On Being with Krista Tippett

Mario Livio

Mathematics, Mystery, and the Universe

Last Updated

March 10, 2022

Original Air Date

May 20, 2010

The astrophysicist Mario Livio spent 24 years at the Space Telescope Science Institute working with the Hubble Telescope, which has revealed the reality and beauty of the Universe to scientists and citizens in whole new ways. The Hubble’s successor, the James Webb Telescope, will become fully operational in 2022, and will further some of the questions about the early formation of the Universe and the origins of life to which Mario Livio has been devoted. Krista spoke with him in 2010, and this conversation has become an On Being Classic, imparting a thrilling sense of all we are learning about the cosmos in this generation in time, our terrible earthly woes notwithstanding. Also: how scientific advance always meets recurrent mystery, from the emergence of life in the Universe to the very heart of mathematics and the puzzle of dark matter and dark energy.


Image of Mario Livio

Mario Livio is the author of seven books, including Galileo: And the Science Deniers, The Golden Ratio, and Is God a Mathematician? His current research centers on the emergence of life in the Universe.


Transcript by Heather Wang

Krista Tippett, host: The astrophysicist Mario Livio spent 24 years at the Space Telescope Science Institute of the Hubble Telescope, which has revealed the reality and beauty of the universe to scientists and citizens in whole new ways. The Hubble’s successor, the James Webb Telescope, will soon be fully operational and further some of the questions about the early formation of the universe and the origins of life, to which Mario Livio has been devoted. I spoke with him in 2010, while he was studying phenomena like dark energy and white dwarf stars. And this has become an On Being classic, a conversation which imparted me, across the years, with a thrilling sense of all we are learning about the cosmos in this generation in time, our terrible earthly woes notwithstanding; also, how scientific advance always meets recurrent mystery, from the emergence of life in the universe to the very heart of mathematics and the puzzle of dark matter and dark energy.

[music: “Seven League Boots” by Zoe Keating]

Mario Livio: Until 1998, we didn’t know that this dark energy exists. And now we know it’s the dominant form of energy of our universe. So whenever you think that you have reached some sort of a — that you cannot go beyond, OK, this is all that there is to know, and so on, somehow we discover that there is yet something even more mysterious that hides behind all of that.

Tippett: I’m Krista Tippett, and this is On Being.

[music: “Seven League Boots” by Zoe Keating]

Mario Livio was born in Romania in 1945. His early childhood was framed by turmoil that came of being born Jewish in Europe in that period. After what he describes as a few “Oliver Twist-like” years, he settled with his mother in Israel, where he became a physicist.  He has written seven popular science books, among them, though he is not a religious person, Is God a Mathematician?

Tippett: This question that is the title of your book, Is God a Mathematician?, I want to honor the fact that — the point you make, that the question itself is what’s most fascinating to you, and I’d like to dwell on that. What is interesting? Why this — what does this question mean to you, and how do you find it arising? Kind of take us there.

Livio: So the question was phrased after — there was a physicist called James Jeans, in the last century, and he once used phrases such as “God is a mathematician,” and so on; and I phrased the question based on his words, more or less. And the meaning of the question really is, how come that mathematics is as powerful as it is in explaining almost everything in the universe? That’s one part of the question. And the second part, which is equally intriguing, is, is mathematics discovered? — namely, mathematics is out there and we are just discovering the truths of mathematics — or is it an invention of the human mind and it really has no existence outside the human mind? So these are the two main questions that I try to deal with in this book.

Tippett: So let’s talk, first of all, about just the — tease out the idea of the power of mathematics. I mean, you and other scientists use words to describe mathematics that are also words that are used to describe the divine, right? Omnipresence [laughs] and omnipotence. What does that mean for you, when you hear that? What does that kind of language connote?

Livio: Well, suppose I want to describe all the basic forces of nature, or I want to describe all the basic subatomic particles of nature, and so on, or I want to describe what does the universe at large do. It turns out that the only way, in fact, that we know how to describe these things is using mathematics. And mathematics turns out to be almost too powerful in describing all of these things.

