Steven Strogatz’s Secrets of Math Communication

[Music] welcome to tonight's conversation i'm very pleased to be here as yvette said i'm the editor of quantum magazine and um so happy that steven strogatz is joining us tonight to talk all about really about his career my goal here tonight is to try to take you on a bit of a journey behind the scenes of steve's evolution as a mathematician and teacher through book writing and public speaking and now with the podcast that he is hosting for quanta i want to start the conversation by talking about you as a teacher because i see you beyond all of your wonderful research and all the books and even all the books and all the public speaking that you've done i see a lot of that at its core as a form of teaching first of all why is teaching so important to you and what is it that you feel like um i'll say that my my own sense of what makes you such a great teacher is a certain level of empathy okay because i think that's one thing that separates great teachers and teachers who maybe you know are trying to communicate something but maybe less successfully but i want to hear from you um why do you care so much about teaching and what is it that you try to do that's maybe a little bit different wow tom you're bowling me over with that introduction and all those super kind words thank you yeah you've really put your finger on things that i do care about the word empathy i would like to single out because um you very astutely i think he really hit the nail on the head that's i think that's the single most important thing in teaching and writing um and communicating to try to anticipate what's in the listener's mind or in the reader's mind or the student's mind if it's a class so um i don't know it's a really interesting question guys why do i care so much about teaching that i don't think anyone ever asked me that before and i'm not sure i know what i would say my instinctive response is because i have something delightful and beautiful that i want to show you how are you able to strip away what you know because i think one of the challenges for people who um especially mathematicians who know a lot about their subject who are very precise i mean it's part of the training i think as mathematicians that you're extremely precise you want to be very rigorous in the way that you do your mathematics so everything that you say you know there's 10 other statements that you have to say to sort of you know make that as precise as possible how are you able to both self-edit and put yourself in the shoes of someone who doesn't know the things that you know right there's certain there's a certain curse of knowledge hurdle here that you have to be able to say okay this person you know doesn't necessarily know all the things i know how do you put yourself in their shoes this feeling of bursting and wanting to share something can also lead someone to be extremely boring right it's almost the definition of a boar someone who is going on and on but you don't care what they're talking about and so that's a key part of good teaching or good writing um is what you first said empathy that i have to but but the specific part of empathy i'm talking about here is i have to help you love the question that's the classic mistake if if the teacher or the writer goes on about look at the great way that this problem was solved or um so you might spend too much time on the process or even on the answer itself look at this amazing theory or a result or theorem let me show it to you that is not going to work the the first thing the student has to have is love which is a bit of a strange thing to say right you don't normally think that math class is about love or or any other class but in fact that's the teacher's first job is help the student fall in love with the question or the topic or whatever it is because once they love it most of your work is done there's this perception that math is this big scary difficult thing and that there's a lot of fear about it in society and i think that um you know a lot of places i've worked as a journalist editors would sort of assume that readers would be afraid of math and so they would you know try to write stories in a particular way um but what you said about love i think gets at the heart of how to sort of overcome that fear right if you can make people care and be interested in it not necessarily giving them something big and scary and difficult at first um maybe you you have a better chance um what are some of the tactics to help someone fall in love with a question humor is one sure if you can get the person laughing if there's something delightful because it's funny or surprising or tantalizing that's why puzzles work so well right if if you give a little kid a puzzle that is at the right level for them you don't really have to teach them or tell them anything they're i mean think about this i i know i've given plenty of lectures where in the course of the lecture i'll ask people to start thinking about a problem if the problem is good they will stop listening to the lecture they want to start thinking about the problem and um that's because problems of the right type are inherently engaging and so surprise humor those are those are good tactics um people are interested in people if you have a story about a person that can work i mean there are many devices and all of your great science writers that at quanta know these things they're all parts of the hook so that's why a good writer starts with a hook right and so i think as a teacher it's the same thing also i like that you phrase uh what i do as being a teacher because i think of myself if in one word as a teacher a lot of my colleagues are driven by a desire to solve mysteries and that's a little bit of a different desire i mean yes you can teach yourself something by solving but um i'm very happy to explain someone else's solution in other words i i think it might be let me say it this way i think in math and in science generally we have in the language of