In this episode, math teacher and author Ben Orlin explores the secret to learning and problem-solving in life. He explains why struggling through challenges (in math and life) can actually be a good thing. Ben also discusses the unexpected power of humor and how we can rethink our approach to learning and change.
Key Takeaways:
- 05:16 – Struggle is a Sign of Learning, Not Failure
- 13:27 – Why We Fear Math (And How to Overcome It)
- 25:06 – The Role of Humor and Play in Learning
- 27:36 – The Paradox of Change and the Infinite Steps of Progress
- 22:03 – Why We Need to Step Away to Solve Problems
- 50:27 – The Link Between Happiness and Expectations
Connect with Ben Orlin Website | X
Ben Orlin is a math teacher, an author, and an inept cartoonist. His books have sold hundreds of thousands of copies worldwide; they include Math with Bad Drawings, Change Is the Only Constant, and Math for English Majors. He has taught math to every age from middle schoolers to undergraduates, and his writing about math and education has appeared in The Atlantic, The Los Angeles Times, and Popular Science.
If you enjoyed this episode with Ben Orlin, check out these other episodes:
How to Find Real Life in Stories with George Saunders
Improvising in Life with Stephen Nachmanovitch
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Episode Transcript:
Eric Zimmer 01:09
Math has always been a challenge for me, so naturally, I figured, why not have a math expert on the podcast? Really is a way to explore how we handle challenges. In general, today I’m talking with Ben Orland, who’s a math teacher and author who makes problem solving feel surprisingly human. We’ll explore why struggling is actually a good sign, how humor helps us push through tough moments, and even what a dog retrieving a ball can teach us about calculus. I’ve spent most of my life intimidated by complex math. But as I talked with Ben, I realized that how we approach math mirrors how we approach any challenge, whether it’s breaking a habit, learning something new, or facing uncertainty. By the end of this episode, you might not just rethink math, you might rethink how you take on hard things. I’m Eric Zimmer, and this is the one you feed. Hi, Ben, welcome to the show. Yeah, Hey, Eric, yeah. Thanks so much for having me. I’m excited to have you on. You are a little bit of an odd guest for us. I don’t mean that you’re odd as a person, although perhaps you are. I think that’s a good thing. But yeah, I get I get that at dinner parties when I show up, though you’re an odd guest for us. Yeah, you’re writing books about mathematics, which is a topic we have literally never covered, except me trotting out some sort of cliched like happiness equations or something. But I was really taken by first the title of your book, and then, as I look deeper into your work, some of the other titles and some of the ideas that you’re playing with. And your new book is called math for English majors, a human take on the universal language. So I think there’s a lot that we can cover that listeners, I think you’re going to be surprised at how interesting this is, particularly if you don’t like math or you’re afraid of math. This is a great conversation. So we’re going to start however, like we always do with the parable. And in the parable, there’s a grandparent who’s talking with their grandchild, and they say, in life, there are two wolves inside of us that are always at battle. One is a good wolf, which represents things like kindness and bravery and love, and the other is a bad wolf, which represents things like greed and hatred and fear. And the grandchild stops. And they think about it for a second. They look up at their grandparent. They say, Well, which one wins? And the grandparent says, the one you feed. So I’d like to start off by asking you what that parable means to you in your life and in the work that you do. Yeah, I think of the feeding as the what you do every day. I think sometimes I give in to the temptation to want to imagine I have this self which is somehow separate from the way I spend my time. There’s like, there’s this me, and I have this high opinion of myself, maybe, but if you look at what I’m doing day by day and week by week, it’s like, well, am I doing those things that I claim to value? And so as a teacher, I think about this. As a teacher, you’re sort of always on the clock in some sense. You know, when the students are in the classroom with you, yeah, they’re taking the lesson from whatever it is you’re doing that day. They’re not taking some lesson you’ve imagined in your head. And so to me, that’s what the feeding is. Is, how are you spending every minute? Every minute, every hour? I love that idea. There’s a concept out there that I know has a name, but I don’t know what the name is. It’s a concept in the mental health world a little bit. And it basically says that if you want to know what somebody values, look at what they do actually do, not what they say. I think that’s a little reductive. I get it because I do think it’s true that that does show at least what our operating values are at the time. But I also think that there are ways in which we can get better at bridging the gap between that idealized self that you talked about in your head and the actual self that shows up day to day, because there’s a lot of time in my life, if you took who I was only measured by what I did, you’d be like, That guy is a piece of shit, right? Like, that guy is a real asshole. Because, I mean, I was a heroin addict. I mean, I was not behaving well, and I like to think that wasn’t all that was true in those moments.
Ben Orlin 05:00 No, I think that’s fair. Maybe that’s. I think having the multiple wolves in the stories is an after metaphor, because we’re not these unified, coherent people. Yeah, you can’t look at someone and say, Oh, yes, this is the explanation for their behavior and who they are and what they do. It’s like, we’re not that tidy, we’re not characters and a fable. We’re something much more complex than that.
Eric Zimmer 05:16
So let’s take that idea there, that we’re something much more complex than that, because we really are. And if there’s one thing that I sort of push against in the space that I’m in is the idea of easy answers, the idea that, like, there’s this one size fits all formula, or there’s these five easy tricks, or all of that. And I heard you say on a different show, I’m not going to get this exact but you basically said that one of the things to be a good problem solver is, instead of trying to immediately solve the problem, is to relax a little bit into what the problem is and explore it a little bit more before you move on to solutions. Say a little bit more about that.
Ben Orlin 05:56
Yeah, yeah. I’ve talked about this with students, and in my writing a little bit. I think if there’s certainly these four stages of solving a problem, and mathematics is a really good place actually, for learning these stages, because mathematics is this series of challenges, of problems that you run into, and some of them are routine, you know, sort of exercises, like doing your weight lifting for the day, and you don’t get stuck on those. You can just kind of move through them. But sometimes you run into a problem and you don’t know what to do. The first thing you try doesn’t work, and then there’s a temptation to just bounce off that problem and go do something else with your day. Especially in math, there’s a lot of ways to spend the day other than doing mathematics. So I know this with my students, like there’s other ways to spend their time. So when a student runs into a problem that they’re stuck with, my first piece of advice is to stop trying to guess the answer, or stop trying to solve it right away. I remember one time it was a class of seventh graders I was teaching, and it gave them a problem that I thought was going to take the whole lesson to solve, but they weren’t accustomed to problems like that, so some of them just started shouting out, guesses, right? But is it 12? Is it 14? And I was like, you’re probably not going to guess the answer in the first 30 seconds. So my advice in those situations, and beyond math too, is to explore the problem, to make the goal for that next 10 minutes, that next half hour, not to solve the problem, but to figure out, what would a solution look like. What are the obstacles here? What’s the what’s the tension in this problem? Why isn’t there an easy answer? What are the things that people have tried, maybe for this problem, you know, to view it as you’re researching and playing with the problem rather than trying to solve it. This is something that research mathematicians, the people who are trying to solve new math problems, tend to be very, very good at, because those problems can take years to solve. I mean, some of them can take centuries, right? They’re sort of passed on generation to generation, and so you have to be patient. And sometimes progress on a problem doesn’t look like a solution. It looks like an idea of what the solution would have to look like, or ruling out possible solutions.
