Exploring the Infinite Powers of Calculus with Professor Steven Strogatz

Jacob Beckey (00:05)
Alright, hello and welcome to the Idealized Science Podcast. I'm here as always with Dr. Brian Wargo. How's it going, Wargo? Hi, to you. And with us today is Professor Steven Strogatz. How are you today, Steven?
Brian M. Wargo (00:11)
Hi, nice to see you.
Steven Strogatz (00:19)
Great. Nice to meet you, Jacob. And hi, Brian.
Brian M. Wargo (00:22)
appears he might have locked up. So we're going to be talking today about infinite powers and some of your other work. And ⁓ I'm just going
to start off until he comes back just by letting you know how much I enjoyed
this book. ⁓ Just wonderful. Right from the get go. ⁓ I'm a physics teacher. And one of the things that as I was going through here, I kept thinking, are you a historian? Are
Steven Strogatz (00:38)
Thank you.
Brian M. Wargo (00:48)
you a physicist? Are you a philosopher?
Are you an educator? And because they're all coming through on this book. mean, and that's what makes a truly awesome book is that like you're just bringing in this collective piece centered around like the beauty of this topic of calculus. So.
Steven Strogatz (01:09)
Thank you very much. That's nice to hear. did try to, I mean, first to answer the question. I'm a math professor, so I'm really a mathematician, definitely not a historian. ⁓ But I'm very interested in history of math and science generally. And ⁓ I wanted to try to do three things in the book, which were,
bring across the great stories of how calculus was invented, why it was invented, who some of the people were who struggled with it. So history, also applications. It's not just math for math's sake. It's math that was very much motivated by problems in science, especially physics and astronomy initially. But since then, in every part of science and technology,
⁓ So history, applications, and concepts, those three things. know, what is calculus? I wanted to write for a reader who never had calculus, or maybe they did have it and didn't see the point of it. ⁓ Or even maybe they did have it and they liked it, but didn't know just how majestic it really is. So anyway, it was a very ambitious undertaking, but I learned a lot while trying to write it.
Brian M. Wargo (02:25)
Well, I have to say, students... Here's what I was thinking. I was thinking, if I would have read this book when I was in my early years of high school, I would have absolutely loved my math classes. Here's how you can tell it was so good. I am sitting here going through this. And you know, like occasionally when you get a chapter, you're like, you know what? I know this. I'm going to skip through this. what a mistake that would have been. I found myself playing with my calculator, doing the calculations alongside you and saying,
my God, that's great. I mean, it's that kind of, of like, ⁓ you're able to find those little nuggets that capture you and pull you in. And I'm telling you, I think every student should read this book before they go into trigonometry or calculus, because I mean, like I actually was having so much fun. Like with, I think it was like your logarithms chapter. Like it was just great. I had never thought of things that way.
And just remember saying to myself, and you almost skipped this paragraph, you know? So, so much fun, masterful piece of writing here.
Steven Strogatz (03:31)
Very kind. Thank you very much, Dr. Wargo. That's great. It's interesting you mention the logarithms, because I originally did not have that in the book. And my editor, who was not a mathematician, probably, I don't know, an English major or history major or something, I don't know what his training was. But he was my kind of target reader, just a generally smart, curious person in the humanities who
wanted in a good hearted, sincere way to what is calculus about? I've heard it's a big deal. I don't have any idea what it is. Can you help me? And so at some point, I did need to talk about exponentials and logarithms. And he said, I don't know what those are. I guess I had them when I was in school. tell me about them again. So I thought, god, now I have to teach pre-calculus too. But it was a smart choice of the editor to say that you've got to have that in there. And I'm glad even for an expert like you, Brian, that it
Brian M. Wargo (04:17)
Yeah!
Steven Strogatz (04:26)
you found that there was something in there of value.
Brian M. Wargo (04:29)
And here's what's great about it. As soon as I was done reading about it, anyone that was in my proximity for the next hour, I was like, look, check out what you can do with these things. And they're like, that is kind of neat. I'm like, you should read the book. I, do you know what OMG is like on texting or whatever? I've never used it before in my life. And I literally put OMG on here because I was running, I always write in my books and ⁓ I didn't have enough space to really say, so I just put wow and then OMG. ⁓
Steven Strogatz (04:45)
Sure, I have kids.
Jacob Beckey (04:46)
Hahaha!
Brian M. Wargo (04:59)
I was like, this is perfect. Now I truly get that piece of it. know? So, all right, enough of that. I'm sorry.
Steven Strogatz (05:05)
Hmm.
Jacob Beckey (05:06)
No, no, I hope.
Steven Strogatz (05:06)
Well, very, very nice.
Jacob Beckey (05:10)
So I also, think Dr. Wargo is okay. So ⁓ Professor Strogatz, it's a little background. So ⁓ Dr. Wargo was my high school physics teacher and is the reason, you know, that I am now, you know, finished with my PhD in physics and in a math department during a postdoc. ⁓ And I just love, so I don't want to jump around too much. And I want to talk more about infinite powers for sure, but
Steven Strogatz (05:20)
wonderful.
Great. Uh-huh.
Jacob Beckey (05:36)
I also, after ⁓ reading Infinite Powers and Joy of X, I wanted to read some of your other ones. And the story about, there's so many parallels about your relationship with your calculus teacher that I really ⁓ feel Dr. Wargo and I have as well. And I just wanted to talk a little bit about this starting point, because the goal of this second season of our podcast is to try and inspire teachers. So our primary audience is in-service and pre-service science and math teachers.
In the first season, we were talking a lot about educational research that we think is fundamental for all teachers to be familiar with. And in this season, we really want to emphasize the importance of nature, philosophy, and history of science and math in courses and how powerful that can be for exciting students. And so, of course, all of your writing is just perfect for this. But I wanted to go back to actually where, you know, at the very beginning, I think it's in sync when you talk about doing the pendulum.
Steven Strogatz (06:19)
Okay.
Jacob Beckey (06:31)
⁓ in high school. So this is one of the main things that we have students and teachers when we do workshops with them, we have them go through the pendulum in like excruciating detail. And Wargo, if you want to say a bit more and then Steve, I would love to hear more about your recollection.
Steven Strogatz (06:47)
go through meaning
like do a lab, they do a lab about it.
Jacob Beckey (06:50)
Yeah, go ahead, Morgan, yeah.
Brian M. Wargo (06:51)
Not a lab.
It's our first nine weeks. literally start off and it's kind of like boot camp and the students come in and I lie to them. tell them that, you know, they found this ancient clock and they need to figure out the pendulum. They're in, right? They want to do this so bad. And then over nine weeks, we just go through trying to figure out the period of the pendulum and they make mistake after mistake. Essentially, we're just doing Galileo's work, right? And they come out at the end.
And most of them realize I've been lying to them about there's no big prize at the end or anything like that. But they truly understand how science came about. And it's just wonderful. And that leads in to every one of these students doing a long-term project. So now they've been through this boot camp where they figured out how do take our basic assumptions of nature and then actually end up with something. And then they all pick something that they like. In fact, ⁓
Dr. Becky, if you'd like to tell them what your long-term was, that might be a nice fit.
Jacob Beckey (07:51)
Yeah, I think so. was just I was like blown away starting sync because ⁓ it was that your anecdote right at the beginning about Pendula. So when I, know, Dr. Wargo again probably lied to me when I was picking my long term in high school and I I ended up doing it on coupled oscillators. So there was ⁓ he put, ⁓ you know, two pendula on a string and and just said, you know, can you figure something out about this system? And I was just blown away.
Steven Strogatz (07:51)
Mm-hmm.
Jacob Beckey (08:19)
For people that haven't seen what we're talking about, there's plenty of videos online, but if you let one pendulum go, it'll start to transfer some small amount of energy through the support, and then eventually it'll switch to the other oscillator fully moving and back and forth like that. And it just fascinated me when I was at the high school. It's a perfect ⁓ long-term, and you're the perfect guest to talk more about these things. But I just wanted to hear more about how you got started ⁓ in high school and what sort of sparked that
⁓ lifelong curiosity for math and science.