I’ll give you a very, very simple example. Sir Isaac Newton, who formulated the law of gravity and so on, so at his time, there were some astronomical observations that were done by Johannes Kepler and others, and so on. And the observations at the time were not particularly accurate. Yet, from these somewhat scanty observations, Isaac Newton managed to distill a mathematical law that describes gravity, and that law, already by the 1950s, was shown to be accurate to better than one part in a million. So the mathematical theory turns out to be even more accurate than the observations on which it was based. How come? I mean, what is it that gives mathematics such powers?

Tippett: And that kind of points at a sense that I’ve had, in conversations with other scientists across the years, that — this idea that mathematics has a reality and truth about it that may even be greater than the reality and truth of human perception or the physical world that it is measuring or describing.

Livio: Right, and I actually know a number of mathematicians and theoretical physicists who speak exactly in the terms that you just described: that they have a reality, mathematical concepts have a reality about them, which is in some sense even stronger than the physical reality that we observe. There are people who absolutely speak in those terms.

There is another aspect of it, which people found always fascinating and I find fascinating, which is, mathematicians, really pure mathematicians, they like to do things with absolutely no application whatsoever in mind. They develop all kinds of mathematical theories, and they don’t think that this will ever have any application. Sometimes they are even proud of the fact that it has no applications. And yet, decades or sometimes centuries later, it is found that those mathematical theories provide precisely the explanations needed for some physical phenomena, and so on. How is this possible? I mean, that’s part of this question of, is God a mathematician?

Tippett: I have to say that until recently, I was under the false impression that in general there was an assumption that basic mathematical truths are discovered, rather than invented, that Einstein discovered E=mc², that he didn’t invent it. And then I was speaking not that long ago with two astronomers, George Coyne and Guy Consolmagno, who told me that there is this ongoing debate about whether mathematics is invented or discovered. And then I read your book, and I find that, in fact, you’ve traced that across the centuries and that it’s very much alive today. I mean, is that something that you’re aware of — that you’ve been aware of throughout your career?

Livio: I’ve been aware of it throughout my entire career. So let me give you a sense. I mean, the “discovered” business started with Plato, I mean, so in ancient times, namely, that truths are out there and all we do is discover them, in the same way that astronomers discover new galaxies. You know, they were always there, but we just discovered that they exist.

There are others who will tell you — in particular, people who come from — neuroscientists and the like, who will tell you that, no, there is no such thing; it’s all an invention of the human mind, really, that we invent all these things, and it’s all like a game. You know, we play a game, we invent the rules of the game, and so on; it’s a bit like playing chess.

The conclusion I reached, which some people aren’t happy with, because we always like things to be black or white — I mean, people can even live with gray, but they cannot live so well with black and white.

Tippett: Right, both/and.

Livio: You see, when you pose the question like this — so is mathematics invented or discovered? — you immediately kind of give the impression that the answer has to be that it is either this or it’s that, and it cannot be both. But what I think happens is that mathematics is a very, very complex mixture of inventions and discoveries.

So I can give you an example. So you may have heard about imaginary numbers? This is like the square root of  -1. You know, there is no number that if you square it, it gives -1, because when you square a number, you multiply the number by itself. Even if the number was negative, when you multiply it by itself it becomes positive, right? So there is no square root of -1. Yet mathematicians invented a new concept, which they call an imaginary number, and they denote it by the letter I, OK? Now, once they invented this concept, then they start to discover all kinds of relations that this concept has. And those are true discoveries. The discoveries are essentially forced upon you. So that’s the difference.

Tippett: So, and like the question, is God a mathematician?, the longer you think about this question of whether mathematics is invented or discovered, you find that just the act of asking the question itself is so rich, right? [laughs]

Livio: It is, yes.