economics a distribution problem not a production problem i think we're producing a lot of great math and science that is not landing in its on the target because we spend so much effort on the creation and the discovery and we're not so necessarily trained or some of us interested in dissemination i think of my own grad students who say i've solved the problem i can't stand writing it up i just want to do the next problem and i understand that for people who love to solve puzzles that is the really fun part but the writing and the explaining is part of the social enterprise of science and and i think the work isn't done until you do that part so uh i love that you uh went through some of the things that go into empathizing and being able to communicate in a way that um helps people enjoy math and and learning and i i want to give this a spin i want to uh do this i'm sorry to put you on the spot but i i want to give you a a a uh something to try out on the crowd and so i i'd like to ask you this um i'd like to ask you to um break down one of the most famous equations and what is widely considered the most beautiful equation in mathematics euler's identity you know for imagine an audience of people who maybe remember some of high school math right and so this is of course e i pi plus one equals zero if you could just use some of those skills and techniques to may i be while i'm stalling to think of how to do it i may ask some questions of course of course for instance does my listener know e should i spend time explaining e or do they know i think that i think that um it would be fair to to assume that that a lot of people wouldn't know a lot about e okay yes so there is a certain equation that is often considered the most beautiful equation in all of math uh that as thomas said is the letter e which i'll tell you what each letter means e to the i pi power plus one equals zero so let's first talk about each of the letters so e e for exponential having to do with things that grow exponentially or decay exponentially so we're seeing that unfortunately right now with the pandemic we've gotten a a very brutal dose of what exponential growth means when something builds on itself and multiplies by a constant factor week after week or day after day so exponential growth we see all over the place in the universe in our own bodies in the case of viruses proliferating unfortunately we also have exponential decay when things decay by a constant factor day after day so there's so e is kind of more broadly a mascot of calculus e is about this kind of continuous change where the thing that's changing keeps changing at a changing rate so it grows but grows faster and the higher it gets the faster it grows or okay so e is to me a kind of personification of a whole branch of math having to do with growth and decay next i so e to the i i for imaginary the imaginary number that enlarged our concept of what numbers could be this this was we think of numbers as little children as magnitudes things that you can mark off on a number line or that have to do with counting cookies or whatever but numbers in more advanced parts of algebra are things that are kind of number like they obey some of the rules that we learned about ordinary numbers but they're more powerful than that and they were so mysterious when they were first discovered they were called imaginary because they didn't act like the usual quantities that we thought about but but i turns out to be crucial in algebra and so speaking with this language of personification i is part is sort of our mascot of algebra pi everyone knows because it's the most famous greek letter that's a number that stands in for geometry but not just geometry of circles remember pi is the ratio of the circumference of a circle to the diameter but so pi is something about converting straight things like diameters into round things like circles and there's a very profound mystery about converting the straight to the round which is that infinity somehow comes into it you you all know that if you write down the digits of pi you get 3.14159 this goes on forever they never repeat they don't show any pattern so somehow in making this conversion from the straight to the round infinity comes into play and infinity is left out of the equation but it's sort of lurking there in pi and um everybody's interested in infinity so now we've got calculus growth and decay we've got algebra we've got geometry but then we have the most basic parts of arithmetic plus equals 1 zero and i don't have to tell you what one and zero are but they're like the beginnings of math right one the beginning of counting zero the void so it's all packed into this one equation and on top of all of that it's unbelievably surprising what does it mean to raise a number to an imaginary power and and somehow the formula is actually true e to the i pi plus one equals zero it has everything in the shortest space so it's it's parsimonious it's beautiful it's surprising it connects i mean in math the aesthetic high point is when you draw connections between things that don't seem connected so here we connect algebra geometry calculus arithmetic i mean that's a pretty beautiful equation absolutely thank you so much wow oh okay that's like a performance yeah sorry for putting on the spot there and for the record this was not rehearsed no it's not real very much just threw that uh out there for steve because i knew he would um nail it and you did thank you so much thank you so much um so i want to now kind of walk back a little bit in in time and i know that you know a little bit about your childhood but we haven't talked a lot about it i know that you know you've played tennis and basketball and you're really into chess you're you know a really good chess player but you weren't particularly outdoorsy um didn't like bugs yeah um but but uh so i just want can you tell us you know how when did math enter the equation when did you know that both that you were you know really good at it and that you wanted to