Jim Simons was a mathematician and cryptographer who realized: the complex math he used to break codes could help explain patterns in the world of finance. Billions later, he’s working to support the next generation of math teachers and scholars. TED’s Chris Anderson sits down with Simons to talk about his extraordinary life in numbers.
Ford had already moved 3,000 miles away from the affluent Maryland suburbs where she says Kavanaugh sexually assaulted her at a house party — a charge he would emphatically deny. Suddenly, living in California didn’t seem far enough. Maybe another hemisphere would be. She went online to research other democracies where her family might settle, including New Zealand.
“She was like, ‘I can’t deal with this. If he becomes the nominee, then I’m moving to another country. I cannot live in this country if he’s in the Supreme Court,’ ” her husband said. “She wanted out.”
.. On the day that Ford publicly identified herself as Kavanaugh’s accuser in an interview with The Washington Post, her husband was driving their 15-year-old son and his friends from a soccer tournament in Lake Tahoe. He couldn’t answer the calls that were blowing up his phone; by the time they reached home, a crowd of reporters was waiting.
.. Russell struggled to explain it to his children. “I said that Mommy had a story about a Supreme Court nominee, and now it’s broken into the news, and we can’t stay in the house anymore,” he recalled. The family was separated for days, with the boys staying with friends and their parents living at a hotel. They’ve looked into a security service to escort their children to school.
.. Quietly, she garnered a reputation for her research on depression, anxiety and resilience after trauma — telling almost no one what she herself had endured.
.. Ford’s inner circle was, “How do you say this? The pretty, popular girls,” explained Andrea Evers, a close friend. “It wasn’t like we were a bunch of vapid preppies, but God, we were preppy then.”
.. the drinking age was 18 then
.. frequently left the girls feeling embattled.
“The boys were pretty brutal,” Evers said. “They would do what they could to get you drunk, and do whatever they would try to do to you.”
.. Kavanaugh and his classmate Mark Judge had started drinking earlier than others, she said, and the two were “stumbling drunk” when they pushed her into a bedroom.
.. Her biggest fear afterward, she recalled 37 years later, was looking as if she had just been attacked. So she carried herself as if she wasn’t. Down the stairs. Out the door. Onto the rest of her high school years, she said. On graduation day, she wore the required white dress and carried red roses. She told no one.
.. Years later, Ford would describe college as a time when she “derailed,” struggling with symptoms of trauma she did not yet understand.
.. She’d been a cheerleader in high school and joined a sorority, but the lifestyle was too much like the place from which she’d come. Despite the talent for math she had shown in high school, one college classmate recalled Ford failing a statistics class.
.. “He said, ‘You’re really smart, and you’re just like totally [messed] up,’ ” Ford recalled. She remembers him saying, “ ‘What are you doing? . . . Everybody’s getting it together but you’re like not.’ It was kind of a harsh talk.”
If she was going to graduate on time, he said, she ought to major in psychology. The major didn’t require students to take classes in a specific order, so Ford could take them all at once.
That was how Christine Blasey Ford came to spend her life researching trauma and if it is possible to get past it.
.. “I think she had really reinvented herself,” said Jeff Harris, her supervisor at the University of Hawaii counseling center. “A surfer from California is a different image than a prep-school girl from Bethesda.”
.. He knew that more than a love of water had brought her west.
“She didn’t always get along with her parents because of differing political views,” Russell said. “It was a very male-dominated environment. Everyone was interested in what’s going on with the men, and the women are sidelined, and she didn’t get the attention or respect she felt she deserved. That’s why she was in California, to get away from the D.C. scene.”
.. As their relationship deepened, Ford told him she’d been physically abused years earlier. He would learn the specifics of the event, including Kavanaugh’s name, during a couple’s therapy session years later. But then, he just listened.
.. Her master’s thesis explored the relationship between trauma and depression.
.. admired by colleagues for her analytical mind and inventive mathematical models.
.. She took a particular interest in resilience and post-traumatic growth — the ideas that people who endure trauma can return to normal and even wind up stronger than before. Ford said she has given speeches about this topic to students, telling them, “You can always recover.”
.. She will probably be asked to detail every moment of the alleged attack. How much she had to drink. Why she went upstairs. What she was wearing.