Tippett: And you end up with all these puzzles or mysteries that feel to me that they’re verging on the philosophical, and the theological as well, by implication. So you can say that our minds give rise to mathematics, but then mathematics are found to explain the physical world …

Livio: That’s right.

Tippett: … which is a very mysterious thing to think about.

Livio: Yeah, you’re absolutely right. And my colleague Roger Penrose, whom — I don’t know if you’ve ever interviewed him.

Tippett: I haven’t, but I know his work.

Livio: So he’s a very famous mathematical physicist. So he once said that there are these three worlds and three mysteries. So the three worlds are, one is the physical world. This is the world where we exist. There are chairs, tables, there are stars, there are galaxies, and so on. Then there is a second world, which is the world of our consciousness, if you like, a mental world, the world where — this is where we love, where we hate, you know, and so on; all our thoughts are there, and so on. And then there is the third world, which is this world of mathematical forms. This is the world where all of mathematics is there: the theorem of Pythagoras and so on and so forth, all these imaginary numbers and all that. So these are the three worlds.

And now come these three mysteries. One mystery is that somehow, out of the physical world, our world of consciousness has emerged. That’s one mystery. A second mystery is that somehow our world of consciousness, or mental world, gained access to this world of mathematical forms; that we were able to invent and discover all these mathematics. And third and maybe most amazing mystery is that we find that this world of mathematics provides the explanations for the physical world.

Tippett: Right. [laughs] So it’s that circle again.

Livio: Right. So there are these three worlds and three mysteries, which, of course, at the end of the day they are all part of one universe, right? But it’s an interesting way of posing the question.

[music: “Electric Counterpoint Fast” by Rainstrick Orchestra]

Tippett: I’m Krista Tippett, and this is On Being, today with astrophysicist Mario Livio.

[music: “Electric Counterpoint Fast” by Rainstrick Orchestra]

Something else that I find to be a bit in the category of something mysterious is how important beauty is to mathematicians, you know? It’s a word —

Livio: Oh, it’s very, very important. It really is very, very important, although, like beauty in the arts and so on, it is somewhat more vaguely defined. Even in the arts, I mean, there was actually a period where artists and people who talk about aesthetics didn’t even want to use the word “beautiful.” They thought they really shouldn’t talk about that, beauty is in the eye of the beholder, and so on.

But in mathematics I think that there is a little bit more of an understanding of what is meant by beauty, and generally what is meant is something that I sometimes call simplicity, and it really means something like reductionism, which means you want to be able to, with as little as possible, explain as much as possible. It’s easier a little bit to explain in physics, is that we try to formulate just a few laws of physics and explain all phenomena with those few laws, OK? And something like this applies to mathematics — I mean, there are these concepts of symmetry, in particular — that many objects in mathematics possess certain symmetries, and we like those symmetries in the way they operate in explaining everything.

Tippett: I would like to talk about group theory, the language of symmetry, which is something else you’ve worked on, in your book The Equation That Couldn’t Be Solved, which does tease out an aesthetic connection between mathematics and art and nature. Would you tell that story a little bit, to introduce that subject?

Livio: Sure. So symmetry is something we all recognize. At least, we recognize — some of us, when we hear the word “symmetry,” we only think of bilateral symmetry, the symmetry that our face has or symmetry that some building of a church has and so on. But in mathematics there are many types of symmetry. So there is what we call “symmetry under translation,” which is a symmetry that you might encounter in, I don’t know, in wallpaper, for example, where you have a certain motif that repeats itself as you move in a certain direction. Or you might encounter it in a work of music, where a certain thing repeats itself as the piece goes along. So that’s one type of symmetry.

Symmetry, basically, is a quantity that describes something that does not change. You do something, and things don’t change. For example, in the case of the bilateral symmetry, it means you basically reflect it in a mirror, and it doesn’t change. Or if you take a phrase like “Madam, I’m Adam,” this is a palindrome, which means if I read it from the back to the front, it also reads “Madam, I’m Adam.” So that’s symmetric, under this back-to-front operation and so on. So there are many symmetries, and we encounter them in shapes, we encounter them in music, we encounter them in a variety of arts, and we encounter them in physics and in the sciences.