pursue it interesting you assume i'm good at it all my lowest grades in college were in math really yeah i don't think i'm especially good at it i i not saying that for false modesty i'm not an inherently modest person i i i'm really good at certain things but math is probably one of my weakest subjects um in terms of pure brain power like to follow a complicated argument all my colleagues are better if i if you ranked me in the math department i would probably be last i'm sure of it i i'm slow uh anything that requires doing a fast calculation i'm not good at but i should come back to the question your question was when did i discover i was good at math or that i loved math and it was a very discreet moment i was in a class well actually i was in a geometry class and i was doing badly uh so i had taken the first freshman you know in high school algebra 2 course i i was a little ahead i had done some algebra already in middle school so i was in this algebra 2 course it was fine they put me in a geometry class taught by the football coach which is a strange thing a lot of times the coach is thought to be someone suitable to teach math i don't know why that like it's a very manly subject or some ridiculous thing and health too right health too okay so anyway mr white the football coach was teaching geometry and i was really bored in the class and not doing well that's always been true my whole academic career when i'm bored i don't pay attention and don't do well so i was bored and getting maybe a c or something and then something great happened which was that the school said you shouldn't be doing this badly rather than punishing me or putting me in some remedial geometry they said we think you should skip geometry and do pre-calculus starting tomorrow and that was great because then suddenly i had something interesting to learn about and my teacher mr johnson had a beard he had gone to mit he he wasn't the football coach he he seemed like oh i thought okay i could learn from mr johnson and he was very difficult um but fair but he asked us a lot of hard questions and so in the course of one of his uh discussions one day he mentioned that there was a certain geometry problem of all things he wasn't teaching geometry teaching pre-calculus he said here's this hard geometry problem and i've been suggesting it to students for years and i've never seen anyone do it he just mentioned that i thought that's interesting let's you know i'll tell you the problem if you're curious it was if two angle bisectors of a triangle are congruent okay so remember an angle bisector cuts the angle in half equally right so if two angle bisectors have the same length the triangle is isosceles sort of seems like it would be true and in fact the other direction is easy if the triangle is isosceles showing that the angle bisectors are congruent is pretty easy but to do it this direction if congruent angle bisectors then the triangle is isosceles mr johnson said that's a hard problem so i thought that's very interesting then he said actually i don't know how to do it and i thought you're kidding mr johnson doesn't with the beard can't do the angle bisector problem how could that be so i thought okay i you know until that time in my life i could do any geometry problem the school asked me to do so i started working on it and i couldn't do it and you know i spent a day or two on it i still couldn't do it i thought about it all day long then it was weeks i still couldn't do it then it was months and the whole time i was in french class and they would say you know conjugate these verbs and they used to have like this kid had to conjugate this verb and then it would go to the next kid and it would go around the room like a train and i could feel it was coming toward me but i was thinking about the angle bisectors so it was really messing me up but both in basketball and in french class and um i got obsessed with this question okay so you're wondering what happened well at some point i thought i had solved it and it was a prep school and mr johnson lived close by uh to the campus and so i asked could i i think i got it can i come over to your house and show it to you it was a sunday morning and he was there in his pajamas his little kids were there and he sat at his kitchen table i showed him each step he carefully sternly checked each step he said it's correct proof and then he wrote a little note to the headmaster of the school stephen has real talent gets me choked up thinking about it so just moving from that point when you used you found you started to love math and you at some point uh did grad school became a mathematician studied became an applied mathematician and studied non-linear dynamics complex networks um you're and then uh sort of the um synchronization emergence of of certain kinds of behaviors um that you know where order appears out of sort of seemingly chaotic right um behaviors and then you wrote your first popular book in 2003 a book called sync related to your work first of all what was the inspiration for that and what were the challenges of going from teaching in a classroom to writing a book you know my whole life i always thought i wanted to be a teacher or if not a teacher a science writer so we skipped over that i always thought i would like to be a science writer and i applied for summer internships and kept getting rejected and including famously to me i mean i saved the letter from the new york times even our copy boys have journalism degrees interesting and i didn't know exactly what that meant but i knew it was insulting so so um okay so i couldn't be a science writer but i always kind of wanted to be so anyway yes um in the course of trying to solve the kinds of problems you need to solve to be a professor and get tenure and do the whole academic track and um there wasn't any place for writing for the public that was not considered a good strategy or advisable it shows misplaced priorities right so discouraged right totally discouraged yeah i mean my department chairman