Eric Zimmer 07:44
I love that, and I do think that that really does apply to challenges in our life, changes we want to make, or problems that we’re having. Is that if we can spend time really looking at the problem or the change that we want to make without immediately jumping to a conclusion of what we should do, it really helps. And you mentioned, like, there’s contradictions and there’s opposing tensions, and it’s like, you know, let’s say I suddenly am like, well, I want to begin reading for 30 minutes a day. I’m just making something up, if you don’t spend some time to acknowledge, like, what’s been blocking me from doing that? You know, what other tensions are pulling on me in those moments like that, sort of exploration can be really, really valuable. We tend to jump right to action and and it’s interesting, I think, a lot about like, one of the most accepted models for behavior change is called the trans theoretical model of behavior change, most commonly known as the stages of change model. And there are three stages before you even ever get to action. And if you don’t do some of the work in those stages, very often, your action just isn’t going to go anywhere. It’s going to just peter out really quickly. And it sounds a lot like what you’re saying, which is like, I’m just going to start shouting out answers, hoping that this problem is solved in three minutes, and I’m on to the next thing.
Ben Orlin 08:59
Yeah, yeah, no. I think that I like the preparation before the solution seems important. And I think another thing that I learned from mathematics is the hardest problems don’t always look hard, and the easy problems don’t always look easy. There’s a very famous one. This is a problem that was first just kind of jotted down in the margins of a book 400 years ago. And it was someone who was reading an old geometry book, this guy Pierre, and he like, he jots it down, and he’s like, Oh, I’ve got an idea for another equation here. There’s a certain kind of equation that I think doesn’t have a solution. And he jots it down in the margin. He says, oh, and I can actually, I know the solution to this. I could prove this to you, but I don’t have quite enough space in this margin of the book. And then it just sort of sat there in the margin of his book for a few years. His son discovered it a few decades later and published it with his writings. And people started looking at what was this proof that he had come up with that he didn’t quite have space for and it took three to 50 years. He probably had it wrong, right? His proof was probably false. But the thing he was trying to prove that this kind of equation didn’t have a solution. It’s a very simple equation. I’ve showed it to eighth graders, and it’s true what he said, but it was one of the hardest problems anyone had ever uttered in mathematics up to that. Moment it took, you know, it wasn’t solvable with the mathematics at the time, you needed 350, more years of mathematical developments for that to be solvable. So it looks really simple. And, you know, sometimes in later, I want to read for 30 minutes a day. It sounds so simple. It’s like I got books on the shelf. I’ve got 30 minutes in the calendar. This seems very easy, right, right, but maybe that’s tapping into issues of attention and patience and anxious worries that keep you from focusing like it can tap into so many different issues exactly, and so, yeah, I find mathematics a very crisp model of those things often, because in math, it seems like, of all places, it should be easy to tell what’s an easy problem, what’s a hard problem, but things can be simple and very hard or complex, and actually not so hard. You know, a lot of surface complication, but if you just understand what the terms are, it’s actually a straightforward problem.
Eric Zimmer 10:45
This is a question about problems like that. Like, how does someone know that they’re proposing a mathematical problem or proof or quandary, versus just writing down a bunch of nonsense? Like, are there points where people are like, we’re trying to prove something that should not be proved because it’s not true or real or like, I know this isn’t a question that probably is like three podcast interviews, but I’m just curious, because I often think about that.
Ben Orlin 11:14
Yeah, that’s another more. I think it’s interesting to hear what mathematicians say about this. I’m a math teacher, right? I don’t do my own mathematical research, but knowing lots of people who do often, they’ll run into a question where you’re trying to decide, okay, Is this statement true or false? And actually, if you sit there wondering whether it’s true or false, you never get anywhere. What they have to do is they have to commit to the thought, Okay, today I’m going to try to prove it’s true. I think it’s true. I’m going to try to prove it, and they’ll work to prove it, and maybe in the process of trying to prove it, they’ll find out that it’s false, or maybe they just don’t get anywhere, and the next day, they go, okay, given I couldn’t find a proof yesterday, I think this is false. I’m going to look for, you know, an example that shows this is false, something that breaks the purported rule, and then they’ll do that. But what I’ve heard from a lot of mathematicians is you can’t occupy both states at once. You have to at least temporarily commit yourself to one side of the ledger. You know, I’m going to push in this direction today. And even if you don’t know which direction to go, you learn a lot by picking a direction and trying that.
Eric Zimmer 12:07
I find that ability to sit with a problem like that for years astounding. I recently, very recently, figured out that I can solve crossword puzzles now, as a 50 year old man, 50 plus years who loves words, I should have known that sooner, but I didn’t, because I would get stumped early on and be like, I can’t do this. Now I realize like, oh, I can do this. I love doing this. This is fun. This is enjoyable. There is some switch in me, and I don’t know if that switch was that I suddenly started to believe that I could do it, and then that enabled me to stick with it. But I think that we could extrapolate this idea a little bit to how do we stick with things that we feel like we can’t do? Now you must face this all the time as a math teacher, right? Because one of the most common things you’ll hear people say is, I’m not good at math. You know, if you ask people what they’re good at or it comes up, you’re gonna hear I’m not good at math a lot. So I think there’s a similarity here to me and my crossword puzzles. So let’s talk a little bit about that process, maybe in how you teach it for math. And then maybe we can broaden it out to how we apply it to other areas of our lives that may be more impactful than a crossword puzzle.
