Transcript for Janna Levin — Mathematics, Purpose, and Truth

May 31, 2012

Krista Tippett, Host: Janna Levin is a theoretical physicist studying the shape of the universe, and whether it is finite or infinite. And she's written a novel that poetically evokes the boundaries where mathematics presses on grand questions of meaning and purpose in human life. Such questions, she says, helped create the technologies that are now changing our sense of what it means to be human: How do we know what is true? And how free are we, really?

Janna Levin: There is no clear way, I don't think, of making sense of an idea of free will in a pinball game of strict determinism or in a game which has elements of random chance that are just sort of thrown in. So it doesn't mean that there isn't a free will. It might be that this convincing feeling I have, I am executing free will, is actually because I'm observing something that is there. I just can't understand how it's there.

Ms. Tippett: "Mathematics, Purpose, and Truth." I'm Krista Tippett. This is On Being — from APM, American Public Media.

Janna Levin is a professor of physics and astronomy at Barnard College. I interviewed her in 2007 after the release of her novel A Madman Dreams of Turing Machines. It centers on the lives and ideas of two pivotal 20th-century mathematicians, Kurt Gödel and Alan Turing. Turing is known as the father of modern computing, and his insights were made possible in part by Gödel's discoveries. In 1931, Gödel shook the worlds of mathematics, philosophy, and logic with his "incompleteness theorems." He showed that some mathematical truths can never be proven. Or, as he says in Janna Levin's novel, "mathematics is perfect, but it is not complete."

Gödel posited hard limits to what any of us can ever definitively know. And Janna Levin's novel evokes the force of this idea in the classrooms and coffeehouses of Gödel and Turing's day, and in her own life as a 21st-century urban scientist.

Ms. Tippett: Many people talk about childhood as a time when we all start to ask for the fist time we ask these great existential questions, like how did this all happen? How did we get here?

Ms. Levin: Mm-hmm.

Ms. Tippett: And I just wonder if you look back to your childhood, do you — can you trace your curiosity in a rudimentary form to some of the things that fascinate you now?

Ms. Levin: Oh, absolutely, I remember asking questions like that, about the origin of the universe, and what we were doing here and what it meant to be a part of the cosmos. I didn't think I would go on to be a scientist, in fact I started as a philosophy major in college.

Ms. Tippett: Right.

Ms. Levin: And I was, um, I was very negative about physics especially, I had no physics experience whatsoever, but I had this kind of comical stereotype of physicists memorizing things and being kind of rote. And I thought philosophy was after the big questions. And it's very ironic, when I look back at my childhood, that I was absolutely mesmerized by cosmology and astronomy, even evolutionary science, ideas of natural selection. They had always captured my imagination, and with these gratifying sorts of ways to think about the world, even if I didn't always understand the answers, it was sort of really a way to think about the world.

Ms. Tippett: Was there science being discussed in your home?

Ms. Levin: Yeah, my father is an M.D., and he for a few years was doing research science, um, medical research and, um, he always talked a lot about sort of scientific explanations for things. You couldn't, you know, say you smelled something without it being a discussion about the molecules, you know, the neurons firing and how neurons worked.

Ms. Tippett: OK.

Ms. Levin: And, um, so it was kind of a natural way to talk in the house. Although again I didn't overanalyze that as a child. My mother was very literary and read lots of books and was not at all scientifically inclined. So I didn't sense that my house had a sort of predominantly science, um …

Ms. Tippett: Right. Was — was there a …

Ms. Levin: … approach.

Ms. Tippett: Was there a religious background?

Ms. Levin: No.

Ms. Tippett: No. OK.

Ms. Levin: Um, you know, in a sense. My grandparents were, um, I shouldn't say no so abruptly. My grandparents were immigrants — Jewish immigrants from Europe and Eastern Europe — and they grew up with a strong religious tradition. And my parents grew up speaking Yiddish and my grandparents kept Kosher until later in their lives when they kind of gave that up. So there was a sense of tradition — very strong tradition and a very strong sense of our European history and our Jewish history. But I myself was never brought to temple. I — I didn't have a bar mitzvah and I didn't practice Judaism actually.

Ms. Tippett: OK.

Ms. Levin: I would have to say.

Ms. Tippett: I mean, tell me how you made that transition when you went to college and you were studying philosophy. How did you get captured by theoretical physics?

Ms. Levin: I think I hadn't really admitted to myself that I actually had loved science. And then I was in a philosophy class, and I was sort of impressed with the subject. We were talking about a lot of interesting things: free will and determinism and what it means to say we're free in a world that's completely, causally, physically determined. And there are all these very deep questions. And one day, a scientist came in to give a guest lecture, and they started to discuss something about quantum mechanics. And everybody in the room got very quiet. And they discussed things about Einstein.

Ms. Tippett: Right.

Ms. Levin: And what I was most impressed with is that philosophers didn't know how to respond. So I thought it was powerful. And I became interested in physics.

