YouSaid · the spoken record

Steven Strogatz

lines on the record: 125
first: 2020-01-07
most recent: 2020-01-07
sittings or episodes: 1
sources: podcast

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“The number of units north-south plus the number of units east-west. You can define a distance like that. It's not the Euclidean distance. It's not the standard one because you're not allowed to take diagonal paths in this geometry. You can only go on the grid. Now, if you ask someone a question like, what is a circle look like in this geometry? That's an interesting question. In other words, what's the set of all points three blocks away from a given point? So try to picture that in your head. You could go three blocks north or you could go two blocks north and one over either east or west. You could go one up and two over. And if you can picture what those points look like, I don't know, are you picturing it?”
2020-01-07 · The Knowledge Project with Shane Parrish · #73 Steven Strogatz: Exploring Curiosities · IDENTIFIED FROM THE TRANSCRIPT
“Oh, yeah, sure. So here's one. You know, we're used to a standard kind of geometry, but there are other geometries. Here's an example. Suppose we're in New York City or some other city that has a grid of streets. So if I say how far is my location from some other location, you could say it in terms of miles or kilometers as the crow flies, but that's not very relevant if you're driving on the grid. You might be more likely to say you have to go three blocks north and eight blocks west or something like that. So you would give units of blocks as measured on the grid. Now that's an interesting kind of geometry. If you define the distance between two points in a plane as being”
2020-01-07 · The Knowledge Project with Shane Parrish · #73 Steven Strogatz: Exploring Curiosities · IDENTIFIED FROM THE TRANSCRIPT
“Yeah, well, we do that. I mean, I teach a course called Math Explorations with students who are required to take a math course before they graduate, and they dread it. These are the people who are the real dead enders. They're putting this off until their last year of college, but they have to get out. They have to go through it to graduate. Then once I teach it this way with them doing explorations together, activities working in groups and thinking and sharing ideas.”
2020-01-07 · The Knowledge Project with Shane Parrish · #73 Steven Strogatz: Exploring Curiosities · IDENTIFIED FROM THE TRANSCRIPT
“You know, the thrill of problem solving and inching your way forward applies to everything. And so we could be spending more time on that rather than here's an established body of techniques that you have to learn, and I'm going to dump it or pour it into your head. That's a very artificial picture of the mathematical enterprise. And why do we do it? I don't know. I mean, maybe there's all kinds of standardized testing. The teacher has to get through certain material to satisfy local authorities because tradition says this is what an educated person needs to know. And there's some truth to that. So I don't know. I mean, I don't have an easy solution to this. But times I've taught courses with this more exploratory mode where there was no place we had to get to. We just had to do the process in an honest way. I mean, the way a real mathematician would do it. Students love that. Math is not boring then. Math is, you know, that's creative.”
2020-01-07 · The Knowledge Project with Shane Parrish · #73 Steven Strogatz: Exploring Curiosities · IDENTIFIED FROM THE TRANSCRIPT
“Though you've hit a bunch of important things there. So one is the feeling that there's a lot to cover. I once heard a teacher say, don't try to cover the material. Try to uncover it. I mean, there's a lot to be discovered, a lot to be uncovered to remove the fog, to remove the crust of difficulty or misunderstanding, reveal something rather than cover it. But that's just a silly use of the word cover and uncover. But the notion that there's a standard curriculum sometimes stifles exploration. There is a certain amount of exploring that even a very young student can do, where if the experience of being a mathematician is so different than that of being a student, where we're frequently in the dark and we're poking around and trying to make sense of some new territory, mathematical or mental territory, and you're an explorer, you're lost, you're in the jungle, how do you get out, or how do you make progress? And that's a very valuable skill in all aspects of life when there's uncertainty and sometimes fear, but excitement, exhilaration.”
2020-01-07 · The Knowledge Project with Shane Parrish · #73 Steven Strogatz: Exploring Curiosities · IDENTIFIED FROM THE TRANSCRIPT
“The structure of the subject partly it's often taught in a very top-down way, you know, that the teacher presents material almost like pouring liquid into a student's head.”
