Jad: Hey, I'm Jad Abumrad.
Robert: Hi, I'm Robert Krulwich.
Jad: This is Radiolab. Our topic today is-
Robert: Mathematics, mathematics, and mathematics.
Jad: I suppose that is our topic, but actually we do have a gripping story for you coming up now from our producer, Soren Wheeler. Hey, Soren.
Jad: This is about math, right?
Soren: Yes. Well, math and friendship really. I heard it from Steve Strogatz. He's a mathematician at Cornell University and he's been on the show once or twice. We sat down in the studio and he told me about, "Why don't you back up and tell me a little bit about high school and about--" his high school math teacher Don Joffrey.
Steve: Well, there were several striking and peculiar things about him. Probably the first thing is that he was physically incredibly impressive. When he would hold the chalk between his enormous fingers and write on the board, the chocolate pulverize with each stroke so that there'll be this cloud of chalk dust all over him and his big sweater. Another thing that was very unusual about him, he'd be in the middle of the calculation, standing at the board, chalk dust all over him as usual, then he would space out. He'd get a look in his eye, a far away look, and then he'd say, "This reminds me," with a hushed tone. "This reminds me of the time Jamie Williams calculated the formula for nth term in the Fibonacci sequence."
Jad: Who's Jamie Williams?
Soren: Jamie Williams was a student. He was just a couple of years ahead of Steve in Mr. Joffrey's class.
Steve: That was part of the mystique, that now he was graduated and it was as if the secret was lost to the ages. The point was that he would talk about a student.
Soren: With reverence.
Steve: With reverence. What was very thrilling about that is that there was this kind of chain that we were now becoming part of. Then I'm off to college and it started very early. I started to write to him. It was an annual tidbit. "Dear Mr. Joffrey. Here's the gym that I learned this year in math."
Soren: Steve would write to him, Mr. Joffrey would write back, add something, ask him a new question. It went on like that for a while, with Steve still being like a student and Mr. Joffrey still like a teacher.
Steve: There was one moment though, where something new happened, where he wrote to me asking for help. He said a question came up in his class about an elliptical swimming pool. Picture a swimming pool. Often there's a little border on the edge of the swimming pool like a piece of concrete that lines the pool. You stand on that part before jumping in. The question was, if you had an elliptical swimming pool with a one-foot border around it, is the outer edge of the border also an ellipse? Something about that really appealed to me. It was a very nice math problem. Probably there was a little bit of a show-off in me. I thought if I could do this, he's going to say something nice.
Soren: You'll become part of the pantheon?
Steve: Yes. Maybe I'll enter the Pantheon. They'll start talking about me like they used to talk about Jamie Williams. I stopped whatever I was doing and I worked hard on that ellipse problem. I figured out two or three different ways. It turns out it's never an ellipse. It cannot be an ellipse.
Soren: Steve sat down and wrote back to Mr. Joffrey about this puzzle, but-
Steve: I didn't just show him the answer. I wrote the answer in a very loving and gentle way that was meant to be empathetic. That is, I know where you're coming from and I'm going to just start from scratch to lead you from where you are, to where you need to be to solve this problem.
Soren: In other words, Steve acted like he was the teacher and Mr. Joffrey played along.
Steve: This was such a generous thing in retrospect, the humility, the modesty, the kindness in playing the role of the student. It's like he knew that that's what I needed. Man, I loved it. I couldn't wait for the next question.
Soren: As Steve went off to graduate school to become a math professor himself, he and Mr. Joffrey kept writing to each other. In fact, they were writing to each other quite a lot.
Steve: There was one sequence in March of 1989 where we wrote to each other almost every day. He sent me puzzle, I worked on it. I showed him a really beautiful answer. He expressed ecstasy in seeing this answer.
Soren: It was a mathematician's dream correspondence of puzzles and equations, and Steve loved it. Every so often Mr. Jeffrey would break the routine.
Steve: A little bit. He would say things about that he was doing some jazz piano gig. He had three sons. He would talk about them a little bit. I feel embarrassed. It feels mean, but I remember not liking those parts of the letters. I didn't write about that. I would say maybe I was playing some tennis but I have lines in some of my letters that say after a few of those sentences, "Enough stalling, here's the math problem." Then in later years he would almost pointedly ask me things, like there was a time when he said that, "Rumor has it that you're engaged. We wish you the best if this is true."
Steve: Guess what? In my letter back to him I didn't say anything.
Soren: Do you remember thinking not to respond?
Steve: Well, I can tell you what was going on, which is that I was already in couple therapy with my fiance. In that time the letters were a refuge from all that. That is, we could go into this pristine world of math where things are simple and logical and well-ordered. There may have been part of me that felt like, "Come on. This is the one place where it's all perfect."
Soren: Over the years, that perfect world got a little less perfect.
Steve: His oldest son died. Marshall died. Marshall died when he was only 27 and I didn't ask about it. Can you believe this? I feel so sick about this when I think about it now.
Soren: You would just write back, " I've got another puzzle."
Steve: "Got another math problem for you. Look at this."
Soren: Then more than 20 years into this relationship with letter writing Mr. Joffery retired, and now that he couldn't teach anymore-
Steve: -He'd write to me. He'd show me these beautiful math problems that he would make up for hiself, usually about hawks flying over the earth and how much spherical area can the hawk see if it's at such and such altitude. What is happening at this time is that now I have just gotten married and we've started having kids and I'm not answering his letters anymore. They're sitting in their envelopes stacking up. He's writing them faster than I can answer them, a lot faster. Then at one point, I got one more letter from Mr. Joffrey. Except as soon as I looked at the envelope, I could see that something was really very wrong.