Ms. Tippett: And I think that this book you've written about Kurt Gödel and Alan Turing takes place very much at that intersection where philosophical questions meet scientific inquiry and scientific truth.

Ms. Levin: Mm-hmm. I think it's — yeah, I definitely came back 'round again.

Ms. Tippett: Did you?

Ms. Levin: Yeah. I mean, in some sense, I came full circle again to start asking those philosophical questions, I think.

Ms. Tippett: I mean, because this kind of — this basic question, I mean, let's start with Kurt Gödel, about truth, right? And I want you to put this into your own words, because I can't say that I can completely wrap my mind around it, but I'm utterly intrigued with it. You know, that truth would ultimately elude us. That some mathematical truths can't be proven within the realm of mathematics, which doesn't necessarily mean they're not true …

Ms. Levin: Yes, that's right. Yeah.

Ms. Tippett: … but that mathematics itself can't demonstrate their truth.

Ms. Levin: Yeah, that's right. It was a time in history when most mathematicians, I think it would be fair to say, believed that mathematics could address every mathematical proposition. And that's a fair enough thing to believe in retrospect. Why shouldn't mathematics be able to prove every true mathematical fact? So when Gödel came along and he found a very surreal kind of tangle, a mathematical proposition that makes a peculiar claim about itself, which cannot be proven within the context of arithmetic — it was in the context of arithmetic that he did this — it really shocked people. It really shook them up.

And I think the way he said it is actually the clearest and nicest way to say it: "There are some truths that can never be proven to be true." And it opens up this idea — which terrified people — that there are limits to what we can ever know. And it's not the first time it happened. If you think about Einstein's theory of special relativity, it was a similar idea. There are limits to how fast we can ever travel. We are limited by the speed of light. There are limits in quantum mechanics to how much we can ever really know. There are fundamental limits to certainty. And this all sort of happened around the same period of time that we began to accept this.

Ms. Tippett: You have a lot of scenes with Gödel in Vienna, early 1930s Vienna, in a coffeehouse, in a famous kind of intellectual gathering, which was called the Vienna Circle. And there's a scene where you have — there's this mathematician, Olga Hahn-Neurath, and her husband, Otto, who's a socialist and — I mean, these are just some of the people. Moritz Schlick was a philosopher and a logician who kind of headed this. And they often just come back to a Wittgenstein's premise — his first premise in his famous Tractatus — that "the world is all that is the case," which is a statement about a basic thing that we can know as real. And you have this moment where Gödel challenges this. And he has been thinking about this and coming up with this theory that you describe.

Reader: "On every previous Thursday, Kurt has been a silent spectator. Tonight, he looks from one person to another as he waits for the right opportunity. His temperature fluctuates while openings come and go until he throws out a question he knows they have asked themselves a thousand times, 'How do you recognize a fact of the world?'

"Moritz laughs, but not rudely, and nods, which loosens his hair only marginally from its proper place before he stops himself, slightly sorry for his reaction, as he takes in Kurt's serious expression. 'It is a fair question,' he confesses. 'How do I verify a fact of the world?' Such a simple question.

"Being honest, he can be sure only he sees. He can be sure only he touches. He watches Olga pull on a mammoth cigar. She has a calm about her, always at ease. The smoke drifts in curly plumes, sifting through her lashes. She doesn't seem to mind and even tends to hold the burning cinder vertically and uncomfortably close to her eyes.

"But what really arrests Moritz, what keeps his fingers in a frozen clutch around the cup, coffee suspended near his chin, is this question: Does Olga exist? He hangs there for what seems like a very long while. The conversation stalls, suspended along with the coffee.


"'Yes, Moritz, I'm here.'

"She reaches over and hooks his thumb with her forefinger. The rest of her fingers scramble over to clasp his hand, but all Moritz concedes is that he can feel what he has learned to describe as pressure on what he believes to be his hand."

Ms. Tippett: In the story, in the novel, all the members of the circle who were sitting at the table with him start to question almost whether they themselves are real, whether the person who's sitting across the table from them is real. And as a reader, I had that same experience. And …

Ms. Levin: That's beautiful, yeah.

Ms. Tippett: It's wonderful. And so, I mean, I wonder if you would kind of describe that scene the way you envisioned it and what's happening there for you?

Ms. Levin: Well, I really hoped that the reader would have that experience, because ultimately I think that's where the book nudges. Do you know that any of this is real, that the book isn't a figment of your imagination somehow?

Ms. Tippett: Even the book itself, right?

Ms. Levin: The book itself. That somehow you aren't the author of the book itself.

Ms. Tippett: Right.

Ms. Levin: And so I was definitely pushing on that limit of what do we know and what don't we know, what do we take to be faith, what's rational to believe, what's not rational to believe. And I think at some stage, I realized that what I was writing about wasn't so much mathematics. What I was really writing about, which I think you've struck on, is belief, what Gödel believed, what the people in the Vienna Circle believed, how they all ultimately struggled with different ideas about reality. And there is this sort of surreal vagueness to our conclusions.

