In our first math episode, Dr. Amites Sarkar speaks with us about mathematical concepts that took the human race millennia to understand. On the other hand, the amazing things people in history did accomplish is mind blowing. Lastly, we discuss the similarity between Erdos numbers and Bacon numbers.
[♪ Blackalicious rapping Chemical Calisthenics ♪]
♪Here we go
♪ Neutron, proton, mass defect, lyrical oxidation, yo irrelevant
♪ Mass spectrograph, pure electron volt, atomic energy erupting
♪ As I get all open on betatron, gamma rays thermo cracking
♪ Cyclotron and any and every mic
♪ You’re on trans iridium, if you’re always uranium
♪ Molecules, spontaneous combustion, pow
♪ Law of de-fi-nite pro-por-tion, gain-ing weight
♪ I’m every element around
Jordan: Welcome to Spark Science, where we explore stories of human curiosity. I’m Jordan Baker: professional improviser, scuba diver, uh . . . science . . .
Dr. DeGraaff: Enthusiast?
Jordan: Host. Nah.
Dr. DeGraaff: [Laughing.]
Jordan: Let’s not go that far!
Dr. DeGraaff: Right. That’ll be like 5 years from now.
Jordan: Right, yeah, once I feel like I know something at all.
Dr. DeGraaff: Yeah.
Jordan: And I’m here with Regina Barber DeGraaff.
Dr. DeGraaff: Yep. That’s me. I teach physics and astronomy at Western Washington University. I am an astrophysicist and a pop-culture enthusiast. And I have seen Jordan improvise; I finally went – listeners – I finally actually went to his show. He’s great; I’m a little biased.
Jordan: Right. You sound like my grandma.
Dr. DeGraaff: [Laughing.]
Jordan: After she saw one of my shows, she was like, “I loved everything that you did.”
Dr. DeGraaff: Right. [Laughing.]
Jordan: Thanks, grandma!
Dr. DeGraaff: But I think, our listeners, if you are in Bellingham, you should definitely check out the Upfront. Jordan’s usually on Thursdays and Fridays?
Jordan: Thursday, Friday, Saturday.
Dr. DeGraaff: Yeah.
Jordan: Depends on my work schedule.
Dr. DeGraaff: Right. Maybe we should tell listeners when you’re on on Facebook in the future.
Jordan: Yeah. Absolutely. Everybody should come see comedy. I mean, everybody likes to laugh, right?
Dr. DeGraaff: Yes. You know, and I think comedy is essential to people’s lives, really.
Jordan: And I think maybe you should watch more of it instead of maybe your TV shows. I mean, this is like a TV show that you’ll never ever ever see again.
Dr. DeGraaff: Wait, are you making fun of my TV!?
Jordan: No.
Dr. DeGraaff: Don’t go see Jordan!
[Laughing.]
Jordan: My goodness.
Dr. DeGraaff: How dare you? Alright well, today, we are gonna talk about the history of the math. And we have with us today an awesome guy, another Western professor, a colleague of mine: Dr. Amites Sarkar. Is that right?
Dr. Sarkar: Yep. Absolutely. Yep. Hi.
Dr. DeGraaff: How’s it going?
Dr. Sarkar: It’s going very well; yeah!
Dr. DeGraaff: And he’s actually seen maybe at least . . . or listened to one of our shows.
Dr. Sarkar: Mhmm. Yeah. [Laughing.] That’s right.
Jordan: Wasn’t he there for the Pluto reveal?
Dr. DeGraaff: Yeah. He was.
Jordan: So yeah. That’s technically . . . you’ve listened to it.
Dr. Sarkar: I’m a veteran!
Dr. DeGraaff: Yeah. You know exactly what’s gonna happen. Well, so, we’re gonna talk about basically the history of math. You teach a class on this?
Dr. Sarkar: Yes. Yes. In fact, I taught it today!
Dr. DeGraaff: Did you really?
Dr. Sarkar: I teach it quite a lot and I enjoy it very much.
Jordan: That’s incredible.
Dr. DeGraaff: Yeah! So you’re on it. You’re gonna answer all these questions. It’s gonna be great. Is it a very popular class?
Dr. Sarkar: It is, actually. It’s surprising.
Dr. DeGraaff: [Laughing.] You’re a mathematician. You’re like: “oh my God!”
Dr. Sarkar: You walk into a classroom and it’s full of people, but, yeah, people are interested. And at the beginning of the quarter, I asked them, you know, what are they interested in specifically. And I get all of these different answers. So it’s interesting.
Dr. DeGraaff: Right, other than just a plain like “math.” They don’t say that.
Dr. Sarkar: Yeah. I think some of them are taking it because they need to get a writing proficiency requirement, but they’re very polite about it. So I’ll try and listen to them all say what their interests are, and then I’m kind of speechless for a little while because I’m sort of happy that they are interested and it’s hard to respond to 20 interested people at once.
Dr. DeGraaff: I do want to let our listeners know is that, one of the first times I met Amites, it actually asked me, “oh! I’m actually interested in astronomy. What did you do?” And I was taken aback. I was like “somebody’s actually asking me what I did and from my research and they’re interested?” So I wanna thank you for that. That was really nice.
Dr. Sarkar: Sure. But I wasn’t faking it. I really was…
Dr. DeGraaff: [Laughing.]
Dr. Sarkar: The trouble with science is that it’s actually too interesting. Because if you’re a scientist or a mathematician, you’re supposed to be doing just one thing, like writing a paper, but then you get side-tracked. You have a conversation with someone. You think “oh. I’ll look into that.” Or you go to a conference and think “I’ll look into that.” And then, sooner or later, you haven’t done any grading; you haven’t prepared your classes. You haven’t written your paper.
Dr. DeGraaff: Right. Yeah.
Dr. Sarkar: You’ve done nothing. And, you know, so that’s . . . so it’s too interesting. That’s the problem with math.
Dr. DeGraaff: I wanted to ask you about yourself. Where did you grow up? I know our listeners will hear you’re our first accented guest, which I’m super-excited about. Where are you from? Why did you come to Bellingham? And what do you do, research-wise? And then we’ll get into, like, the history of math.
Dr. Sarkar: Yeah. I was born in London. And I actually had an Indian accent until I was 13. My parents sent me away to a boarding school and I got this posh accent.
Dr. DeGraaff: [Laughing.]
Jordan: Wow!
Dr. Sarkar: I came to Bellingham . . . if you’re an academic, you apply to jobs all over the place. And Bellingham, Western was one of the places that I applied to. Out of all the places that I got jobs, it was by far the best and I absolutely love it here.
Dr. DeGraaff: Really?
Dr. Sarkar: So I’ve been here for 8 years and I think it’s great, yeah.
Dr. DeGraaff: Did you go to undergrad in London?
Dr. Sarkar: In England, so in Cambridge, and then I did a PhD there as well.
Dr. DeGraaff: You went to Cambridge. You came here. Where did you go for grad school?
Dr. Sarkar: Also Cambridge.
Dr. DeGraaff: Just Cambridge all the way through!
Dr. Sarkar: But the whole thing was wasted on me. I mean, you’re walking around these quadrangles where Newton and Maxwell and all these people . . .
Dr. DeGraaff: Yeah! Right?
Dr. Sarkar: But you just think “yeah, yeah . . . Newton, Maxwell.” And now I think, “Wow! Newton and Maxwell.” I should’ve been kind of like, you know, taking mental photographs of every step I took.
Dr. DeGraaff: So let’s get to the history of math.
Dr. Sarkar: Mhmm. Yeah.
Dr. DeGraaff: So like how do you bring your students into this course? Like what’s the beginning of this course like?
Dr. Sarkar: Well, the beginning is like I ask them what they’re interested in. But very soon after I’ve got their very sophisticated responses, I just ask them to write down what mathematics is.
Dr. DeGraaff: Right.
Dr. Sarkar: So I give them index cards and I say, “well, write down what you think mathematics is.” I get 20 completely different answers. But they’re all very well-thought-out things. And I compare them with the dictionary definitions, which are almost always much more boring.
Dr. DeGraaff: Right.
Dr. Sarkar: And then we talk about just what mathematics has been throughout the ages. Because the meanings of words change.
Dr. DeGraaff: Right.
Dr. Sarkar: This is one of the things I bring up. The meaning of the word “mathematics” has certainly changed. That just gets us into thinking about mathematics before getting into the kind of “it began with the dinosaurs” kind of thing.
Dr. DeGraaff: When the dinosaurs were doing algebra!
Dr. Sarkar: It’s always nice to kind of start off and just not go straight into it.
Dr. DeGraaff: What are some of the definitions that they give you, like, some in your memory that have stood out?
Dr. Sarkar: Yeah. They sort of say things that it’s about ideas, which, of course, always pleases me a lot. So it’s about ideas and the connections between ideas. Some of them go completely overboard. The more overboard they go, the more exciting it is. Like “it’s about understanding the meaning of life” and all this stuff. And some of them are much more kind of like down-to-Earth and say it’s about numbers and patterns and shapes and connections and logic.
Dr. DeGraaff: Right.
Dr. Sarkar: So there’s a whole spectrum.