Ben Orlin 13:27
Yeah, although I love crossword puzzle that’s pretty high impact. You can spend 15 minutes a day sort of enjoying the New York Times puzzle. That’s a nice way to spend the time. It is, it is, yeah, it’s definitely true what you say about people identifying as not a math person. It’s sort of funny, because everyone, when they present it, they present it as sort of this idiosyncratic fact about them personally. It’s like, oh, you know, it’s just me. I’m just this funny person who’s like, ah, it didn’t really math. Didn’t really click with me. It’s like, yeah, there’s hundreds of millions of people like that in the United States. Like this is a solid majority of the country, I would say. So it’s obviously not, and maybe that’s, I think, the first step for people, you know, it’s not some personal failing of yours, and I try not to blame me. I’m a teacher. I love lots of other teachers. I try not to blame it’s not the teachers have failed. It’s a weird thing we’re trying to accomplish in math education. We’re taking these five year olds and sending them down on this 10 year journey where they’re supposed to come out the other side having learned, sort of like centuries worth of mathematical ideas, becoming expert in stuff that really only a very small elite would have ever had to learn in a lot of past generations. You know, these very abstract ideas that come with their own language that’s presented in pithy, very sometimes too short, too brief, the glimpse you get of these ideas. To me, there’s no shock when someone struggles with mathematics or with mathematics education. That’s sort of the default state. And I think for me, that’s a first step. When there’s something that I’m struggling with mathematical or something else, or when I see a student struggling, is to de personalize it a little bit. It’s not some shortcoming, some gap within you, you know, there’s some missing jigsaw piece in your brain that you’re never gonna be able to get this. It’s like not things are hard to learn. It takes time. That takes effort. It takes the teacher to walk you through it. So that’s the first step. For me, the second step is often motivational. Why would I want to learn it? For a lot of students, the benefit to learning math is you can pass math classes and then stop taking them. That’s really it’s it’s a thing you want to learn. So you can cease ever having to think about it. And so this varies a lot from person to person, but I try to find something that that feels meaningful to them, that will open something up for them in their life. Just a student the other day, actually, it was their first day coming to my class. They enrolled late and missed the first week, and we were doing a little bit of work in spreadsheet programs, just in Microsoft Excel, and the student was saying was just sort of like, mouth open. They were like, my mom’s been running a small business for years and doing the accounting with literal spreadsheets, like sheets of paper spread out and a hand calculator and adding up the numbers hours every month to get that to work. I was like, oh, yeah, no, take this home. By the end of the semester, you’ll be able to do that hours of work and 5-10 minutes of updating the spreadsheet. So for a lot of people, I think it’s personal finance. It’s you can give you a grasp on money and where you’re putting it, and how it’s flowing and and where it goes. You know, when, when the money’s gone from the bank account, where did it go? Just a little bit of extra grasp on mathematics and mathematical tools can can really help with personal finance. So especially for a lot of the adults I teach at community college, that’s a very relevant one. And then especially for younger students, but for some adults too, mathematics is just this kind of beautiful set of ideas. It’s connected to to everything a little bit it’s like, kind of like this underground water source or something underground river that sort of connects all these different parts of the landscape that you wouldn’t have thought were connected. And so, you know, one of the things I love to do is kind of collect great thinkers who are fascinated by mathematics. And you know, Abraham Lincoln loved mathematics, right? He read a lot of Euclid the geometry. In fact, memorized the whole geometry book while he was in law school, he was sort of working on his legal studies. He goes, Oh, I’m never going to be a good lawyer unless I really understand argument and logic and proof. So okay, so I guess I’ve got to go read ancient geometry texts and learn it that way and memorize them. Israel, yeah, he memorized the arguments. Yeah,
Eric Zimmer 17:07
I guess you can just get a lot done if you don’t have TVs or cell phones or, you know,
Ben Orlin 17:13
right, right? All he had to do back then was Chop,
Eric Zimmer 17:16
chop electric lights. I mean,
Ben Orlin 17:19
that’s what I’ve been saying for years, is electric lights are a huge distraction for us. It’s really, you know, it’s shorten our attention span. It’s really gotta, gotta go back to candles. This is rambling here in this answer. But, yeah, I think reason I ramble a little bit is because every person needs to find their own connection here. You know, for Lincoln, it was logic. It was mathematics as a model of logic. And for people who love Sudoku puzzles, that’s a little bit the same thing. That’s, all, you know, airtight logical reasoning. And for some people, it’s, you know, mathematics being connected to the arts and sort of the ways geometry plays into into different artistic traditions. Cosmology is a topic that I’m always fascinated by, like, what is this universe, and how does it work? And what on earth is going on here? How did we get here? And mathematics is really central to answering some of those questions. So for some people, they sort of you get excited about science and maybe learning a little bit of mathematics will help open doors there.
Eric Zimmer 18:07
That is a quandary I run into often, which is the last time I took math would have been a long time ago. My main attempt in most of high school was simply, how do I not go to school? How can I get out of going? So if I could have used mathematics to help with that, I probably would have. But I love Popular Science, but a lot of it, I’m reading the introduction, and I’m like, Okay, I’m cruising along here, and then start the equations, and all of a sudden, I’m like, You know what? To understand this, I’m gonna have to go back a little ways, and I just never quite take the time then to go back and go, You know what? Some basic algebra has served me really well in getting into all of these ideas.
Ben Orlin 18:51
Yeah, yeah. I think of algebra especially. It opens a lot of doors. It’s a key. It’s a key that’s very hard to acquire, right? It takes a few years of education. And, you know, in the US, we teach a course called algebra to, you know, usually 14 year olds or so, and I’ve taught that course, and students don’t really internalize it. Don’t really learn it until, usually three, four years later, at the earliest, when they’re when they’re taking calculus or something like that, that it’s having to use those algebra skills later on that really forces you to absorb them. So it’s not easy to learn algebra, but it just opens up so many doors down the road that you wouldn’t have guessed, yeah, especially in the sciences. But, well, I don’t know sciences touch everything. So you know, if you want to learn about economics or finance or or astronomy or or population biology or epidemiology and think about predicting the next pandemic, any of that, yeah, just having the language of algebra really pays off.
Eric Zimmer 19:39
I’m trying to balance the desire to keep this conversation somewhat about what the one you feed talks about, versus chasing it down mathematical rabbit holes. So I’m gonna pull back up here for a second and say, like, let’s keep going with this question of, okay, there’s something in life that I can’t seem to do, or I’m intimidated. By, how do I work through it? We’ve talked about how recognizing you’re not alone in doing it is really important, right? Recognizing that this is a problem lots of people share, humanizing it. We’ve moved on to trying to connect it to why it matters. And I think that’s really important too. Same thing with like, reading a book for 30 minutes. Like, okay, why? Why does that actually matter to you? If we’re unable to articulate that, well, we’re not going to have sufficient motivation to stick with it, which I think is what you’re saying about math. You’ve got to get the student interested somehow. So okay, now you’ve got the student recognizing I’m not alone and not liking math. Okay, I can see why this might be valid to me. You know, I have always wanted to read Brief History of Time by Stephen Hawking, and I can’t. And so, okay, algebra, where do we go next?
Ben Orlin 20:48
Yeah, yeah, for solving any particular problem. What I like to say sort of the next step. Once we’ve we’ve kind of walked around the outside of the problem and we’re motivated to solve it is getting a wrong answer down on the page, deliberately wrong, right? Like you’re not trying to answer it correctly, yet, you’re trying to get sort of maybe an obvious wrong answer. And then that gives you something to work on that sort of solves that blank page problem, right? Anyone who’s written knows that it really helps to have a draft in front of you. Getting that first draft down is pulling teeth. That’s that’s the hard part, yeah, when solving a problem, just getting an answer down in math, one of the questions I like to ask students is, you know, what’s an answer you know is much too big, and what’s an answer you know is much too small, you know, for trying to solve for some number. And that can start to build some intuition. It sort of says, Okay, this is the sort of thing we’re looking for. Or, you know, if you’re looking for some problem solving method, you can say, Okay, well, why wouldn’t this work? It’s another way of teaching yourself about the problem, introducing something that you know isn’t quite the right solution. Yeah, it gives you a first draft to build on.
Eric Zimmer 21:45
Excellent. I want to jump back to a loop I didn’t close earlier, which is you talked about, like, I think you talked about four steps of solving the problem, or four stages, and I think we got through about half of them. So maybe we can pause right now and close that, because I think it’s relevant to where we are in the conversation. Yeah.
Ben Orlin 22:03
Yeah. This doubles, I think making mistakes sort of like getting a wrong answer down. I would call that, yeah, sort of my second step there. Once you explore the problem, once you’ve explored it further, and you’ve worked for a while, one very important step, I think, is to step away from it, to not have a false sense of urgency that you have to solve it in the next 10 minutes, and just give it some time, especially once it’s kind of circulating around your mind, the back of your brain, can do incredible things given a little space to breathe. So for me, it’s, you know, putting on headphones and going for a walk or going for a run, although I have to be careful. When I’m on a run, often, I’ll have ideas that I think are brilliant at the time, and then I get home and look at like that little note I took on my phone. It’s like waking up after a dream like, Oh, that wasn’t, wasn’t the idea I thought it was.