Ms. Tippett: You know, you write of both Gödel and Turing, that they were besotted with mathematics. And I have to say that I feel that you, I don't know if you're completely like them in that way, but you have a real sympathy for that. You know the way you seem to delight and just in the way they live with mathematics and wrestle with it. And is that true? I mean, for you, are numbers maybe not more real than the Sun and the Earth, but as real as the Sun and the Earth? And, you know, if so what does, what does that mean exactly? How would you explain that?

Ms. Levin: Well, I would absolutely say I am also besotted with mathematics. I don't worry about what's real and not real in the way that maybe Gödel did. I think what Turing did, which was so beautiful, was to have a very practical approach. He believed that life was sort of, in a way, simple. And you could relate to mathematics in a concrete and practical way. And it wasn't all about surreal, abstract theories. And that's why Turing is the one who invents the computer, because he thinks so practically. He can imagine a machine which adds and subtracts, a machine which performs the mathematical operations that the mind performs. And the modern computers that we have now are these very practical machines that are built on those ideas. And so I would say that, like Turing, I am absolutely struck with the power of mathematics, and that's why I'm a theoretical physicist. If I want to answer questions, I love that we can all share the mathematical answers. It's not about me trying to convince you of what I believe or of my perspective or of my, sort of, assumptions. We can all agree that one plus one is two, and we can all make calculations that come out to be the same, whether you're from India or Pakistan or, you know, Oklahoma …

Ms. Tippett: Right.

Ms. Levin: … we all have that in common. And so there's something about that that's deeply moving to me and that makes mathematics pure and special, and yet I'm able to have a more practical attitude about it, which is that, well, we can build machines this way. And there is a physical reality that we can relate to using mathematics.

Ms. Tippett: So I want to pose a question to you that you pose in different ways to Turing and Gödel, or you have them contemplate in the novel. And I'll say it this way, you know: In your mind, does the fact that one plus one equals two have anything to do with God?

Ms. Levin: Are you asking me that question?

Ms. Tippett: Yeah, I'm asking you that question. I'm asking you how you think about that.

Ms. Levin: I think it's — I am — oh, you're tough. I think that it raises — if I were to ever lean toward spiritual thinking or religious thinking, it would be in that way. It would be, why is it that there is this abstract mathematics that guides the universe? The universe is remarkable, because we can understand it. That's what's remarkable. All the other things are remarkable too. But it's really, really astounding that these little creatures on this little planet that seem totally insignificant in the middle of nowhere — we're not special, we're not in a special place — can look back over the 14-billion year history of the universe and understand so much and in such a short time.

So I think that that is where I would get a sense, again, of meaning and of purpose and of beauty and of being integrated with the universe so that it doesn't feel hopeless and meaningless. Now, I don't personally invoke a God to do that, but I can't say that mathematics would disprove the existence of God either. And it's just one of those things where over and over again, you come to that point where some people will make that leap and say, I believe that God initiated this and then stepped away, and the rest was this beautiful mathematical unfolding. And others will say: Well, as far back as it goes, it seems to be these mathematical structures. And I don't feel the need to conjure up any other entity.

Ms. Tippett: Right.

Ms. Levin: And I think I fall into that camp, and without feeling, again, despair or dissatisfaction.

Ms. Tippett: I'm Krista Tippett, with On Being. Today: "Mathematics, Purpose, and Truth," with physicist and novelist Janna Levin. We tend to think time is like a straight arrow, always moving forward. But Einstein called that a stubbornly persistent illusion. And Janna Levin's novel, A Madman Dreams of Turing Machines, is structured to evoke time the way physicists know it — as relative and curved, with past, present, and future in a fluid interplay. And Janna Levin also occasionally brings herself into the story, commenting from modern-day New York City. Here's one of those passages:

Reader: "I have tried to stay out of these stories, but I am here too. I am standing on a street in a city.

"In the park, over the low wall, there are two girls playing in the grass. Giants looming over their toys, monstrously out of proportion. They're holding hands and spinning, leaning farther and farther back until their fingers rope together, chubby flesh and bone enmeshed. What do I see? Angular momentum around their center, a principle of physics in their motion, a girlish memory of grass-stained knees.

"I keep walking and recede from the girls' easy confidence in the world's mechanisms. I believe they exist, even if my knowledge of them can only be imperfect, a crude sketch of their billions of vibrating atoms. I believe this to be true.

"I am on an orbit through the universe that crosses the paths of some girls, a teenager, a dog, an old woman.

"I could have written this book entirely differently, but then again, maybe this book is the only way it could be, and these are the only choices I could have made. This is me, an unreal composite, maybe part liar, maybe not free."

Ms. Tippett: I sense that what you know about mathematics and the kinds of ideas that you spend your life with do leave you with a real nagging question about human freedom, about free will.