Dr. DeGraaff: Well how big is the index card? You need to give them smaller index cards.
Dr. Sarkar: Yeah. I give them a [inaudible.] But some of them write, fill the whole thing, you know. And some of them just write, I don’t know . . . well they just write some very short thing.
Dr. DeGraaff: Right. “Math is math.”
Dr. Sarkar: Mhmm.
Dr. DeGraaff: Have you ever got that one?
Dr. Sarkar: I’ve never got that one. But they’re all kind of fresh for the quarter so they’re trying to be in a good mood and trying to impress, not me, maybe, but trying to kind of just take it seriously.
Dr. DeGraaff: And you were saying the idea of mathematics has changed. So how has it changed?
Dr. Sarkar: Yeah. I think now, much more, it’s somehow . . . maybe it was a more practical thing in the past. Maybe people were only doing if there was some pressing need to do it. Although, always there’s been this theoretical aspect.
Dr. DeGraaff: Yeah.
Dr. Sarkar: But I think, for example, in the 19th century, it was tied very much more to kind of specific areas of study.
Dr. DeGraaff: Right.
Dr. Sarkar: And now, somehow, you know, there’s mathematics in lots of different areas. And people have sort of expanded the definitions to include really any type of chain of precise reasoning is now called mathematics.
Dr. DeGraaff: Okay.
Dr. Sarkar: Whereas before, it would have had to have been about calculus, or geometry, or algebra, or something like that.
Dr. DeGraaff: Okay.
Dr. Sarkar: So it’s become a more kind of soft definition, rather than tied to a specific thing.
Dr. DeGraaff: Yeah. I do not understand the soft definition either, I mean, so maybe I should take this class. I could sit in.
Dr. Sarkar: You’d be very welcome.
Dr. DeGraaff: Then what do you get into? Do you get into people of history? Or do you get into ideas of history?
Dr. Sarkar: Yeah. Both actually. I try and weave the 2 together. But one of the things is that access to information is everywhere. Unlike when I was a child, if you want to go and find out about Newton or Leibniz or Descartes, you can just go and look up about Newton or Leibniz or Descartes. So I try and keep it, you know, I’m not gonna go through these mathematics in this order, but I try and weave it into one story, which is difficult because it’s a pretty long story.
Dr. DeGraaff: Yeah.
Dr. Sarkar: And I only have got 30 classes. And I want to involve the students as well. So it shouldn’t just be me talking. So I have various discussion topics. But I try and find some kind of theme. You know maybe like, this is: we’re gonna talk about equations for a while. And now we’re gonna talk about, you know, geometry for a while.
Dr. DeGraaff: Yeah.
Dr. Sarkar: And just how geometry has changed, and also how maybe how the Greeks . . . just the paradoxes that the Greeks couldn’t resolve. Like, they couldn’t resolve Zeno’s Paradox and just talk about, you know, how this looks from a modern perspective.
Dr. DeGraaff: Okay. What’s Zeno’s Paradox?
Jordan: I don’t know why they couldn’t figure that one out, heheh…
Dr. Sarkar: Yeah. So Zeno’s Paradox is . . . So, Achilles and the Tortoise… So, they’re running a race and the tortoise starts ahead, but it’s going more slowly. And the idea is that when Achilles has got to where the tortoise started, then the tortoise has moved on.
Dr. DeGraaff: Right.
Dr. Sarkar: And then so when Achilles has caught up with the tortoise then, the tortoise has moved on a little bit further . . .
Dr. DeGraaff: But he’s going slower.
Dr. Sarkar: He’s going more slowly, so, of course, we know he’s gonna catch up. And it’s second-nature to students now to visualize graphs of Achilles and the tortoise. But for the Greeks, somehow, this was a paradox. And so, it requires a bit of brain rotation to figure out why it was a genuine Paradox to them, and they couldn’t just say, “well, look; these graphs cross.”
Dr. DeGraaff: Right.
Dr. Sarkar: And so sometimes the thing is to put yourself in the shoes of people who thought in a different way. So, they didn’t have zero. They dealt with fractions in a different way. They didn’t have algebra.
Dr. DeGraaff: Yeah.
Dr. Sarkar: So, all this stuff, I mean, and you can really . . . it’s really quite mind-expanding thinking about how they thought of these things. But you can’t do that too much otherwise you never get very far.
Dr. DeGraaff: Well you’re amazing me about this graph. Because, when you said that, it’s funny that I instantly did go to the graph in my head. I mean this is just the way we were taught. This is how we were raise in university to think in these graphs.
Dr. Sarkar: Mhmm.
Dr. DeGraaff: But when did that start?
Dr. Sarkar: Yeah; with Descartes, I guess. Descartes had the idea of sort of combining algebra and geometry.
Dr. DeGraaff: Okay.
Dr. Sarkar: And actually it’s a coincidence for me because, just today, one of my students is doing a paper on Descartes and she brought Descartes’ book: La Géométrie with her and it had the French and the English. And we were looking through trying to find out where this idea of drawing graphs of equations comes from.
Dr. DeGraaff: Yeah!
Dr. Sarkar: And the original context was amazingly complicated. It was a problem of Pappus. You have 5 lines. You have a point. You want to draw lines to those 5 lines, making various angles and so that the distances have a relationship, so, an incredibly complicated problem.
Dr. DeGraaff: Wow.
Dr. Sarkar: And that’s the problem that sparked Descartes to have this, nowadays, very simple idea of drawing a graph.
Dr. DeGraaff: So what year was this exactly?
Dr. Sarkar: This was 1637.
Dr. DeGraaff: Okay.
Dr. Sarkar: And so this book was an appendix to this famous book: Discourse on the Method, where he says “Je pense, donc je suis.”
Dr. DeGraaff: I don’t . . .
Jordan: Oh, yeah!
Dr. Sarkar: It means “I think, therefore I am.”
Dr. DeGraaff: There we go!
Dr. Sarkar: But then this preface was actually kind of . . . this is the famous thing that everyone reads about it in philosophy. But it was actually just a preface to 3 books, one on optics, one on geometry, and one on meteorology.
Dr. DeGraaff: Oh, wow. Is it just Descartes or were there other people in other parts of the world that were doing similar things around the same time or maybe before or after?
Dr. Sarkar: There were people doing similar things at the same time. For example, one of the things that Descartes does in his book is he draws tangents to curves. He finds an algebraic way. And that was also being done by Fermat and Newton and so on around the same time but maybe a bit later.
Dr. DeGraaff: Right.
Dr. Sarkar: I think one of the things that you find is that, a lot of the time, the same thing was done by people in different places at different times.
Dr. DeGraaff: Yeah.
Dr. Sarkar: Or maybe the same time.
Dr. DeGraaff: It’s just they didn’t have as many published books I guess. I don’t know.
Dr. Sarkar: Yeah. And also just . . . right. I mean it’s a bit of a coincidence where they were born. Did they have access to other books?
Jordan: They should’ve just posted it on the internet!
Dr. Sarkar: [Laughing.]
Jordan: That way they could’ve collaborated.
Dr. DeGraaff: Why didn’t they?
Jordan: Who knows? But they should’ve invented it earlier.
Dr. DeGraaff: They should’ve. What amazes me, and, as you’re talking about is, and from other discussions I’ve had with people: the idea of zero is just so hard.
Dr. Sarkar: The idea of zero, yeah, absolutely. And this is one of the things that, you know, students have a hard time with math. And I think it’s really important for them to know that the human race had a hard time with it. And the inventors of the stuff that they’re learning about had a hard time with it, too. People are always telling me “fractions are so easy. How come, you know, my child can’t learn fractions? Or how come my teacher couldn’t teach fractions?” It’s like, fractions took a long time for the human race to get their heads around.
And zero is another thing. The Greeks didn’t have zero. This came from India, and only about a thousand years ago, which is a lot more recent that a lot of the math that people learn in school, like Pythagoras’ Theorem.
Dr. DeGraaff: It came to us from India about 1,000 years ago. How did it come about?
Dr. Sarkar: Yeah. I don’t know. But I was reading . . .
Jordan: [Laughing.] Well there was: somebody had nothing!
Dr. DeGraaff: And he was sad about it.
Dr. Sarkar: It’s interesting because you say that you don’t know much about history. The embarrassing thing is that I don’t know much about history either. Because when I was a child, we were taught basically the history of battles that were won by the English. You know, that’s how they teach. I think George Orwell said this is what you teach history in British schools: just these battles. And, of course, mathematics doesn’t really come into it. And why would anyone want to learn about battles that were won by the British or the English?
Student: Well, English people do!
Dr. Sarkar: Well, but really? I mean, I don’t know. I was probably not the only person who was not. . . But now that I’m interested in math, I can go back and say, “well, okay, now I’m interested in this. So let’s look at the life of Cardan, Leibniz, Descartes, Galois.
Dr. DeGraaff: Yeah.
Dr. Sarkar: And then, as I get interested in that, then I get interested in thinking about how did they live. You know, what were they thinking of other than mathematics? And I hope my students kind of think that as well.
Dr. DeGraaff: Right.