Steven Strogatz (08:50)
Well,
yeah, you put your finger on it. I was in ⁓ my freshman year of high school, a class called Science 1. And the school was a little unusual in that typically a first year student would take biology as their first science course. And but the.
Where I was, they had the idea that if students had extra math coming into high school and knew enough algebra that they could understand this science one course, which was essentially like a little physics course, that you could do it in the opposite order. You could do physics first and then chemistry and then biology, the thinking being that there's a certain logic to it, that chemistry builds on principles of physics and biology on chemistry. So. ⁓
Brian M. Wargo (09:15)
Mm-hmm.
Steven Strogatz (09:38)
So I was in this class, science one, and one of the first experiments we did was to figure out the period of a pendulum of different lengths. So we had a pendulum that you could stretch to make it. It was retractable, so you could make it longer or shorter in discrete clicks, like da-da-da-da, and a plastic rod that could click.
And we could also put different masses on as the bob. And we were given stopwatches. This was the old days when, I mean, nowadays, I guess you could do it on your phone with a timer. But in those days, it was old school with a stopwatch, a stem. Anyway, whatever. And so we were asked to time 10 swings of the pendulum back and forth. And then really, the lab was supposed to teach us how to use graph paper. Because remember, we're just beginning in high school. And so we're learning about.
Jacob Beckey (10:14)
Yeah
Steven Strogatz (10:30)
You graph the length of the pendulum in centimeters on the x-axis, the time for 10 swings on the vertical axis, or maybe divide that by 10, so the time for one swing. And so I remember doing that and plotting four or five dots on this picture and noticing that ⁓ they didn't fall on a straight line. I thought they would, but they don't. Yeah, I mean, it's true that the longer pendulum takes longer.
Jacob Beckey (10:54)
as all students, I think,
Steven Strogatz (10:59)
to swing back and forth, but it isn't directly proportional. so that was already interesting. But then Mr. DiCurcio, my teacher, said, well, graph the time squared against the length instead of just time of swing versus length time squared. OK, I don't know why, but I tried it. And of course, we all did. And then we got a very nice looking straight line, which was
very spooky to me because it meant that the ⁓ underlying relationship was roughly speaking something like y is related to x squared or maybe it's more like y squared is related to x. But the point being it makes a parabola, right? That thing that didn't look like a straight line, those dots were falling on a parabola and that really creeped me out.
Jacob Beckey (11:27)
You
Steven Strogatz (11:49)
in an epiphany kind of way, because I had learned about parabolas in my algebra 1 class. And I just had this feeling like, what the heck? could this pendulum know algebra? That is so weird. It's just a weight hanging off of a rod. How is that possible? And one aspect of the story that I don't normally tell, but I will tell here, is in this other way of doing it, where we graph time squared against length,
Jacob Beckey (12:02)
You should have seen that.
Steven Strogatz (12:19)
The teacher asks us to calculate the slope. You have a straight line. The slope is meaningful. And what is that slope? And as I recall, it comes out something like, I might get this upside down. I think it was something like, if I measure time in seconds and length in centimeters.
I'm going to either, okay, it's either, it's either times squared is 25 times the length or times squared is the length over 25. I can't remember which, but the number 25 came into it. We could quickly figure it out. But anyway, what was really weird is that the slope involved this number 25. And even as a 13 year old, I remember thinking that's weird because 25 is only a special number to us because we have 10 fingers.
Brian M. Wargo (12:44)
Yeah. Yeah.
Jacob Beckey (12:48)
Sure,
Steven Strogatz (13:05)
Right, because we have five fingers on each hand, it's natural for us to be interested in the numbers five and 10. Five squared gives us 25. You know, we have 25 cents for a quarter. 25 is very intimately connected with five, and five is an accident of our biology that we have five fingers. And so I remember thinking, now this is really getting crazy, because why should a pendulum know anything about our fingers?
Jacob Beckey (13:27)
you ⁓
Steven Strogatz (13:31)
OK, so that part turned out to be a coincidence. That number is not really 25. Years later, I came to understand that what that number is is 4 pi squared divided by little g, the gravitational constant, 980 centimeters per second squared. So acceleration due to gravity. And 4 pi squared.
Brian M. Wargo (13:44)
Mm-hmm.
Steven Strogatz (13:55)
turns pi squared turns out to be a number pretty close to 9.8. So when you divide 9.8 by 980, you get 1 over 100. And then the 4 that I mentioned earlier gives 4 over 100. That's 1 over 25. So the 25 is not really 25. It's just an approximate thing that involves pi and gravity. Anyway, that's really going into the weeds for you and your audience. But I mean, you guys might like that kind of stuff.
Jacob Beckey (14:18)
No, no, this is...
Brian M. Wargo (14:20)
No, that's it. That's it right there.
Right?
Jacob Beckey (14:23)
It
is literally at the end of at the end of ⁓ Dr. Wargo wrote a book sort of outlining exactly how he does this with the students so that new teachers can try and take them through a similar thing, usually abbreviated doing a full nine weeks is a hard sell for for for most teachers. But ⁓ literally the last few pages of the actual unit are describing exactly what you just described. The fact that you can get
Steven Strogatz (14:49)
⁓ okay.
Jacob Beckey (14:51)
⁓ this number that seems almost exactly like ⁓ pi squared being close to G is like this crazy realization when you plot it and find the slope and stuff. It was so funny reading this and I was just like, Dr. Orgas is, couldn't think of a more fitting guest. It's just, ⁓ yeah, I just love this. I love your way of storytelling and I wanna, for students, I've watched a lot of your interviews over the years and I think,
Steven Strogatz (15:02)
huh, huh.
Hahaha
Jacob Beckey (15:19)
I don't want to be repetitive with some of them, but I also think your story of how you got into sort of math and science at the undergrad level and then into a life as a research mathematician is really inspiring. And I think the thing that I appreciate the most is that you maintained an interest in teaching the entire time, which I feel like the incentive system of academia is actually not set up to incentivize excellence in teaching in large part. And so I just want to hear about your sort of
Steven Strogatz (15:37)
yep. Yeah, yeah.
Jacob Beckey (15:48)
thought process as you went through your academic career and how this blends with your love of teaching and if there was ever tension between those and whatnot.
Steven Strogatz (15:58)
Wow, that's a really interesting question. no, I felt that tension my whole life, in fact. ⁓ So I always wanted to be a teacher from the beginning. I admired my teachers a lot. I was grateful to them, including my own parents. Just something about it, I always really liked the whole process of learning and teaching, and not just science and math, all the subjects, my English courses, history, everything French. ⁓
So I always had this dream of someday wanting to be a teacher. But when I was in college, I started to see certain phenomena that I hadn't really seen in high school or elementary school, which was that there was this whole concept of getting tenure. Some professors would be kept on.
for their whole life as long as they wanted. And other professors, so to speak, would not get tenure. was, I didn't as a kid in college, I didn't really understand what that meant exactly. But in practice, it meant that they left. You wouldn't see them the next year. And what was very dismaying about that is some of the best teachers that I had were the ones that weren't getting tenure. And conversely, I don't want to be too
rude about this, but there were some other people who, let's say, their heart was not in their teaching. They might have had other priorities or whatever. And those are the people who sometimes we had as our teachers. And I really wished I had the other people. They cared more or had more of a knack for it. So in thinking, am I going to have the right stuff to be a professor someday? I thought, what happened to those guys that didn't get tenure?
Jacob Beckey (17:30)
You
Steven Strogatz (17:43)
what did they do wrong or why did that happen to them? And I didn't have a very deep understanding, but simplistically I thought maybe they didn't publish enough papers or good papers or something. I don't know. I thought it was really about quantity. So at that time I sort of resolved as a little secret to myself that I'm going to do my best with research, but I'm going to always make sure when my time comes that nobody can say I didn't publish enough.