His handwriting didn't look normal. My address, my name was written in a craggy, shaky. I knew what that looked like because my dad wrote like that when he had Parkinson's. I thought, "What's this?" I opened the letter and the first sentence is, "I just had a mild stroke." I didn't write back to him right away. I didn't call him.
Soren: Then just a couple months later-
Steve: My brother died very suddenly. He heard about it from someone else and immediately wrote to me that he and his wife had heard and they were very sorry to hear that my brother had died. I still had never said I'm sorry about Marshall all those years ago. It kept nagging at me, "Why won't you to talk to him." I obviously care about him. It's like in math there's this concept of bifurcation, which really means a fork in the road, a splitting. When the forces on a system get too large, there can be a moment when the dynamics of that system change abruptly and qualitatively.
This was a moment of bifurcation. I should have just said how sorry I was to hear about Marshall. I thought, "I got to go talk to him," and asked him, "Can I come to your house?" He seemed a little reluctant about it, but said, "Fine." I bought a little pocket tape recorder, just a cheap thing. Drove up route 95 to his house in Connecticut on the shore and knock on the door. I hear the piano that was playing inside stop. He comes in rushes to see me. We give each other hugs, take out a big plate of cold cuts and say, "Let's sit out on the porch."
Does that work? Hello? We're eating and it seems to be recording. Then he takes out his journal-
Don: I decided that I would keep a journal since I was retired.
Steve: -where he's drawn pictures of all kinds of birds.
Don: Here's a picture of me doing an eagle watch out in the Connecticut River.
Steve: There's a lot of stuff about-
Don: Hank and his typical ways of discovering things.
Steve: -people I don't know.
Don: This is a bird that's moved up from the South too. You never saw these, well, what some people call buzzards. They've moved up here. This is one of my favorite birds. It's a marsh hawk and it flies low over the meadows. More about that. Hank says, "I'm going to take you over to see a rough-legged hawk." He didn't say, "we're going to see if we can see a rough-legged Hawk." He produced.
Steve: I'm thinking to myself, "I'm not really interested in this. I want to talk about him about all these things that we never talked about that are emotional hard things like 'What happened? How did your son die?'"
Don: -of a lot of work. They're just trying to make guys put in extra hours to pay guys extra hours.
Steve: There was a fidgeting feeling inside me.
Don: -and benefits and all of the other stuff.
Steve: There was a pause. My heart was beating fast. Then I thought, "I'm going to ask him now." I don't think we ever talked about Marshall, but I wanted-- Then I did, I asked. I didn't really know him either, but I know that he died very young, what happened? What happened to Marshall?
Don: Well, that's-
Steve: You don't want to talk about that? I think he was going to say, "That's something we don't talk about." I remember him as a star.
Don: He had a wonderful 27 years, music was going to be his thing.
Steve: It was so beautiful, so uplifting, and sweet.
Don: He'd be at home and we'd sit around the piano, and I'll get out the Cole Porter songbook, and just turn to a page. Something that he'd never seen, he could cite, read it, play it and sing it all at one time with us. I thought, "God, this guy has got a multichannel mind that I wish I had."
Steve: He talked about what a great life he had in his 27 years.
Don: Even in his waning moments, he'd stay up all night long playing the piano, just the house would just fill with beautiful music. He had made plans to get a job at the New England Conservatory and things like that, but the fates were wrong for him. We miss him.
Soren: In that moment, did it change the way you see him?
Steve: I have to tell you how that day ended. We talked more and asked him at one point, "Do you think Marshall had a religious feeling?" And he said-
Don: Yes, I think he felt close to having to come to terms with somebody out there. That was a good thing, that I think he went peacefully.
Steve: Then the actually conversation drifted to ease or things like calculus problems. We talked some more about math, and then he said, "How about a swim or let's go to the beach."
Don: How would you like to go out to the beach?
Steve: Yes. I would do something where I get outdoors a little bit. We did go to the beach, and it was a beautiful evening and there were waves coming in from Long Island. In fact, we were talking about a math problem about waves, about Fourier analysis. Which is really about infinity and the fact that.
Soren: If you take an infinite number of simple waves, you can create any shape of wave you want,
Steve: As long as it's a wave that repeats.
Soren: Then Mr. Joffrey asks, "How do you create waves that don't repeat, waves that change?"
Steve: Sometimes waves don't exactly repeat. They can grow or die out.
Soren: Steve told him that to deal with those kinds of waves, you need a different kind of infinity. Not the kind where you just keep adding and adding and adding numbers, but the kind that sits in the space between two numbers.
Steve: This higher kind of infinity than Don had thought about before.
Robert: Thanks to Soren Wheeler, our producer who interviewed Steve and produced that story.
Jad: Thanks to Steve Strogatz, who has a book out now which tells this very story, called The Calculus of Friendship. I'm Jad Abumrad.
Robert: Three seconds to go.
Jad: You are?
Robert: Robert Krulwich.
Paul Hoffman: I'm going to leave some credits for you. This is Paul Hoffman. Radiolab is produced by Soren Wheeler and Jad Abumrad. Our staff includes Michael Rafiel, Ellen Horn, Jonathan Mitchell, and Lulu Miller, with help from Adits Narayan and Tim Howard. Special thanks to Ben Calhoun, Steven Vitello, Ron Graham, Ike Sriskandarajah, Ted Gibson, Amanda Aronchick, Rob Replay, [unintelligible 00:15:08], David Krulwich, Ken Baum and Eric Cherries. Thanks.
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