Dr. Sarkar: And then you start to get drawn into it. Like, I became very interested in revolutionary France in the 1830s and books by Louis Blanc, and Strömdahl [sp?], and all these people. But only through reading about the mathematician Galois, whose story I was captivated by.
[♪ Magic Number by De La Soul♪]
♪Three
♪That’s the Magic Number
♪Yes it is
♪It’s the magic number
♪Somewhere in this hip hop soul community
♪Was born 3 Mase Dove and me
♪And that’s the magic number
♪(What does it all mean?)
♪Difficult preaching is Posdnuos’ pleasure
♪Pleasure and preaching starts in the heart
Dr. DeGraaff: Spark Science is an all-volunteer-run show and if you’d like to help out, go to KMRE.org and click on the button “donate.”
♪Something that stimulates the music in my measure
♪Measure in my music raised in three parts
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♪’Cause seein’ and doin’ are actions for monkeys
♪Doin’ hip hop hustle, no rock and roll
♪Unless your name’s Brewster, ’cause Brewsters are funky
♪Parents let go ’cause there’s magic in the air
♪Criticising rap shows you’re out of order
♪Stop look and listen to the phrase Fred Astaires
♪And don’t get offended while Mase do-se-do’s your daughter
♪A tri-camera rolls since our music’s now set
♪Fly rhymes are stored on a D.A.I.S.Y. production
♪It stands for “Da Inner Sound Y’all” and y’all can bet
♪That the action’s not a trick, but showing the function
Dr. DeGraaff: Today we are joined by a colleague of mine at Western Washington University, awesome guy, mathematician. He teaches the history of math but he also teaches many other math classes: Dr. Amites Sarkar.
♪And that’s the magic number
♪This here piece of the pie
♪Is not desser but the course that we dine
♪And three out of every darn time…
Jordan: Welcome back to Spark Sience. We’re talking with Amites about the history of math. So, when we talked about zero, basically they thought it was an impossible number. How did they come up with zero like zero money? Like, coins and everything like that and monetary values? Like, once they ran out, what did they call it?
Dr. Sarkar: That’s a great question. So one of the things is that coins were invented a long time before the concept of zero was really created in the way that we know it. One of the things that I learn about when I’m teaching this course is just the impact of other things that happen. So, the history of counting even . . . counting came before writing. I didn’t realize this.
Dr. DeGraaff: Oh yeah!
Dr. Sarkar: It was only known recently how this happened. People would have various tokens which represented property. And then they would seal them. They would make these tokens and put them in a clay ball and bake the ball and seal them in this clay ball. And then if there was a property dispute, they would break open these clay balls and see who had what tokens.
Dr. DeGraaff: Oh wow. I did not know that.
Dr. Sarkar: Right. I didn’t know it either. What people used to do is they used to press the tokens into the side of the clay ball to avoid breaking the clay ball. And that was counting, really. So you could own 200 goats. You would press the “hundred goat” token in twice, making 200-goat shape. And then that was counting. And that became writing eventually.
Dr. DeGraaff: Wow.
Dr. Sarkar: So I learned about the history of writing through this, and also, coins. Coins was a really key discovery because when people started making them, it meant that trade could be facilitated but also people could accumulate huge amounts of wealth because it’s probably very difficult to store 5,000 sheep, but if you just have a load of coins, and you can store it. And so there became this concentration of wealth, so an inequality of wealth, and that led to a leisure class. And so that leisure class could then spend their time being freed from farming the fields. They could do math and science. This isn’t my theory. I think this is actually Aristotle’s theory; he wrote it down that the invention of coins led to the formation of this leisure class who could study astronomy, science, mathematics, geometry.
Dr. DeGraaff: Right. Leisure class in the betterment of human not just “leisure class” in like, you know . . .
Dr. Sarkar: I’m not sure, actually. This is the sort of thing that we don’t really know about.
Dr. DeGraaff: I know, yeah! Yeah.
Dr. Sarkar: I mean, it’s just that it was important to have people who didn’t have to do anything.
Dr. DeGraaff: Oh my . . . No; it totally is. And it goes against everything I believe in, right? I mean, this whole . . . I’m a class warrior inside. I mean, like our Superman episode that we were talking about. But you’re right. I mean, if you aren’t, you know, being a farmer or you’re not working hard, then you can do science. So, that’s so horrible. [Laughing.] I’m so conflicted right now.
Dr. Sarkar: I’m also a class warrior. But it’s just interesting to read this stuff and you sort of read it putting everything to one side.
Dr. DeGraaff: Yeah.
Dr. Sarkar: But yeah. The connection is that, you know, the invention of coins, the invention of the printing press, the invention of the telescope; these were things that happened and you can see then how quickly they affected mathematics, science, and society in general.
Dr. DeGraaff: Right. Well, I mean, Kepler and Tycho, right? I mean, Tycho Brahe had all the money. And he was the financier. And you know, you I mean, he liked science and he took data. But if he didn’t have money then none of that stuff would’ve happened.
Dr. Sarkar: That’s absolutely true. And one of the things I really did learn the first time I taught this course is I always thought he had a telescope.
Dr. DeGraaff: No. He didn’t!
Dr. Sarkar: But he had no telescope. He had a 37-foot quadrant instead.
Dr. DeGraaff: Yes. He did.
Dr. Sarkar: Because the telescope hadn’t been invented.
Dr. DeGraaff: Well, it had. Will had been.
Dr. Sarkar: It had been invented?
Dr. DeGraaff: So, Galileo was experimenting with using a telescope that was invented for nautical reasons. And he started pointing it to the sky. And he was modifying it and playing with lenses. And he actually sent one to Kepler. And Kepler got to use it for about a month when he was working under Tycho.
Dr. Sarkar: Oh, okay.
Dr. DeGraaff: But yeah, Tycho and Kepler were not using a telescope. They did see one for about a month.
Dr. Sarkar: It’s amazing to me that they made all those observations without one, though.
Dr. DeGraaff: Yeah. It is. And it’s very sad actually because Galileo was giving all these telescopes away to like rich people as gifts and Kepler was like “uh . . . I would like one.”
Dr. Sarkar: Yeah, yeah! [Laughing.]
Dr. DeGraaff: And he only got it for a month.
Dr. Sarkar: So Galileo held back the history of science by his generosity, you know.
Dr. DeGraaff: Well, or, yeah . . .
Dr. Sarkar: Maybe he didn’t like Kepler or something.
Dr. DeGraaff: I don’t know what that was about. This is all stuff I read.
Jordan: Yeah. I heard about a crazy feud between them, too, it was like 300 goats or something.
Dr. DeGraaff: Well, it’s funny you talk about feuds; Tycho’s body has been exhumed twice.
Dr. Sarkar: It’s been exhumed twice. And this is one of the things that I talk to my students . . . they’re trying to find out how he died. They’re trying to find out what his nose is made of.
Dr. DeGraaff: Correct.
Dr. Sarkar: And I never read the news story. So what was his nose made of?
Jordan: What his nose is made of? Why is this a controversy?
Dr. Sarkar: So the reason it’s interesting: he got interested in alchemy because he lost his nose in a duel.
Dr. DeGraaff: In a duel!
Dr. Sarkar: At age 20. And then he had to have a prosthetic nose made out of . . . I don’t know. What was it made of?
Dr. DeGraaff: Bronze.
Dr. Sarkar: Bronze.
Jordan: Bronze beak! That’s . . .
Dr. DeGraaff: Yeah. And this famous story is that he died because he had this big banquet and it was manners at the time to not get up and go to the bathroom during the meal.
Jordan: Oh.
Dr. DeGraaff: But the meal was so long that he was just sitting there and sitting there and sitting there. And people thought his bladder burst and then he died. So, this was the rumor.
Dr. Sarkar: Did that happen?
Dr. DeGraaff: They think it might’ve actually happened. Because so many people were like, “no. It wasn’t the bladder. Kepler poisoned him.”
Dr. Sarkar: Right. Right. That’s what I heard. Or maybe he poisoned himself accidentally with his alchemy.
Dr. DeGraaff: Right. No, but they don’t think it was poison. They said it’s inconclusive. But they were saying the bladder thing isn’t as farfetched as people thought.
Dr. Sarkar: Mhmm.
Dr. DeGraaff: So that’s what I read for my class because we also talk about Kepler and Tycho. And this is . . . when is all this? 17 . . .
Dr. Sarkar: Yeah. When is…? Yeah . . . I… hmm. Kepler’s laws are about 1690. So Tycho must’ve been about 1600 or something like that.
Jordan: Is that right when he started making RC cars? The Tyco?
Dr. DeGraaff: [Laughing.] Yes. Same guy.
Jordan: Well. Duh. He’s got a bronze nose.
Dr. Sarkar: That was just he was faking his own death, you know, like James Bond.
Dr. DeGraaff: That wasn’t really his body.
Dr. Sarkar: That’s right.
Dr. DeGraaff: I’m glad we have you on, because talking about these historical things . . . we’re jumping around, kind of, not chronological. But these great stories that exist associated with science or associated with math really do open up your eyes. Like you said, you didn’t even know that they didn’t have telescopes
Dr. Sarkar: Mhmm.
