Janna Levin —
Mathematics, Purpose, and Truth

An astrophysicist who studies the shape of the universe, Janna Levin has also explored her science by writing a novel about two pivotal 20th-century mathematicians, Kurt Gödel and Alan Turing. Both men pushed at boundaries where mathematics presses on grand questions of meaning and purpose. Such questions, she says, help create the technologies that are now changing our sense of what it means to be human.

Share Episode

Shortened URL


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.

Pertinent Posts

About the Image

Located in the Bolivian Andes, Salar de Uyuni is the world's largest salt flat. The irregular, hexagonal cells are naturally occurring phenomena called Bénard cells. Scientists are trying to understand why these convective cells adhere to deterministic laws at the microscopic level but result in a non-deterministic arrangement, as you see here.

Episode Sponsor

Share a Reflection



I don't think that's a fair reflection on the history of science. I think we can say we are improving our understanding (of the universe, for instance), but every major turning point in the history of science has opened up for us far more questions than it has answered. It has allowed us to open our minds and our understanding to a whole new variety of possibilities. To paraphrase Bertrand Russell's famous comment regarding philosophy: it is not the goal to find THE answer, but to keep us moving forward.

Sorry to put this here, but I can't find another feedback form.

The question you posted:

How do you reflection on Levin's statement that "we're getting closer to the truth even though we can't always prove it.

doesn't seem to be grammatical.

It SEEMS to mean "what are your reflections on..." or "how do you reflect upon..." but I'm really not sure.

Perhaps you'd like to fix the question to help others.


there is no "R" in Godel (with an umlaut). The lips are puckered to pronounce the umlaut, but it doesn't make an "R" sound. Saying "Gerdel" is not the correct pronunciation.

I am "truthfully" intrigued by the use of reflection as a verb. In effect, that is a truth that is becoming more and more prevalent in the American reality. Thank you, Krista, for such a program. Always engaging, always stimulating. Reflecting on Levin's statement that "we're getting closer to the truth even though we can't always prove it." is not an exception. The reality is just when, where and how we define "truth". Time and space in conjunction with the "howness", a term frequently used by philosopher, mystics especially Sufis, all affect what falls in or out of truth. What is this truth to which we are getting close? Throughout human history, humans have been getting closer and closer to a truth, no matter what that truth is, be it scientific (mathematical, physical...) on one side or philosophical (metaphysical, spiritual, religious...) on the other. The cumulative knowledge make it so, in general, that truth is clearer, more so as we incrementally advance that knowledge. I believe that this doesn’t mean that someone, somewhere throughout the time of accumulating the human knowledge, did not reach, somehow, the truth at its utmost certainty. I believe that Levin’s statement might have been more accurate had it stated that we are getting closer to proving the truth rather than “… we can’t always prove it”. If the question is about the universe, the truth is more so provable mathematically in the most primordial and physical sense of Mathematics, than ever before. If the question is the creation, particularly beyond the “zero nanomoment” and the creator of that Universe, the truth is still so fluid and not as physically provable without the help of some other finite or infinite dimension, be it faith, metaphysics or some other logical or illogical way, since proving non-physical is not always achievable with the physical alone. The truth is that, admittedly, we are limited in what we can know about the “Truth”, if at least temporarily. Great show, great subjects, Krista. Thank you, Moulay

"with the truth one cannot live" Otto Rank

Scientists assume that there is "A Truth", lying in state, waiting to be discovered. That each step we take to uncover it takes us closer to The Truth one additional iota.

Every description of reality, be it by observation or physical model, is necessarily partial and incomplete. We all resemble the proverbial blind Indians describing an elephant they know by touch.

The attempt to explain the universe and human existence using physics and brain chemistry alone is necessarily a reductionist, "blind Indian" view.

This is where God comes in. It is the indescribable infinity that encompasses the universe, of which we can receive fleeting, partial, imperfect glimpses -- guided by the power of awareness.