Brian M. Wargo (17:54)
Thank
Steven Strogatz (18:13)
And here, depending how deep you want to go into this, it's possible to get pretty cynical here. ⁓ Because ideally, the merit system should care about the quality of your discoveries, not just the quantity. Or maybe you could even say not even the quantity. But on the other hand, the reality is it's very hard for anyone to understand anybody else's work at the frontier of science. It takes a huge amount of effort to understand what someone did.
Brian M. Wargo (18:31)
Mm-hmm.
Steven Strogatz (18:43)
And so it's much easier to just count the number of papers on their record. And I think that happens more than it should. And so I decided if I have even something that is a little marginal but publishable, I'm going to publish it because it'll mean I have one more paper. And so ⁓ I of went through the whole academic track.
Publishing the stuff I was proud of as well as stuff that I wasn't proud of but that I thought was publishable and not embarrassing I don't don't recommend doing publishing bad stuff but anyway So I was very acutely aware of it in the course of my career and the other thing I guess I would say is that in my heart of hearts I always really wanted to be as I said earlier a teacher
Jacob Beckey (19:12)
Yeah.
Mm-hmm.
Steven Strogatz (19:30)
And that's not normal. The normal thing is you want to be a professor because you love the mysteries of science or nature. And you call teaching a teaching load. The word is a giveaway about what you respect and what you don't respect. If teaching is a burden or a load, you'll take a certain attitude toward it. I mean, to me, teaching is a privilege. Teaching is what I'm there to do.
And so I wouldn't say research was the load. mean, research is fun, too. I love doing that, too. But I like the whole thing. Yeah, they're both important. So anyway, I'm giving too long of an answer. But the gist of it is that throughout my whole life, even to the present, I still think of myself mainly as a teacher. That's what I'm in this for. And I love the research. But if I had to pick, my heart of heart is in teaching.
Jacob Beckey (19:59)
Yeah, possible for both of them to be enjoyable and they should be, ⁓ you know. Yeah.
Oh, it's a-
Brian M. Wargo (20:08)
No.
Jacob Beckey (20:23)
Yeah, think that's a fantastic answer and yeah, no worries on like this is.
Steven Strogatz (20:28)
I wouldn't say that to my when I was coming up for tenure, you know, you can't admit that this this thing got me in trouble. I don't want to make it sound like, it's all sweet and everybody agrees with this. They don't. I as an assistant professor, my chairman, when I was an assistant professor, my chairman told me, why are you working on writing this textbook? I was working on a textbook about.
Jacob Beckey (20:32)
I am
chaos.
Steven Strogatz (20:49)
the area
I was specialized in, yeah, was in nonlinear dynamics and chaos. And as a teacher, I was frustrated that I couldn't find suitable material to teach beginners. So I just thought I'm going to write what I think a beginner should learn. And my
Jacob Beckey (21:04)
And now it's a celebrated
textbook that everyone in the field uses to learn from. ⁓ And that is a service that for some reason is viewed as not as important. Yeah.
Steven Strogatz (21:09)
Well, that's done. Yes, thank you.
It was viewed as questionable. But my
chair told me explicitly, this shows wrong priorities. You're going to take away time from your research if you do this, and it's not going to help you. So we don't recommend it. And I just felt like, well, OK, I hear you. this was before tenure.
Jacob Beckey (21:28)
And was this pre tenure or post tenure?
And you still said, bet, yeah.
Steven Strogatz (21:35)
I really want to do it. I think it's
important. And I paid the price. I was told that I wouldn't get tenure. Now, I didn't actually come up. This was at MIT in the math department. I didn't actually come up for tenure. The process was that I had a review two years before the tenure decision, sort of like a dress rehearsal. And at that time, I was told, well, the outlook is not good. ⁓ But.
We like you, we hope you'll do something great in the next two years, but at this point, we don't think it's positive. So that's what I look for.
Jacob Beckey (22:07)
What was that
experience ⁓ like? I I imagine at the time, I don't, you know, I can only imagine, but it just feels like, yeah.
Steven Strogatz (22:15)
Well,
on the one hand, it wasn't a surprise because that department had a tradition of not giving tenure to their young faculty. It was almost like you would go there knowing that it's another postdoc and that you're going to have to leave. It was just fairly common. In fact, people before me that were a little older than I was, that I thought were better than I was, they weren't getting tenure. So I knew the odds were not good. That was not a mystery.
Jacob Beckey (22:23)
Flip a foc-
Steven Strogatz (22:40)
But nevertheless, everybody is always hoping somebody has to get tenure. And I had lived in Boston for quite a number of years at that point. I had a lot of connections. I didn't want to leave. But I was being told that prospects didn't look good. And then Cornell, which was really the best place in the country for my specialty, for chaos, said, well, we will give you tenure right now if you want to move here. ⁓
You know, we think you're great. So I was very confused about this. I asked my brother. I have a big brother who is 12 years older, and he's a lawyer and a good negotiator. And I asked him, well, what do you think? This is a tough decision. I really like it at MIT. But Cornell is saying, he said, it's not a tough decision. could just, actually, I won't say what profanity he said. But he said, you could tell MIT such and such.
Jacob Beckey (23:12)
That's.
Yep.
Steven Strogatz (23:36)
And Cornell is great, and you'll have a nice life. You should just accept it. It's a nice offer. And so I spent my whole life since then, more than 30 years now, there. And it's been very nice. Of course, I don't hold it against MIT. I have a lot of friends there still, and it's a great place.
I do think it was a short-sighted system. It's important to develop young talent. And they let go a lot of good young professors that I think they regret in retrospect, not to talk about myself here. For example, this guy I mentioned that I thought was better than me that was a little bit older became a professor at Oxford and then was recently elected to the National Academy of Science and is a fellow of the Royal Society. So they had absurd standards.
Jacob Beckey (24:06)
Yeah, it's...
Yeah, it's no, I mean, so I appreciate the insight. mean, as I, you know, I'm in my first postdoc and I'll be in. Yeah, so it's, ⁓ you know, it's a daunting and I think, you know, the climate currently is perhaps ⁓ as bad as it could be in terms of but without being too doom and gloom, I mean, the thing I really wanted to sort of emphasize is that I think it's, ⁓ you know, to be able to
Steven Strogatz (24:24)
Okay.
Sure, you're gonna be facing this stuff.
Jacob Beckey (24:51)
get tenure and be a leader in your field, but also maintain the passion for teaching. just really appreciate it. I know a lot of your students do. And I've heard so many people that have used your book, not just the books that are written for the general audience, but also the textbook that maybe MIT wasn't supportive of, but a lot of people really appreciate it. it's great that you stuck to your guns.
Steven Strogatz (25:13)
Well, they do use that.
They use that book at MIT still. And it's funny, of all the different work I've done over the years, I hear from students more than anything else, not about some research paper, but about that book. They're really grateful for that book. So I'm very proud of it. It was the first book I ever wrote.
Jacob Beckey (25:29)
Mm-hmm.
Brian M. Wargo (25:35)
Well, I want to jump in and say, this should be
a book at the university. Imagine if you have students that are not going into research, or maybe they're not at MIT, and you want them to understand some history and this notion of like, what do scientists and mathematicians do? This is it. This shows you how difficult it is to come up with an idea. I mean, you do an excellent job of just showing how long it took to get away from just thinking of something
Steven Strogatz (25:45)
Sure.