Dr. DeGraaff: And, for me, it gives me so much more respect for people. And when people say, “oh. Things are backwards. You know, they just didn’t understand it because people were dumber back then.” I’ve heard students say that. I’m like “no no no no. It wasn’t that they were dumber at all!”
Dr. Sarkar: Right. This is absolutely kind of a myth which is very interesting to dispel. Because, when you’re learning mathematics, you kind of think, okay, so the Greeks got to here, and then the Romans did nothing at all. And then Newton and Leibniz, they got to here, but then Euler got to here. And I got through all of it in the first year of university. So therefore I’m at a higher level of sophistication.
Dr. DeGraaff: So I’m a genius!
Dr. Sarkar: So the thing is, you know, one should go away and look at one these people did. And it’s amazing.
Dr. DeGraaff: Mhmm.
Dr. Sarkar: And also, the thing about math is: when you’re told the answer to something, then it all seems very easy. But when you don’t know the answer to it, which way do you go?
Dr. DeGraaff: Right.
Dr. Sarkar: So, yeah, it’s amazing for the students to discover and for me to discover just how smart some of these people were.
Dr. DeGraaff: Yeah. We talk about astronomy. Like we were just talking about Kepler and the idea that they could predict when planets were gonna be in the sky. They could predict when certain constellations . . . I mean, that’s very hard to do. And I was like, and some of my students don’t even understand that the moon rotates! Give them some credit.
Dr. Sarkar: I’ve got a remedy for this, which is: they figured out how far it was to the moon.
Dr. DeGraaff: Mhmm.
Dr. Sarkar: And the way they did it was basic math, totally sort of like middle-school math. But, you ask a thousand people who don’t know the answer how they worked out the distance to the moon, it’s very hard. It’s very hard. And it was Aristotle who figured out the key, which is that a lunar eclipse is the moon passing through the earth’s shadow. And that’s an act of genius, I think.
Dr. DeGraaff: Yes.
Dr. Sarkar: You know, just to figure that out, just to take that first step. And then once you figure that out, then you can maybe − I mean it’s all with hindsight − but maybe it’s not so hard to actually do the math.
Dr. DeGraaff: Well, yeah.
Dr. Sarkar: And then work it out. But there’s so many steps. I mean, there’s not just that one step. There’s quite a few clever steps in that. And so that’s my illustration to people: that even though the math that they did, you know, maybe is just plain geometry, no calculus, they were incredibly clever. They were incredibly good at it and incredibly good at putting it to use.
Dr. DeGraaff: Right. My example is that I said, “prove to me . . . what can you tell me to prove that the Earth is going around the sun? What would you do to prove to me without a telescope?”
Dr. Sarkar: Right. And they can’t do it. I’m not sure I could do it from cold you know.
Dr. DeGraaff: No one can!
Dr. Sarkar: Right.
Dr. DeGraaff: And what happened is that Galileo pointed the phases of Venus, you know. And that explained that Venus was going around the Sun and we were also going around the Sun.
Dr. Sarkar: Mhmm.
Dr. DeGraaff: Because if you don’t have a telescope, you can figure out all of predicting where the planets are, all that kind of stuff. You could do it with, what these called, epi-cycles or epi-circles or whatever you want to call them.
Dr. Sarkar: Mhmm.
Dr. DeGraaff: And it still works.
Dr. DeGraaff: Right. Ptolemy had a theory of epi-cycles. Exactly.
Dr. DeGraaff: Exactly. So it is a testament to how brilliant, you know, humans were. And our brains really haven’t changed very much in thousands of years. So, I mean, it wasn’t that they were dumber. It’s that they didn’t have the tools. They didn’t have the knowledge that we have.
Dr. Sarkar: Yeah. Going back on the [inaudible], they could do it actually. In order to figure out all this stuff, you need to know various stuff. So I’m just left in total admiration. I mean, look at all these great mathematicians of the past. You realize just how much much better they were than the cleverest person I’ve ever met.
Dr. DeGraaff: Right. But it makes me sad they need the leisure class
Dr. Sarkar: They needed the leisure class. Yeah.
Dr. DeGraaff: They did. Aww. Yeah. Even Kepler. He was very poor. But he needed it, right?
Dr. Sarkar: Mhmm.
Dr. DeGraaff: And Faraday, which we’ve talked about on a previous show . . . he was very very poor.
[♪ Music playing ♪ – “Magic Number” by De La Soul]
♪Time is a factor so it’s time that counts
♪Count not the negative actions of one
♪Speakers of soul say it’s time to shout
♪Three forms the soul to a positive sum
Dr. DeGraaff: If you’re just joining us, this is Spark Science, and you are listening to KMRE 102.3 FM in Bellingham. I’m Regina Barber DeGraaff.
Jordan: And I’m Jordan Baker. Today we’re talking about math history with mathematician: Dr. Amites Sarkar.
♪But it just won’t go away
♪Three times one?
♪(What is it?)
♪(One, two, three!)
♪And that’s a Magic Number
♪(Yo, wassup?)
♪(One, two, three!)
Dr. DeGraaff: Anyway, let’s keep on talking about this idea that people have really struggled with understanding math. You said that in the very beginning of our show and how these are hard concepts. But, even though they’re hard, people are still interested in them. Right? I mean, we still see all these things everywhere. Like you were saying: baseball stats. You were telling me that earlier.
Dr. Sarkar: I think this just ties in with lots of little mini-rants that I have that math is sort-of a creative process. And a lot of . . . sort of dispels some myths . . . it hasn’t all been done already. And so math is still being done, both for applications and for its own sake. And, unlike using math that’s already been discovered, the process of discovering math is a creative one. I think it has a lot in common with being a writer or being a songwriter, being a musician. I think you do rely on sort of luck and sort of insight, or on thinking about something for a long time. But there’s no rules for doing mathematics.
Dr. DeGraaff: Like you were saying, it’s more broad. I think you were telling me earlier, like, sudoku, right? I mean, this is patterns. This is like . . .
Dr. Sarkar: Yeah! So this is the thing. I kind of, like . . . a lot of people . . . actually my colleagues at Western, they say, “well, you know, we feel sorry for you because you have to teach math and no one wants to be in your classes.” And I tell them well, actually, like “not only would you be surprised how interested are in mathematics, not my class necessarily . . .”
Dr. DeGraaff: Right.
Dr. Sarkar: But, I mean, you see people doing sudoku . . . that is math. And it’s not just the numbers part. The logical reasoning part is math.
Dr. DeGraaff: Right. Exactly.
Dr. Sarkar: Anyone doing sudoku . . . and I don’t even do it. My mom does it. I’m not even interested in sudoku.
Dr. DeGraaff: I don’t even like sudoku.
Dr. Sarkar: I don’t like it!
Dr. DeGraaff: [Laughing.]
Dr. Sarkar: So it turns out that I’m actually less interested in math than everybody else because everyone who does sudoku is into math. Everyone, and like, baseball statistics is the other thing . . . I mean, you watch baseball . . .
Dr. DeGraaff: Right. I am not interested. But I love baseball but I don’t do the statistics.
Dr. Sarkar: Right. I have no interest in baseball stats at all. But if you . . . you know, sometimes I watch the television and they just have all these baseball stats and it’s almost like they’re using the numbers to make it more interesting. And I think people must have some kind of mathematical kind of . . .
Dr. DeGraaff: Urge or need?
Dr. Sarkar: Some mathematical urge, yeah! Because otherwise, you know, they would just be watching how amazing it is, this person playing baseball. And they wouldn’t be interested in how many . . .
Jordan: I think they’re just making up those numbers, I mean, really . . .
[Laughing.]
Jordan: It’s like, the bigger the number, the better the person is at whatever it is.
Dr. DeGraaff: Well, like, the batting average . . . do you ever . . . do you watch?
Jordan: No. I don’t ever . . . [laughing.]
Dr. DeGraaff: Okay. You don’t watch baseball, Jordan.
Dr. Sarkar: So none of us actually know anything.
Dr. DeGraaff: Well, batting average is okay . . . [laughing.] I mean, it’s just like how many times a player is up to bat, how many times they get a hit. And a hit is . . . we don’t wanna go down this road.
Jordan: No. We don’t.
Dr. DeGraaff: But, I mean, they score tells you something about how good of a hitter that baseball player is. So you’re looking at this value, which, if you are interested in math, you understand what that value means, and then that helps with your anticipation on what you think is gonna happen next. Is this person gonna get on base? Is this person gonna give you a home run? So, I mean, these numbers are predictive. They help you predict.
Dr. Sarkar: Yeah! But it’s weird to me that people who, you know, claim to have no interest in math, actually do actually participate in things that are kind of fairly mathematical.
Dr. DeGraaff: Absolutely.
Dr. Sarkar: Even reading a detective story, I think, is a mathematical-type thing to do, you know?
Dr. DeGraaff: Absolutely.
Dr. Sarkar: So I kind of think that somehow, I mean, you know, people associate it with trying to follow instructions at school. And then they could sort of never quite do that. And then they were a bit slow or something like that. But I hate following instructions as well. So, it’s not . . . parts of math that people associate with it aren’t really representative, I don’t think.
