Being Comfortable with the Presence of Mystery
Krista Tippett, host
I am so happy to be back in the studio making radio, though these last few months of public conversations about Einstein’s God have been fascinating and energizing. And we continue to build on our cumulative conversation with and about science and the human spirit. I picked up Mario Livio’s book, Is God a Mathematician, sometime last year, and knew I wanted to speak with him.
Given that title, it is perhaps surprising to learn that Mario Livio is not himself a religious man. But in his science, he is working on frontiers of discovery where questions far outpace answers — exploring the nature of neutron stars, white dwarfs, dark energy, the search for intelligent life in other galaxies.
In vivid detail and with passionate articulation, he reinforces a sense that has come through in many of my conversations with scientists these past years. That is, in contrast to the 19th- and 20th-century Western cultural confidence that science was on the verge of explaining most everything, our cutting-edge 21st-century discoveries are yielding ever more fantastic mysteries. The real science of the present, Mario Livio says, is far more interesting than science fiction could ever be.
For example, the fact that the universe is expanding rather than contracting is new knowledge. That has led to the discovery of what is called, for lack of precise understanding, “dark energy,” which is accelerating this expansion. And this utterly unexplained substance is now thought to comprise something like 70 percent of the universe. Likewise, the Hubble telescope has helped humanity gain intricate new detail on the unimaginable vastness of the cosmos and the relative insignificance of the space we take up in it. At the same time — and this is one of Livio’s intriguing mysteries — this new knowledge and perspective also shine a new kind of light on the inordinate power of the human mind.
Livio’s question, “Is God a mathematician?,” is actually an ancient and unfolding question about the uncanny “omnipotence and omnipotent power” of mathematics as experienced by science and philosophy across the ages. The question itself, as Livio says, is as rich to ponder as any of its possible answers. And so is the fact, behind it, that our minds give rise to mathematical principles, which are then found to have what one great physicist called “an unreasonable effectiveness” in describing the universe.
Livio also picks up on an intriguing theme left dangling in my lovely Easter conversation with Vatican astronomers Guy Consolmagno and George Coyne — the enduring question of whether mathematical truths, laws of nature, are discovered or invented. He unapologetically offers his conclusion that there is no either/or answer possible here — that mathematics is both invented and discovered. That is to say, as he tells it, scientists habitually “invent” formulations and theories with no practical application, which generations or centuries later are found to describe fundamental aspects of reality. Even mathematical ideas that are at first invented yield real discoveries that are relevant, true, and wholly unexpected.
I was also interested, as I went into this conversation, that when Mario Livio is not doing science he is a lover of art. “Beauty” is a word that recurs across my cumulative conversation with scientists, and Mario Livio infuses that word with his own evident passion. He is not quite sure, when I press, what that might have to do with his simultaneous passion for art. And yet there is something intriguing — mysterious even — about his description of how echoing allusions from science and art come to him effortlessly in his writing.
And in the backdrop of our conversation, images from the Hubble Space Telescope have brought a lavish beauty of the cosmos into ordinary modern eyes and imaginations. One senses that of all the accomplishments in which he has played a part, Mario Livio is most proud of this one. For him, science is a part of culture — like literature, like the arts. And he wants the rest of us, whether we speak his mother tongue of mathematics or not, to experience it that way too. This conversation (listen above) brings me farther forward on this path.
And I kept thinking, as I spoke with Mario Livio, of Einstein’s references to the reverence for beauty and open sense of wonder that Einstein saw as a common root experience of true science, true religion, and true art. His use of the word “God,” Mario Livio tells me, is similar to Einstein’s grasp for the word “God” as a synonym for the workings of the cosmos. I am struck once again with the capacity of modern scientists to be more comfortable with the presence of mystery, and bolder in articulating its reality than many who are traditionally religious.
Astrophysicist Mario Livio: A Twitterscript
Shubha Bala, associate producer
For the past few interviews, we have been diligently tweeting away while Krista converses with our guests. We hope that this is a unique way for you to experience some of the highlights — and get the conversation started — before you experience the full edited (or unedited!) show.
After our interview with Mario Livio, we all sat down to discuss what constitutes a good tweet. So, this week, we ask you: seeing the entire tweeting transcript below, what tweets are helpful? Do links help? Is it too much to break information between tweets?
- For the next 90 minutes, we’ll be live-tweeting Krista’s ISDN interview with Mario Livio, a Romanian astrophysicist who grew up in Israel.
- Mario Livio’s latest book is “Is God a Mathematician?”
- Livio asks if mathematics discovered or is it an invention of the human mind. Picks up from Krista’s interview with two Vatican astronomers.
- “Mathematics turns out to be too powerful in describing all these things.” -Mario Livio
- Mario Livio: Newton takes observations that aren’t so accurate, + his mathematical equations are more accurate than the observations!
- Livio: the theory of knots are very important application for string theory even though it was initially thought to have no application.
- Livio: The conclusion I reached about math being discovered or invented is that the question is being posed wrong. It’s a mixture.
- Ex. of mixture: imaginary numbers like square root of -1. We invent the concept and then we discover the relationships among these concepts.
- Ancient Greeks invented concept of prime numbers. And then the discoveries were forced upon us.
- Livio: Roger Penrose, mathematical physicist: three worlds and three mysteries - physical world, consciousness, mathematical forms.
- Penrose’s 3 mysteries: 1) out of the physical word, consciousness 2) consciousness gives access to math forms 3) math explains phys. world
- Livio: Chomsky will tell you that there is more universality to languages than we think.