Brian M. Wargo (26:03)
being a straight line, right? And what a challenge that was. And then you make these little steps and the great minds that we had were able to add a little something to it. So you get rid of this, you dispel this idea of genius. And it's like, no, it's about ingenuity and hard work. And quite honestly, I mean, like I thought you're ⁓ dealing with Newton was just fantastic because we all instantly accept Newton was handed down from the heavens and he instantly wrote
you know, on these tablets. And you're like, no, he's a normal kid who's, you know, he's got some trouble at home and this, that, whatever. But, right? But what does he do? He just keeps working at it. And so to me, I think that this book would be great for a general audience who maybe they need to take a history class, maybe they need to take a math class and so on. And none of them are going to be specializing in this. I think this would be the book. I think you'd inspire so many students to say, you know what?
Steven Strogatz (26:35)
Yeah.
stuff yeah
Brian M. Wargo (27:02)
I can actually do this, albeit history or mathematics or science.
Steven Strogatz (27:06)
Thank you, that's nice to hear. And I think, ⁓ Dr. Wargo you're putting your finger on a really interesting point, which is, who are we trying to reach when we teach? ⁓ Even in high school, elementary school, or college, we have courses, kids often ask, why do I need to learn this? Why am I taking French? I'm not going to live in France. I'm not planning to go to Montreal. Or why am I taking calculus? I'm not going to be an engineer. So.
Brian M. Wargo (27:15)
Yes.
Steven Strogatz (27:34)
That's a complicated question to answer. There's a lot of interesting answers that you can give to that kind of question. But one of them is, OK, let's suppose you're never going to speak French or read French or do calculus, because that is true for a large part of the population. You don't want to dismiss them. ⁓ Is there still something valuable you can get by being exposed to this? And if you just teach the person how to conjugate verbs,
Brian M. Wargo (27:57)
Yes.
Steven Strogatz (28:00)
or how to do complicated integrals in calculus class, you might be shortchanging them as opposed to setting this in a much broader cultural sense. Like, look, you're a human being. You want to see what your fellow human beings have come up with, what great books they've written or poetry or the funny swear words you could say in French or what calculus. Like when people watch the movie Hidden Figures about those women mathematicians at NASA that helped put
people on the moon and got them back safely. That's a very thrilling story. Everybody likes that story. And that's calculus in that story. So my point being that often when we teach subjects, we're aiming at the students who are going to be practitioners. And that's not the main population. Just like you take a music class, I mean, some people will become professional musicians, but a lot of people just want
Brian M. Wargo (28:34)
Yes.
Steven Strogatz (28:55)
a better appreciation of music because it makes their life richer. And we could do that with math and science too, that it's not just about the technical specialists. I we need to train them, of course, but there's a lot more people who just need to see what's glorious about these subjects. we don't, I understand the pressure that teachers are under, know, there's a lot to cover. The tests are high pressure, the kids need to get into college. There's a lot to do.
So I'm not criticizing the teachers, but I wish that we would in our curriculum make space for these, I don't know what you want to call it, like a bigger picture view of different subjects.
Brian M. Wargo (29:34)
Yeah.
Jacob Beckey (29:35)
Totally.
100%.
Brian M. Wargo (29:37)
One of the other things that
you do is you give real world examples chapter after chapter. You're talking about AIDS research, know, PET scans, everything. And so I think that's another reason because let's face it, you can take all the calculus you'd like and it can be completely inert. And yeah, you might be very good with manipulating symbols, but what can you do with it? And that I think is what students, if they knew what they could do with this, like if you're going into finance or something like that.
Steven Strogatz (30:00)
Mm-hmm.
Brian M. Wargo (30:06)
you should know calculus, right? I think if they knew that, they would suddenly say, wait, I can use calculus to make money, right? I I think you nail it on that. You give enough practical examples that, and of course the music major, you talk about how music is mathematical. And then of course you bring in like Kepler and so many others that are just mystics with this. I mean, it's like great story, great application. And again,
Steven Strogatz (30:07)
Yep. yeah.
Well, yeah.
Brian M. Wargo (30:35)
I think no matter what you're interested in, you're going to find something that relates to one of the greatest ideas of all time, The changes in rates. Yeah. Amen. I told you when I read this, I felt like I knew you were right away. And by the way, I just realized something, the joy of X. ⁓ I just remembered where my book is because I didn't get to finish it. I lent it to a student and I just remembered and they never gave it back.
Steven Strogatz (30:45)
Wow. Tell it, brother.
You
You
Brian M. Wargo (31:05)
Because I remember starting it and going, this is great. And I said, take a look at this. Never got it back.
Jacob Beckey (31:05)
Yeah.
It is always anytime war go get started talking about books. It is we have to reel them back in and get so excited. But I when I when this one like when I read this, I was like that you we have to we have to read this and review it. And the what you said, I think ties in perfectly with the whole goal of our of the season of our podcast, which is to try and get, know, the
science standards, the next generation science standards in the US call for a certain fraction of time to be spent on nature of science and not just on content. ⁓ And you go into a lot of classrooms still today and it is mostly content, right? It's a teacher speaking at students and if they have an AP curriculum to stick to, they have to get through everything. And I think what books like Joy of X and Infinite Powers do is like,
Steven Strogatz (31:44)
good.
Jacob Beckey (32:02)
Even if you're not going to have the student read the entire book, if you can bring in pieces of it and humanize the story, I think you're just going to reach, like you said, so many more students, the students that we really need to reach if we want to see a change in society at large with opinions towards math and science. ⁓ These are the types of books that can do it. Absolutely. ⁓ It is so yeah, Infinite Powers was fantastic. And the story of calculus is hard to. ⁓
Steven Strogatz (32:12)
Mm-hmm.
Jacob Beckey (32:29)
I mean, when you tell someone, it's a book about the history of calculus. mean, if they're not a math person, they're like, well, I'm never in. Yeah, no, please keep that away from me. But then when you actually get into it, you realize, OK, like, you know, the way you tell it, it's like these are these are people and they're, you know, they're having an actual battle over, know, the discovery and the credit. there there's people that are, know, there's like real emotion involved. And it just it I thought it was just great. It was ⁓ yeah, it was a great telling of the story.
Brian M. Wargo (32:33)
All right.
Steven Strogatz (32:34)
All right.
Brian M. Wargo (32:41)
Everything
Steven Strogatz (32:58)
Well, actually,
Jacob, about that, you you raise an interesting issue about like branding or marketing. If you market it as this is a book about calculus, which it is, OK, you may have to climb a certain hill to get the reader. But if you say there's a book about infinity, I find that most people like infinity or at least find it creepy or disturbing or intriguing because it suggests so many things like
Brian M. Wargo (33:14)
Yeah.
Yeah.
Steven Strogatz (33:27)
the idea of the universe going on forever or God is infinitely powerful or when I'm dead, will I be dead for all eternity? I mean, there's just a lot of deep things connected to the infinite. And also just the mystery of kids, like I talked at one point in the book, and it was true. I used to argue with friends of mine on the schoolyard like.
Jacob Beckey (33:42)
tied up with.
Steven Strogatz (33:54)
you'd be naming some number and somebody would say it. Someone would eventually pull out infinity and think they won the argument. And someone else would say, well, infinity times infinity. And then someone else would but that's just infinity. Anyway, it's just there's something inherently interesting about infinity. So I think calling it infinite powers, which has a little bit of a quasi-religious vibe to it, it also ⁓ is true to what calculus is about, which is the strategic use of infinity.
Brian M. Wargo (34:14)
Yeah.
Steven Strogatz (34:23)
And it's not easy to get a handle on that because it's such a mysterious concept. First of all, that's truer to what calculus is about. it's also dense to grab people, find. Once you talk, I I told the editor of the book, I really want infinity to be in the title somehow. And it was the editor who came up with that title. I had been calling it the language of the universe or something like that, which made it sound like a textbook or a little more.
Jacob Beckey (34:27)
Absolutely.
Mm-hmm.
Steven Strogatz (34:52)
I don't know, anyway, he came up with infinite powers and I'm happy. I think it has worked pretty well.