Now, mathematicians came up with a language to describe all these symmetries, and I mean all these symmetries. Everything I just mentioned falls under one type of mathematical language, and that is the language that’s called group theory.

Tippett: And it has relevance, as you said, for wallpaper and the human perception of the beauty of a face and a melody, as well as great scientific principles. It’s really fascinating.

You know, I can’t help but make a connection here, and maybe this isn’t right, but the fact that you also in your life are a lover of art …

Livio: I am.

Tippett: … I mean, that there’s an aesthetic side to you.

Livio: You seem to be very well prepared. [laughs]

Tippett: I am. So I don’t want to force a connection here, but let me ask you this way. As you study this, especially this implication of symmetry and how that figures into the human response to beauty, did that give you insight into this passion you have for art?

Livio: I must say, it didn’t.

Tippett: No?

Livio: Yeah, no — I honestly don’t have a very good explanation for my passion for art. My family was vaguely connected to art; I, personally, I have no talents really in that area. Maybe it simply came out of admiration of what other people can do, of which I cannot do at all. But I mean, I did develop relatively early on a passion for art, and that ran kind of parallel to my passion for science. I do try to combine the two when I write, and so on, so forth, and of course, these things sort of come to my mind effortlessly. I mean, I talk about science, and some of the metaphors that I use will come from art and so on, but I do not feel that my passion for art was inspired by my love for science.

Tippett: So Einstein would sometimes talk about this core sense of wonder that was there, that was animating for him as a scientist, and he would talk about how he had that in common with the arts and religious people. I mean, so do you sense some impulses that are in you that animate these two passions?

Livio: There is no question, but these are subtle, and they may be very deep, but they are nevertheless subtle connections. Nevertheless, I mean, I think it will be false to say that science and art have in a substantial way influenced each other, or that science and religion have in a substantial way influenced each other. So I don’t think that has happened. But they all stem from this sense of wonder.

Tippett: Right. And see, that’s more interesting to me than trying to force that relationship. But I think that particularly happens in American culture that when we talk about science and religion, not to mention art in the same breath, we try to come up with something more linear. [laughs] I mean, I’m curious —

Livio: I completely agree with you on this. I mean, there is a certain way in which I — and I’ve given this some thought. I have — I am not myself a religious person, but I have great respect for religions of everybody, and I have many colleagues who happen to be religious people. And by that I mean Jews, Christians, Muslims — from various religions. And I think that the way that I find that that develops is by something — exactly by not forcing these things. Namely, a person who feels a need for God does not want, I think, a God that created the universe however many years ago and then left this universe to its own devices. A person, I think, who has a need for God needs a God that is there for him or her every day, every minute, every second. Science has nothing to say about a God like this. This is in a completely parallel plane than the plane in which science operates. So I think that the places where you generate these unnecessary clashes are when actually people try to force the connection, which is exactly what you said. I really don’t want to offend anybody, but I think that this does a disservice both to science and to religion.

Tippett: Right. You know, something that’s intriguing —

Livio: I mean, I hope that you agree with me. I mean, I …

Tippett: I do. I do agree with you. [laughs] I agree with you, but — I agree with you, but I —

Livio: But feel free to disagree with me, too.

Tippett: No, no. Well, I would, but I also — I think that we have to keep putting — I mean, the way you say it is different. It comes out of your experience and your perspective. And something that also intrigues me, I mean, you said you’re not a religious person. And of course, Einstein wasn’t a religious person in the sense of believing in a personal God. Something that interests me in his work and that I find coming up again in your writing is — in your writing and in the writing of other scientists, is that even scientists — perhaps because, as you said, however much we discover, there’s still so much that’s largely inexplicable — that people end up using the word “God.” You know, like he would say, “I needed to know what God was thinking.”

