way.
Speaker 4: Yeah.
Speaker 1: Yeah, I think about athletes too. When I see athletes,
Speaker 1: there can be a time when it's quite painful to
Speaker 1: be doing what you're doing, you know, Michael Jordan during
Speaker 1: the flu game or whatever. Yeah, but the resistance is
Speaker 1: in their case maybe negative. They're not resisting the pain.
Speaker 1: They're they're embracing it. You can't do that all day,
Speaker 1: as you say, or even for an hour, but yeah,
Speaker 1: people can find moments.
Speaker 3: Yeah, that's another great example of being able to look
Speaker 3: at that from a slightly different perspective. The last one
Speaker 3: that I want to talk about, and this is one
Speaker 3: where I haven't quite figured out why the equation is
Speaker 3: written as it is, which is that happiness equals reality
Speaker 3: divided by expectations. So the core idea makes sense. Our
Speaker 3: happiness tends to be higher when reality meets or exceeds
Speaker 3: our expectations, right, and when it disappoints us, we feel
Speaker 3: less happy. I don't quite know why it's a division, though,
Speaker 3: I'm asking the mathematician I happen to have on this
Speaker 3: call here to say why any ideas?
Speaker 4: Yeah, yeah, I think division seems right to me there.
Speaker 1: Okay, because what division does is it if you have
Speaker 1: a vast number right, say the it was reality over expectations. Yeah,
Speaker 1: m so take someone whose reality looks tremendous to any
Speaker 1: outsider right, Like we would call that a million, you know,
Speaker 1: somebody a celebrity who's got sort of every material comfort
Speaker 1: and adulation and followers and all the social media platforms,
Speaker 1: you know, whatever you'd be hoping for. And what we
Speaker 1: tend to think is we sort of bring our very
Speaker 1: mortal expectations. I'm expecting one hundred out of life. So
Speaker 1: if I had a million and I was only expecting
Speaker 1: one hundred, my happiness would be huge, right, A million
Speaker 1: divided by one hundred is an enormous number.
Speaker 4: It's ten thousand.
Speaker 1: But if you're in that situation as a celebrity, probably
Speaker 1: your expectations are very similar to that yeah million they're having.
Speaker 1: In fact, maybe you look over there and you know
Speaker 1: the two other people in your field, yes, who have
Speaker 1: a bigger audience, who have better reviews. You know, like
Speaker 1: your comparison set becomes very restricted to the absolute top performers.
Speaker 1: And so now you have a million, but you're expecting
Speaker 1: two million, and so that's only half of what you're expecting.
Speaker 1: That's you know, your happiness is at one half rather
Speaker 1: than even being at a comfortable you know, one where
Speaker 1: reality meets expectations. So there's something that the ratio has
Speaker 1: the nice property that if you double the reality, but
Speaker 1: you also double the expectations in terms of happiness, nothing
Speaker 1: has changed.
Speaker 3: Yep, yep. Would subtraction not do essentially the same thing.
Speaker 1: It would do very similar, but it wouldn't quite have
Speaker 1: that exact doubling property. So for example, let's say that
Speaker 1: you're expecting it to make up numbers. You're expecting five
Speaker 1: and you have a ten. Yep, if you double both
Speaker 1: of those, now you're expecting a ten, but you have
Speaker 1: a twenty. So you've a sort of gotten the happier
Speaker 1: have you in a ratio?
Speaker 3: No?
Speaker 1: Because twenty divided? So yeah, if you well, we're getting
Speaker 1: into the into the weeds. I need to whiteboard to.
Speaker 3: Draw this, okay, and I'm not going to understand.
Speaker 1: It was subjection, so right, I think subtraction would capture
Speaker 1: a similar a similar thing. Given that these aren't precise numbers, anyway,
Speaker 1: you could probably write the same thought with subtraction.
Speaker 3: Division works. Yeah, As it was preparing for this interview
Speaker 3: and thinking about these two equations that I've used, and
Speaker 3: here I decided to say what other equations are out
Speaker 3: there for happiness? And there was some crazy out of it.