Eric Zimmer 22:41
Yeah, what’s interesting about that is, I do think it mirrors an experience I used to have when I was a heavy substance user. Is I would write some part of a song or something, and be like, this is incredible. Wake up in the morning, be like, not so much. And for some reason, walks seem to do a little of the same thing. Some of the ideas are great, but I’m a little bit astounded by how some of them, I’m like, there must be something about the state of flow, or it is what you want to have happen when you’re initially brainstorming, which is the critic takes a vacation for a little bit. You’re like, go away. Critic. And walking seems to do that for me.
Ben Orlin 23:14
Yeah, yeah. That puts me a little more at ease. And it’s a good reminder to us. Someone who very much lives in my head, I think math induces this, and people sort of like you, spend a lot of time with your thoughts and looking at screens, looking at paper, but you could remember, I’m a body, you know, that’s what I am. That’s what I have. And then it moves around the world. I’m not a just a computer where you can predictably feed me inputs and get the right outputs. You know, I need, I need a little bit of serendipity. I need some surprises and things in front of my eyes that I didn’t expect to see, I think, stepping away and going for a walk or cooking a meal or whatever it is that gives you something to keep your hands or your feet busy, and then your brain can keep working in the background. And then the final step is sort of the counterpoint to that, which is, then you got to go back to work. Yeah, you can hope that some inspiration will come. But this is true even of artists, right? A lot of the artists I admire, they have a very strict writing regimen. I mean, Paul Simon, when he was writing albums, he would just be writing a certain number of hours every day, and that’s how he generated it. Stephen King wrote 3000 words a day, or some completely superhuman number of words. And I think most working artists, I should say they do, yeah, they have to, right? Otherwise you don’t create what you don’t create what you need to create, otherwise, you don’t solve the problems you’re trying to solve within each work. Even if you feel uninspired, you’ve got to go back to it.
Eric Zimmer 24:42
Let’s shift direction just a little bit here. We’re still talking about sort of overcoming fear or overcoming being stuck. I want to talk a little bit about the role of play in that and all. Also the role of humor, because your first book was, I think, called math with bad drawings.
Ben Orlin 25:06
Yeah, that’s right, yeah. It’s always fun seeing how translators handle that. There’s one word because translate as math with the worst drawings got demoted here.
Eric Zimmer 25:14
So yeah, you draw humorous little drawings that are intended to illustrate the concept, but also oftentimes just have fun, right? There are times I see they help me figure out the concept, and there are other times I think they just sort of make light of the whole thing a little bit, which I think causes a reduction in the strain around trying to figure it out. So talk to me about play and humor and why that is the direction you’ve chosen to go.
Ben Orlin 25:41
For me, the bad drawings. There’s a few things that led me to them, and one is my inability to draw. I just can’t do it. And, and math is very visual, so you need, you need pictures to explain things, and you need pictures to kind of punctuate, you know, the end of a thought. So I needed to draw. And I’ve never doodled as a kid, I really, I should have practiced more, yeah. But anyway, so I arrived in adulthood and wanted to write these books about math and wasn’t able to draw. So they’re okay, we’re gonna do stick figures. We’re gonna do you embraced your limitation. Yeah, exactly. Yeah. And I think it wasn’t a calculation on my part. It was sort of a shrug of the shoulders, like, okay, I guess that’s the best I can do. But I think it creates a different tone or a different kind of space for people coming to mathematics, maybe not super enamored with the subject, because you come thinking, Oh, I’m not really a math person, and it sort of activates people’s defenses around being good at things, being bad at things. And so to have the person you’re learning this stuff from be very self evidently, leading with something they’re bad at, right? Kind of putting their worst foot forward. Yeah, yeah. I think it kind of demystifies a little bit we’re coming here as fellow human beings, with our strengths and our weaknesses and our gaps and our knowledge sets. We’re here to share things. I’m not here to stand on a mountaintop and pronounce the truths of mathematics.
Eric Zimmer 26:48
One of your earlier books is called Change is the only constant. It’s about calculus. I may not have that title exactly right, but as a person who studied a lot of Buddhist and Eastern thought, this idea of impermanence is central to the whole game. Talk to me about the role that change plays in mathematics, yeah, and maybe how math brings that concept alive. And I’ll say one last thing, and then I turn it over to you. There’s a phrase from the Japanese poet Basho who says, I’m not gonna get it exactly right. You learn more about impermanence from a falling leaf than like, 1000 words about it. So, but math probably shines a different light on that same idea, right? There’s another way of learning more about impermanence. Talk to me about it mathematically.
Ben Orlin 27:36
Yeah, changewas something that mathematics always struggled with. I think, is one way to put it, that somehow a lot of mathematics that was developed by brilliant mathematicians dealt with static situations, and it was actually change in motion that presented some of the most vexing mysteries. And, of course, one of the most ancient ones. And this comes up in the Western tradition, comes up in the Chinese school of names, was a philosophical school, is what we call Zeno’s paradox. So the idea that, you know, if you and I are going to high five each other, Zeno would have phrased it a little differently. But if we’re going to do a high five, like to complete that high five, we need to get halfway there, right? Like our hands start three feet apart, we got to get to a foot and a half apart. And then, okay, that takes some amount of time, but then to complete the high five, now we need to go halfway again and get to three quarters of a foot apart, or nine inches apart now, but we’re still not there. Yet. There’s another step. We got to go halfway again. And now our hands are really close, but there’s still another step. You got to go halfway again and halfway again. And so there’s this infinite series of actions you have to complete just to high five, somebody. And this is sort of true of all motion. It feels like all change, anything that you want to happen. You can decompose it into an infinite series of steps, which certainly from a perspective, making change in your life is very daunting. Thought that somehow any change is infinite in scope.
Eric Zimmer 28:49
It often is. I think there is change that is goal oriented, as in, I’m going to run a 5k but if your bigger goal, the reason you want to run a 5k is that you value your physical health, then change is infinite, because there’s never a day that your physical health is like, Okay, I have established it now. It is set. I will go about all my other business and it will remain in place. It’s the same thing with like, we can’t just eat once, right?
Ben Orlin 29:20
I’ve locked in healthy eating. I had a salad for lunch yesterday. It was delicious. That was it. Now I’m done. Now I can have cinnamon buns every day. Yeah, exactly, yeah. So maybe that’s right, that yeah, Zeno was on to something. I think Zeno was certainly on to something. Obviously, as you know, understood, you can complete an action, right? We see people walk across a room and they get all the way to the end. So clearly, there’s something a little a little tricky about his logic, but Bertrand Russell, the 20th century philosopher, said that sort of every generation since Zeno has had to reckon with that paradox. Right on the one hand, we do complete actions. On the other hand, there’s this sort of compelling argument that it’s impossible, that it’s infinite, that we’ll never get there, and so every generation has sort of had a different answer to that. Question,
Eric Zimmer 30:01
What does your generation I think we’re probably sort of a generation apart, not quite so, what would Russell say your generation’s wrangling with Zeno’s paradox is.