2020-01-07 · The Knowledge Project with Shane Parrish · #73 Steven Strogatz: Exploring Curiosities · IDENTIFIED FROM THE TRANSCRIPT
“It's a long way down off the tower. It's a very linear architecture, whereas the reality is that math is a web, not a tower, that you can jump in at different points in the network of ideas and then find your way around from there. And so it's not really true. I mean, it's complicated. In some ways, it is sort of like a tower. The idea of algebra and variables and functions, and I know you know computer science, so you will know what I'm talking about here. Those are fundamental ideas. If you can't think abstractly about a variable rather than a concrete number, you're going to have trouble with a lot of math because that's a fundamental idea. So if you don't get that pre-calculus is going to be trouble, algebra 2 is going to be trouble. So some things are indispensable. But there are other things which, okay, maybe you missed the idea of an asymptote you can get on, you can still keep going without that. I mean, it's the part.”
2020-01-07 · The Knowledge Project with Shane Parrish · #73 Steven Strogatz: Exploring Curiosities · IDENTIFIED FROM THE TRANSCRIPT
“These different places, but it seems it sort of happens to everybody at some point or almost everybody. And so why? There's a few explanations. One is that the subject, the way it's traditionally taught, is made to seem like a tower. Each thing builds on the topic before it. And if you fall off at any stage,”
2020-01-07 · The Knowledge Project with Shane Parrish · #73 Steven Strogatz: Exploring Curiosities · IDENTIFIED FROM THE TRANSCRIPT
“You're right about that, aren't you? I mean, if you just look around and ask your friends, the average person did not have a good experience in math class, although it tends to be a little more complicated than that. Most people will say, I did like math until, and then they'll tell you until we got to fractions. Those were really confusing with the common denominators. Or I liked it until we got to algebra, and then it was all those x's and y's instead of numbers, and I didn't really know what was going on or I even liked algebra, but then I lost it in geometry, or I hit the wall in calculus. So different people have...”
2020-01-07 · The Knowledge Project with Shane Parrish · #73 Steven Strogatz: Exploring Curiosities · IDENTIFIED FROM THE TRANSCRIPT
“It's not really that hard. You can do better than my old teacher did. Show some pictures, give some intuition, talk about how it's connected to the real world, tell some history. You know, bring it alive, Jesus. It's a really exciting subject. You don't have to suck all the blood out of it. So the idea of being made to feel like a weed. You know, you hear this idea of weeding out the people who have the right stuff from those that don't. I really don't accept that idea. People have a lot of potential more than that kind of superficial analysis would lead you to think. So I could have easily been weeded out except that I just loved the subject so much. I stuck with it even though I was always one of the weakest math majors in my cohort. I just loved it more than most.”
2020-01-07 · The Knowledge Project with Shane Parrish · #73 Steven Strogatz: Exploring Curiosities · IDENTIFIED FROM THE TRANSCRIPT
“So it was a real, yeah, very demoralizing experience and it made me think, wow, maybe I don't have the right stuff for this. Maybe math is different in college. I stuck with it for one more semester and took a second course in that same Wizid sequence honors this time honors multivariable calculus and I could feel the same thing was happening again in that second semester I was on track for another lousy performance well and meanwhile I saw other kids doing fine I mean they were raising their hand they seem to know everything so even in a relative sense not just an absolute sense I could see that I was weak compared to the people around me and It was a formative experience because I think it's given me a lot of sympathy as a teacher when I see students struggling. I don't always assume that they're hopeless or they can't be rescued or they have no future. In my case, I mean, it has stuck in my craw now 40 years later when I teach linear algebra, I realize.”
2020-01-07 · The Knowledge Project with Shane Parrish · #73 Steven Strogatz: Exploring Curiosities · IDENTIFIED FROM THE TRANSCRIPT
“Well, okay. But it was a low grade. And it was discouraging because I didn't deserve a B- I really knew that I knew nothing. I probably should have failed, but they didn't want to do that for some reason.”
2020-01-07 · The Knowledge Project with Shane Parrish · #73 Steven Strogatz: Exploring Curiosities · IDENTIFIED FROM THE TRANSCRIPT
“Go ask for help from the teaching assistant. I didn't know. I had never done that stuff before, so it didn't occur to me. I thought I should be able to understand and I was having trouble. And so I did end up getting a B minus, which was a pretty low grade.”