And this is the explanation of free will. We all possess free will, whether or not we are aware of it. One cannot make the simplest moral choice without free will.

It is not the narcissistic, "New Age" free-will that purports to wield control over our entire existence; rather, it's the fleeting ability, guided by awareness, to navigate between constraints of reality and the free-will actions of our neighbors.

So if physics or biochemical models cannot describe free will, its source must come from the realm beyond them.

It makes me personally think of a few passages from Rebecca Goldstein's book about Kurt Gödel ("Incompleteness - The Proof and Paradox of Kurt Gödel"). I guess my attitude about that statement depends very much upon "how much" truth we're shooting for, and if it matters to you that there might be an endpoint to the game, that we can't overreach, with a vast array of truths still "out there" forever beyond our reach. If you're going for broke so to speak, assuming that in principle it's possible for us to zoom in on each and every truth, then I do think that assumption must always be a matter of faith not proof, precisely because of Gödel's work. Here are the passages that statement made me think of. Mull over them a bit, and I think you might get the gist of why I feel the way I do:

From "Incompleteness - The Proof and Paradox of Kurt Gödel" (pg. 202):

Gödel himself was far more reserved about drawing conclusions concerning the nature of the human mind from his famous mathematical theorems. What is rigorously proved, he suggested in his conversations with Hao Wang as well as in the Gibbs lecture that he gave in Providence, Rhode Island, 26 February 1951 (which he never published), is not a categorical proposition as regards the mind. Rather what follows is a disjunction, an "either-or" sort of proposition. That is, he was admitting that nonmechanism doesn't follow, clean and simply, from his incompleteness theorem. There are possible outs for the mechanist.

According to Wang, Gödel believed that what had been rigorously proved, presumably on the basis of the incompleteness theorem is: "Either the human mind surpasses all machines (to be more precise it can decide more number theoretical questions than any machine) or else there exist number theoretical questions undecidable for the human mind."

What exactly did Gödel have in mind with this second disjunct. I "think" that what he is considering here is the possibility that we are indeed machines -- that is, that all of our thinking is mechanical, determined by hard-wired rules -- but that we are under the "delusion" that we have access to unformalizable mathematical truth. We could possibly be machines who suffer from delusions of mathematical grandeur. What follows from his theorem, he seems to be suggesting, is that just so long as we are not delusional as regards our grasp of mathematical truths, just so long as we do have the intuitions that we think we have, then we are not machines. If indeed we truly have the intuitions that we do, then it is impossible for us to formalize (or mechanize) all of our mathematical intuitions, which means that we truly are not machines. Of course there is no "proof" that we know all that we think we know, since all that we think we know can't be formalized; that after all, is incompleteness. This is why we can't rigorously prove that we're not machines. The incompleteness theorem, by showing the limits of formalization, both suggest that our minds transcend machines and makes it impossible to "prove" that our minds transcend machines. Again, an almost-paradox.

An extremely interesting conversation. I made me want to run right out and buy her books. The conversation regarding her thinking on religion and the last statement about there being no space until it happened (or words to that effect) is the most interesting to me. Would like to read more about her thoughts.
I have a room of books on Religion and I would like to get outside of it.

I agree! I just listened to the latest interview on her new book, and have the same reaction. I see your note from 2010 and wonder how your experiences have been and would you recommend running out and buying her books? Did you find an interesting path, or a dead end?
I'm intrigued.

I really enjoyed listening to the mathematics, + truth, purpose podcast. I think that the truth can be proved and defended. We may differ on the basis for the proof or defense; I would rely on the scriptures more than a mathematical or scientific test as the method for the demonstration. First, I believe the words of Jesus: “I am the way the truth and the life. . .” John 14.6. This is not to minimize the beauty or progress that has been achieved through developing the concepts of particle theory, quantum mechanics, unraveling DNA and mapping the human genome. When I consider the question about truth I also think of the words of Pilate to Jesus: “What is truth?”