Ben Orlin 30:11
Oh, that’s interesting, right? I guess I’m sort of a squarely in the millennial generation. Yeah, yeah, I don’t know. I think millennials looking at us from the outside. I think we have a reputation for being a little square, a little earnest, you know, compared to Gen X, which was always steeped in irony, and Gen Z, which sort of finds Millennials hopelessly straightforward and earnest. I think there’s something about millennials maybe that just want to be like, no, no, I’m going to get there. I’m going to I’m going to go halfway and halfway again. I’m going to complete that sequence of of actions. Yeah? So maybe, yeah, maybe the the lesson for millennials would be to embrace a little more, a little more mystery in that, a little more, uh, accepting it as a paradox.
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Eric Zimmer 30:49
So there’s a recent post on your blog about the poet Adrian rich, and really about this idea of change. Can you share a little bit more of what you wrote there?
Ben Orlin 30:59
Yeah. I came to Adrian rich very sideways. It was just through I came across the quotation of her totally out of context, that the moment of change is the only poem. And I thought that was lovely. Didn’t know anything about Adrienne Rich, because I’m not particularly knowledgeable about poetry, and so this was actually while I was working on that calculus book, I went and read a few of her collections and essays she’d written, and found her a fascinating figure, and really someone who embodied change in her life, because she had say she was living in the right doing her best work in the 60s, 70s, 80s, and so as of the late 50s into the early 60s, she was living a very sort of conventional looking life. You know, she was, I think, mostly a homemaker, housewife. She had a few kids. Her husband was a professor at Harvard, and she wrote very careful and sort of Immaculate but fairly traditional poetry. And anyone who knows Adrienne Rich knows her as a radical feminist lesbian you know, who had female lovers and then wrote about, sort of breaking loose from societal constraints and completely re imagining out of the world around us. And so how did she get from the one spot to the other? And it was sort of this gradual process. One of the things she started doing was putting the date, the year, in parentheses at the end of each of her poems. You know, I’m sure it was just a sort of artistic intuition when, but later, when she reflected on it, she said they were starting to feel more more like snapshots, less like completed works, and more like yeah, moments of an ongoing dialog. Exactly, yeah, something ongoing and evolving. And that poem that has the the line the moment of change is the only poem. It’s dedicated to that French film director, Goddard and so yeah, it begins. The opening line is driving to the limit of the city of words, which I love as a line. The word limit happens to be a very important word in mathematics and calculus. She’s coming at kind of the same idea from a different direction. She’s saying, What are you trying to do in film or in poetry? You’re trying to go right to the edge of what words can tell us, and let those words gesture at something beyond themselves. And then towards the end of the poem, she kind of circles around this thought, or uses this thought to propel herself forward. She says the notes for the poem are the only poem which I sort of like that. You know, the idea is that the poem itself is too polished, too too final, and like, really the magic the poetry is, is in those notes, is in that, that first impression. And then a few lines later she comes back, she says, No, the mind of the poet is the only poem. Like, no, even, even the notes, there’s something, there’s something recorded and documentary about that. And really it’s just what’s happening in the inner space. And then the very final line of the poem is the moment of change is the only poem. It’s like, no, no. It’s not even really the mind. It’s something I don’t know, like, I can’t I can’t explain in words, because she’s gesturing beyond words. Anyway, I wrote a whole chapter that I wound up cutting from the calculus book because it was more about poetry than it was about calculus. But it really shaped my thinking about when I was writing that book about calculus. I suspect I’m the first author of a calculus book to really have my thoughts on the subject, shaped by Adrienne Rich and her radical poetry, but it really, it felt very true to the insights of the math to me that there’s something about trying to reach towards something infinite that you can’t ever quite attain, but there’s a lot of meaning and purpose in that reaching.
Eric Zimmer 34:17
Yeah, that whole thing is such a Zen idea. I mean, Zen is a form of Buddhism that really talks a lot about how, yeah, words, you need them, because they’re the main thing we have. And yet they’re only pointing at something, you know, they’re only trying to get you to look in a certain direction, in a certain way. And then that same idea of we tend to think that the end output is the thing. And Zen would say, No, no, no, it’s much more the doing, the being one with the doing. And then ultimately it would go on to say, sort of that last level is that even the mind itself is in change. You can’t. It down to anything. You know, what you think is your mind is this constellation of conditions that have come together extraordinarily temporarily, right? And that you’re freezing and so Change is the only poem resonated so much with me. I thought the way you wrote that up and her lines are really beautiful,
Ben Orlin 35:18
yeah? And I think I really do. I love that poem. So fun. One to revisit.
Eric Zimmer 35:23
On the subject of your calculus book, I read your latest book, which is the math for English majors, a human take on the universal language and and really enjoyed it. But I sometimes dig a little bit deeper with guests. And so I opened up your calculus book about change and the the chapter titles. If I wasn’t, like, an hour and a half from an interview with you, I would have bought that book and been like, I’ve got to read this. And I may go back, because the chapter titles are so good, but I thought maybe we could talk about a couple of them. And the first is, when the Mississippi ran a million miles long, how calculus plays a prank.
Ben Orlin 36:01
yeah, so there’s this, this fun passage in Mark Twain. One of his non fiction books is the history of the Mississippi. And he talks about this funny fact about rivers, which is that they create these meanders right over time. They sort of have these curves, and so you get these wide, you know, almost circles. And every so often, the river will actually complete the circle. So just time going on and the water changing course, it’ll sort of jump the gap, especially during a flood. And so this has happened periodically on the Mississippi. We have, we have decent records of this. And so in the century or two, you know, sort of before, when Twain was was writing this, you could sort of chart the decrease in the length of the Mississippi as it sort of jumped those gaps. And so a long, kind of circular meander became a straight jump. He’s just sort of applying arithmetic he learned in school. He said, Well, here’s what you can do. You can say, Okay, if the Mississippi River has I’m gonna get the numbers wrong, but the Mississippi River has gotten 100 miles shorter in the last 100 years. Well, that means the Mississippi is shrinking by about a mile a year. So a million years ago, the Mississippi River would have been a million miles long, right? It would have stretched out four times past the moon. It would have been this visible from deep in the solar system, just this extraordinary, astronomical river, or maybe wrapping many times around the Earth. Who knows how you want to do it. And then his line, which I love, Twain, is such a brilliant stylist, he says that’s the marvelous thing about science or mathematics is nowhere else can you get such a wholesale return of conjecture from such a trifling investment of fact, which is very astute, I think, as to what science and mathematics can often do. Say that again, a wholesale return of conjecture from a trifling investment of fact,
Eric Zimmer 37:41
I would say that might be shaping a lot of our online political discourse at this point, also
Ben Orlin 37:47
very limited investment. Effect,
Eric Zimmer 37:52
We’ve got a whole lot of conjecture, not very fun conjecture, to be honest, for a trifling amount of fact,
Ben Orlin 37:57
no, I think we’d be better off. I’m gonna spend more time reading social media than I do Twain. But I should probably divert that into into reading more twain. The lesson I take away from that Twain knows that that’s not what happened, right? Like, obviously the Mississippi River did not wrap many times around the Earth, but it’s actually, it’s quite an important lesson in mathematics I’m going to think in life, which is that there’s growth patterns that mathematicians talk about, and in particular, linear growth, which is what Twain was talking about, where sort of every time period the same thing happens. You know, each year it gets one mile shorter. And then there’s other growth patterns. So we saw this very vividly in COVID, for example, where from day to day you would get big increases. Where I’m thinking like March 2020, when the case loads were starting to explode. You know, day to day wasn’t the same change, you know? March 2, you get 100 new cases. March 3, you get 300 new cases. March 4, it’s 500 new cases. So it’s the change is not linear. It’s accelerating. But the funny thing about changes like that is that if you zoom in enough, they always look linear, yes, so it’s only at a big scale that you see the actual pattern of the change, yes, which is almost never linear forever. It’s sort of analogous to how the Earth looks quite flat. You know, every experience I’ve ever had of the Earth, it looks very flat, but I know it’s a sphere. It’s just that I’m very small. The earth is very big. And so if I got up in a spaceship, I could see the whole thing and see the curvature. But from the zoomed in perspective, it just looks linear. Everything looks flat, right? And so the same thing is happening there with Twain. Obviously, over time, the Mississippi River has grown and shrunk and changed length in a very non linear way. It’s probably in over 1000s of years. It’s gone up and down, you know, extends a little bit through those lakes, and it gets cut off and, you know, some new tributary joins it. So at the big scale, it’s very non linear, but over a few 100 years, that’s actually a pretty small scale for for a geological feature like a river, yeah. So that’s the takeaway lesson in that chapter. Is that if you zoom in really close on something, you’re going to think it’s a more predictable kind of change. But over large scales, you get surprises.