Ms. Levin: Absolutely.

Ms. Tippett: Talk to me about that.

Ms. Levin: Um, I think it's a difficult question, to understand what it means to have free will if we are completely determined by the laws of physics, and even if we're not. Because there are things — for instance, in quantum mechanics, which is the theory of physics on the highest energy scales, um, which imply that there's some kind of quantum randomness so that we're not completely determined. But randomness doesn't really help me either.


Ms. Levin: So either …

Ms. Tippett: It doesn't suggest to you that there is space for human decisions and for people to change the way things would go, no?

Ms. Levin: I don't see how it does. I don't see how it does.

Ms. Tippett: OK.

Ms. Levin: You know, if something randomly falls in a certain way, how is that a gesture of will? So it's either will has to do with determinism — my will strictly determines an outcome — or it doesn't. So it's very hard. There is no clear way, I don't think, of making sense of an idea of free will in a pinball game of strict determinism or in a game which has elements of random chance that are just sort of thrown in. Where does my will come in there? So it doesn't mean that there isn't a free will. I've often said maybe someday we'll just discover something. I mean, quantum mechanics was a surprise. General relativity was a surprise, the idea of curved spacetime.

Ms. Tippett: Right.

Ms. Levin: There are limits to mathematics. All of these great discoveries were great surprises, and we shouldn't decide ahead of time what is or isn't true. So it might be that this convincing feeling I have, I am executing free will, is actually because I'm observing something that is there. I just can't understand how it's there. Or it's a total illusion. It's a very, very convincing illusion, but it's an illusion all the same.

Ms. Tippett: So for you, as a scientist, you said this convincing feeling, you simply can't, you can't take that as seriously as a calculation that you can prove no matter what?

Ms. Levin: No, I can't — and no matter what. You know, our convincing feeling is that time is absolute. It is a very convincing feeling that time is absolute.

Ms. Tippett: Oh, right.

Ms. Levin: Our convincing feeling is that there should be no limit to how fast you can travel. You just go faster and faster and faster. Our convincing feelings are based on our experiences because of the size that we are, literally, the speed at which we move, the fact that we evolved on a planet under a particular star. So our eyes, for instance, are at peak in their perception of yellow, which is the wave band the sun peaks at. And so it's not an accident that our perceptions and our physical environment are connected. And so we're limited, also, by that.

That makes our intuitions excellent for ordinary things, for ordinary life. And that's how we evolve. That's how our brains evolved and our perceptions evolved, was to respond to things like the Sun and the Earth and these scales. And if we were quantum particles, we would think quantum mechanics was totally intuitive. And it's not intuitive for anybody else, but we would think that things fluctuating in and out of existence or not being certain or whether they're particles or waves or — these kinds of strange things that come out of quantum theory would seem absolutely natural.

And what would seem really bizarre is the kind of rigid, clear-cut world that we live in. So I guess my answer would be that our intuitions are based on our minds, our minds are based on our neural structures, our neural structures evolved on a planet, under a sun, with very specific conditions. So we reflect the physical world that we evolved from. So I guess — I guess the bottom line is that our intuitions are good, our intuitions are good …

Ms. Tippett: Yeah.

Ms. Levin: … for a lot of things. And that's why they're good. It's not a miracle.

Ms. Tippett: And so, I mean, as you have come to see things this way through your work as a scientist — I mean, do you live differently because of that? Do you raise your children differently because of that? Or is it just a puzzle that you hold, that you carry forward?

Ms. Levin: The question about free will?

Ms. Tippett: Mm-hmm.

Ms. Levin: If I conclude that there is no free will, it doesn't mean that I should go run amok in the streets. I'm no more free to make that choice than I am to make any other choice. And so there's a practical notion of responsibility or civic free will that we uphold when we prosecute somebody, when we hold juries or when we pursue justice …

Ms. Tippett: Right, right.

Ms. Levin: … that I completely think is a practical notion that we should continue to pursue. It's not like I can choose to be irresponsible or responsible because I'm confused about free will.

Ms. Tippett: OK.

Ms. Levin: That's being even more confused than me.

Ms. Tippett: In her novel, A Madman Dreams of Turing Machines, Janna Levin writes: "One plus one will always be two. Turing and Gödel's broken lives are mere anecdotes in the margins of their discoveries. But then, their discoveries are evidence of our purpose. And their lives are parables on free will. Against indifference, I want to tell their stories."

Kurt Gödel became delusional while at Princeton's Institute for Advanced Studies. And for fear of poisoning, he starved himself slowly to death. Alan Turing helped invent modern computer science and he was celebrated in England for helping crack Nazi codes during the Second World War. But he was later imprisoned and chemically castrated for admitting to a consensual homosexual affair. He committed suicide in 1954 by eating an apple he had soaked in cyanide.