One of my sincere questions on how it happened is the stopping and turning back of time on earth, as recorded in the scriptures: Joshua 10.12-13 and 2 Kings 20.11. As a matter of faith I believe these events occurred as they were written. Perhaps the space-time understanding that Einstein developed brings some degree of explanation to this. My mother-in-law recently challenged me on God’s first creation. I was thinking well of course it was the heaven and the earth. Her proposition to me was that the first creation was time, and the continuation of that thought is that God, being outside of and not limited by the time created, will at some point in the future cause the cessation of time. Even the concept of future is only from my perspective, not God’s.

As concerning the concept of free will, and I would by-and-large agree with Levin’s conceptualization, especially the difference between the human constructs and the forces described through mathematical formulae. It may be a bit of a quip, that freedom is not free, but I think it speaks to the concept that we have limitations, responsibilities and purpose that define our understanding of freedom. Perhaps when we escape the boundaries of one reality – human or scientific – we then enter a new freedom that later we will challenge, and so on.

One poem that came to my mind during the podcast was Mary Oliver’s poem “The Summer Day”. If you have a moment, take some time to read this poem and reflect. It takes me from an abstraction of things we may not know to a specific grasshopper that we can see, handle and enjoy. This is kind of a passage from ethereal truths we can only dimly see, to the physical ones we can.

Mathematics, Purpose, + Truth was a segment that featured Janna Levin, a theoretical physicist who wrote a novel named A Madman Dreams of Turing Machines. She began her career in science with little interest, instead she thought that philosophy was asking all of the really good questions. Obviously she still pursued her career as a physicist but she has a special interest in areas where the scientific meets the philosophical. Specifically, she is interested in areas where truth cannot be defined or where truth is entirely humanly constructed.

One of the underlying concepts of her book was the idea that not all mathematical truths can be proven to be true but rather must just be accepted. Along these lines she talks extensively about what is real, what is not, and how we can tell the difference. Another idea that she brought up was that our convincing intuitions are specific to the type of beings that we are. An example that she brings up is that our visual perception quality peaks at the frequency for the color yellow, which is the color of the sun. She states that we are formed in a way that helps us decode the world around us. One of the other interesting points that she brings up is the idea of voting for government officials. This is an entirely humanly created process that she thinks is peculiar that we can all come together and agree to respect and follow the leadership of one man. As a student who is studying sociology at the same time, this podcast stresses the value in having the ability to distill the elements and the means of sociology and examine them individually for their truths. Janna Levin is not confined by social norms but chooses to see past them, not out of rebellion but as an exploration of what might be real that lies outside what we think is real.

Prof Levin,
I really enjoyed your unedited interview with Krista Tippet, especially the part that talks about a "Finite World". I'm and aircraft technician with Continental Airlines and a Chief in the Navy Reserves who enjoys learning about Space. What prompted me to email you was in your interview you said that the "World is Finite". After that I recalled a story in the news that a father & son team placed an I Phone with a video camera into a styrofoam capsule and launched it into Space (80 miles short) by using a weather ballon as it's power. The unit was launched from Newburgh N.Y. and it was retrieved 30 miles away from it's launch point. I discussed this with my coworker's but the didn't understand how this could land so close to is starting point. Could this be a "micro view" of something that travels in a straight line and arrives back or close to where it started? I have to purchase you books now... There's so much interesting things in books. Thanks again. Reggie Spence

Krista, i sent this email to Janna Levin. Take Care. Reggie.

I think Levin is speaking to the process of science, whereby scientific theories must be falsifiable. This self-correcting process of science (that religion, for example, lacks) results in a catalog of tested theories that provide the most reliable way of seeing nature as it actually is, which for Levin is where the truth lies regardless of our cherished beliefs. Nonetheless, because our senses evolved in a relatively confined natural environment, powered by a three-tiered evolutionarily jury-rigged brain notoriously prone to error, we have to be careful in claiming to have proofs of truth.