Brian M. Wargo (34:57)
One of the things that I love about it, if we go from infinite and infinitesimal, you're talking about like philosophy here. Like does anyone actually think this thing is real, like this infinity? I mean, there's no way to get around not talking about epistemology and philosophy. So I think it's just great. Now, if we go back to the finite, one of the other things that I got to throw in here, and I think this was at the end and your acknowledgments that you were talking about, like I've wanted to write this book for a while and I...
Steven Strogatz (35:02)
Hmm
yeah.
Brian M. Wargo (35:26)
hadn't gotten around to it. you're like, and then I realized like most people every day is another day that I'm getting closer to the limit. Right. And, and you're like, get going, get going. And all I can think of, and cause I'm, I'm getting older too. And I'm thinking the same way, but imagine if like teenagers started to think, look, my life, life is finite. Get going now. Right. I mean, like, um, and this is one, one of the things why books are so important and you, you can't read an infinite number of books.
Steven Strogatz (35:33)
Yes it is.
Yes. Right.
Brian M. Wargo (35:56)
So only read great books. And that's the ticket. Never ever read a book that's like a five out of 10. It's gotta be a 10, a nine, an eight, but don't waste your time on anything else. I'll be quiet about the books, but all right.
Steven Strogatz (35:59)
Uh-huh.
Ha
ha ha!
Jacob Beckey (36:11)
No, it's great. It's great. Yeah, no. I will say that we had recently, so every Monday and Friday, we upload a quick quiz to our YouTube channel. And these are sort of the gateway into what we want teachers to do. So we want teachers to engage their students in authentic science in the classroom. And this is done via dialogue amongst one another and through all of the practices of science.
of scientists. And the one quick quiz that happened to go viral, think it might, we might have you and Grant Sanderson and others to thank in small part because it is somewhat related to the brachistochrone curve, at least on the surface. So the question is simple. We have four ramps of different shapes. And the question is simply, how do the speeds at the bottom relate? Okay, so you just say four different
Steven Strogatz (36:54)
yeah?
Brian M. Wargo (36:54)
Bye.
Jacob Beckey (37:08)
four different curves that they're gonna take and how do the speeds at the bottom really. And I can't tell you the number of comments that just say with no other explanation, brachistochrone, done. that was, and it is of course closely related because it has to do with the time of descent on a curve under the, but I honestly think because of your guys' popularization of this problem, we ended up getting a lot of traffic to this. ⁓
video and then we ended up getting some phenomenal dialogue about, because the simplified model of this is just conservation of energy. They start with the same energy at top. It's gonna have roughly the same speed at the bottom. And so of course this is what you, but then people say, well, what about friction? What about air drag, all these things. So we got a really good, of course you can always refine the model and go deeper, but it's funny how many, I just would not think so many people would know what the brachistochrone curve is. And I feel like it's, you know, it's,
Steven Strogatz (37:44)
They should have the same speed at the bottom, yeah.
Yeah. wow. That's
so interesting because I've been finding this too. The reach of of Grant Sanderson on Three Blue, One Brown and Derek Muller on Veritasium.
Brian M. Wargo (38:10)
Come on.
Jacob Beckey (38:13)
Crazy.
Steven Strogatz (38:13)
And
some of the other channels, the guy Destin that does Smarter Every Day, I don't know if you've seen his channel, they're uh physics girl. They're just a lot of really interesting influencers and science and math teachers, physics teachers, that are reaching sometimes tens of millions of people around the world. So it's incredible.
Jacob Beckey (38:19)
Yep. Yep.
Crazy.
Steven Strogatz (38:36)
⁓ I am constantly when I meet young people, they'll say to me, I saw you on, you know, Veritasium. It's not like I read your book. It's I saw you on this video. So that's the mechanism for reaching people nowadays. I'm not really surprised that the brachistochrone got traction. You know, you're seeing that effect.
Jacob Beckey (38:43)
People on Brown are very tough in there. Yeah.
I guess
I was just surprised because it seems a little bit esoteric. But it's just such a cool story in the history of calculus. I do understand why. But it is funny because I think maybe one in every hundred comments was probably about the recreation.
Steven Strogatz (39:13)
You want
to say for your listeners or viewers what the problem is in case they're not familiar?
Jacob Beckey (39:17)
Yeah,
that's a great idea. Yeah, so the brachystochrone problem, as you describe in the book and also in these great videos with with Three Blue and Brown and did you have one with varitacin as well on maybe it was a different topic.
Steven Strogatz (39:29)
Not about
that topic. I've had several with them on other topics. I think also Michael Stevens that does Vsauce, he had a brachistochrone. So, yeah.
Jacob Beckey (39:33)
synchronization things, but.
right. You're right.
is. Yeah. So maybe maybe I'll let you explain the problem to the listener, though. I think that you're
Steven Strogatz (39:45)
Well,
first of all, this funny word that we keep saying is two Greek words stuck together, brachisto, which is the shortest, and chron, like chronometer or chronograph or chronology about time. So shortest time.
And it refers to the problem of ⁓ if I have a chute and I need to get from a point ⁓ A to another point B, I can connect them with some kind of a slide. I could connect them with a straight line like a ramp, or could put something that looks more like a chute that a kid would go down a slide at the playground, whatever. What's the best path in the sense of that a particle that's sliding down without friction along this path?
will get from A to B in the fastest time. What's the the path of shortest time? So in Greek, what's the brachistochrone? And that was a big challenge in the late 1600s that one of the Bernoulli brothers, these two very genius brothers who are bitter rivals with each other, ⁓ one of them, they're always trying to show who's smarter, not only than each other, but then all the other mathematicians and physicists of Europe.
Jacob Beckey (40:55)
at the time.
Steven Strogatz (40:56)
Yeah,
at the time. And there were some great people alive at the time, Leibniz, Newton, guy named Lopital, who was very good. Anyway, there were a bunch of very powerful people mathematically. so, yeah, I think it was Johann Bernoulli posed, I'm forgetting which one it was. I think it was Johann posed the problem to the great mathematicians of Europe. And five people wrote in with solutions for the curve of the fastest descent.
Brian M. Wargo (41:04)
.
Steven Strogatz (41:23)
They all got it right, which is interesting, the five. And ⁓ one of them was an old Isaac Newton at that point, kind of more or less retired from math. But the legend and probably true is that he found this. We know he did solve it and he went home and solved it in one night. He felt very, very powerful, ⁓ sort of like Michael Jordan, you know, coming off out of retirement to show the Steph Curry how it's done or something like that.
Anyway, so the legend is that Newton solved it, and Bernoulli's brother said they recognized the lion by his claw, because Newton didn't sign his solution. But they could tell it was Newton. Anyway, and the answer, in case you're wondering, is that the curve is this interesting curve called a cycloid. So it's not a straight line. It's not the path of the shortest distance. The path of shortest time.
Jacob Beckey (42:04)
Yeah, it submitted it anonymously, right?
Steven Strogatz (42:20)
involves going straight down at first and then taking a curved path that is the path that if you put a little light bulb on a wheel of a bicycle and then ride the bicycle, you'll see the light making this shape called a cycloid. So that turns out to be the curve. An arc of the cycloid is the fastest. anyway, it's classic old problem. But OK.
Jacob Beckey (42:30)
Enroll.
Yeah, no,
so thank you for the explanation. A question that we got in the comments, and I'm curious to have your initial thoughts on it. If you take into account, they were asking if you do take into account friction, say rolling resistance or some lost term, ⁓ how would the answer change? I thought it was an interesting question. I think the math would get unwieldy very quickly. Yeah.
Steven Strogatz (43:06)
the answer to that,
Jacob Beckey (43:07)
But it was a fascinating question. But yeah, a lot of people, the natural answer would be that it is a straight line. Of course, it has to be. It's the shortest distance between two points. And I think it is a very intuitive thing. So the fact that it isn't that is rather counterintuitive.