Livio: Or when he says, “I don’t think God plays dice.”

Tippett: Well, and right. That was not a — that was about quantum physics, right? [laughs]

Livio: Right; no, but you see, when he said that, he did not mean to say that he knows how God spends his time. What he meant to say by that is, “I don’t think that the universe works in this way,” and so on. And that’s the same sense of the question, is God a mathematician?, namely, how come mathematics is as powerful as it is in explaining the universe? It’s not meant to ask what is the profession that God has.

Tippett: Right. Right. But is there something revealing in the fact that that word, “God,” in these moments when the great questions are being posed, that even scientists reach for that word, “God”? Not, I’m saying, as a statement of belief, but there’s —

Livio: Yeah, I’m not sure. I think that, yeah, in a way, yes, that is taken to mean some unifying feature of the universe.

Tippett: And is that kind of what’s behind that word for you, even when you use it in the title of the book Is God a Mathematician?

Livio: Yeah, I like — somebody asked me something like that, and, oddly enough, because you actually wrote a book with that title, I said that I mean “God” exactly as an Einsteinian God: that it’s in some sense a synonym to the workings of the cosmos.

[music: “As the Stars Fall” by The Cinematic Orchestra]

Tippett: After a short break, more with Mario Livio.

[music: “As the Stars Fall” by The Cinematic Orchestra]

I’m Krista Tippett, and this is On Being. Today, I’m with the theoretical astrophysicist Mario Livio. He spent 24 years at the Space Telescope Science Institute, which coordinates the science operations of the Hubble Space Telescope, which launched in 1990, and the James Webb Telescope, which will be fully operational in 2022. This science has allowed the rest of us to see some of the phenomena Mario Livio has studied — extrasolar planets, neutron stars, white dwarf stars — and the formation of galaxies in the early universe. This is a classic On Being conversation, taped in 2010, and it is as illuminating today. It’s formed me across the years with a basic sense of how scientific advance meets recurrent mystery, including the very heart of mathematics as the element and language of science.

In the book Is God a Mathematician? and in a lot of your work, you do take a long view of time and history, and so you trace the history of human fascination with mathematics and scientific work with mathematics, beginning with Pythagoras and Plato, to the present day. And I wonder if there was anything that you saw in tracing that history that you learned about our present reality that really gave you something to work with, as context that you hadn’t quite seen before.

Livio: Well, the same type of questions that mathematicians or scientists dealt with even thousands of years ago continue to intrigue us today. And in mathematics, even more so than in other sciences — I mean, physics, for example, the physics of Aristotle is not the same as our physics today. I mean, the questions were the same, yes? I mean, he also tried to explain the universe around him, and so do we, but we don’t use the same physics. In terms of mathematics, we largely use the same — well, mathematics has evolved, but the mathematics that the ancient Greeks did is still true today, in those areas where it applies. So I mean, students today in school learn the same geometry that Euclid did at 300 B.C.

Tippett: Right. It’s the closest thing science has to eternal truths, I guess. [laughs]

Livio: Right, although somebody once told me, and I think they were right, that philosophy is actually another area where — as you may know, Alfred North Whitehead once wrote that all of Western philosophy is just a series of footnotes to Plato. So in philosophy we also still use many of the ideas of the ancients. But in many of the sciences we don’t, really.

Tippett: That’s interesting. I mean, one thing that strikes me, reading and getting an historical view of this, is it’s only really a couple hundred years ago that religion overtly was taken out of the equation, right? I mean, Galileo, Kepler, Copernicus, to some extent Darwin, I mean, they lived in a world that was infused with religion, and their religious imagination was not quite separate from their scientific imagination. But then that changed, culturally, and it changed in the culture of science, and we have ever more increasingly sophisticated systems of logic. And yet, in science right now, and especially in physics, it seems to me that there’s as much mystery as there ever was, or more mystery; that’s there’s less determinism; [laughs] that there’s more that is simply bizarre and unanswerable. And that just seems like kind of a paradox to me, to have those two phenomena side-by-side.