said even when i wanted to write a textbook the book that you mentioned it that you had read um the chair said it won't help it won't really hurt you but it takes away time from your research and it definitely won't help you so you shouldn't do it but i did anyway because i really wanted to and i i was frustrated that there weren't any books in my subject in nonlinear dynamics and chaos that i felt were readable for a beginner so i just felt this compulsion glad he did it i'm glad you disregarded that advice uh i think it was turned out to be a good choice i mean a lot of people have thanked me for that book over the years and also set you down a path right to yeah i did what i wanted to do i also didn't get tenure at mit so i mean they they played their cards they they were open about what mattered to them and what mattered to me wasn't exactly what but on the other hand cornell said well move here and we'll give you tenure two years early so i thought that sounded better [Laughter] but but to the question of sync um the book sync i well a bit of a i had just gotten married to carol who's here uh in the audience [Laughter] ready to crawl under her seat and we um were having our first child at that point and there was a popular tv show called who wants to be a millionaire and we were starting to think about how would we ever pay for college on a professor's salary um this is honestly what was in our head i'm sorry maybe you don't regret asking this question but i was thinking i would like to find a way to make some money and some i was aware of people getting big advances for writing books for the public about science and carol said to me if you always say you want to do this if you are serious and you want to do it i think this would be a good time to do it because um who wants to be a millionaire i kept trying to get on they wouldn't call me back so so anyway i did put in a proposal to write this book for the public um used an agent you know that other science people my friend brian green had used the same agent and he said use these people they'll get you a big advance and that all turned out to be true and it was good and our kids are now in college now i did have the story that i wanted to tell yeah i i did but that was true my whole life the question why then was for the money you have the contract you have to deliver a manuscript now yeah yeah there are certain challenges to producing an entire book that people want to read right yeah what was like maybe the the top challenge and how did you overcome it the top challenge is self-censorship um i i start typing and immediately want to hit the backspace or the delete button i you know as you mentioned mathematicians are trained to be critical they only want to say what's exactly true and it always requires a million caveats so as a writer i was very troubled by the difficulty of writing a true sentence and um so i was painfully slow writer and i had friends advise me the first draft has to be terrible don't worry about that don't you can edit later just spit it out but i had trouble doing that and it was a painful book to write it was a slow process but what has helped me since then because you mentioned to me before we started the conversation you were hoping maybe i could share some tips i do have a tip which is if you're a self-censoring person and a lot of us are um the dictation function on your phone is very hard so i i turn on my nowadays when i write a book i turn on my phone and talk into the phone and dictate in the notes app and don't expect it to be any good and just talk while i'm walking the dog so i'll think of what section do i want to write and then just start talking and it gives the book a very conversational sound with automatic rhythms that are like spoken english because that's how it was generated and most of it is bad but it's easy enough to delete it later but sometimes there are good nuggets right but it gets rid of the problem of trying to constantly self-edit yeah i'm also i never learned to touch type so my typing is very bad which makes it easier to delete so so i think the dictation gets me to generate thousands of words in a day which is otherwise impossible for me and then editing i love to do afterward let's just skip forward one uh again quickly to your most recent book um infinite powers which came out in 2019 2019 i think of it as your magnum opus and it's about calculus what it is the history of it and just to me like reading that book anyone can read that book and come away with a very very good sense of what calculus is and how it works without actually having to do any calculations right and so talk talk through a little bit of your evolution as a writer from sync now to oh thank you infinite powers and that's a very astute question i really wanted to tell the story it was a love story of calculus and i love the subject of calculus it's my favorite part of math i think it's one of the all-time greatest ideas right up there with democracy and quantum mechanics you know and darwinism and you know they're just a few relativity there are a few ideas that really change the world and calculus absolutely is one of them but you wouldn't get that from a calculus book you would get a thousand pages of integration by parts and related ratings so it seems terrible there's something so monumental here and this needs to be told a large part of the population doesn't know anything about it our population either doesn't know it or has a distorted picture of it from the course that they took right okay so i wanted to convey that but how is it just about the ideas of calculus is it about the people stories of calculus or is it about how calculus changed the world and i want it to be about all three so i want it to be both the applications but not both i want three i want the applications i want the history and i want the ideas and i didn't really know how to do that but i knew that that's what i wanted to do and so rather than write an outline of something that i couldn't imagine i just