Steven Strogatz (43:14)
Mm-hmm.
Nope,
it's not that. And also, other people who were very clever got it wrong. Galileo thought that it would be an arc of a circle. He realized that going straight down at first to build up speed is a good idea. But he put, I think, some arc of a circle that had its vertical tangent at the beginning point, build up a lot of speed, then come curving into the final point. He had the right idea, but that isn't actually the correct curve.
Brian M. Wargo (43:28)
Yeah.
Jacob Beckey (43:28)
Hmm,
so close. So it's on other.
Right, very cool, very interesting. Wargo, do you have?
Brian M. Wargo (43:49)
This all makes me think about,
about like, like I had mentioned, we make all of our students do a long-term project and you can't Google it. You can't like look it up. If you do, it's already been done. There's no need to do it. Some of these ideas would be just marvelous. And we really do push doing math long-terms, but we've had limited success. And I think it's because the way that math is taught is you're
supposed to know these algorithms and you're supposed to know truth and you're supposed to know the exact thing instead of like what the great mathematicians have done. They've tried things that hasn't worked out and they said, okay, let me tweak this. That's what we're after. So this would be, you know, I just heard about five great ideas of things that you could test and then say, and by the way, with our long-term, you don't have to come up with some correct answer. You just show this is what I did. This is what I, I found out.
Steven Strogatz (44:26)
Mm.
Brian M. Wargo (44:43)
And so I'm really excited about all of these and I need to write them down so I can say to students that are like, I want to do a math one and I don't know what to do. Well, here's a bunch that you can start to think about.
Steven Strogatz (44:54)
I could provide you with an old high school notebook of my own because I did lots of them in those days. They were me at 13, 14, 15. And I'm just reminded, of course, this is a sign of getting old, that things were different then. Life was slower. I had time to sit in the library and read.
Brian M. Wargo (44:58)
Yes!
Jacob Beckey (45:00)
That would be awesome. Yeah, yeah.
Brian M. Wargo (45:01)
That would be great.
Steven Strogatz (45:16)
I mean, I had sports after class every day and had a job. I was supposed to either be mopping the floor in the dining room or cleaning the dishes or something. This was at a boarding school. So the school gave students a balanced life. It wasn't just homework and classwork. But ⁓ there was more time. We didn't have social media. I mean, it's a long time ago. I didn't have a phone to look at. I don't even think there was a phone in the whole building, practically. It was hard when I
Brian M. Wargo (45:38)
Yeah.
Jacob Beckey (45:45)
Yeah.
Steven Strogatz (45:46)
parents wanted to call me up. But how it's relevant to today is I worry that we, in what we think of as making a rigorous curriculum, I think we're packing too much in there. And we're not giving students enough time or teachers enough time. Like going slow has big advantages in terms of depth. If you can help a student love a problem like these long-term questions you're mentioning, Dr. Wargo, what's the rush?
Brian M. Wargo (45:47)
Yes.
Yes.
Steven Strogatz (46:13)
It's much better. You learn much more if you spent a week or two thinking about something that you really like and doing experiments and maybe looking stuff up on the internet and trying things. Anyway, it's harder to assess. I mean, it's much easier to just have students do these multiple choice tests or fast, fast, fast. But that's so shallow. And students pay the price later in their career.
Brian M. Wargo (46:33)
Hmm.
Steven Strogatz (46:39)
that they've never come to grips with a hard problem and really wrestled with something, which is how real creativity happens.
Brian M. Wargo (46:43)
And one of the things,
one of the words that you use in this book, and I don't remember where it was, I think it was at the end, maybe in the acknowledgements, you talk about falling in love with calculus, right? And, you know, that's the thing. I think a lot of students don't realize how interesting and how enjoyable it is to work with numbers and symbols because it's so foreign at first. But, ⁓
Steven Strogatz (46:58)
yeah.
Brian M. Wargo (47:10)
If we could give a little bit more time for students to play, to develop that, to stumble into something that excites them that they say, my gosh, that was really cool, with numbers, and then encourage them, imagine the level of, you know, I don't have to tell you that the math scores in the United States are not where they should be. And I think part of that is because we've taken the joy out of X, right?
Steven Strogatz (47:15)
Mm-hmm.
Absolutely.
Yeah, sure, sure. Because I think we're in a big rush. And we think that we're doing ourselves a favor, that this is how we're going to do better if we demand more and hold people accountable. You hear about this word about accountability for the teachers and the students. I think it's a, I understand where that's coming from, but I think it's easy to do wrong. You know?
Jacob Beckey (47:36)
Thank
It's absolutely easy to do wrong. think
the pressure, so where Dr. Wargo, so where I grew up and where Dr. Wargo still teaches is a rural school in Pennsylvania. It's ⁓ severely underfunded and we just make do with what we have. And I will say a persuasive argument for the speed of some of these, they have a lot of AP courses and college dual enrollment.
Steven Strogatz (48:25)
Mm-hmm.
Jacob Beckey (48:27)
is a big push and it's always this back and forth between what the research says about depth over breadth and the benefit, like you point out, of going deeply into something. But I think there is, ⁓ unfortunately, hard to rebut argument about the economics for a lot of students that can save so much money by doing either AP or dual enrollment when they actually get to the university level. I think that is a challenging thing. All I can say is that it's, like you said,
Steven Strogatz (48:37)
Mm-hmm.
Fair enough. yeah.
Jacob Beckey (48:56)
you're sort of, we're cutting a lot of the experience out of high school short if we try to pack in all of this stuff and never have students actually fall in love with the content. And once you get to the university.
Steven Strogatz (49:06)
Well, a lot of ⁓
things have gotten twisted. The rush to calculus is a good example, if we're talking about this. ⁓ There's a feeling that everybody needs to have some calculus to get into a good college. And that's putting a lot of pressure on everybody. The truth is that there's a lot of material before calculus that's very rich and interesting about vectors and complex numbers and trigonometry and.
curvature of curves and things. mean, there's a lot you can do that's not calculus, that's very deep. And I can tell you seeing in the college level, a lot of my students don't know that stuff, and it hurts them in college. That they've zoomed through, some are even taking linear algebra or differential equations or multivariable calculus in high school, producing this extremely accelerated but very thin
usually, I mean, not everyone, some kids can handle it and they're very accelerated, that's fine. But a lot of kids, I think, are being hurt by this rush. And if we made it so that you could get into a good college without having taken calculus, but you did really well in your high school math courses, I do think ⁓ that might be healthier for a lot of people, not maybe for everyone, but for many.
I don't know. don't claim to have an answer to these things because these are really complicated issues of education at the nationwide scale. And as you say, there's economic aspects. Because if you can get farther ahead faster through AP, you could maybe graduate in three years from college and save yourself a whopping amount of money. I hear you. I hear you, Abudat.
Jacob Beckey (50:48)
I mean, yeah, that's,
yeah, so that is, ⁓ you know, actually because of Dr. Wargo's influence, that is what I ended up being able to do, graduate. ⁓
Steven Strogatz (50:58)
Tell
a little bit about that. How many APs did you take in high school? ⁓
Jacob Beckey (51:02)
Well, it actually, it was a lot of the
dual enrollment. So because we're kind of a smaller underfunded school, there wasn't a lot of AP, but I took what I could. What they did have was dual enrollment with local community colleges where I was able to take. So I got all of my prerequisites out of the way and to, know, if there are students listening and stuff, I would highly recommend this because it, you know, I was able to avoid debt ⁓ in large part because of this. So that's the only case that I feel is persuasive for
Steven Strogatz (51:15)
I see, I see. That's what you're saying. OK.
Wow.
Jacob Beckey (51:32)
packing content into the high school level is an economic one. I do feel though that it's still when students ask how they should be spending their time at the high school level and stuff, I do think that experiences like doing a long-term project or really falling in love with something along these lines can have more of a lasting impact. It's just, it's a tough, it's a tough balance.