Dr. DeGraaff: Right. It’s a very inquisitive thing.
Dr. Sarkar: Mhmm.
Dr. DeGraaff: I agree with like if people like to solve puzzles and stuff.
Dr. Sarkar: Mhmm.
Dr. DeGraaff: I hate puzzles. [Chuckling.] And I’m a physicist, or an astrophysicist.
Dr. Sarkar: Right. But you should like them.
Dr. DeGraaff: I should like them, right? I keep on being told, “you should like this,” you know? But I hate it! I hate those big picture puzzles.
Dr. Sarkar: Me too.
Dr. DeGraaff: Hate them. And I hate the wooden puzzles you get at the craft stores, and they’re like “oh and then you do . . .” I mean . . .
Dr. Sarkar: Yeah. I would be interested in those if I could do them.
[Laughing.]
The jigsaw puzzles are just not interesting.
Jordan: I’m just recreating a picture, basically.
Dr. DeGraaff: Right. So it’s funny the things that, you’re right, that people actually like that are associated with this broader idea of math that you keep on talking about, this idea of logic, really, not numbers and equations.
Dr. Sarkar: I mean, logic somehow also has these kind of negative connotations because people kind of say “you’re not being logical” or whatever. But there’s no way of really saying it without sound incredibly pretentious. But it is about ideas and connections between ideas really.
Dr. DeGraaff: Right, which is really all of science.
Dr. Sarkar: Mhmm.
Dr. DeGraaff: And, again, our listeners and Jordan are just hearing me rant about our students, but, you know, a lot of my students get into my physics class and it’s a kind of science that they’ve never dealt with before. They have to make connections. They have to problem-solve. It’s not an instructional, you know, step-1, step-2, step-3 thing.
Dr. Sarkar: Right.
Dr. DeGraaff: Almost all science is like that, too. It’s just, I think, in my class, it’s maybe it’s just more obvious that there’s no instructions. But yeah. Math, science; it’s all about, like you said, problem-solving, making these connections, ideas. I agree with you.
Dr. Sarkar: Right. And that’s really good of you to actually make it obvious to them that it’s about that.
Dr. DeGraaff: I’m really loud.
Dr. Sarkar: [Laughing.]
Jordan: She yells at them.
Dr. Sarkar: I get this thing sometimes where I set students’ homework and they say “well this isn’t really math so I didn’t really know where to begin.” And I say “well, that’s where the subject begins. You don’t know where to begin.” That means you’re actually doing math. And of course people aren’t very happy with that.
Dr. DeGraaff: No.
Dr. Sarkar: But if you could just do it all, then we would just program a computer to do it all. And they wouldn’t make any mistakes. So it would be easy.
Dr. DeGraaff: Right. Well, I mean, I don’t know why, but this makes me think of the Curiosity Rover on mars. When Melissa was here and when I’ve had discussion with it and they say like what the Curiosity Rover can do in like a week, a human can do in a minute, right? You know, because a human can think through these problems, make a decision on what to do, like, in the next minute, analyze what . . . you know, decide where to go . . . these split-second decisions that humans make: these are things that I try to teach in science. I mean, we’re using our brain. We’re solving problems. And, like you said, it’s not instructional because that’s what computers do
Dr. Sarkar: Yeah. It’s nice to have the edge somehow. It’s nice to have the edge on the machine, you know.
Dr. DeGraaff: For now.
Dr. Sarkar: Yeah; for now.
Jordan: Yeah. Down with the machine!
Dr. DeGraaff: So let’s go back to history. Because, you know, we’re advertising this as the history of math.
Dr. Sarkar: Mhmm. Yeah, yeah. I should just stick to the point. Focus.
Dr. DeGraaff: Oh no! I wanna go back to this idea, again, of zero. Because we’re talking about ideas, what math is. And what were some other, like, big revolutionary kind of ideas in math. And like when did that happen and where in the world did that happen?
Dr. Sarkar: Algebra would be a good one.
Dr. DeGraaff: Yeah.
Dr. Sarkar: Al-Khwārizmī wrote a book in which he . . .
Dr. DeGraaff: Where was he from?
Dr. Sarkar: Persia, Iraq.
Dr. DeGraaff: Okay.
Dr. Sarkar: So, he was one of the great Islamic mathematicians around 800 AD, I believe. So, the word “algorithm” is named after him. The word “algebra” is also named after him. But it’s interesting because there was sort of, you know, the pre-cursors of algebra even in the Babylonians, but I think he made one of the decisive leaps, which was to sort of talk about the unknown quantity, which we now call “X” or “Y” or something like that.
Dr. DeGraaff: Or I call it “happy face” in my class.
Dr. Sarkar: Happy face.
Dr. DeGraaff: Because I’m so angry that people are so used to like “5 plus X equals 10.” They’re always used to the unknown being called X. And I was like “no. It’s elephant. It’s house. It’s happy-face.” Because I just try to get them away. They need to associate something with an unknown, a variable.
Dr. Sarkar: Right. Right. Right. Yeah. No, I should try that as well.
Dr. DeGraaff: Seth does that.
Jordan: It’s harder to do on a calculator. “Smiley face.”
Dr. DeGraaff: It is. But it forces them to understand what that means. They really, when they see “X” over a and over again, then they store in their minds “X is always 5.” And then when they see X again, they come to this like 5, or they come to like the most common number that they keep on getting for X.
Jordan: I think if I see “X” in any sort of like a number thing, I keep just wondering why they just threw consonants into numbers. And I throw the paper away.
Dr. DeGraaff: You’re right. They don’t use vowels a lot for unknowns.
Dr. Sarkar: Actually I was just reading about this. But I can’t remember the exact details. But somewhere along the line, someone decided to use, I think, consonants for unknowns and vowels for knowns, or maybe the other way around. But this kind of convention goes back hundreds of years anyway, so I didn’t realize that.
Dr. DeGraaff: Wow. Jordan was totally right!
Jordan: Yeah!
Dr. Sarkar: I thought it was just some kind of, like, thing, from the 50s or something. But no. It goes back a long way.
Dr. DeGraaff: Wow. Yeah. Well, yeah. I want them to be okay with calling an unknown anything, right? Because if you have to make up your own equations, and you have to be like, you know: “there are 15 students for every teacher.” They can use “S” for the number of students and “T” for the number of teachers, or, you know, “star” for the number of teachers.
Dr. Sarkar: But this is one of the things where it really helps people to realize that things that they struggled with when they were learning things were things that don’t really come naturally to the human mind, which is why the Babylonians did not have it and the Greeks did not have it. And then it took anything thousand years for someone in a completely different part of the world to come up with this concept, which then just took off. Because, once you can do this, it’s an incredibly empowering thing. I mean, you can write down equations. You can describe the laws of physics.
Dr. DeGraaff: Yeah.
Dr. Sarkar: But without this idea that you have unknowns which you solve for, then you can’t really do physics, you know.
Dr. DeGraaff: No. Yeah.
Dr. Sarkar: You can’t do physics or chemistry or anything really, anything in science. But it wasn’t the first thing that came to mind. The Greeks were doing really complicated stuff before that.
Dr. DeGraaff: Wow. That makes me think I need to be nicer to my students. [Laughing.] Because I’m like “come on!”
Dr. Sarkar: Yeah. They’re running through the whole of human history, but just like really quickly.
Dr. DeGraaff: Yeah. That’s true.
Dr. Sarkar: And it’s not just they have to learn all the stuff that happened, like who won this battle; they actually have to understand this stuff.
Dr. DeGraaff: Right.
Dr. Sarkar: Which we know from the historical record does not come naturally.
[♪ Music playing ♪ – “Magic Number” by De La Soul]
♪But odd as it may be
♪Without my 1 and 2 where would there be
♪My three: Mase, Pos and me
♪And that’s the Magic Number
♪(What does it all mean?)
♪Focus is formed by flaunts to the soul
♪Souls who flaunt styles gain praises by pounds
♪Common are speakers who honor the scroll
♪Scrolls written daily creates a new sound
♪Listeners listen cause this here is wisdom
♪Wisdom of a Speaker, a Dove and a Plug
♪Set aside a legal substance to feed ‘em
♪For now get ’em high off this dialect drug
♪Time is a factor so it’s time that counts
♪Count not the negative actions of one
♪Speakers of soul say it’s time to shout
Dr. Sarkar: My name is Amites Sarkar. I’m a mathematician. And you’re listening to KMRE LP, 102.3 FM in Bellingham: your community, your voice, your station.
♪Now you may try to subtract it
♪But it just won’t go away
♪Three times one?
♪(What is it?)
♪(One, two, three!)
♪And that’s a Magic Number
♪(Yo, what’s up?)
♪(1, 2, 3)
♪(I say, children, what does it all mean?)
♪(Woah-woah-wo, 1, 2, 3)
♪(I wouldn’t lie to you)
♪(No more no less, that’s a magic number)
♪(No more no less)
♪(What it is?)