Speaker 3: Some Chinese research lab equation that like, I think would
Speaker 3: take me literally the rest of my life to try
Speaker 3: improve or disprove because it was so convoluted. But their point,
Speaker 3: which they then summarize this crazy long who knows what
Speaker 3: went into this equation, I just think this is interesting
Speaker 3: And they said, well, essentially it comes down to, you know,
Speaker 3: reality divided by expectations, except if you take your expectations
Speaker 3: too low. That doesn't work either. To suddenly expect that
Speaker 3: everything is always going to be terrible is not a
Speaker 3: recipe for happiness either, because then I guess you don't
Speaker 3: try to do anything and pessimism invades every aspect of
Speaker 3: your life. But I just thought it was interesting that
Speaker 3: they then had some fancy equation to sort of then say,
Speaker 3: but you can't have zero expectation or that's going to
Speaker 3: be problematic.
Speaker 1: Yeah, yeah, yeah, I think that's right. And to me
Speaker 1: that suggests not so much a shortcoming of the equation itself,
Speaker 1: like it's a nice equation. Then yeah, the reality about
Speaker 1: of expectations, but actually just a shortcoming of equations writ large,
Speaker 1: like equations are not as complicated as reality. Reality is
Speaker 1: very complex, and equations have a couple of terms. They're
Speaker 1: meant to show us a little a little schematic picture
Speaker 1: which yeah, to close the loop actually on Jeevans and
Speaker 1: the graph of your happiness that mountain range where I
Speaker 1: land on it in the book is that like just
Speaker 1: doesn't work.
Speaker 4: It's not right. I like social psychology research.
Speaker 1: So there's a nice set of studies where one of
Speaker 1: the things they did is they made people stick their
Speaker 1: hand in ice for a minute.
Speaker 4: You know, you're right familiar with this study.
Speaker 1: So you know, you spend a minute with your hand
Speaker 1: in ice water, really cold, and then half of the
Speaker 1: people that's it. You take your hand out. You've spent
Speaker 1: sixty seconds in ice water. You're done, and half the
Speaker 1: people you stick your hand in ice water, and then
Speaker 1: you get another thirty seconds in slightly warmer ice water.
Speaker 1: You know, the original bucket was maybe thirty five degrees.
Speaker 1: The next bucket is forty degrees, so it's still still
Speaker 1: uncomfortably cold, but not as cold. And then when they
Speaker 1: looked back on their experience, the second group liked it better.
Speaker 1: They rated that as less unpleasant. They rated that as
Speaker 1: like a happier time than the first group did. The
Speaker 1: first group thought it was more unpleasant. The conmoments diversity.
Speaker 1: The researchers talk about peak end theory that when you
Speaker 1: look back on a memory, you're not actually looking at
Speaker 1: the whole mountain range. That's not how we remember. We
Speaker 1: look at the peak, what was the most extreme experience,
Speaker 1: you know, the greatest bliss or the greatest pain, and
Speaker 1: we look at how it ended, like what happened at
Speaker 1: the end of the day. Yeah, and that actually matters
Speaker 1: much more than the specifics of the mountain range, because
Speaker 1: the mountain range theory would tell you another thirty seconds
Speaker 1: of pain, even if it's less pain, it's still more pain,
Speaker 1: more total pain. That should that should be worse. Yeah,
Speaker 1: So that's the limitation of you know, again, a little
Speaker 1: graph of a mountain range of your happiness. That's not
Speaker 1: actually your mood. That's a little picture. One of the
Speaker 1: reasons I like trying to spread a little more awareness
Speaker 1: of math is that it makes people were able to
Speaker 1: call bs you know, like mathematics is often it's simplified.
Speaker 1: It's useful, but simplified. And if you viewed as magic,
Speaker 1: you can't call BS on it. You can't be like, no,
Speaker 1: that there's something missing from that picture.
Speaker 4: And here's what it is.
Speaker 3: I had not heard that version of the study. There
Speaker 3: seemed to be a whole bunch where they plunge people's
Speaker 3: hands into ice water. I love reading psychology studies. They've
Speaker 3: gotten more ethical as time has gone on. You can't
Speaker 3: get away with quite what you used to be able to,
Speaker 3: but there's still a lot of really funny things. The
Speaker 3: version i'd heard of that was people getting to dental
Speaker 3: procedure and for the last couple minutes, the dentist just
Speaker 3: hangs out in their mouth, don't do anything really particular right.
Speaker 3: But you would think that then you would rate the
Speaker 3: whole thing as worse because you had a dentist in
Speaker 3: your mouth for longer, which is inherently uncomfortable. But the
Speaker 3: people whoe are it ended relatively low pain compared to
Speaker 3: maybe what it was before. Like you said, they rated
Speaker 3: it as a better overall experience. I think this is
Speaker 3: also really fascinating because the other thing that I think
Speaker 3: factored into this this Chinese paper, in its equation, is
Speaker 3: another idea that I'm often fascinated by and that psychologists discuss,
Speaker 3: and what they're discussing is two broad ways of measuring happiness.