So again, I want to ask if from what you know as a scientist how do you think about, "is there purpose to the universe," or to our lives, even if we don't have free will …

Ms. Levin: Well, I certainly think that both Turing and Gödel are examples of people living out their purpose. Even though they came to tragic ends, those were people who were committed, really, to meaningful pursuits. And if you look at Turing, for instance, he was honest to the end. He really believed in being blunt and truthful. He couldn't pretend. He couldn't be a fake. He hated this idea of fakes and phonies. And he couldn't pretend to be somebody he wasn't. He couldn't pretend to be heterosexual even if it meant imprisonment or …

Ms. Tippett: Right.

Ms. Levin: … or lethal poison. And there is a person who, even though he might not have believed in free will, still behaved in a way that I think most people would hold up as being responsible, responsible for himself and believing in truth. And Gödel also, even though he went very astray in his sort of compulsions and his paranoia and his imaginings, was very committed to being truthful, in a sense, to really following logic where it lead him and to not deceiving himself or taking an easier path. And so I think both of those are admirable examples of people living up to their innate purpose.

Ms. Tippett: And those are two extreme stories. And I do want to say that although there is real tragedy in them, you present them in a very human light. And we also see what was wonderful about these human beings and what they brought into the world. So I don't want to say that, you know, here are these stories just of tragedy.

Ms. Levin: Right.

Ms. Tippett: But, you know, just — I mean, a more kind of mundane question is, you know, how does the messiness of just of experience, you know, of all of us, you know, not just our, what we can know, but just how life unfolds, how does that impinge on, kind of, the ultimate reality of what we can know and achieve through logic and through science?

Ms. Levin: I myself would argue that we should never turn away from what nature has to show us, that we should never pretend we don't see it, because it's too difficult to confront it. I mean, I guess that's something that I don't understand about other attitudes that want to disregard certain discoveries, because they don't jell with their beliefs. And one of the painful but beautiful things about being a scientist is being able to say, it doesn't matter what I believe. I might believe that the universe is a certain age, but if I'm wrong, I'm wrong. There's something really, I think, thrilling about being committed to that. Um, and so, in my own life, I don't feel that that causes me problems. I mean, I've also, in a lot of ways, made easier choices than my two heroes, whom I wrote about.

Ms. Tippett: Right.

Ms. Levin: I do have children; they did not have children. I do have a certain sense of having a physical comfort around me that they don't have or didn't have. And in a way, I'm a much more connected person than either of those two people, even though I still have some of the affinities that they have. Maybe that means that I'll never go as far as they went in my own discoveries. I hope that's not the case, but I can imagine maybe it will be. And maybe there is a trade-off. Maybe sometimes you just have to abandon everything and pursue nothing but that. I'd like to think that if I'm lucky, I'll just get better at honing in on the jugular of things, so that I can still make progress and discoveries as a scientist or have epiphanies as a writer. But yeah, I guess we all just have to find that particular balance.

Ms. Tippett: I also sense that you're pursuing questions, beliefs, I don't know, hunches about the meaning of life or just about what matters to you in a form that calculations simply can't contain or convey, that simply can't be captured in numbers.

Ms. Levin: You mean by writing a book, for instance?

Ms. Tippett: Yeah, by writing a book.

Ms. Levin: Mm-hmm, Mm-hmm, or being engaged with the arts.

Ms. Tippett: Right, right.

Ms. Levin: Well, I think that's true. I think that the answers that we're going to get, the discoveries that we're going to make are going to be in mathematics. But they're going to be meaningless to us unless they're integrated into a sort of human perspective where we understand why we ask the questions, what the significance of the answers is for us, and how the world is going to change as a result of having made those discoveries. So I think that probably is true. I think that's why I can't quit one and become completely committed to the other.

Ms. Tippett: Right, right.

Ms. Levin: And I continue to sort of go back and forth between the two subjects.

Ms. Tippett: Janna Levin has more to say on engaging with the arts along with science. You can hear my entire, unedited interview with her on our website, In 2009, two years after I spoke with Janna Levin, the U.K. government did issue an apology to Alan Turing for charging him with "gross indecency" and chemically castrating him. Prime Minister Gordon Brown called this treatment "horrifying." However, in 2012, the British government refused to fully pardon Turing, since the fact remains that homosexual behavior was illegal at the time.

Coming up, why it matters that the universe is finite or infinite; and how Janna Levin is formed as a citizen and a mother as she spends her days with such questions.

I'm Krista Tippett. This program comes to you from APM, American Public Media.

I'm Krista Tippett, and this is On Being. Today, "Mathematics, Purpose and Truth," with physicist Janna Levin. We've been talking about her novel, A Madman Dreams of Turing Machines. It's about two 20th-century scientists, Kurt Gödel and Alan Turing, who helped bring us modern computing and who also pressed on the boundaries where science meets great questions of human life.

Your book about two scientists kind of led me on this path of reading other biographies of scientists. So I've been reading James Gleick's biography of Newton …

Ms. Levin: He's a great writer.