2020-01-07 · The Knowledge Project with Shane Parrish · #73 Steven Strogatz: Exploring Curiosities · IDENTIFIED FROM THE TRANSCRIPT
“I mean, this was a really pathetically terrible person for teaching. I mean, the first day of class, he came in and sort of slithered along the wall, didn't make eye contact with the students, very shy person who didn't say welcome to Princeton, welcome to, you know, this is going to be exciting, nothing. You just started with the definition of the key ideas at the beginning of linear algebra, the definition of a field, blah, blah, blah. Here are the axioms it satisfies. Anyway, extremely dry. And I couldn't understand what the heck was going on. And the textbook had no pictures. And as a visual thinker, I found that very problematic. I couldn't really understand what was happening. And weeks would go by. I could feel myself falling behind and not my homework was getting worse and worse grades. I didn't know certain basic things like, well, try reading a different book. You idiot, or go to the...”
2020-01-07 · The Knowledge Project with Shane Parrish · #73 Steven Strogatz: Exploring Curiosities · IDENTIFIED FROM THE TRANSCRIPT
“That is true. That was my first year. Well, that was that class. So I was just describing how our freshman, the first year students, can do astonishing things. I was supposedly one of those students when I went to college. So they grouped a bunch of us together in WizKid linear algebra. And for this was for all the kids who had done extremely well in calculus and high school. So it's sort of like you had a mark on your head. This is a future professional mathematician, or at least potential to be. And the other thing, though, is that professors know that kids who are good in math and high school, a lot of them are going to get, so to speak, weeded out. They don't really have the right stuff to be mathematicians of the future. At least that was the thinking at the time. It's a pretty nasty pedagogical philosophy, I must say, but they would throw all of us in with one of the worst teachers in the school. I don't know why they assigned him to us.”
2020-01-07 · The Knowledge Project with Shane Parrish · #73 Steven Strogatz: Exploring Curiosities · IDENTIFIED FROM THE TRANSCRIPT
“Sometimes it does, especially younger ones. You can really, you know, by the time they're seasoned, if they've been in college a few years, they start to know the game. But freshmen don't really know what college is going to be like. And so you can do mercilessly unreasonable things to the bright freshman in math. And they will astonish you with what they can do. Yeah, we see that all the time.”
2020-01-07 · The Knowledge Project with Shane Parrish · #73 Steven Strogatz: Exploring Curiosities · IDENTIFIED FROM THE TRANSCRIPT
“And so if the teacher expects something really hard, kids don't even know it's impossible. They'll try. I try to do that myself with some of my students.”
2020-01-07 · The Knowledge Project with Shane Parrish · #73 Steven Strogatz: Exploring Curiosities · IDENTIFIED FROM THE TRANSCRIPT
“Yeah, of course. I mean, partly that he really set the bar very high, but also he was humble. He was strong enough to admit there was something he didn't know. And apparently other, he probably mentioned that in other years and other students hadn't either risen to the challenge or weren't interested. Why would you do homework if you didn't have to? But something about it caught me. Yeah, he was a very inspirational teacher. And it's interesting too that he's not the Hollywood inspirational teacher. It wasn't like, you know, such a loving, sweet guy, or certainly not interested in building your self-esteem. He was just all business. But there's a line in that movie about another great teacher stand and deliver about Jaime Escalante, who taught in East Los Angeles. Who says in one's critical scene?”
2020-01-07 · The Knowledge Project with Shane Parrish · #73 Steven Strogatz: Exploring Curiosities · IDENTIFIED FROM THE TRANSCRIPT
“give some verbs to conjugate and you'd feel that it'd be going around the room and you could feel it's going to be my turn soon. But I was still thinking about the angle bisector. So I was obsessed with it and I didn't realize it at the time, but I was doing research where I was thinking about something for just the pure pleasure of trying to understand it. And ultimately I got something that I thought was a proof. It was a boarding school. My teacher lived nearby and I asked if I could come over to his house on a Sunday morning. I could still remember him there and his beard and his pajamas and his little kids running around in his house at breakfast. He checked this proof line by line very slowly and with his serious stern face said, well, yes, that's a correct argument. Very good. And then he wrote a little note to the headmaster of the school, which meant a lot to me that my teacher said something like Stephen has real talent.”