♪(No more no less)
♪(No more no less)
♪(Do the shang-a-lang)
♪(No more no less)
♪(No more no less)
Dr. DeGraaff: Let’s talk about prime numbers.
Dr. Sarkar: Yes. Let’s talk about prime numbers. It’s kind of an interesting thing. Because, to my mind, it’s sort of an example of just math of math’s sake. You know, these are numbers which have no factors other than themselves and 1. So, 2, 3, 5, 7, 11, 13, and so on.
Jordan: Keep going.
Dr. DeGraaff: [Laughing.]
Dr. Sarkar: 17, 19, 23 . . . I could go on . . .
Jordan: Alright. You’re done.
Dr. Sarkar: But yeah. So, Euclid, for example, 2300 years ago, proved there were infinitely many primes. We still don’t know if there are infinitely many pairs of prime numbers which differ by exactly 2. So, 5 and 7, 17 and 19, 29 and 31. That’s an unsolved thing in math. So that’s just one thing. But another thing is that people often say about math: “well that’s all very well, but what is the point of that?” And prime numbers actually, to everyone’s complete surprise, about 40 years ago, turned out to be very useful in cryptography, public-key cryptography. So that every time you purchase something on the internet, your credit card number is encrypted using prime numbers, another mathematical algorithm.
It’s just interesting to me that something which was always thought to be the purest of pure mathematics actually gets applied quite a lot. You probably know this. I’m sure it’s come up on this program before. But radio waves were discovered by Heinrich Hertz in the 1880s.
Dr. DeGraaff: That has come up. [Chuckling.]
Dr. Sarkar: And it probably also came up that his original comment about their use was “it’s of no use whatsoever.”
Dr. DeGraaff: No. That hasn’t come up yet.
Dr. Sarkar: And someone did and he was very very happy that he had confirmed Maxwell’s predictions of electromagnetic waves. He said he thought it was amazing. He was writing in German. So not only an I misquoting him . . .
Dr. DeGraaff: [Laughing.] In anything language!
Dr. Sarkar: But he was amazed that there were these waves that you can’t see them, you know, but they’re there everywhere. And then within a few years, of course, Bose in India, Marconi, I think in London actually, were doing these demonstrations of radio waves. So, to me, that’s a perfect example of how . . . I shouldn’t say “perfect” because I just came up with the example.
Dr. DeGraaff: [Laughing.]
Dr. Sarkar: But, I means, it’s a good example of how you don’t know what’s gonna be useful.
Dr. DeGraaff: Right.
Dr. Sarkar: And that happens in mathematics as well.
Dr. DeGraaff: It happens in all the sciences, right? When we have questions that we ask and we ask for money from the government and grants and science-for-sceince’s-sake vs. science-of-application’s-sake and knowing that science-for-sceince’s-sake will someday turn into something that’s application is a wonderful thing and history has shown us that that’s true.
Dr. Sarkar: Mhmm.
Dr. DeGraaff: So I agree. We were saying that the pairs of prime numbers haven’t been proved yet. There are many of these, like, unsolved things, right?
Dr. Sarkar: Yeah. There’s a whole lot of questions just involving prime numbers. Is every even number greater than or equal to the sum of 2 prime numbers? That was stated by Goldbach in a letter to Euler in 1742. No one knows the answer. It’s about the simplest thing you could imagine about prime numbers. And no one knows that yet: Goldbach’s conjecture. And so math is full of these very simple questions that, you know, we can’t solve.
Dr. DeGraaff: Or we haven’t yet.
Dr. Sarkar: We haven’t yet solved. But interestingly, the struggle to solve them often, you know, leads to the development of interesting branches of mathematics which connect with other branches of mathematics and also have applications.
Jordan: So I watched this video a little while ago. And it was like “The 5 Weirdest Ways to Become a Millionaire.”
Dr. Sarkar: Yeah?
Jordan: And one of them . . . there was like a million dollars for some math equation that hasn’t been solved yet. Because somebody was trying to solve it. I think it was a Russian guy.
Dr. Sarkar: Yeah. There are 7, actually, there are 7 Millennium Prize problems. And 2 of them, the Riemann Hypothesis and the Birch and Swinnerton-Dyer Conjecture involve prime numbers and number theory. And if you solve those, you get a million dollars. The one that you’re talking about was actually solved by a Russian mathematician Grigori Perelman in 2003. But he refused the prize. He refused the Fields Medal, which is a well-known prize in mathematics
Dr. DeGraaff: Why?
Dr. Sarkar: I don’t know. And he sort of lives in seclusion somehow in Moscow and people have asked him, “why did you decline it?” And he says it’s because there’s somehow . . . that the culture of mathematics is very unfair and gives credit to the wrong people.
Dr. DeGraaff: Oh.
Dr. Sarkar: But I’ve never really understood his reasons.
Dr. DeGraaff: Oh. Well we have 3 listeners in Russia now.
Dr. Sarkar: Uh huh?
Dr. DeGraaff: So maybe they know him.
Dr. Sarkar: Maybe he’s one of them.
Jordan: Yep. Right. That’s a fact! [Laughing.]
Dr. DeGraaff: That’s sarcasm, international listeners.
Dr. Sarkar: [Lauhging.] Yeah. So no one really knows. But that prize has been deemed to be solved. He actually said about that prize: he said that an equal share of the credit should go to Richard Hamilton, who invented the method. So, a lot of the time, someone invents a method and then someone else does something with it. So it’s a collaborative thing. But the other 6 are unsolved. I should say that a couple of my friends 15 years ago won a million pounds for solving a jigsaw puzzle.
Dr. DeGraaff: What!?
Dr. Sarkar: And they used math to do it.
Jordan: Wow.
Dr. Sarkar: The Eternity Puzzle. It was a 209-piece jigsaw puzzle.
Dr. DeGraaff: Well and pounds are way more than dollars, so!
Dr. Sarkar: Yeah, yeah. So that, to me, was, you know, like, evidence that mathematicians can really . . .
Jordan: So have you thought about devoting your life to solving one just to become a millionaire?
Dr. Sarkar: I don’t know. I mean, you have to be very clever to do this kind of thing.
Jordan: You have an accent, so that’s a start!
Dr. Sarkar: [Chuckling.] I could sort of just speak at the pieces . . .
Jordan: Right. Yeah. Exactly.
Dr. DeGraaff: People fall into line!
Dr. Sarkar: A lot of people have a British accent, though, you know?
Jordan: What?
Dr. DeGraaff: What? Not here!
Jordan: Yeah. Not that I know of.
Dr. DeGraaff: Not in Bellingham. You win, Amites. But you were saying this collaborative thing and you were talking about giving credit and not being fair. And this just makes me want to bring us to our next section of Erdős. Am I saying his name right?
Dr. Sarkar: Oh yeah. Erdős, yes; Paul Erdős.
Dr. DeGraaff: Erdős, yeah. And where is he from? And tell us his story because it’s a good story.
Dr. Sarkar: Yes. So he was from Hungary. He was the most prolific mathematician who ever lived. He wrote 1500 papers with about 500 co-authors.
Dr. DeGraaff: Was he the first author on that many papers or with . . .
Dr. Sarkar: It’s interesting in math. They have a diplomatic system where everything is alphabetical order. So in engineering, and I understand, physics, people have first author, second author, and so on. But in math, it’s kind of nice. They just list the authors in alphabetical order.
Dr. DeGraaff: That is very nice. Being Barber-DeGraaff, I would’ve been earlier. So that would be great.
[Laughing.]
Dr. Sarkar: But yeah. I mean, mathematics, I think, through most of its history was something that people did in isolation. And then Erdős was one of the people who really collaborated with people. He knew which problems that he was working on were suited to which mathematicians.
Dr. DeGraaff: Wow.
Dr. Sarkar: So he created just a huge amount of mathematics. He was a child prodigy, I mean, an amazing mathematician. But he traveled around the world. He had no permanent job. He had no permanent home. He lived out of 2 half-empty suitcases, just really . . .
Dr. DeGraaff: I love that he had 2 half-empty ones instead of one full one.
Jordan: Yeah. Like you were there!
Dr. Sarkar: It might even have been one half-empty suitcase. But he had very very few possessions, never married, and just really devoted his life to mathematics. Towards the end of his life, he took, I think benzadrine, and did 19-hour days of mathematics. The amount of stuff he did . . . I mean he made really fundamental contributions in combinatorics, number theory, set theory, graph theory − just all these different branches of mathematics. He started some branches of mathematics; just this amazing figure in mathematics.
Dr. DeGraaff: So what was the timespan of this?
Dr. Sarkar: 1913 he was born. And he died in 1996.
Dr. DeGraaff: Oh. Okay.
Dr. Sarkar: So in math, there is this Erdős number kind of association that people talk about. And it’s very similar to the Kevin Bacon: the degrees of Kevin Bacon. So, for our listeners, I’m gonna try to explain it and Amites, you can . . .
Jordan: You can explain it to me, too. I don’t know what a degree of Kevin Bacon is!
Dr. DeGraaff: Oh my gosh! Okay. So I’ll do this for everyone. Kevin Bacon is a wonderful actor. He has most recently been seen in . . . the one I’ve seen him in is X-Men: First Class. He was a villain in that one. He was in Footloose.