Ms. Tippett: … another very complicated character also. And something that reminds me of is, you know, how, what Newton discovered. You know, it wasn't just important, it absolutely changed the way people thought about the world. And I'm curious about, like, you know, what are you working on right now that is probably not accessible to most of us, wouldn't even know that these kinds of discussions are taking place? What are you working on that also, you know, starts to reshape the way you see the world around you and the way you move through it?

Ms. Levin: Well, it's funny, people have often asked, when I've been describing the work that I'm doing, they'll say, "Well, who — why should I care about that?" I'm telling something about extra dimensions and maybe the universe isn't three-dimensional, but maybe there are extra spatial dimensions. It is very abstract. We could do a whole show hammering that out.

Ms. Tippett: Yeah, yeah, yeah, yeah.

Ms. Levin: But supposing we grasp the notion of multidimensional space and spaces are finite, people say, "Why should I care about that? You know, my taxes are high. We have a war in Iraq." And these are fair questions, but my feeling is that it changes the world in such a fundamental way. We cannot begin to comprehend the consequences of living in a world after we know certain things about it. I think we cannot imagine the mindset of somebody pre-Copernicus, when we thought that the Earth was the center of the universe, and that the Sun and all the celestial bodies orbited us.

It's really not that huge a discovery in retrospect. In retrospect, so we orbit around the Sun, and we take this to be commonplace, and there's lots of planets in our solar system, and the Sun is just one star out of billions or hundreds of billions in our galaxy, and there are hundreds of billions of galaxies. And we become, you know, little dust mites in the scheme of things. That shift is so colossal in terms of what it did, I think, to our world, our global culture, our worldview, that I can't begin to draw simple lines to say, "This is what happened because of it" or "That's what happened because of it."

Ms. Tippett: Right, right.

Ms. Levin: We see ourselves differently, and then we see the whole world differently. And we begin to think about meaning, and all of these questions that you've brought up, completely differently than we did before. And I'd feel the same way if we discovered that the universe is finite or if we discovered that there are additional spatial dimensions, if these things will impact us, I think, in ways that we can't just draw simple cause and effect arrows.

Ms. Tippett: And, I mean, does it make you react to simple things differently in your life because you are closer to, you know, that cutting edge of knowledge right now?

Ms. Levin: Well, I think I will often look at what people feel is very important and not identify with what they think is very important.

Ms. Tippett: Yeah, OK.

Ms. Levin: You know, I think that's probably true. I have a hard time becoming obsessed with internal, um, social norms, how you're supposed to dress or wear your tie or …

Ms. Tippett: OK.

Ms. Levin: … who's supposed to — you know, for me, it's so absurd, because it's so small and it's so — this funny thing that this one species is acting out on this tiny planet in this huge, vast cosmos. So I think it is sometimes hard for me to participate in certain values that I think other people have. So in that sense, yeah, I guess there is a shift of what I think is significant and what I think isn't. And if I try to look at that closely, I would say the split is, things that are totally constructed by human beings, I have a hard time taking seriously, and things that seem to be natural phenomenon, that happen universally, I seem to take more seriously or feel is more significant.

Ms. Tippett: Well, give me an example. I mean, I think sometimes it's hard to draw the line. Give me an example of something for you that would be totally humanly constructed and then the other one.

Ms. Levin: Actually, this is going to sound really dangerous, but even things like who we elect as an official in our government. Of course, I take very seriously our voting process and I'm, you know, very, try to be politically conscious. But sometimes, when I think about it, I have to laugh that we're all just agreeing to respect this agreement that this person has been elected for something. And that is really a totally human construct that we could turn around tomorrow and all choose to behave differently. We're animals that organize in a certain way. So it's not that I completely dismiss it or don't take it seriously, but I think a lot of the things we are acting out are these animalistic things that are consequences of our instincts. And they aren't, in some sense, as meaningful to me as the things that will live on after our species comes and goes. Does that make any sense?

Ms. Tippett: No, it does — it makes a lot of sense. It's perspective that you bring, that you have that's different …

Ms. Levin: Yeah.

Ms. Tippett: … that's a bit larger, that's cosmic.

Ms. Levin: And it doesn't mean that I'm dismissing things as unimportant either. You know, I take very seriously what's going on in the world right now, and I'm really pained by what's going on in the world. But my perspective is to look on it as just as animals acting out ruthless instincts and unable to control themselves even though other people think that they're being very heady and intellectual.

Ms. Tippett: So I do believe and I — I mean, I think I know this that something deep is met in human beings in a sense of being part of something larger than oneself, being part of something big. And …

Ms. Levin: Well, I think we are a part of something larger than ourselves.

Ms. Tippett: Right, I think you — yeah.

Ms. Levin: I think we know that for sure. And it's a remarkable thing to know that for sure. We definitely are made up of material that was synthesized in the cores of stars, a previous generation of stars. We literally are made up of something larger than us, you know? We come from a very specific series of events in this universe, that if they hadn't happened, we wouldn't be here.