Speaker 3: One way would be to simply like ping you randomly
Speaker 3: throughout the day and say how do you feel? Right,
Speaker 3: plot your mood on a chart, you know, four seven, one, whatever,
Speaker 3: and you just add all that up and basically that's
Speaker 3: kind of how happy you are. There's another way of
Speaker 3: doing it, which is you actually ask people, broadly speaking,
Speaker 3: how happy are you? How satisfied you are with your life?
Speaker 3: And those can produce different results, and I find that
Speaker 3: sort of fascinating. This equation apparently also tried to take
Speaker 3: some measure of that into effect, or maybe it was
Speaker 3: a different paper, but it was this idea of they
Speaker 3: were calling it you demonic versus hedonic happiness, right, hedonic
Speaker 3: meaning moments of pleasure, you demonic meaning overall broad satisfaction.
Speaker 3: And I just always think about how you measure those
Speaker 3: two things, and there's a lot of debate about which
Speaker 3: is the right method.
Speaker 4: Yeah, yeah, that's nice though. That's interesting.
Speaker 1: The right the trying to decompose happiness. So it's such
Speaker 1: a vast word with so many meanings that it makes
Speaker 1: that that's a good start I think on decomposing it.
Speaker 1: You say, okay, right, moment to moment pleasure and then
Speaker 1: of life satisfaction and you're kind of the narrative you're
Speaker 1: telling about your life, but I'm sure you could decompose
Speaker 1: it into many more elements than that exactly.
Speaker 3: I mean, like, no equation solves us as a human right,
Speaker 3: It's just it's not possible. You mentioned children earlier, and
Speaker 3: that's another one of these weird findings is that they
Speaker 3: find that if you measure moment to moment happiness, most
Speaker 3: parents will end up with a net negative when they
Speaker 3: have children. But if you're measuring meaning and purpose and
Speaker 3: overall fulfillment and satisfaction, people will say they will rate
Speaker 3: children much higher than that. And so it's sort of
Speaker 3: this like what we think we're experiencing versus what we're
Speaker 3: telling ourselves we're experiencing, or the story that we're putting
Speaker 3: on it, which are not separate from each other.
Speaker 4: Right, They're intertwined and complicated ways.
Speaker 1: Yeah, yeah, may be misremembering this, but I think another
Speaker 1: another study along similar lines was that if you ask
Speaker 1: parents if young children, how are you doing? How satisfied
Speaker 1: are you? You get one answer, but if you want
Speaker 1: a higher answer, you just first asked them how are
Speaker 1: your kids doing? Okay, they talk about their kids for
Speaker 1: a minute, and then and they say, Okay, now, how
Speaker 1: are you're doing interesting and just activating that different side
Speaker 1: of what they're thinking about. This hard to say because
Speaker 1: I've read about this for a lot of psychology studies
Speaker 1: in the last twenty years to trouble replicating and this
Speaker 1: defects generalize, but they still give I think, an illustrations
Speaker 1: of intuitive effects sometimes. That's one I can vouch for
Speaker 1: that as a parent of young kids. If you if
Speaker 1: you ask me, you know, sort of how's my mood
Speaker 1: compared to before I had kids, Like you know, day
Speaker 1: to day, probably a little rock here, But if you
Speaker 1: start get me talk about my kids and then ask me,
Speaker 1: it's like, oh, I'm going to be glowing exactly right.
Speaker 3: It's a priming effect to some degree, right, It's what
Speaker 3: it's bringing to your mind. My version of this that
Speaker 3: I would play, And this is a story I tell
Speaker 3: often that I kind of go back to just because
Speaker 3: it was so illustrative, right, was you know, me complaining
Speaker 3: that when the boys were like middle school age about
Speaker 3: every single day driving them to some sporting event one
Speaker 3: or the other of them and finding myself saying like
Speaker 3: I have to do that, I have to do that
Speaker 3: and then finally ultimately realizing I didn't have to do it,
Speaker 3: I was choosing to do it. But I think a
Speaker 3: version of the study would have been would be to
Speaker 3: ask me like, what's your son get out of soccer?
Speaker 2: You know?