2020-01-07 · The Knowledge Project with Shane Parrish · #73 Steven Strogatz: Exploring Curiosities · IDENTIFIED FROM THE TRANSCRIPT
“If two angle, two perpendicular bisectors are congruent, or something called medians. All these questions are pretty easy to prove that you would get an isosceles triangle. But something about angle bisectors made the question very hard. And when I tried it, I couldn't do it. And that already caught my interest. And I worked on it a lot. I spent a day or two on it. I still couldn't do it. And then days became weeks and weeks became months. And I think I spent about maybe six months on this question, trying things, getting stuck, trying other things, getting stuck. And sometimes it would come close to working out, but I could never get the argument to go all the way through. And my friends would get annoyed with me, like, come on, let's go to a movie. No, I feel like thinking about the angled bisectors. Or in French class, you know, when the, we used to have this conjugation train where the teacher would”
2020-01-07 · The Knowledge Project with Shane Parrish · #73 Steven Strogatz: Exploring Curiosities · IDENTIFIED FROM THE TRANSCRIPT
“It was a question about a triangle that sounded like many other geometry problems. It says if the angle bisectors of a triangle are congruent, prove the triangle is isosceles. So what that means is angle bisectors, that would be a line that cuts through the angle, picture a triangle, like say standing there flat on the table with its point sticking up. If you divide the angle in half at the base, there are two of them down there. If they're divided in half by a line, and then that line meets the opposite side of the triangle, that's the angle bisector. And so if you have two of those crisscrossing and they're equally long, that's what congruent means. prove that the triangle is isosceles meaning that those two angles at the base are actually the same angle have the same number of degrees and so it sounded like many other questions there are similar questions if”
2020-01-07 · The Knowledge Project with Shane Parrish · #73 Steven Strogatz: Exploring Curiosities · IDENTIFIED FROM THE TRANSCRIPT
“Candidly mentioned it to the whole class, and I thought that was interesting because I had always been able to do any geometry problem. Any teacher asked me. So he said, yeah, no one had ever solved this certain question. And then he also said that he didn't know how to solve the problem. And that was very surprising because I had never heard a teacher say that. He didn't know how to do the problem. So I started thinking about it. I could tell you the problem in case you're.”
2020-01-07 · The Knowledge Project with Shane Parrish · #73 Steven Strogatz: Exploring Curiosities · IDENTIFIED FROM THE TRANSCRIPT
“And it just felt good. So I'm not saying this is a noble reason to be interested in math, but it was just an early memory that it was very objective. You could say, I'm better than you, and it actually meant something, which to a 13-year-old boy, that was important. But on a more elevated level, I'd say the real turning point was high school, so by then I was about 14 or 15. And a teacher said something that took me aback. I had never heard any teacher say something like this. He was, this was Mr. Johnson who had a beard and had gone to MIT. And to me, he looked like what I imagined a brilliant math professor might have looked like. He was very serious, not a smiler, but fair. And he said that there was a certain geometry problem that he had never seen any students solve, just off hand.”
2020-01-07 · The Knowledge Project with Shane Parrish · #73 Steven Strogatz: Exploring Curiosities · IDENTIFIED FROM THE TRANSCRIPT
“Well, I was interested in all of school, and I still am. I like all the different subjects. So math didn't stand out for me, I'd say really pretty much for most of my childhood. It was just one among many. But then I do remember one or two moments where it started to take special significance. One was I had two friends when I was about, well, let's see, we used to call a junior high school, so with seventh and eighth grade, I must have been about 12 years old. Two other boys. They were both good at math and vocabulary and geography and everything else. I used to like to compete with them. We would play chess against each other and other things. And at that age, just being better than your friend meant a lot to me. I don't know, or having them feel better than me inflicted a kind of pain. So I do remember one time getting a little higher score than this other kid on a math exam.”
2020-01-07 · The Knowledge Project with Shane Parrish · #73 Steven Strogatz: Exploring Curiosities · IDENTIFIED FROM THE TRANSCRIPT
“A great discovery that no one appreciates is not really a great discovery because science is a social enterprise. It's not just enough to do the work. You have to communicate it and help other people understand why it matters.”
2020-01-07 · The Knowledge Project with Shane Parrish · #73 Steven Strogatz: Exploring Curiosities · IDENTIFIED FROM THE TRANSCRIPT