Livio: Yes, I mean, but you must realize that something somewhat similar happened, also, in terms of the relationship between philosophy and science. You know that Galileo’s position was called a philosopher; so all the people who dealt with natural sciences were at one point called “philosophers.” But once physics in particular started to become more mathematical and more quantitative, then, philosophy and science, like physics, sort of parted ways in some way. I mean, even though they continued to some extent to deal with the same or similar questions, they still went on somewhat different paths. The parting of religion and science I think happened roughly around the same time. So as physics became in particular more predictive, then this is when people started to talk less in terms of religion and so on, and more in terms of, when they want to describe nature, they talk in terms of precise sciences and so on. So I think that that happened.

Now, you’re absolutely right that with the realization of quantum mechanics and so on, we did discover that our world is not deterministic, it’s not fully deterministic, in the sense that we cannot really predict the results of an experiment; we can only predict the probabilities of different results, which is not the same thing, yes? I mean, the probabilities are actually fully deterministic. I mean, we can use quantum mechanics to calculate the probabilities for different results. But we cannot calculate the results themselves. So that is an interesting development of the 20th century.

[music: “Arrumacao” by Uakti]

Tippett: I’m Krista Tippett, and this is On Being, today with astrophysicist Mario Livio. His career working with the Hubble Telescope at the Space Telescope Science Institute spanned three decades.

[music: “Arrumacao” by Uakti]

My sense is that — so, for example, there’s the part of you that loves art and there’s the part of you that does science. And my sense is that you don’t need your science to reflect on that one way or the other. You don’t need your science to tie up all the questions of life.

Livio: Well, the questions of life are very, very complex, of course. I try to answer much simpler questions, as some very distinct phenomena that we observe in the universe and which we don’t understand, like this phenomenon of dark energy that is pushing the universe to expand faster and faster. So we don’t — at the moment, we hardly have a clue what that is. And I’ve given quite a bit of thought to what this might be, and, I must say, not with much success so far. But so I do try to use my science to answer very specific questions.

I mean, the thing is that in science, unless you have a well-defined problem — and in mathematics, too — then it is virtually impossible to actually answer it. So I try to, when I look at some phenomenon that is about the universe, I try to ask myself, OK, what is the biggest question we don’t understand about this? And then I try to see if I can do anything to try to answer that question. Now, when it comes to things such as life and things like that, these are inherently very complex situations, where I wouldn’t even dare try to — very often, I don’t even know what question to pose, let alone to try to find an answer.

Tippett: [laughs] That’s a good way to make that distinction. That’s true of life, we’re often not even asking the right question.

Livio: No; I mean there are, of course, people that do very, very important work in this respect, but they try to take — I mean, the people who do the best work are those who try to take baby steps, instead of trying to — so like, I don’t know, Jack Szostak, who tries to do work on the origin of life, OK?, so very simple experiments. I mean, they don’t try to take a test tube and see whether a baboon walks out of that. They try to do very, very simple experiments on how, for example, a membrane can form, or something like that, and so on. And I think that that’s the way to make real progress in these areas.

Tippett: I just want to ask you a couple more questions.

Livio: Please.

Tippett: I’ve read that something that’s important to you is that science and mathematics should be communicated better in the same way that literature and poetry are: as part of human culture. And I think that’s —

Livio: That is absolutely true, yes.