- Livio “The Microsoft Effect”: once a particular OS starts to dominate, all have to adapt it. Mathematical notation is a little bit of that.
- Mario Livio: “Our perception system is universal. This had to help in inventing natural numbers like 1,2,3,4,5…”
- “Like beauty in the arts, it is somewhat more vaguely defined [in mathematics] …but perhaps it is a little bit more defined.” -Mario Livio
- We try to formulate a few laws of physics + try to explain all phenomena. We do the same thing in mathematics - like in symmetry. -M. Livio
- “I have heard very few people think that Einstein’s general theory of relativity is not beautiful.” -Mario Livio, astrophysicist
- Mario Livio: You could argue that the principal behind Einstein’s general relativity is simpler than Newton’s gravity.
- M. Livio: Symmetry is a quantity that does not change. Mathematicians came up with a system to describe ALL these symmetries. Group Theory.
- Funny moment where Krista starts to ask Livio about his love of art and Mario Livio responds, “You seem to be well prepared.”
- Mario Livio, in response to Krista’s question: “I don’t have a good explanation for my passion for art.”
- Livio: “…it would be false to say that science + art have influenced each other. Or that science + religion have influenced each other.”M. Livio: “A person who feels a need for God does not want a God that created the universe and then left the universe to its own devices.”
- M. Livio, picking up on that last point: “Science has nothing to say about this. … People try to force the connection.”
- M.Livio-ppl who try to say Genesis is completely accurate scientifically does science & religion a disservice
- M.Livio-Is God a Mathematician? “I mean God as an Einsteinian God-synonym to the working of the cosmos.”
- M.Livio-Physics has changed over time but “Mathematics has evolved, but the math the ancient greeks did is still true today.” Eternal truth?
- M.Livio-As physics became more predictive, people went away from religion to talk about nature - talked about precise sciences
- M.Livio-cont. a development of 20th century-with quantum physics, things are no longer deterministic, can only calculate probabilities
- M.Livio-“Biology today is..at the state physics was…..-many of the major breakthroughs are yet to be made”
- Krista tells a funny story of Goedel, accompanied by Einstein, applying for US citizenship - http://www.ias.edu/people/godel/institute
- M. Livio - About math and life… well “in science, unless you have a well defined problem it is virtually impossible to try to answer it”
- Livio-“Things like life these are inherently complex situations where..often I don’t..know what question to pose, let alone find the answer”
- Livio-April 24 is Hubble 20 year anniversary. He talks about the importance of Hubble images - http://hubblesite.org/gallery/album/
- Krista and M. Livio recall SOF interview about human & mathematical limits with Janna Levin - http://bit.ly/axpPBy
- M.Livio-pushing boundaries-we used to think the earth was the center of a universe, and now “200 galaxies like ours just in the observable”
- M.Livio - but each discovery we make, we find out there’s something “even more mysterious”
- M.Livio-In all this, our physical selves seem more&more minuscule, but our minds making the discoveries are more&more important & central
- Thank you Mario Livio! For more information on him and his book : http://www.mariolivio.com/
Who Ordered This Show Title?
by Colleen Scheck, senior producer
With each new program, we carefully consider the show’s title so that it reflects the tone and substance of Krista’s interview, but also so that it intrigues you, hopefully, and makes you want to listen. This week’s title, “Who Ordered This?,” comes directly from Krista’s interview with astrophysicist Mario Livio:
Krista Tippett: One of the places this takes me back to, 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 …
Mario Livio: Lord Kelvin, you know, has been claimed to have said that everything has actually been 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, you know, surely this is how things are happening, and we have had a number of occasions of, there are those things where — you know, another famous physicist once said “Who ordered this?” I mean, so, who ordered dark energy? As if we didn’t have enough to explain as it was already, and then suddenly this thing appears and its now the most perhaps intriguing question in all of physics.
Krista Tippett: Right.
Mario Livio: 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, you know, there is really so much there to do and there is so much room for imagination and creativity ….
Livio is adapting a phrase by Nobel Prize winning-physicist Isidor Isaac Rabi who once said “Who ordered that?” when the muon was identified. A New York Times book review traces this line of scientific compounding back even farther, blaming Democritus.
Interestingly, in Livio’s dual passion for science and art, and his work to make a deeper understanding of the universe more accessible to humanity, it seems he shares the perspective of the man he quoted. According to one biographical entry, Rabi once wrote, “What the scientist really desires is for his science to be understood, to become an integral part of our general culture, to be given proper weight in the cultural and practical affairs of the world. Like the poet, the scientist would rather be read than praised.”
Mathematics in Sunflowers
Shubha Bala, associate producer
This week’s show with astrophysicist Mario Livio explores, amongst other things, how math is implicated in the nature of the world. The Nobel physicist and mathematician Eugene Wigner, who wrote “The Unreasonable Effectiveness of Mathematics in the Natural Science,” argued that math is so successful in predicting events in physics that it could not be a coincidence. Even on our previous show, “Asteroids, Stars, and the Love of God,” the astronomers pointed out the complexity in declaring whether math is discovered or invented.
While producing these interviews, I happened upon the video above. The visualization helped me by filling in some of the specific examples in nature that mathematicians can easily visualize on a daily basis. It shows how three mathematical concepts, including the golden ratio, translate into simple objects in nature.
What I really love is the about page, which deconstructs how the Fibonacci series and golden ratio translate into the spiral of a shell, and the spirals within a sunflower. When listening to Livio, what examples of math explaining the cosmos came to mind for you?