Steven Strogatz (51:34)
hear you.
Hmm.
As the the youngest person here, can you tell us a little how did it all happen for you? Did did you grow up in a family that was interested in science or I don't know.
Jacob Beckey (52:03)
⁓
No, yeah, no, I truthfully, Dr. Wargo is he's always uncomfortable when people give him praise, but it is it is because of Dr. Wargo. So I, I as a first generation college student and ⁓ my parents were always supportive, but ⁓ they did not when I said I wanted to go into physics, they were like, what do do with a degree in physics?
Steven Strogatz (52:11)
Go for it.
nice.
Yeah, sure, my parents
too. Yeah.
Jacob Beckey (52:28)
super supportive,
but that was not their specialty. And so they've been supportive through the whole process, but really Dr. Wargo has been that mentor to me through ⁓ all of these years now through my PhD and now into the postdoc and starting this nonprofit together, it really is in large part because I feel I want so many, it's not just me, we have an alumni meetup at our high school where 30,
Steven Strogatz (52:32)
Okay.
Wow. Nice.
Jacob Beckey (52:54)
years worth of students, you know, he started in 95, 96, all these alumni come back to just to meet other alumni and talk about how Dr. Wargo has sort of, you know, helped them in their career and stuff. And we help each other and it's, we just want to share it through the, through the nonprofit and try and get other teachers to realize what, you know, change agent they can be at the high school level when you start.
Steven Strogatz (53:17)
This is a really
good story. So first of all, that we keep referring to Dr. Wargo as dark doctor is itself something I would like to know more about. There aren't that many. You teach at a high school, is that right?
Jacob Beckey (53:28)
This is true. is true.
Yeah, ⁓ Wartow, would you like to take this one or would you?
Brian M. Wargo (53:30)
Yeah.
Steven Strogatz (53:32)
So, yeah, just
tell me for a minute, because I want to tell you about my old teacher.
Brian M. Wargo (53:35)
I'll let you. I'll let you.
Jacob Beckey (53:37)
Yeah, we're gonna be uncomfortable. So this is another synergy though with what you were talking about, I believe now that I have them a little mixed up, it's one of the books I've been reading ⁓ of yours. And talking about your first research project, having something to do with understanding DNA and had having some background in x-ray crystallography. I thought that was a great synergy as well because yeah, Dr. Wargo did his master's in x-ray crystallography. So as a master's in physics, and then when I had him in high school,
Steven Strogatz (53:47)
Hahaha
Yes.
really?
Jacob Beckey (54:03)
He was about to defend his PhD in science education at University of Pittsburgh. And the expertise is directly in having students engage in science and engineering practices in the high school, in the secondary classroom.
Steven Strogatz (54:08)
⁓ okay.
I see, wonderful, wonderful.
That's really what these teachers, when I said that my ⁓ freshman year in high school, we were supposed to do these physics style experiments, ⁓ there were teachers there who really should have or could have been PhDs themselves. They weren't, they had master's degrees, some of them. ⁓ My one main mentor, my teacher, Mr. DiCurcio.
really was a natural college professor. His life didn't work out that way. for my, I mean, it was great for me because I had him teaching me in high school. And I can remember, I've told this story in one of my books that when I was reading about Einstein one time in like my junior or senior year, and I was sitting at it, like I say, it was a boarding school. So we would eat dinner together sometimes. I was sitting next to him.
at a table and he's there with his family and other students sitting around the table. ⁓ I said something about I really want to teach myself multivariable calculus because this is what I would need to understand Maxwell's equations and Einstein was very, you know, of electricity and magnetism and Einstein was very impressed with them and I would like to learn what they are. And Mr. DiCercio said, you want to see them right now?
And I said, what? And he just started writing them down on the placemat or something, you know. Then started speaking in tongues. Divergence of curl is grad div minus del squared. you know, or no, curl of a curl is grad div minus del squared and blah, blah. And then you get the wave equation. And from this, see that E and electricity and magnetism can propagate at the speed of light. And I just couldn't believe it. Like he's deriving the whole thing for me in real time at the table because he was so
such a superior mind who spent his life devoted to young people teaching. I mean, this is what a great high school teacher like you can do. And that's really, you know, such a secret weapon. If we could have more people like you, you know, think of what a multiplier, it sounds like these reunions, you have all these students coming back, you've changed so many lives. So congratulations, and we're happy to have people like you in the business.
Jacob Beckey (56:20)
100%.
Brian M. Wargo (56:33)
There's a couple of things. First of all, our big event is we have our science conference at the end of the year. And it's a true science conference, and you can only present original research. Every student's been working all year doing that. Well, the alumni come back on that day. And we might have like 25 that come back to see what the young kids are doing and to help along. And we realized that they never got to speak to one another because they're so excited about helping the younger students that we needed to have one
It's like the day before Christmas, which is crazy, but people still show up, right? And then that way we don't let students come so they can finally talk to each other. But out of many of these, you know, I think a lot of them, a lot of people that we talked to, they're like, I would love to teach. I can't afford it. And this is what ⁓ Becky was talking about. Like you go into university and if you don't do it right, you could be in real debt. And so now
Steven Strogatz (57:09)
No.
Uh-huh.
Brian M. Wargo (57:32)
I have to get a job and I have to get a job that pays me enough so that I could pay off that debt. ⁓ We are not doing it right in America. We should be investing in our teachers, in our schools, but you can't come out with $100,000 in debt and become a high school teacher or a middle school teacher. mean, how are you gonna pay that off? How are you gonna have your own kids?
Steven Strogatz (57:53)
Absolutely.
Brian M. Wargo (57:59)
Until we can really take care of that problem, we're probably not going to have very many of maybe our most enthusiastic or highest flyers coming back to school. Not that they don't want to. They can't, they literally can't afford to teach.
Steven Strogatz (58:14)
Mm-hmm.
Mm-hmm. Very important point. Great point. And sad.
Brian M. Wargo (58:18)
One of the things that we're trying
Jacob Beckey (58:18)
Yeah,
Brian M. Wargo (58:19)
to do with our nonprofit,
Jacob Beckey (58:21)
it's sad indeed.
Brian M. Wargo (58:21)
if we can build this and gain capacity, we would like to start supporting science teachers that might not be able to go back. Imagine if we could help them financially to say, like, look, we'll take care of some of that debt for you if we can get you into the classroom. You know what mean? And I think...
Steven Strogatz (58:43)
Uh-huh.
Brian M. Wargo (58:44)
You know, it is unusual to have advanced degrees at the high school level, but I don't think that's typical worldwide. I think many other countries, you expect that. I think ⁓ that is something that we should really consider. What do we want out of our schools and how do we achieve those goals?
Steven Strogatz (59:02)
Well, maybe a more positive note about this, because I think you're really on the mark with this. There is an organization that agrees with you and that has the money to help called the Simons Foundation. So there is maybe, Jacob knows about this, or maybe you all both do, a program called Math for America. So Math for America through the.
Jacob Beckey (59:14)
Silence Foundation.
Steven Strogatz (59:28)
the ⁓ philanthropy of Jim Simons and Marilyn Simons is a program that does a lot of the things that you, Dr. Wargo, just suggested for math. Now, we could do it for science, too, that they will help teachers get master's degrees. They fund them. They will have a special category of what they call master teachers who then teach other teachers some of the techniques that they've developed.
And this is, as you say, around the world. In Japan, for instance, there's a whole culture of master teachers helping other teachers improve. ⁓ And also constructive feedback. I nobody's an expert on everything. So we can all help each other get better. But we need to respect teachers more, expect more of them, reward them appropriately. These are the people that teach our children. You'd think it would count for something.