Speaker 3: Or how much does your son like soccer? And I
Speaker 3: would have answered that question. Then you would have said like, well,
Speaker 3: how do you feel about driving him to soccer? And
Speaker 3: I'd been like, I feel great about it, right, Like
Speaker 3: it just would have reset my mind in a direction
Speaker 3: of something that matters, which is honestly a lot of
Speaker 3: what the mental psychological game is is how do you
Speaker 3: sort of move your mind from here to over to here? Yeah?
Speaker 4: No, that makes sense. Yeah, yeah.
Speaker 1: I think something I find from writing about math and
Speaker 1: then putting it in contrast with lots of more human
Speaker 1: social topics or the social sciences and philosophy, is that
Speaker 1: math always gives us this vision of simplicity and you know,
Speaker 1: singularity and very straightforward things you can define, and those
Speaker 1: are useful, but you need multiple lenses like that. You've
Speaker 1: got to move between different models because we are so
Speaker 1: much weirder and more complex than that, you know, with
Speaker 1: each got a city inside our minds of these different selves,
Speaker 1: and so how do you coordinate.
Speaker 4: Them and lead them?
Speaker 1: You know, how to get them to agree on goals
Speaker 1: like it helps to adopt a simplified lens for a
Speaker 1: little bit, but precisely because it's yes only for a
Speaker 1: little bit.
Speaker 3: So listener in thinking about all that and the other
Speaker 3: great wisdom from today's episode. If you were going to
Speaker 3: isolate just one top insight that you're taking away, what
Speaker 3: would it be? Not your top ten, not the top five?
Speaker 2: Just one? What is it?
Speaker 3: Think about it? Got it? Now? I ask you, what's
Speaker 3: one tiny, tiny, tiny, tiny little thing you can do
Speaker 3: today to put it in practice? Or maybe just take
Speaker 3: a baby step towards it. Remember, little by little, a
Speaker 3: little becomes a lot. Profound change happens as a result
Speaker 3: of aggregated tiny actions, not massive heroic effort. If you're
Speaker 3: not already on our Good Wolf Reminder SMS list, I'd
Speaker 3: highly recommend it as a tool you can leverage to
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Speaker 3: totally free and easy to unsubscribe. If you want to
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Speaker 3: to one ufeed dot net, slash SMS all right back
Speaker 3: to it. Knowing when a broad principle of well being
Speaker 3: or happiness or whatever will serve you, even of parenting
Speaker 3: anything will serve you, like Okay, that's useful, and then
Speaker 3: also recognizing when it's like okay, that sort of applies.
Speaker 3: But I have to trust myself that that's not useful
Speaker 3: here anymore. Yeah, ultimately trusting ourselves. You and I are
Speaker 3: going to continue for a few minutes in the post
Speaker 3: show conversation because I have realized I cannot get away
Speaker 3: without knowing about Professor Dogg. That's Professor Dogg to you,
Speaker 3: in which calculus vaults a dog to start them, so
Speaker 3: you and I are going to cover that in the
Speaker 3: post show conversation. We may also talk about how mathematics
Speaker 3: makes us want to quantify everything, which we've been doing
Speaker 3: for the last fifteen minutes, trying to quantify happiness or
Speaker 3: expectations or put a number on everything, and you know
Speaker 3: what are some of the costs of that. So, listeners,
Speaker 3: if you would like access to the post show conversation
Speaker 3: we're about to have if you like ad free episodes
Speaker 3: as well as a special episode I do each week
Speaker 3: where I share a song I love, I teach you
Speaker 3: something useful based on the show. Then you can go
Speaker 3: to one feed dot net slash join and become part
Speaker 3: of our community. Ben, thank you so much. This was
Speaker 3: really fun. I've enjoyed being in the math world a
Speaker 3: little bit for the last week and diving into your
Speaker 3: world a little bit. It's always hard when we have mathematicians,
Speaker 3: which we've never done before, but I have had visual
Speaker 3: artists on before whose drawings are a big part of
Speaker 3: what they do, and obviously we couldn't do that here.
Speaker 3: So I will make a call out for listeners, which
Speaker 3: is his books are much better with the drawings than
Speaker 3: they may have sounded in you know in our discussion.
Speaker 3: So his latest book is Math for English Majors, a
Speaker 3: human take on the universal language.
Speaker 4: Thank you, Ben, Yeah, thanks so much, Eric, I appreciate
Speaker 4: the conversation.
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