Well, falsifiable is a good start but Lakatos and others showed that it's really not a sufficient condition for a theory to be considered scientific. While I certainly agree with you that the issue is how to deal with the fallibility of our assessments I think the search is still on for the best way to do that.

An interview with an author who is "besotted with mathematics"

Levin's "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" is the dimness before the dark. See Adam Curtis' BBC documentary The Trap for the lights out on quantification.

These ideas always give me the "wow" sensation. Though I am a redneck, I do have a degree in Physics. OK, I flunked out of it at grad school., but the blogger who said she likes the Iris DeMent song...I get it as well.

I just discovered On Being and Krista Tippet and am really excited about scanning the archives. Though I'm really looking forward to it, I haven't listened to this show or read Levin's book yet. Therefore I should probably obey Wittgenstein's injunction but what the heck, this is the age of impatience. Re. the line in the blurb: "Their work laid the foundations for computer intelligence while challenging fundamental notions about how we can know what is true." it's always been my contention (despite having spent a career as a physicist) that nobody has yet been able to show that Godel's incompleteness results didn't forever damm attempts to argue that scientists are converging on any sort of definable truth. As a human activity it seems fine to me that scientists proceed with a belief in convergence but I think Godel's result present a profound challenge to epistemology and as a result lower the high horse of arguments about scientific omniscience a bit. But maybe Levin and Tippet clear this all up. Hope so !

The below is something I wrote earlier. Apologies, It's long, but it fits.... Thank you for your fine program.

Two rules of thumb in physics:

The simpler and more elegant a theory, the more likely it is to be correct.

To know is not to know what—but to know how.


Observation and common sense agree: Systems in conflict do not cohere. But while the forces in the universe seem to work together well enough, our models of them don’t. Something is wrong, and that is why finding the Theory of Everything has become the “Holy Grail” of physics. It’s done with math. One way math does it is to see what happens inside a universe of more than the four familiar dimensions of breadth, depth, height, and time (e.g., “movement”), and what they find is, by adding one or more dimensions to the right equation, they can enhance its simplicity, its resonance and, strangely enough, its chances of revealing reality.

Spiritual phenomena also unify when viewed from a higher plane. And since, like with physics, we have to start somewhere, why not begin with the assumption right action has intrinsic worth: that virtue is its own reward? And, again, we must define our terms if they are to reveal themselves. For example: Faith joins doubt because faith is not fact. It can’t be. By definition. Yet faith is concrete. We wouldn’t walk down the street without it, but it is the doubt in faith that gives us room to maneuver. Which is why, in a world where anything may be possible, it actually makes sense to cast our lot with the highest good we can conceive. If only to reveal us to ourselves. If for no other reason than to be happier. Don’t we do this already in every other field of endeavor? As a matter of course? Why should “religion” be different? The optimist thinks, "There’s got to be a way." The pessimist thinks, "Why try." (Who do you think stands the better chance of winning?)

Rising above the bickering gods of polytheism, monotheism, too, is a Theory of Everything. Just as physics addresses the how of everything, monotheism addresses the why. But monotheists who regard the idea of one God as nothing more than a number end up spawning as many gods as there ever were (and we are right back where we started). We need to go deeper and we can. For instance: By challenging religion, heresy helps faith understand more plainly what it is not, and see more clearly what it is. Heresy is not the enemy. (In fact, where would faith be without it?) And God: “Is there a God” is the wrong question. “Should there be a God” is what we need to know. And, interestingly enough, this is the question that puts theists and atheists on the same side, right where they ought to be.

If God is One, we don’t join the True Faith, we are born in it, and whatever God we talk to, hears.

-- Kirk Perrow III

As a physician who undertook both formal and lifelong education joyfully and seriously, even now that I am retired, I really get what Janna Levin is talking about when she states that the truth is beautiful and is like that old comedy line: "Ah knows it when ah sees it." When I would see a patient, usually I knew the diagnosis before I could complete my examination or perform any testing. Mathematical symmetry is often associated with truth, and even with beauty of a person or a scene such as trees perfectly reflected in water stained black. Therefore, I agree that we often know the truth based upon experience and gut feeling, though we are still required to try to prove it.