Jordan: That’s recent!
Dr. DeGraaff: Well I’m trying now to give you more examples. What other Kevin Bacon movies are there? I’m looking to our crew here at KMRE.
Speaker: Hollow Man.
Dr. DeGraaff & Jordan: Hollow Man?
Dr. DeGraaff: He’s basically a side character in many movies. But there’s something called “7 degrees of Kevin Bacon” and if you’re in a movie with Kevin Bacon, you’re number 1. Oh it’s 8 degrees of . . . oh, 6 degrees. Oh, sorry.
Jordan: Well yeah. Because it’s 6 degrees of separation.
Dr. DeGraaff: Oh, right.
Jordan: 6 Degrees of Kevin Bacon. Is that just an alteration.
Dr. DeGraaff: I’m sorry. I don’t know. So 6 degrees . . . if you’re in a movie with him, that’s 1; your Kevin Bacon number is 1. If you are in a movie with somebody who was in a movie with Kevin Bacon, your number is 2, and so on and so forth. Now, with Erdős, how does that work, Amites?
Dr. Sarkar: Yeah. It works that if you have written a paper with Erdős, you have number 1. If you’ve written a paper with someone who’s written a paper with Erdős but you haven’t written one with him yourself, then you have an Erdős number of 2, and so on. So, the same thing with the Kevin Bacon.
Dr. DeGraaff: Right. So if you’re an actor and your number is 1, I think it’s kind of good because Kevin Bacon has been in so many movies. It means that you are kind of more connected with the Hollywood crew.
Dr. Sarkar: You’re like almost famous or something. Or maybe you are famous.
Dr. DeGraaff: Exactly. You are famous. But the higher your number, I guess, the less famous you are. And with math, it’s kind of the same way, right? People are more proud of having lower Erdős numbers.
Dr. Sarkar: It seems so. I mean, of course, there’s different branches of mathematics. I mean, if you were to work in algebraic topology or algebraic geometry, maybe it’s just a different area of study, so…
Dr. DeGraaff: Right.
Dr. Sarkar: But, yeah . . . people do definitely . . .
Dr. DeGraaff: It’s a bragging right!
Dr. Sarkar: If you go to Wikipedia pages, people do seem to put people’s Erdős numbers on there.
Dr. DeGraaff: Really?
Jordan: Hahaha. That’s so lame.
Dr. Sarkar: I shouldn’t really reveal that I go to Wikipedia.
Dr. DeGraaff: We all go to Wikipedia.
Jordan: Do people do that as like their . . . on Facebook, they’re like, “I’m interested in long walks on the beach and I have an Erdős number of 3.”
Dr. Sarkar: I’ve never seen it.
Dr. DeGraaff: If they’re mathematicians, they might, though.
[♪ Music playing ♪ – “Magic Number” by De La Soul]
♪Time is a factor so it’s time that counts
♪Count not the negative actions of one
♪Speakers of soul say it’s time to shout
♪Three forms the soul to a positive sum
♪Dance to this fix and flex every muscle
♪Space can be filled if you rise like my lumber
♪Advance to the tune but don’t do the hustle
♪Shake, rattle, roll to my Magic Number
♪Now you may try to subtract it
♪But it just won’t go away
Dr. DeGraaff: If you’re just joining us, this is Spark Science, and you are listening to KMRE 102.3 FM in Bellingham. I’m Regina Barber DeGraaff.
Jordan: And I’m Jordan Baker.
Dr. DeGraaff: We’re talking about mathematical connections today with mathematician Dr. Amites Sarkar.
♪(I say, children, what does it all mean?)
♪(Woah-woah-wo, 1, 2, 3)
♪(I wouldn’t lie to you)
♪(No more no less, that’s a magic number)
♪(No more no less)
♪(What it is?)
♪(No more no less)
Dr. DeGraaff: So I first learned . . . I actually didn’t know that much about Paul Erdős until my friend, who we’ve referenced on the show many times: Dr. Seth Rittenhouse. He calls me up while we’re in grad school and he starts talking about Erdős numbers and how frustrated he is that I have a lower Erdős number than he does. And he’s a mathematician and I am not. And I was like, “who is this guy? I don’t know what Erdős numbers are.” And it turns out that I have a number of 2.
Dr. Sarkar: Tell us the story.
Dr. DeGraaff: Yeah, so . . .
Jordan: Yeah!
Dr. DeGraaff: And then you have to tell us yours.
Dr. Sarkar: Yeah. For sure; yeah.
Dr. DeGraaff: Okay. So I have a number of 2 because I went to San Diego State University for a Master’s Degree; I didn’t know what I wanted to do with my life. So I just got a Master’s Degree in physics.
Jordan: We’ve all been there.
Dr. DeGraaff: We’ve all been there. There was one female professor. There was one female grad student: me. She was from Holland. My last name was DeGraaff, so some reason she liked me. I worked with her and she’s a computational physicist and she was on a paper with Erdős in like 1988.
Dr. Sarkar: Wow.
Dr. DeGraaff: So my first ever paper that I was on was hers. And so my first ever paper gave me an Erdős number of 2.
Jordan: I have a number of 3.
Dr. DeGraaff: Do you?
Jordan: Yeah. Because I know you.
Dr. DeGraaff: You weren’t on a paper with me though.
Jordan: Dang it!
Dr. DeGraaff: If we wrote a scientific paper together, you would have an Erdős number of 3.
Jordan: Oh. I have to write a paper with you?
Dr. DeGraaff: Mhmm.
Jordan: Well I have a radio show with you. Is that pretty close?
Dr. DeGraaff: No.
Jordan: Oh, well.
Dr. DeGraaff: It has to be scientific. Oh! It is scientific.
Jordan: [Whiny grunt.]
Dr. DeGraaff: To add to that: when I was 5, I was in a movie with River Phoenix…
Jordan: Kevin Bacon?
Dr. DeGraaff: No, River Phoenix and Sideny Portier and then the guy who played River Phoenix’s dad was in a movie with Kevin Bacon so I have a Bacon number of 2.
Dr. Sarkar: That must be a record, no?
Dr. DeGraaff: Well, there are actors out there that have done scientific work as well. So they do have Erdős numbers and Bacon numbers. But I would challenge any listener to try to find a lower lower Erdős and Bacon number combined – it’s 4 – than anyone else.
Dr. Sarkar: I think it’s probably a record, actually.
Dr. DeGraaff: I think it is!
Dr. Sarkar: It has to be the record for Erdős-Bacon.
Dr. DeGraaff: Right. I think the Kevin Bacon thing, you have to be, like, credited. Granted, I was like an extra. And you can see me for a couple seconds as a kid. But I think it still counts.
Dr. Sarkar: The question is: was Erdős in a movie with Kevin Bacon?
Dr. DeGraaff & Jordan: [Laughing.]
Dr. Sarkar: That would be crazy, you know? That would just blow my mind.
Jordan: Absolute Zero!
Dr. DeGraaff: Alright. Tell us your story. I think you have a low number as well.
Dr. Sarkar: I have an Erdős number of 1, actually. My very first paper was a joint paper with Baylor Bolabash [sp?], my research supervisor, and Paul Erdős.
Dr. DeGraaff: What!? When was this?
Dr. Sarkar: This was in 1999.
Dr. DeGraaff: Oh, wow.
Dr. Sarkar: But it’s a bit strange because this paper was published 3 years after he died because we continued something that he did, so he wasn’t really doing math from the grave. But we continued something that he was working on.
Dr. DeGraaff & Jordan: [Laughing.]
Dr. DeGraaff: Your story is way better! Doing math on the grave.
Dr. Sarkar: That’s right! That’s my plan: I plan to do math after I die.
Dr. DeGraaff: Right. Well, we need to, you know, start on a project before, when you’re 98 or something.
Jordans: Sounds like a movie: “He’s doing math from the grave!”
Dr. DeGraaff: Having a number of 1. I mean, I didn’t know at the time, my advisor; she also had a number of 1. But I haven’t met anyone else.
Jordan: What’s your Bacon number?
Dr. Sarkar: I’ve never been in any movies. So I have an infinite Bacon number. Infinite Bacon.
Dr. DeGraaff: Well. Yeah, that’s true.
Dr. Sarkar: I think so. I think for me, the interesting part of it isn’t so much kind of like bragging rights. It’s just seeing how much people collaborate with each other. So I think actually this 6 degrees of separation . . . my hero, Stanley Milgram, did one of his famous experiments was to try and . . . I think there was a stock broker in Boston and he was trying to get people to send a letter or a message to this stock broker via a chain of acquaintances.
Dr. DeGraaff: Oh, yeah!
Dr. Sarkar: And the idea was that, you know, is everyone connected to everyone else by short links?
Dr. DeGraaff: Yeah.
Dr. Sarkar: And I think a lot of the letters never actually got to their target. But the ones that did got there by very short links. So it’s the same kind of thing: that everyone knows somebody. On Facebook, for example, I wonder how many Facebook links it would take to get from you to —
Dr. DeGraaff: Beyoncé.