Ms. Tippett: But I think some people might listen to this and feel that if you really internalize this, that possibly everything is predetermined, that we, in fact, are not free in any way, that we are behaving like animals even when we think we're at our most civilized, you know, that life would somehow be robbed of joy and hope and transcendence. I don't experience you as a person without joy, hope, and transcendence.

Ms. Levin: No, I don't feel that way at all. I have a 15-month-old daughter and a 4-year-old son. And the overwhelming feelings I have for them, even if I believe that they're instinct, do not fade one bit, because of that. It matters to me not at all that I have evolved to feel that way. It doesn't take anything away from me whatsoever. That feeling is as real, as strong, as beautiful, as meaningful as it is for somebody who believes otherwise. And I've never really understood the argument that it takes the shine off of things, when for me, it really doesn't take the shine off of things.

For instance, let's say somebody said that they had a belief system in which it was simply posited that carbon came out of, I don't know, a blue sky one day. That wouldn't make me feel any more meaning about who I was in the world. It feels much richer to me to imagine that a cold, empty cosmos collapses with stars, and stars burn and shine, and they make carbon in their cores and then they throw them out again. And that carbon collects and forms another planet and another star and then amino acids evolve and then human beings arise. I mean, that's, to me, a really beautiful narrative.

Ms. Tippett: Physicist and novelist Janna Levin. Here's another passage from her book A Madman Dreams of Turing Machines.

Reader: "I am looking on benches and streets, in logic and code. I am looking in the form of truth stripped to the bone. Truth that lives independently of us, that exists out there in the world. Hard and unsentimental. I am ready to accept truth no matter how alarming it turns out to be. Even if it proves incompleteness and the limits of human reason. Even if it proves we are not free.

"They are here in our minds, Turing's luminescent gems, Gödel's platonic forms. There are no social hierarchies to scale. No racial barriers. Given to us along with our brains. Built into the structure of our thoughts — no bullying into blind faith, no threats of eternal damnation — just honesty, truth, and reason.

"I am here in the middle of an unfinished story. I used to believe that one day I would come to some kind of conclusion, some calming resolution, and the restlessness would end. But that will never happen. Even now, I'm moving toward a train. My heart is thumping. My lungs are working. There is a man, a woman, a bench, the glasses, the smooth hair, an umbrella. We are all caught in the stream of a complicated legacy — a proof of the limits of human reason, a proof of our boundlessness. A declaration that we were down here on this crowded, lonely planet, a declaration that we mattered, we living clumps of ash, that each of us was once somebody, that we strove for what we could never have, that we could admit as much. That was us — funny and lousy and great all at once."

Ms. Tippett: I'm Krista Tippett, and this is On Being. Today, "Mathematics, Purpose, and Truth," with physicist and novelist Janna Levin.

It seems to me that there is so much beguiling kind of mystery in science right now. I mean, even language, like dark matter. What is it? It's …

Ms. Levin: We can be pretty corny too, you know?

Ms. Tippett: No, I know, but …

Ms. Levin: There's all kinds of acronyms and …

Ms. Tippett: Right, right. But it's so, I mean, it's certainly — it is very mysterious. Whether that's the same way religious people talk about mystery or not, there's real mystery in it. Isn't that right?

Ms. Levin: Yeah. I think the secret you are uncovering is that scientists often share a very childlike wonder for the world. And so a lot of the language that we invent about the universe reflects that kind of childlike experience. So there is really, at some level, that feeling of excitement over learning about the universe and wanting it to sound a certain way. Wanting the language to reflect the mystery and the magnitude of what we're learning. So, um, so I think that's what you're picking up on.

Ms. Tippett: I know that you're now working on the idea of whether the universe is infinite or finite. And somewhat against the grain, you are pondering whether the universe is finite. Explain that to me.

Ms. Levin: There are a handful of people for — several years ago who started getting interested in this around the world. And what it would mean is it's similar to the idea of the Earth. If you're standing, as I am, in New York City and you walk in a straight line, and then you swim in a straight line, and then you walk again and swim again, you keep going in a straight line as far as you possibly can go, you will end up coming back to New York City because the Earth …

Ms. Tippett: OK.

Ms. Levin: … is not infinite. It is also not — it doesn't have an edge off of which you would just sort of fall off. And so in spacetime, it might be something like that. I travel in a rocket ship in several different directions and I find myself coming back to where I started. I think I left the Earth behind me, I see it go away behind me. And as I approach some planet in front of me, I realize, "Whoa, that's the Earth again."

Ms. Tippett: And you've made this interesting observation that several times in history when science has acknowledged limits, right? I mean, you'd be putting finitude to infinity, that that in fact has made great leaps forward possible.