Jacob Beckey (1:00:20)
Well,
and ⁓ it should be viewed as an investment as well, it is, in fairness, hard to quantify the return on that investment. But I also think that you can make very strong arguments on purely economic basis that it would be money extremely well spent. ⁓ The Simons Foundation, the difference, there's really only one difference between them and us. it's about
Steven Strogatz (1:00:40)
Mm-hmm.
Jacob Beckey (1:00:48)
$10 billion or something. But if we were just, we're right on their heels. But yes, now ⁓ the Simons Foundation for listeners that don't know this organization, Jim Simons was a mathematical physicist that then went on to sort of start the quant revolution in the financial markets. And he was the first to
really do quantitative finance at scale and as a result more or less printed money for about three decades and fortunately put that to very good use to fund education, to fund autism research and many other fantastic things. It is a great model. It's one we're trying to do on a smaller scale with our teacher fellowships
that would be really great.
Brian M. Wargo (1:01:30)
One of the things
that we need to really keep in mind though is we've got teachers that have been taught in this traditional fashion and it's just been handed down. You walk into most math classes and it's really decontextualized. mean, they're afraid, they feel such terrible pressure to only do content. They never have a chance to bring in the history or make the connections to science. They feel this terrible push.
Steven Strogatz (1:01:41)
Sure.
Brian M. Wargo (1:01:59)
I've got to get the students to this point so they can go on to their next class. So one of the things that I think you're doing in some of the videos that you were talking about, one of the things we're trying to do is here, try these things. Maybe you don't have access to going for a master's or something like that. Watch these videos and try to engage your students in dialogue the next day. You don't need a degree for this. Just try it. Because once you can get, because let's face it, a lot of teachers are quitting.
Steven Strogatz (1:02:22)
Mm-hmm.
Brian M. Wargo (1:02:28)
within the first five years. mean, the attrition rate is terrible. we need to have them have success, get students instead of fighting mathematics saying, no, no, no, this is something that I can find joy in.
Jacob Beckey (1:02:41)
⁓ Okay, so maybe because I think anytime we go down a tangent on ⁓ some of the shortcomings of our education system, it can be pessimistic. We should end on a high note. ⁓ This whole season we're having on authors, great science and math communicators to talk about ⁓ the importance of including nature of science and math and history into the classroom. And so one of the things that we wanna ask is like,
So Dr. Wargo is an avid birder and he told me this concept of a spark bird, birds that ignited your interest in birding. ⁓ And so we started just referring to them as spark books. What is your spark book that was like, you read this and it changed for me. It was Cosmos by Carl Sagan when I was younger. And I'm just curious if you have a book that comes to mind. ⁓
Steven Strogatz (1:03:30)
Well, there is one, but it doesn't exactly qualify because it's four volumes. So it's a series of books and it was called The World of Mathematics. So you can probably find it still. It was four volumes and it was a collection of essays by mathematicians or by math teachers talking about math.
All aspects, math and music, math and history, pure math, applied math, math of warfare, math of weather prediction. But the thing was, it wasn't textbook-y. You would read Heisenberg talking about the uncertainty principle and how did he discover it, or Ramanujan and the story of Hardy discovering this great genius from India and the work they did together.
Brian M. Wargo (1:04:00)
you
Jacob Beckey (1:04:02)
That's the end.
Steven Strogatz (1:04:24)
and or Poincaré, you know, thinking about topology of higher dimensional spaces in their own words. And these were very carefully selected essays that were really well written and inspiring and fun. ⁓ And so I used to sit in the library in the 1970s when I had time and just go back to the same spot in the library and pull out one of these volumes of the world of mathematics and just pick a random essay and start reading it. ⁓
I loved it. yes, that book, and I even mentioned it to my parents and they, for graduation present, got me these four volumes. I probably added up to, I don't know what, it wouldn't have been cheap because it was four books, but ⁓ I still have it. It's really great. Yeah, definitely a life-changing spark for me.
Jacob Beckey (1:05:12)
That's fantastic. I'll have to
see if I can, can you remind me the title?
Steven Strogatz (1:05:17)
World of Mathematics by James R Newman. Yeah, I think R is the middle initial. But anyway, James Newman, it's a 1950s vintage series. It's not cool. It's not, you know, it's really old school, but it was good.
Jacob Beckey (1:05:18)
Word of Netflix.
Mm-hmm.
Yeah.
That's fantastic.
That's fantastic. ⁓ And I want to be mindful of your time, but one final question maybe is, as teachers, so one of the things we see with a lot of teachers that we work with is a lot of pressure from administration, as we said, to get content, content, content. So if we're trying to encourage them to make small steps in their classrooms to start bringing in more of these inspiring methods of storytelling, like you mentioned, and getting
you know, their students actually hooked on math rather than seeing it as something, you know, that they should be fearful of. ⁓ Do you have any, you wisdom you might impart to a young teacher trying to dip their toes into this whole world of teaching?
Steven Strogatz (1:06:13)
⁓ Hard to know what to say because I you know, even the way that we're phrasing the question We don't want a short change content either, right? I don't want anyone coming away from this discussion thinking we're trying to as they would say dumb it down Soft or any that you want to feel technically strong. You can do every problem in the book But there's more
Jacob Beckey (1:06:28)
No. Yeah.
You're
right.
Steven Strogatz (1:06:37)
There's the question of why. Why am I doing this? What is this good for? Why did people think of it in the first place? How did it change the world? Because all these things really are world changing. And that will make you want to master the content. So these are not fighting each other. I want it all. I want the context and the content. I want them both. And now, of course, the schedule's already packed. So now I'm saying I want even more from the teachers and the students.
And what can I tell you? Yes, I do. I do want more. So what's got to give? Well, maybe less time on TikTok. ⁓ I don't know. If you don't want to do it, don't do it. But I think you'll love it once you get into these things, these feelings of strength and interconnection. All of school will become more interesting for you. I mean, obviously, if we need to say it.
Jacob Beckey (1:07:08)
Yeah.
Mm-hmm.
Brian M. Wargo (1:07:24)
That's it.
Steven Strogatz (1:07:33)
this is a road to high paying careers. know, the person who has mastered math and science, the world is your oyster, whether it's quantitative finance or high tech or biotech or, you know, and if those aren't your thing, that's okay too. There's a lot of great stuff to do with your life, but ⁓ just like, you know, I said earlier that loving music doesn't mean you have to become a professional musician. think everybody can benefit from seeing
Brian M. Wargo (1:07:36)
Yes.
Jacob Beckey (1:07:37)
It's important, yeah.
Absolutely. Yeah.
Steven Strogatz (1:08:03)
these great things that people have thought of in the past and what they've done for our world.
Jacob Beckey (1:08:08)
Absolutely. Yeah, think a lot of what you said. Yeah, yeah. Fantastic. Awesome. Well, thank you for taking the time. It's really, it's an honor. I have looked up to you as a researcher and as a ⁓ expositor for a long time. it's fantastic to meet you virtually. And thank you for sharing some of your insight and stories about these things. I think.
Brian M. Wargo (1:08:09)
I don't think we could say it better. Yeah, that's perfect.
Steven Strogatz (1:08:29)
very very kind of you.
Well, thanks to both of you. I mean, you guys are very inspiring to me. I love hearing this story because it does remind me of my own story. And I think it's probably a story replicated all around the country and the world of a teacher and a student and people who are just very genuine in their love for learning and how far it's taken them. I wish you the best in your career, Jacob. You're off to a great start. And Dr. Wargo, keep it up,
Jacob Beckey (1:09:00)
Thank you very much.
Steven Strogatz (1:09:04)
You're an inspiration. I love what you're doing. So this has been fun. Thank you very much.
Brian M. Wargo (1:09:07)
Thank you for, thank you and
thank you so much for writing so well.
Steven Strogatz (1:09:11)
Ha
Jacob Beckey (1:09:12)
Yes, awesome.
Brian M. Wargo (1:09:12)
Alright, very good.
Steven Strogatz (1:09:14)
All
right, bye everybody.