Mathematics, Purpose, and Truth: The World Feels More Spacious
by Krista Tippett, host
I picked up Janna Levin’s novel off a table at a bookstore, drawn to it initially perhaps because we had just completed our show with Paul Collins and Jennifer Elder on autism. Mathematician Alan Turing — known as the father of modern computing — is one of the autistic personalities who was mentioned in that interview. I was immediately taken by Janna Levin’s lush prose and the alluring, provocative ideas that she brings to life through human stories in space and time.
A Madman Dreams of Turing Machines sounds depths I had never considered before, between mathematical truths and great existential questions. It does so by probing the parallel lives and ideas of Turing and another pivotal 20th-century mathematician, Kurt Gödel. Turing’s discoveries were made possible in part by Gödel, who shook the worlds of mathematics, philosophy, and logic in 1931 with his “incompleteness theorems.” They demonstrated that some mathematical truths can never be proven. Or, as Gödel says in Janna Levin’s novel, “Mathematics is perfect. But it is not complete. To see some truths you must stand outside and look in.” This held unsettling scientific and human implications; it posited hard limits to what we can ever logically, definitively know.
Janna Levin is an atheist, if we care to categorize her. And while that simple fact informs our conversation along with her exquisite intelligence and her mathematical training, we cover territory that can’t be bounded by such definitions. Janna Levin’s most certain “faith” is in the conviction that we can agree on basic realities described by mathematics — that 1 plus 1 will always equal 2. Putting God into that equation, or barring God from it, is not her concern. Yet this conversation is a beautiful example of the deep complementarity of religious and scientific questions, if not of answers. The ideas and questions Janna Levin lives and breathes open my mind to new ways of wondering about purpose, meaning, and ultimate reality.
There is much in her thought that I struggle to comprehend and will continue to ponder. I’m intrigued, at the same time, by echoes with the wisdom of ordinary life. Gödel’s idea that there are some truths we can only see at an angle — by standing outside, looking in — is a fact even in the work I do, of speaking of faith. The deepest truths are usually impossible to see and articulate straight on.
And I feel a kindred pull to Janna Levin’s delight and passion in the great narrative of the world and humanity, epitomized in these lines from her book that we read in the show:
"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."
Of all the ideas Janna Levin presents, the most provocative and disturbing, perhaps, is her doubt that there is free will in human existence at all. She cannot be sure that we are not utterly determined by brilliant principles of physics and biology. Yet she cleaves more fiercely in the face of this belief to the reality of her love of her children and her hopes and dreams for them. She sees “evidence of our purpose” in figures like Gödel and Turing, even though they did not the find the clarity in life that they wrested from mathematics on all our behalf.
Paradoxically, perhaps, the world feels more spacious to me after this conversation with Janna Levin — even, to use her words, if it suggests incompleteness and the limits of human reason and faith; even if it suggests we are not free. She possesses a quality that keeps me interviewing scientists as often as a I can — a delight in beauty, a comfort with mystery, a limitless ambition for one’s grandest ideas combined with a humility about them that many religious people could learn from.
Will My Smart Phone Be Smarter Than Me?
by Colleen Scheck, APM producer
Perhaps you’ve asked yourself this question while speaking to Siri on your iPhone. It surfaced at yesterday’s World Science Festival event “The Creator: Alan Turing and the Future of Thinking Machines” where a panel of scientists and filmmakers discussed the nature and future of artificial intelligence.
The conversation was framed through the premiere of the film “The Creator” by artists Al+Al - a surreal, mythical journey of computers into the dreams and memories of Alan Turing as he contemplates suicide in his final hours of life. Wired UK recently interviewed Al+Al about the film.
It was a wide-ranging dialogue that touched on both the scientific and the ethical aspects of artificial intelligence work to create machines that will capture not just what we do, but the reasons we do what we do. I appreciated the historical perspective of NYU computer scientist Yann LeCun who noted that until recently computer science was about being exact, and artificial intelligence has forced computer science to deal with the unsolvable, or the “approximately solvable” - how we deal with uncertainty. This echoes Janna Levin’s perspective on the coexistence of mathematics and mystery that she so eloquently discusses in this week’s repeat broadcast. Is this a “Golden Age” in mathematics history?
In the photo above (l-r): Janna Levin, Josh Tenenbaum, and Yann LeCun discuss the nature and future of artificial intelligence at the World Science Festival.
The Creator: A Film That Explores Alan Turing’s Enduring Question
by Susan Leem, associate producer
This week’s show with physicist Janna Levin spends a great deal of time discussing her novel about Alan Turing. Tonight, Ms. Levin is helping launch a short film about the legacy of the computer scientist and code breaker called The Creator, which makes its world premiere at the World Science Festival:
"[it] follows sentient computers from the future on a mystical odyssey to discover their creator: legendary computer scientist Alan Turing. Decades ago, Turing famously asked, ‘Can machines think?’ and ever since, the notion of computers exceeding human intelligence has transfixed researchers and popular culture alike."
The Wonder of the Cosmos (through an Upgraded Lens)
by Colleen Scheck, producer
Last week NASA published pictures from the newly-refurbished Hubble telescope. Beautiful. Mysterious. Divine. And, simply, Wow. These were the words that ran through my head when I saw them. It’s worth reading the descriptions of the photos on NASA’s site for more detail on these galactic happenings. I also liked this online comment:
"These photos, and the multi-billion year life behind them make me think I’ve wasted the better part of my life looking down at my feet, instead of looking up into the sky."
I don’t have profound thoughts to add, but comments from two cosmologists who have been on SOF seem to apply. From our show "Science and Hope," George Ellis, a practicing Quaker from South Africa:
How do you — because you’re telling me that you also, I believe, you’re telling me you have concluded that there is a God and there can be a God in your cosmology. But how do you think your way around into that question?
It’s a very valid question, and it’s one for which we haven’t got any clue to the answer. But that is the same for every attempt to understand the foundations of the universe. Science runs into that and religions run into that. My colleagues are producing theories of what they call creation of the universe out of nothing. But when you probe them, you find they’re not producing theories of creation of the universe out of nothing. They are assuming a huge machinery of quantum field theory and fields and particles and interactions, which generates universe, not creation of the universe out of nothing.
Which had to come from somewhere.
Yeah, it had to come from somewhere else….And in the end, we run into a metaphysical blank, whether you pursue it scientifically or religiously, and you simply have to give up in wonder and awe and say, ‘I don’t know the answer, and it’s just marvelous the way things are.’
And, Janna Levin, a novelist and professor of Physics and Astronomy at Barnard College, spoke with Krista for our program "Mathematics, Purpose, and Truth":
….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?
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.
But supposing we grasp the notion of multidimensional space and spaces and finite, people say, ‘Why should I care about that? You know, my taxes are high. We’re on 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.’
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.
"On Truth and Beauty"
by Trent Gilliss, senior editor
When we originally released our program with physicist and novelist Janna Levin, we included a short clip of a conversation from Seed magazine (a great science publication that recently featured Andy’s Art Shanty Project). Now that we’re rebroadcasting an updated version of "Mathematics, Purpose, and Truth," we thought it was a good time to feature the complete salon with acclaimed fiction writer Jonathan Lethem and Ms. Levin from March 2007. They discuss the importance of truth in their art and the impurity of metaphor — and therein lies elegance and beauty. Enjoy.