Eric Zimmer 40:21
I love that idea. It really echoes a couple of things that I talk about and teach, and one of them is that idea of, you know, little by little, little becomes a lot, right? That day to day doing a little thing and a little thing and a little thing, you don’t really see much, but you zoom out far enough and you’re like, oh, that actually really did add up to something substantial. And then the second is that idea of zooming out, in general as a way of having a different perspective, right? I mean, there’s that phrase that people use, like making a mountain out of a molehill. The way you make a mountain out of a molehill is you get really close to a little bump on the ground, and you stare at it, right? It looks really big. Then you stand up and you’re like, Oh, it’s just a little bump on the ground. And so that same idea of if we can zoom out, if we can change our perspective, would be the core thing. But zooming out is just a really easy way to do it.
Ben Orlin 41:13
Yeah, I think that’s right. Not always easy to do. It’s actually easier on a graphing calculator. And then it isn’t like graphic hit the minus button, you might Zoom out. Zoom Out, Zoom out.
Eric Zimmer 41:20
100% okay, what about there’s so many great titles in here. I’m just gonna read a couple. We’re not even gonna talk about them, but that’s Professor dog to you, in which calculus vaults a dog to stardom. That’s a pretty good one. What the wind leaves behind when calculus poses a riddle. Another great one. But the one we’re gonna talk about is, if pains must come in, which calculus takes the measure of your soul?
Ben Orlin 41:47
Yeah, which I don’t know. It makes my soul shudder a little bit. I’m not sure I want calculus taking that measure precisely.
Eric Zimmer 41:52
It would come up with an equation I’m certain that I wouldn’t be able to solve, and I would be no further along in understanding soul than I am today. You might be able to understand it,
Ben Orlin 42:02
right? I think one of the things I take from math, and actually it’s very much the theme of this chapter, is that math, although it feels complex when you’re learning it, math is designed to offer us simplified answers, and because they’re simplified, they’re almost never quite right, right? They’re always capturing some feature of the world, but leaving something else out. But they can still be useful because they’re these simple schematics. They’re sort of these stick figure drawings of reality. So the one there, I think it opens with a quote from The Economist, jeevans, a 19th century economist, and he was writing at a time when there was sort of a lot of excitement about math is doing so much for us, right? Like, look at what math did for physics. You know, we went from a world where it was kind of hard to explain how things move and just the basic mechanics of stuff in the world, to we’ve got great equations for this. We can predict it with exquisite accuracy. And economists in his day were hoping like, maybe we can do the same thing for a lot of human behavior, you know, not just for markets, but for, maybe for individuals, for sort of, you know, your moral sentiments, or even your sort of sense of happiness in life, what he does, what Jesus does, he sort of imagines a graph of your happiness, your state of mind. And he says, Well, you know, imagine over time, sort of got this line going up and down, and if you feel bad, it goes down. If you feel good, it goes up. Maybe that’s it. Maybe that’s the model of what happiness is. You can sort of picture this line going up and down, and you get to the end of the day, and what you actually want is you want to maximize the area under the curve, because if it’s very high all day long, there’d be a lot of area under there. And if it’s very low all day long, right? It’d sort of be very close to the bottom of the graph, and there’d be very little area under the curve. And you can sort of make up for things, right? If it’s kind of low most of the day, but then it has a really high spike, then you’ll get a lot of happiness total but it’s sort of about adding up the area under the curve, which is what the calculus teacher would call an integral, and what jeevans calls an integral, help me understand the curve. I’m not visualizing this. Oh, sure, sure. Picture. Imagine. Let’s say you’ve got a big piece of paper on your wall, and you mark it along the bottom. You know, midnight, 1am, 2am all the way to the next midnight. And every hour, even every minute, you go and you sort of extend a line starting from the left. And if you’re feeling really unhappy, the line goes down towards the bottom of the page, yep. And if you’re feeling great, you’re feeling really happy, the line goes soaring up towards the top, yeah. And what you’d be able to do at the end of the day is look at this picture, and it would be kind of this abstract picture of your experience of that day, right? And, you know, maybe, you know, if you had a great breakfast, it sort of starts out low, but then it spikes really high, because they’re called delicious eggs. And then it maybe goes back towards the middle as you go to work, and it’s kind of, it’s hovering around the middle. You have a boring meeting. It dips towards the bottom. You have a nice afternoon. It kind of rises up you get home and you’re, I don’t know, for me, getting home and having my little ones run up to me is like the. It’s my happiness spiking way up high. Two year old jumps into my arms. I gotta, I gotta extend the paper at the top. And then she throws a tantrum. Yeah, I was gonna say, you’re exhausted, yeah, that’s right. And that now we’re back towards the bottom. And then, you know. So anyway, so you get this, this kind of abstract picture of your day, this mountain range, and what jeevans is suggesting. He wasn’t the first to suggest it. He just, he just, he put it very nicely. Is why, I quote him, is that maybe this mountain range, maybe that’s your day, maybe that’s it like, that’s, you know, it’s the highs, the lows. And what you want in a day is you want kind of a big mountain range. And there’s a few ways to have it. It could be a very flat mountain range and not a lot of up and down, but it’s just at a pretty high level, yeah. Or maybe it has some real lows, but also some incredible highs, and that would be another way to get a big mountain range. Robert Frost has a poem that’s titled, happiness makes up in height what it lacks in length. Wow, maybe getting the phrasing slightly wrong there, but anyway, but same idea, right? Happiness can be kind of an intense, exultant happiness can make up for its brevity. Say that again, happiness, yeah, happiness makes up in height what it lacks in length. I think that’s it. I see something along those lines.