Dr. Sarkar: I don’t know whether this can be proved, but I’m guessing it’s only about 3 or 4 links.
Jordan: It’s 3.
Dr. Sarkar: You think it’s 3. Yeah?
Jordan: I know a friend who’s actually a record producer.
Dr. DeGraaff: Really? Oh!
Dr. Sarkar: So 3 links. There you go. Think of a non-celebrity. But it’s gonna be a very short link. And that’s the phenomenon that’s interesting to me is that, somehow, you know, whether by appearing in movies or writing papers or being friends, we’re all a lot closer than we think we are.
Dr. DeGraaff: I love that because it’s very true, even outside of physics and astronomy. I always think to myself, I’m sure you do, too. You go to these conferences and you see people that know somebody that you know, or whatever.
Dr. Sarkar: Mhmm.
Dr. DeGraaff: And it’s a very small, small group. But what’s weird is that I’ve gone to astronomy conferences where I have met people that aren’t astronomers or figured out that I’ve known somebody who is an astronomer. Or I’ve gone to general science conferences and figured out that I know people through various, you know, connections, that are in no way connected to physics or astronomy or even science, you know, so it’s very weird.
Jordan: And a great movie that kind of encapsulates this whole idea was “My Date with Drew Barrymore.”
Dr. Sarkar: Uh huh.
Jordan: Where this guy just borrows a camera from Best Buy or whatever it was for 30 days, and tries to track down and get a date with Drew Barrymore. He does the whole 6 degrees of separation. He goes to, like, her esthetinologist, or whatever, I don’t know, skin, whatever.
Dr. DeGraaff: Uh.
Jordan: Esthetician, yeah.
Dr. Sarkar: “Esthetinologist.” [Laughing.]
Jordan: But yeah. I don’t know.
Dr. Sarkar: Yeah. I think that’s kind of really cool. There’s lots of ideas that are related to that. One of the things that I think is interesting is that, if you think about it for long enough, it’s not surprising that you can get from you to Beyoncé in about 4 steps. And the reason is, if that wasn’t the case, then all your friends feel like about a thousand people who would be like your “friend bubble” and all of those thousand people wouldn’t know anyone outside of that group.
Dr. DeGraaff: Right.
Dr. Sarkar: That’s really unlikely.
Dr. DeGraaff: Right.
Dr. Sarkar: So it’s actually not even all that surprising. But it always strikes us as surprising. But it’s nice. It’s nice that we’re all connected in this way.
Dr. DeGraaff: Right. I mean you have an Erdős number of 1 and you’re from an island!
Dr. Sarkar: That’s right. Yeah. That’s right.
Dr. DeGraaff: [Laughing.] But yeah, no, I think that it’s an amazing thing. And it definitely dispels the idea of scientists and mathematicians and anyone kind of in these technology-STEM fields that we are very isolated people, that we are hermits, that we work alone. It definitely dispels that idea.
Dr. Sarkar: It’s funny, actually. On a personal level, almost all the scientists and mathematicians I know are just interested in every single thing like literature, music, and so on.
Dr. DeGraaff: TV.
Dr. Sarkar: TV. I don’t think we want to just do science and math. I think people, you know, we’re interested in stuff just like everyone else.
Dr. DeGraaff: But yet that persists. I mean, like, yet that idea is still out there and it still gains momentum. And this is what still gets people to not want to get into science, you know, or math.
Dr. Sarkar: Yeah. But I think it all is changing very rapidly I think, you know. I think all these cultural norms are kind of breaking down quickly.
Dr. DeGraaff: I totally agree. And I’m just going to . . . I wanna say one last thing about TV. You were saying that there is a movie coming out about a mathematician.
Dr. Sarkar: Yes!
Dr. DeGraaff: So I want to hear about that before we end today.
Dr. Sarkar: Yes. This famous Indian mathematician, Srinivasa Ramanujan, e was an Indian clerk. He had a book on mathematics. And he was going through, developing all these mathematical theories by himself. And then in 1913, he wrote a letter to mathematician G.H. Hardy, sending him some of his discoveries. Hardy and his friend, Littlewood, soon discover that these letters must come from a genius. And so this kind of unknown Indian from Madras traveled to Cambridge, which was the center of the mathematical world, to work with Hardy and Littlewood on number theory, prime numbers.
So, it’s just kind of an amazing story. You can’t really imagine it happening now.
Dr. DeGraaff: Well it could; social media.
Dr. Sarkar: Well, it could happen. Actually, in some sense, it’s more likely to happen now because the internet is everywhere. So yeah, but, I mean, at that time, it was like an amazing thing to happen.
Dr. DeGraaff: Yeah.
Dr. Sarkar: And so . . .
Dr. DeGraaff: And just, you know, the bravery of him to just like send him things and be like “hey, this is going on.” I have so much admiration for people that have the guts to do that. It’s like, “I’m doing this. What are you doing?”
Dr. Sarkar: Right. That is what one’s supposed to do at conferences.
Dr. DeGraaff: Right. But we hide in corners.
Dr. Sarkar: [Laughing.] I’m glad it’s not just me.
Dr. DeGraaff: [Laughing.]
Dr. Sarkar: But yeah. It’s also the international language of mathematics. You know, Ramanujan was doing this stuff in India and then Hardy and Littlewood were doing this stuff in England. And then they worked together with their completely different styles of doing mathematics and created this amazing mathematics together. And so there’s a movie starring Jeremy Irons as G. H. Hardy. Hardy wrote this book: A Mathematician’s Apology, which, if anyone’s listening and interested in the culture of mathematics, it’s a very short book. You can get it on the internet: A Mathematician’s Apology.
Dr. DeGraaff: I’m gonna get it.
Dr. Sarkar: And Dev Patel from Slumdog Millionaire is playing Ramanujan. And they were filming, actually, in Trinity College, Cambridge, I read. And that’s gonna come out next year.
Dr. DeGraaff: I’m totally gonna watch it.
Dr. Sarkar: Yeah. Alongside the movies about Turing and Stephen Hawking, there will now be a third movie about a Cambridge mathematician.
Dr. DeGraaff: I think in the math department, we should just get . . . we should watch those first 2, the Stephen Hawking and the Alan Turing one. And then we should all go out and watch this one when it comes out.
Dr. Sarkar: Yeah! So who was it who said that mathematicians don’t like doing stuff? We should totally . . . yeah, absolutely.
Jordan: He goes outside!?
Dr. Sarkar: Yeah, yeah. And then go inside to watch a movie.
[Laughing.]
Dr. Sarkar: I got 5 minutes of sunshine.
Dr. DeGraaff: Alright, well, thank you for coming to talk to us. We’ve actually learned a lot in our random walk around the history of math. I might actually ask you back on when we see this movie.
Dr. Sarkar: Sure, absolutely.
Dr. DeGraaff: And we can talk more about this mathematician and talk more about things that we didn’t quite get to today.
Jordan: Hey. It’s all about not following instructions.
Dr. DeGraaff: It is. It’s about ideas! Alright. Thank you so much.
Dr. Sarkar: Thank you.
[♪ Magic Number by De La Soul♪]
♪Three
♪That’s the Magic Number
♪Yes it is
♪It’s the magic number
♪Somewhere in this hip hop soul community
♪Was born 3 Mase Dove and me
♪And that’s the magic number
Jordan: Thank you for joining us. We just spoke with Dr. Amites Sarkar about math history. If you missed any of the show, go to our website: KMRE.org and click on the podcast link.
♪Casually see but don’t do like the Soul
♪’Cause seein’ and doin’ are actions for monkeys
♪Doin’ hip hop hustle, no rock and roll
♪Unless your name’s Brewster, ’cause Brewsters are funky
Dr. DeGraaff: This is Spark Science. I’m Regina Barber DeGraaff.
Jordan: And I’m Jordan Baker. We’ll be back again next week. Listen to us Sunday at 5:00pm, Wednesday at 9:00pm, and Saturday at noon.
Dr. DeGraaff: If there’s a science idea you’re curious about, send us an email or post a message on our Facebook page: “Spark Science.” If you liked our show and would like to help us out, go to KMRE.org and click on the button “donate.”
Jordan: Our theme music is “Chemical Calisthenics” by Blackalicious.
Dr. DeGraaff: Our feature song today was “The Magic Number” by De La Soul.
♪And three out of every darn time
♪The effect is “Mmmm” when a daisy grows in your mind
♪Showing true position, this here piece is
♪Kissin’ the part of the pie that’s missin’
♪When that negative number fills up the cavity
♪Maybe you can subtract it
♪You can call it your lucky partner
♪Maybe you can call it your adjective
♪But odd as it may be
♪Without my 1 and 2 where would there be
♪My 3
♪Mase Pos and Me
[♪Blackalicious rapping Chemical Calisthenics ♪]
♪ Lead, gold, tin, iron, platinum, zinc, when I rap you think
♪ Iodine nitrate activate
♪ Red geranium, the only difference is I transmit sound
♪ Balance was unbalanced then you add a little talent in
♪ Careful, careful with those ingredients
♪ They could explode and blow up if you drop them
♪ And they hit the ground
[End of Transcript.]