walked around talking into my phone for a long time it was extremely painful to write that book i keep using the word pain don't i writing is hard writing all right let's let's just get that you know yeah i wrote a first draft that i was moderately happy with and my great editor ayman dolan said it's it's really nice but wouldn't it be great this is editor speak you know wouldn't it be nice if every chapter had something like that chapter where you explain how calculus helped make hiv into a manageable chronic illness rather than a near-certain death sentence which was the way it was when aids was ravaging the country so he said that was a compelling example wouldn't it be nice if every chapter had that and i thought yes it sure would be nice that's what i meant to do the first but i hadn't written that book yet so then i had to rewrite the whole book and then after i did that he said the book is so much better now it's really great wouldn't it be nice if there was a whole story that went all the way through from beginning to end like one principle or one big idea that would so i said you're right that would be good and then i had to write that book so it was unbelievably hard for the family i i keep the pain wasn't just me like psychic pain of my own work it was very hard for the family i was upstairs in my attic working my dog missed me my wife missed me kids i mean it was really not easy no but i'm very proud of the result it feels to me like and actually the ending of the book came to me on one of those walks and as i was dictating i started crying it was such a perfect ending really a weird out-of-body experience those of you who are creative musicians or artists or whatever you know sometimes your art takes you you didn't see it coming and this is what an outline will not do for you a real writer like real but you know some let yourself go i didn't know how to do that when i wrote sync and i and i was very happy with um these weird deep wells of subconscious stuff that the words came out like paul mccartney has talked about that with writing i'm not saying i could write lyrics like paul mccartney but you know what i mean you're a writer yourself so sometimes your own art can really um transport you so the last few minutes i i want to talk also of course about our podcast yes thank you spent the last few years producing uh first the drivex and now the newest um podcast uh that you are uh hosting for quanta is called the joy of why and i wonder if you could maybe just start from talking a little bit about what was uh the joy of x about and what did we change for the joy of y well yeah so the joy of x was our first of all thanks a lot for letting me be part of the quanta team i love your whole enterprise your magazine your stories you are yourself fantastic as no no no no okay we don't have to go well let me let me say this since we're going back and and uh complement each other okay in thinking about a new podcast for quanta i remember being on vacation with my family and thinking you know what should this new podcast be about who should be the host and it just sort of dawned on me the host has to be steve strogatz it really it occurred to me i reached out i was so thrilled that you said yes because i was thinking i would love to figure out a way to do a podcast tonight to me the timing was perfect as the rolls-royce of science journalism i just was delighted to do it okay well um joy of x to me was based on the vision that the radio is intimate that podcasts are coming into your ear and that's the most intimate thing to listen to someone else's stories and words so i felt i wanted to have scientists and mathematicians talk about their inner lives what does it feel like to make discoveries why are they in love with the questions they work on what were their own journeys so it's a very intimate show about the scientists themselves it tended to be meandering i i deliberately wanted a very spontaneous conversational vibe with them and we didn't have much planned out we let it go where it went the joy of why is uh about the questions it puts the big questions first so are you more interested in black holes or the scientists who work on black holes both are reasonable answers if you're more interested in black holes and then you will learn a lot about you know the origin of life black holes why do we have to sleep it's all about the great timeless mysteries of science and i mean it's not like we're neglecting the scientists we are talking to living breathing scientists and they do tell their stories and there are very um spontaneous and animated moments in our conversations but we're really sticking to the conversation about the big questions and current thinking about them part of this conversation has been about transitions right your transition from a mathematician teacher to a writer and now to a podcast host like what did you have to learn so the teacher side of me sometimes hears my guess saying things in a way that i'm imagining my listeners may not exactly get it and so i might rephrase uh what the person has just said and a lot of times i'm truly confused by what they just said i'm not playing possum it's not a gimmick like are you saying such and such i really don't know are you saying something so i will ask those what i hope are clarifying questions and um sometimes those really land i think absolutely absolutely i think you know again it just shows what a great teacher you are i think we're really lucky to have you as the host for the joy of why i hope all of you will listen to it uh we have a trailer out right now next thursday is the first full episode uh you can subscribe all your all the major podcasting platforms so thank you all for coming tonight you

Channel: Quanta Magazine

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Keywords: science, quanta, quanta magazine, explainer, science explainer, science video, educational video

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Length: 31min 46sec (1906 seconds)

Published: Fri Mar 25 2022