Eric Zimmer 46:11
Love that. So that makes me think about the sort of half baked equations I occasionally hear for happiness or for well being. There’s two that I really like, there’s one that I love, and it’s suffering equals pain times resistance. And I like the mathematical precision of this one. Actually, if you assume suffering is the total amount of overall suffering that you have in relation to something, you can break that down and say, well, some of that is pain, so let’s just take like my back hurts, there’s there’s a physical sensation of pain, and then there is all the things I’m thinking about that pain. Oh, God, it shouldn’t be happening. Oh, if I feel like this at 50, what am I going to feel like at 80? My mom has all that. And so a lot of that is we could call sort of resistance to the pain. And so if you were to make this mathematical, and let’s say you might say that your pain is a five and your resistance is a five, you’ve got 25 total units of suffering. What I love about this is, oftentimes, I can’t change the pain, right? A lot of situations in life, you can’t change the thing that’s wrong, so I’m gonna have five units of pain no matter what I do. But if I can lessen that resistance from a five to a three, well now I have 15 total units of suffering, which is way better without changing the underlying problem. And I’m not a believer that resistance ever goes to zero. Maybe that’s what enlightenment is when resistance goes to zero. But for most of us, we’re not gonna get there. But if we can turn down the what would be the way to say it turn the dial, all of a sudden, you have less units of suffering. So that’s one that I’ve always really loved, and I’ve understood the math of,
Ben Orlin 47:59
oh yeah, to jump in, no. I like your thought on zero, the unattainability of zero there, because that was my first thought when you, when you multiply two things, if one of them is zero, then it’s gone, you know. So if you can get that resistance down to nothing, then then somehow you could have pain without suffering, yeah? And maybe that, maybe when I think about, yeah, I’m a very amateur student of Buddhism, but when I think about the Buddha like that, sort of seems to be the image that that’s conjured for me, that somehow, if the resistance vanishes entirely, then there can be pain. But maybe it’s not pain that really matters. Maybe it is suffering.
Eric Zimmer 48:27
yeah. I mean, that is a core Buddhist idea and core Buddhist message. I’ve had big enlightenment, like experiences, you know, that were like everything you read about in the book. And I would say, Yeah, resistance was near zero, but boy, it just doesn’t want to stay there, right? Because it does seem to me that if you look at things from an organism perspective, we move away from what causes pain and we move towards what is nourishing or causes pleasure. You can see this in an amoeba, right? Put something that’s toxic to it on one side, and put something that’s nutritive to it on the other side. You know which side it’s going to go to. And so if you try and push it towards the toxic side, it’s probably going to be like, No thank you. And so it almost feels like some degree of resistance to me, seems built into being an organism. You know, it’s so deep that hoping to make it go away on any kind of permanent basis is to hope to be something that as a living creature, I don’t know that will ever be, but I do think you can turn that resistance down in a truly meaningful way.
Ben Orlin 49:34
Yeah yeah. I think about athletes too. When I see athletes, there can be a time when it’s quite painful to be doing what you’re doing. You know, Michael Jordan during the flu game or whatever, yeah, but the resistance is, in their case, maybe negative. Not only they’re not resisting the pain, they’re they’re embracing it. You can’t do that all day, as you say, or even for an hour, but yeah, people can find moments.
Eric Zimmer 49:52
Yeah, that’s another great example of being able to look at that from a slightly different perspective. The last one that I want to talk about. This is one where I haven’t quite figured out why the equation is written as it is, which is that happiness equals reality divided by expectations. So the core idea makes sense, our happiness tends to be higher when reality meets or exceeds our expectations, right? And when it disappoints us, we feel less happy. I don’t quite know why it’s a division though. I’m asking the mathematician I happen to have on this call here to say, why any ideas?
Ben Orlin 50:27
Yeah, yeah. I think division seems right to me there. Okay? Because what division does is it, if you have a vast number, right, say the it was reality over expectations, yeah. So take someone whose reality looks tremendous to any outsider, right? Like we would call that a million, you know, somebody, a celebrity, who’s got sort of every material comfort and adulation and followers and all the social media platforms, you know, whatever you’d be hoping for, yeah. And what we tend to think is we sort of bring our very mortal expectations, where I’m expecting 100 out of life. So if I had a million and I was only expecting 100 my happiness would be huge, right? A million divided by 100 is an enormous number. It’s 10,000 but if you’re in that situation as a celebrity, probably your expectations are very similar to that. Yeah, million they’re having. In fact, maybe you look over there and you know the two other people in your field, yes, who have a bigger audience, who have better reviews, you know, like your comparison set becomes very restricted to the absolute top performers. And so now you have a million, but you’re expecting 2 million, and so that’s only half of what you’re expecting. That’s, you know. So your happiness is at one half, rather than even being at a comfortable, you know, one where reality meets expectations. So there’s something that the ratio has the nice property that if you double the reality, but you also double the expectations in terms of happiness, nothing has changed.
Eric Zimmer 51:47
Yep, yep. Would subtraction not do essentially the same thing.
Ben Orlin 51:51
It would do very similar, but it wouldn’t quite have that exact doubling property. So for example, let’s say that you’re expecting it to make up numbers. You’re expecting five, and you have a 10, yep, if you double both of those, now you’re expecting a 10, but you have a 20, so you’ve actually sort of gotten happier. Have you in a ratio? No, because 20 divided. So yeah, if you Well, we’re getting into the into the weeds. I need a whiteboard to draw this.
Eric Zimmer 52:16
Okay, okay, and I’m not gonna understand. So Right?