Ms. Levin: Yes, it's a funny thing. It doesn't mean that we throw up our hands and say we can't know anything, you know? Mathematics is limits. "Oh, no, we don't do mathematics anymore. Or the speed of light is a fundamental limit, we stop doing physics." It's really been exactly the opposite. Mathematics has limits, and somehow, that leads people to invent a computer. The speed of light has a finite limit, which is what Einstein proposed, and he invents special relativity, and eventually a theory of curved spacetime based on this observation.

So it opens up this huge way of thinking about the world, when we kind of accept our limits and just move on. And quantum mechanics was the other example, where quantum mechanics implies a fundamental uncertainty in what we can know about physical reality. And by accepting this, we make these enormous discoveries. So I think, similarly, if we come to accept that maybe the universe isn't infinite — I mean, Einstein had this funny thing — which I'm probably overusing, because I've said it a bunch of times — but he said only two things are infinite, the universe and human stupidity. And then he said, "I'm not so sure about the universe."

So he knew that it was conceivable that the universe wasn't infinite, but he wasn't sure how to go about it. And only later did we understand how to kind of actually handle it. And if we were to discover that the universe was finite, I think it would again be something like what happened with Copernicus or like understanding that there was a Big Bang. I think it's hard for us to remember what it was like before the discovery of the Big Bang itself. That's just such a part of our worldview now.

Ms. Tippett: That there was a beginning point.

Ms. Levin: That there was a beginning, that the universe hasn't always been here, that it isn't permanent and unending and unalterable.

Ms. Tippett: This is a nuance of — we spoke at the very beginning about Kurt Gödel, this, one of the two scientists you wrote about in your novel. And, um, he said there are things that are true that mathematics — there are things that mathematics cannot prove. They might still be true, but the idea was you would have to go outside mathematics to know that. And you use phrases like, we can't see the logic of them until we step outside the logical framework. You said something like, "We have to look at them out of the corner of our eye." And to me, that again seems so resonant with life as I know it. And I just, you know, I wonder if that's a kind of idea that you also find you can translate into other aspects of knowledge and experience.

Ms. Levin: Well, I definitely think it's the reason the book was structured as a novel. I tried to stick as close to fact as possible. It's not the facts that I'm changing, it's the approach to the facts. And it's a sort of confession that no matter how I list these facts, I am somehow not able to get at the truth. The truth doesn't just drop out like a theorem if I follow certain logical steps. And I think maybe it's saying something also about maybe my own approach to science.

No matter how much I follow these logical steps, no matter how much I make real discoveries that will be unambiguous, I hope, the — in some sense, my approach to the truth, in the bigger sense of the meaning of the word, will always be a little bit out of the corner of my eye, or the visceral experience of what it really means or what the implications are. There are no true things really out — except for things as crisp as one plus one equals two — that are unambiguously true.

Ms. Tippett: Right.

Ms. Levin: And yet we know we're getting closer to the truth even though we can't always prove it.

Ms. Tippett: Janna Levin is a professor of physics and astronomy at Barnard College of Columbia University. She's the author of two books, How the Universe Got Its Spots and A Madman Dreams of Turing Machines. In closing, here's a reading from the final chapter of that book:

Reader: "Here I am, in New York City. It is the twenty-first century. This is as good a place, this time as good a time, as any.

"I am stepping off the curb. The subway entrance is just across the street. Big green orbs signify that the downtown entrance is open. Artificial light competing against the sun. There are children in the park; a woman with silver hair and a long, old coat; a couple on a bench. A yellow plague of taxis infests the streets. I walk behind some and in front of others. We all move along fixed trajectories, following our prescribed arcs. The plague disappears behind the stone wall as the old steps take me down into the subway.

"… There is no ending. I've tried to invent one but it was a lie and I don't want to be a liar. This story will end where it began, in the middle. A triangle or a circle. A closed loop with three points. A wayfaring chronicle searching for a treasure buried in the woods, on the streets, in books, on empty trains, craving an amulet, a jewel, a reason, a purpose, a truth. I can almost see it on the periphery, just where they said it would be, glistening at me from the far edges of every angle I search."

Ms. Tippett: Listen to this show again and download it at You'll also find more there about Kurt Gödel and Alan Turing. In fact, as this show is going to air, Janna Levin is helping launch a British-made short film, "The Creator," about Turing's legacy. The film is showing at the World Science Festival in New York. We'll be blogging from the festival as well, at

We've also posted some videos of Janna Levin speaking, including her thoughts on what it sounds like when two black holes collide. Take a listen at And like us on our Facebook page, that's On Twitter we're @Beingtweets.


Next time, oceanographer Sylvia Earle, a scientist with the nickname "Her Deepness." Please join us.

This is APM, American Public Media.

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is an astrophysicist and writer. She has contributed to an understanding of black holes, the cosmology of extra dimensions, and gravitational waves in the shape of spacetime. She is the author of A Madman Dreams of Turing Machines, which won the PEN/Bingham prize.