Really interesting conversation. In spite of her nuanced language, I think she ought to look a bit more closely at the history and sociology of science and technology because her assertion that scientists accept that they may be proven wrong is, well, wrong. She treads the timeworn path here that scientists are somehow above their socialization and are somehow more honest about their work is just not borne out by the history of science - the literature abounds with examples of how science and technology have been shaped by the personal beliefs, political commitments, and other "external" factors (I use external in quotes because as a sociologist of science I do not believe that there is anything truly external to the practice of science). To believe otherwise perpetuates what scientists seem to like - that they are beyond and above the rest of us.

This radio show was terrific, and intriguing. I literally couldn't leave the room till it was finished, and can't wait to read Janna's new book. Well done, and thank you!

your interview on N P R was great although it was done in 2007 it is still relevant today 2014 .But there is one point where the

interviewer were ask you about your views that may be world changing and you gave a very excellent response about not

making fore going conclusion in math, science or anything that can help make our world more beautiful so I would like to give

you mine and that is mistakes. what are they can we as people afford some of the great mistake we make in the past in live the

more beautiful live in the future? but what is a mistake what math formula works!

OMG. It is so nice to know that someone thinks exactly like me. Exactly. It isn't really so much about us and are rediculous, smart ape constructs that we sadly cling to. Thinking from a scientific, reality based point of view doesn't detract from spirituality it magnifies it.

Janna Levin discusses how important math and science are in life, even if everything in them are not completely understood. It makes me question what is real and what is not. Her book that she wrote on Turing and Godel really explains how the mathematicians shaped the technology that we have today (i.e. Turing and the computer). She also explains just how amazing the universe really is. She says in the interview that although she doesn't necessarily believe that God created the universe but she also says that Math \cannot necessarily disprove the existence of God either. She also explains that free will is not completely free because we are all binded by the laws of physics. "If something randomly falls in a certain way, how is that a gesture of will?" (25:32)

I really enjoyed this broadcast and interview because I myself really like math along with her as she describes. I think that science today has really opened up almost another world to us as human beings. Science really changed the way that we live life and how we do things that we do on a daily basis. I think that her research and her novel is very interesting the way that it sounded in the broadcast. Kurt Godel and Alan Turing are two vey intelligent men that really revolutionized todays life. Math and science can bring a person very far and allow you to do many things in life and this really shows it. They took math and really took it to the next level with the way that they looked at certain aspects. They did stuff and tried to do stuff that other mathematicians never tried or never thought of trying. Overall this On Being discussion was one that i really enjoyed listening to and makes me want to check out her novel.

As to Belief, I completely disagree with your knowledge (from Belief) that "It doesn't matter what I believe." This theorem is an element of the set of all theorems which cause the Epistemology level of abstraction to show incompleteness. Epistemology is one of the levels of abstraction referenced by van Gigch. Epistemology is realized from Ethics & Aesthetics. However, I am not aware that van Gigch ever included C.W. Churchman's Morals non-system. Ethics & Aesthetics is realized from Morals. Morals is realized from Transcendence. Belief is in Transcendence and is our only “latch point” in Transcendence. Belief informs taxonomies of realizations through the layers of abstraction, which then results in what we form in Reality. It is, therefore, of paramount importance; singularly foundational to our Being. It is both the most abstract notion (“surreal vagueness”) we have and yet is the source of all realizations from Transcendence. I would hope that you might reconsider the importance of Belief. There is, of course, more words to be offered on this topic.

Math is false and cannot and should not be used for engineering and nature. Can you add one apple with one orange? No, you cannot. Similarly, you cannot even add two apples, because no two objects of nature are equal. You cannot even describe any property of an apple using math. Thus math is false. For more examples take a look at The real numbers are false, because they are not objects of nature, they do not grow on trees nor can they be mined from earth. How can you create something true by using something false, like math?