Ben Orlin 52:20
I think subtraction would capture a similar a similar thing, given that these aren’t precise numbers anyway, you could probably write the same thought with subtraction. Division
Eric Zimmer 52:27
works. Yeah, as I was preparing for this interview and thinking about these two equations that I’ve used and here, I decided to say, what other equations are out there for happiness? And there was some crazy out of it, some Chinese Research Lab equation that, like, I think, would take me literally the rest of my life to try and prove or disprove, because it was so convoluted. But their point, which they then summarized this crazy long, who knows what went into this equation? I just think this is interesting. And they said, Well, essentially, it comes down to, you know, reality divided by expectations, except if you take your expectations too low, that doesn’t work either. That to suddenly expect that everything is always going to be terrible is not a recipe for happiness either, because then I guess you don’t try to do anything, and pessimism invades every aspect of your life. And but I just thought it was interesting that they then had some fancy equation to sort of then say, but you can’t have zero expectation, or that’s going to be problematic,
Ben Orlin 53:29
yeah, yeah. I think that’s right. And to me that suggests not so much a shortcoming of the equation itself, like it’s a nice equation, yeah, the reality of expectations, but actually just a shortcoming of equations writ large, like equations are not as complicated as reality. Reality is very complex, and equations have a couple of terms. They’re meant to show us a little, a little schematic picture, yeah, which, yeah, to close the loop, actually on jeevans and the graph of your happiness at mountain range, where I land on it in the book, is that like this just doesn’t work. It’s not right. I like social psychology research, so there’s a nice set of studies where one of the things they did is they made people stick their hand in ice for a minute. You’re familiar with this study. So you spend a minute with your hand in ice water, really cold, and then half of the people, that’s it. You take your hand out, you’ve spent 60 seconds in ice water, you’re done. And half the people, you stick your hand in ice water, and then you get another 30 seconds in slightly warmer ice water. You know, the original bucket was maybe 35 degrees, the next bucket is 40 degrees, so it’s still still uncomfortably cold, but not as cold. And then when they looked back on their experience, the second group liked it better. They rated that as less unpleasant. They rated that as like a happier time than the first group did. The first group thought it was more unpleasant. The convent University, the researchers, talk about peak end theory, that when you look back on a memory, you’re not actually looking at the whole mountain range. That’s not That’s not how we remember. We look at the peak what was the most extreme experience, you know, the greatest bliss or the greatest pain, and we look at how it ended, like, what, what happened at the end of the day? Yeah. And that actually matters. Much more than the specifics of the mountain range, because the mountain range theory would tell you another 30 seconds of pain, even if it’s less pain, it’s still more pain, more total pain. That should that should be worse. Yeah, so that’s a limitation of you know, again, a little graph of a mountain range of your happiness. That’s not actually your mood, that’s that’s a little picture. One of the reasons I like trying to spread a little more awareness of math is that it makes people more able to call BS. You know, like mathematics is often it’s simplified. It’s useful, but simplified. And if you view it as magic, you can’t call BS on it. You can’t be like, no that there’s something missing from that picture. And here’s what it
Eric Zimmer 55:33
is. I had not heard that version of the study. There seemed to be a whole bunch where they plunge people’s hands into ice water. I love reading psychology studies. They’ve gotten more ethical as time has gone on. You can’t get away with quite what you used to be able to but there’s still a lot of really funny things. The version I’d heard of that was people getting to dental procedure, and for the last couple minutes, the dentist just hangs out in their mouth. Don’t do anything really particular, right? But you would think that, then you would rate the whole thing as worse, because you had a dentist in your mouth for longer, which is inherently uncomfortable, but the people where it ended relatively low pain compared to maybe what it was before, like you said, they rated it as a better overall experience. I think this is also really fascinating, because the other thing that I think factored into this, this Chinese paper and its equation, is another idea that I’m often fascinated by and that psychologists discuss. And what they’re discussing is two broad ways of measuring happiness. One way would be to simply, like, ping you randomly throughout the day and say, How do you feel? Right? Plot your mood on a chart, you know, 471, whatever, and you just add all that up. And basically, that’s kind of how happy you are. There’s another way of doing it, which is you actually ask people, broadly speaking, how happy are you? How satisfied you are with your life. And those can produce different results, and I find that sort of fascinating. This equation apparently also tried to take some measure of that into effect, or maybe it was a different paper, but it was this idea of they were calling it eudaimonic versus hedonic happiness, right? Hedonic meaning moments of pleasure, eudaimonic meaning overall, broad satisfaction, yeah. And I just always think about how you measure those two things, and there’s a lot of debate about which is the right method,
Ben Orlin 57:32
yeah, yeah, that’s nice, though. It’s interesting that right the trying to decompose happiness. So it’s such a vast word with so many meanings that it makes sense that that’s a good start. I think on decomposing it, you say, Okay, right? Moment to moment, pleasure and then a sense of life satisfaction, and you’re kind of the narrative you’re telling about your life. But I’m sure you could decompose it into many more elements than that
Eric Zimmer 57:52
exactly. I mean, like, no equation solves us as a human right? It’s just, it’s not possible. You mentioned children earlier, and that’s another one of these weird findings is they find that if you measure moment to moment happiness, most parents will end up with a net negative when they have children. But if you’re measuring meaning and purpose and overall fulfillment and satisfaction, people will say they will rate children much higher than that. And so it’s sort of this, like what we think we’re experiencing, versus what we’re telling ourselves we’re experiencing, or the story that we’re putting on, which are not separate from each other, right?
Ben Orlin 58:27
They’re intertwined in complicated ways. Yeah, yeah. I may be misremembering this, but I think another, another study along similar lines, was that if you ask parents of young children, how are you doing? How satisfied are you? You get one answer, but if you want a higher answer, you just first ask them, How are your kids doing? Okay? They talk about their kids for a minute, and then they say, Okay, now how are you doing? Interesting and just activating that different side of what they’re thinking about. This hard to say, because I’ve written about this for a lot of psychology studies in the last 20 years, of trouble replicating and Erdos effects generalized, but they still, they still give, I think, nice illustrations of intuitive effects. Sometimes that’s one. I can vouch for that as a parent of young kids, if you if you ask me, you know, sort of, how’s my mood compared to before I had kids, like, you know, day to day, yeah, probably a little rockier. But if you start getting me talking about my kids and then ask me, it’s like, Oh, I’m gonna be glowing Exactly,
Eric Zimmer 59:12
right? It’s a priming effect to some degree, right? It’s what it’s bringing to your mind. My version of this that I would play. And this is a story I tell often that I kind of go back to, just because it was so illustrative, right? Was, you know, me complaining that when the boys were like, middle school age about every single day, driving them to some sporting event, one or the other of them, and finding myself saying, like, I have to do that. I have to do that. And then finally, ultimately realizing I didn’t have to do it. I was choosing to do it. But I think a version of the study would have been, would be to ask me, like, what’s your son get out of soccer, you know, or how much does your son like soccer? And I would have answered that question, then you would have said, like, Well, how do you feel about driving him to soccer? And I’d been like, I feel great about it, right? Like, it just would have reset my mind in a direction of something that matters. Which is honestly a lot of what the mental psychological game is, is, how do you sort of move your mind from here to over to here?
Ben Orlin 1:00:08
Yeah? No, that makes sense. Yeah, yeah. I think something I find from writing about math and then putting it in contrast with lots of more human social topics, right, the social sciences and philosophy is that, right? Math always gives us this vision of simplicity and, you know, singularity and very straightforward things you can define, and those are useful, but you need multiple lenses like that. You’ve got to move between different models, because we are so much weirder and more complex than that. You know, we’ve each got a city inside our minds of these different selves, yeah. And so, how do you coordinate them and lead them? You know? How do you get them to agree on goals like it helps to adopt a simplified lens for a little bit, but precisely because it’s only for a little bit,
Eric Zimmer 1:00:46
knowing when a broad principle of well being or happiness or whatever will serve you, even of parenting anything will serve you like, okay, that’s useful. And then also recognizing when it’s like, okay, that sort of applies, but I have to trust myself that that’s not useful here anymore. Yeah, ultimately, trusting ourselves. You and I are going to continue for a few minutes in the post show conversation, because I have realized I cannot get away without knowing about Professor dog. That’s Professor dog to you, in which calculus vaults a dog to stardom. So you and I are going to cover that in the post show conversation. We may also talk about how mathematics makes us want to quantify everything, which we’ve been doing for the last 15 minutes, trying to quantify happiness or expectations or put a number on everything. And you know, what are some of the costs of that? So listeners, if you would like access to the post show conversation we’re about to have, if you like, ad free episodes, as well as a special episode I do each week where I share a song I love. I teach you something useful based on the show. Then you can go to one you feed.net/join and become part of our community. Ben, thank you so much. This was really fun. I’ve enjoyed being in the math world a little bit for the last week, and diving into your world a little bit. It’s always hard when we have mathematicians, which we’ve never done before, but I have had visual artists on before, whose drawings are a big part of what they do, and obviously we couldn’t do that here. So I will make a call out for listeners, which is his books are much better with the drawings than they may have sounded in, you know, in our dry discussion. So his latest book is math for English majors, a human take on the universal language.
Ben Orlin 1:02:30
Thank you so much, Eric. I appreciate the conversation.
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