Tippett: So I wonder, you’re at the Hubble Telescope. We’ve hardly even spoken about that. But so how, if I ask you how you would like people to imagine the work you’re doing there as part of culture —

Livio: So actually, the work I do with the Hubble, that’s the easiest part, actually, deal with that, because if Hubble has done one thing — other than all the scientific discoveries, what Hubble has done is it has literally taken the excitement of discovery and brought it into the homes of people. I mean, you see now Hubble images everywhere. I just saw, the other day, one of these late-night shows, where a person just started showing Hubble images one after another and so on. And the rock group Pearl Jam chose a Hubble image for the cover of one of their albums. So Hubble images are so astounding, and they are so visually beautiful, that people really can appreciate this, because in that case they do something that is in some sense even more than a work of art, because on one hand they are extraordinarily beautiful, and at the same time people realize that this is something real that exists out there; it doesn’t come out just from somebody’s imagination. So they realize that there is all this incredible beauty in the universe that surrounds us. So Hubble has really been fantastic in communicating science to the public, and hopefully inspiring young people, in particular, to get more into the sciences.

Tippett: Again and again, scientific discovery has reframed our cultural imagination about who we are, and what the cosmos is, and our place in it. So I want to ask you, what are you working on now that comes closest to doing that for you? What are you working on now that you think might ultimately reframe, not just your imagination but all of our imagination about some of these big questions?

Livio: Well, one thing I mentioned is that I’m involved in these studies of this dark energy. I mean, we knew that our universe is expanding, we knew that since the 1920s, but we thought that this expansion should slow down. Instead, in ’98, we discovered that the expansion is speeding up. It is propelled by something. For lack of a better name, we call this something dark energy, and we now know that this dark energy is more than 70 percent of the energy of the universe, but we still don’t know what it is. So that’s one thing we’re trying to basically find more of, the properties of this dark energy.

On the other hand, I try to work on extrasolar planets. By that, I mean planets around other stars. Until 1995, we did not know of a single planet outside the solar system that revolves around a sun-like star, and we now know about such planets that revolve around other stars.

Tippett: Because we’ve been able to see them?

Livio: Well, mostly we discovered them just by their small gravitational pull on their parent star. But in a couple of cases, and Hubble actually played a very important role in this, we were able to actually image a planet like this. With any luck, we will eventually be able to even see them directly, and we have started to determine the composition of the atmospheres of some of these planets, and so on. And of course, the ultimate goal would be eventually to find if there is life elsewhere, and intelligent life in particular. So part of my work is about this. So in some sense I work about some of the smallest things, namely, planets around other stars, and about some of the biggest things — I mean, things that push the universe as a whole.

[music: “The Lion” by CTB]

One of the things that we have done, in science in general and in physics in particular, is we continuously push both farther and farther back in time, and into areas that we didn’t know before. So for example, until, I don’t know, Copernicus we thought that the Earth is the center of the universe. We then discovered that the Earth is not even at the center of the solar system. We then discovered that the solar system is not at the center of our galaxy, the Milky Way galaxy; we are about two-thirds of the way out. Then, astronomer Edwin Hubble discovered that there are billions of galaxies like ours, and in fact, with the Hubble Space Telescope we have shown that there are about 200 billion galaxies like ours just in the observable universe. And so on. And of course, we also — in terms of time, we now can talk about things that happened a fraction of a second after all space and time of the universe came into being.

Now, the interesting thing is that even though we keep pushing these boundaries and so on, we somehow always find new mysteries. Until 1998, we didn’t know that this dark energy exists, and now we know it’s the dominant form of energy of our universe. So somehow, whenever you think that you’ve reached some sort of a — that you cannot go beyond, OK, this is all that there is to know, and so on, somehow we discover that there is yet something even more mysterious that hides behind all of that. And this is very interesting, because it also plays a very interesting role in terms of the human mind, because, you see, our physical existence has become more and more miniscule in all of this, but our minds somehow manage to get around all of this. All of these things are discoveries that we made. So in that sense, we are very central to all of this. I mean, if we didn’t make these discoveries, we wouldn’t be talking about them.

Tippett: We are very central, even as everything we are discovering makes us smaller and smaller in the grand scheme of things.

Livio: Exactly. Physically smaller, physically smaller and smaller, but our minds become more and more important in all of these things, because our minds expand at the same rate — well, our knowledge if you like, expands at the same rate that everything I talked about in the universe. I mean, we will discover more and more things about life, about how the brain works, about how life originated, all these things. So this is really very, very fascinating, how we are doing all of this, and just imagine what would happen if, or when, we discover intelligent life elsewhere. This will be a revolution that humankind has never experienced, actually.

Tippett: And one of the places this takes me is back to just — and I don’t know what the future will be of the science–religion discussion or interplay or whatever that is, but part of where it came to in the 20th century was this idea that science was pushing religion farther and farther out of the picture, because science ultimately was going to answer all the questions, right? But as you’re saying, what’s happened in the 21st century, as we’ve built on these discoveries of the 20th century, is that in fact there’s just this exponential increase in questions and even in what you call mystery — or religious people even —

Livio: Lord Kelvin, you know, has been claimed to have said that everything has been actually solved already, and there are just two small problems that remain to be solved. And as it turned out, those two problems led to quantum mechanics and general relativity, the two greatest scientific revolutions of the 20th century. So surely, this is how things are happening, and we have had a number of occasions of — there are those things where — another famous physicist once said, “Who ordered this?” I mean, so who ordered dark energy? I mean, as if we didn’t have enough to explain as it was already, and then suddenly this thing appears, and it’s now the most, perhaps, intriguing question in all of physics.

You know, some people sometimes ask me if I’m fascinated by science fiction, and I like to say that actually, real science is way more fascinating than any science fiction I’ve ever read, because there is really so much there to do, and there is so much room for imagination and creativity that I certainly hope that people will go more into that and do more of mathematics, science, engineering, and so on. And I don’t mean by that that everybody needs to become a mathematician. Absolutely not. I mean, [laughs] God forbid if everybody was a mathematician.

Tippett: Even if God is a mathematician. [laughs]

Livio: Yeah. But what I mean by that is that understanding, indeed, that mathematics and physics and so on is a part of human culture and a very important part of human culture, which has also led us to where we are to a large extent right now, is something that is extraordinarily important for society in general. And even for people who at the end don’t become professional scientists, I mean, thinking in those terms and learning those logical systems and the tools that are provided by things like mathematics are very important for every aspect of our everyday life.

[music: “Kit and Pearle” by Dosh]

Tippett: Mario Livio is an astrophysicist and science educator, who spent 24 years with the Hubble Space Telescope. His current research centers on the emergence of life in the universe. His most recent book is Galileo: And the Science Deniers, and he’s also the author of The Golden Ratio and Is God a Mathematician?

[music: “Kit and Pearle” by Dosh]

The On Being Project is: Chris Heagle, Laurén Drommerhausen, Erin Colasacco, Eddie Gonzalez, Lilian Vo, Lucas Johnson, Suzette Burley, Zack Rose, Colleen Scheck, Julie Siple, Gretchen Honnold, Jhaleh Akhavan, Pádraig Ó Tuama, Gautam Srikishan, April Adamson, Ashley Her, Matt Martinez, and Amy Chatelaine.

The On Being Project is located on Dakota land. Our lovely theme music is provided and composed by Zoë Keating. And the last voice that you hear singing at the end of our show is Cameron Kinghorn.

On Being is an independent, nonprofit production of The On Being Project. It is distributed to public radio stations by WNYC Studios. I created this show at American Public Media.

Our funding partners include:

The Fetzer Institute, helping to build the spiritual foundation for a loving world. Find them at fetzer.org;

Kalliopeia Foundation, dedicated to reconnecting ecology, culture, and spirituality, supporting organizations and initiatives that uphold a sacred relationship with life on Earth. Learn more at kalliopeia.org;

The Osprey Foundation, a catalyst for empowered, healthy, and fulfilled lives;

And the Lilly Endowment, an Indianapolis-based, private family foundation dedicated to its founders’ interests in religion, community development, and education.

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