Nobel physicist Frank Wilczek sees beauty as a compass for truth, discovery, and meaning. His book A Beautiful Question: Finding Nature’s Deep Design is a long meditation on the question: “Does the world embody beautiful ideas?” He’s the unusual scientist willing to analogize his discoveries about the deep structure of reality with deep meaning in the human everyday.
.. “Each of us is born to become an accomplished, if unconscious, practitioner of projective geometry.”
.. That’s right. That’s one of our most impressive abilities that humans, children, do routinely without thinking about it — although they have to learn it, or parts of it — and yet, we have not been able to teach sophisticated computers to do it. That is, humans do an astonishing feat, routinely and very quickly. That is, they interpret the messages coming through little, little openings in their eyes and project it on a two-dimensional screen, the retina at the back, which then, the light gets turned into electrical signals. And from that crazy, scrambled encoding, we reconstruct an external world of three-dimensional objects in space. We recognize that if we move our head, they’re still the same objects, and we determine these effortlessly. We do a job which is — it literally is impossible. We use all kinds of tricks and rules of thumb to guess what the external world is, and sometimes it’s wrong, with optical illusions, but basically, in most circumstances, we do this remarkable feat of reconstructing a three-dimensional world from two-dimensional information that’s all scrambled up with things on top of each other
MR. WILCZEK: We take it for granted, but nature has equipped us with extraordinary abilities in geometry. I knew this abstractly, but in preparing the book I decided I should actually learn something about [laughs] perspective and projective geometry. And it was a real revelation. I’m terrible at drawing, just terrible — the worst person I’ve ever met. But I [laughs] learned some of the rules of perspective that artists use, and they are just so beautiful. They’re so elegant. And using them, I was empowered to create accurate buildings and town squares and so forth. I just astonish myself. And I wasn’t able to reproduce it consciously, but now, with knowledge, I was able to do it. And it was just magic to suddenly see these things emerging from geometric constructions, and it looks like the external world. And it had a tremendous effect, historically and psychologically, when these rules were discovered in the Italian Renaissance. It’s one of the things that really powered the Renaissance — the artists took enormous joy in their sudden ability to render the world the way it actually looked.
.. Yes. And people who started to work on artificial intelligence thought at the beginning that would all be trivial, because it’s so easy, [laughs] we don’t have to work very hard. They thought that would be very easy, whereas, say, teaching a computer to play chess would be very difficult. But it’s turned out to be just the opposite. The things that we do unconsciously and are part of our daily lives and are important for survival are things we’re really, really good at.
.. But in science, we need to have a more precise concept. And the concept that we use that’s more precise, that has something in common with the common usage but is a special case of it and gets amplified in different directions, is that symmetry in physics and mathematics means change without change.
Now, that seems kind of mysterious and mystical, but it means something very concrete. Einstein’s theory of relativity, it says that if you ride by the world at a constant velocity, any constant velocity, although things will look different — so some things will be coming at you, other things will be moving away, faster — that the same physical laws will apply to this new configuration of the world. So, you can make a change in the way everything looks, [laughs] but you don’t change the laws.
A simpler example might be helpful here. We’re used to the idea that a circle is a very symmetrical object. What does that have to do with change without change? Well, a circle is an object that you can rotate around its center by any angle, and although it might have changed, and every point, in fact, moves, the circle as a whole does not move, and that’s what makes it symmetric. If you take a more lopsided shape and you rotate it, there’s no way — it won’t come back to itself until you go all the way around. So if you take an equilateral triangle, it’ll come around after you turn it one-third of the way. So it has some symmetry, but much less than a circle. So that’s a concept, change without change — things that might have changed, but don’t — that picks out special kinds of objects, like circles.
.. It turns out that very symmetric laws seem to be the laws that nature likes. Nature likes laws and likes equations that support enormous possibilities for transformation, where things look different, get different names, and different situations are described, but the same equations apply.
.. “Deep propositions have a meaning that goes beyond their surface.” This is so interesting. “You can recognize a deep truth by the feature that its opposite is also a deep truth.”
.. MS. TIPPETT: So one of the conflicts was, is light a particle or wave? And, in fact, it is both.
MR. WILCZEK: It’s both, and…
MS. TIPPETT: It’s both, right.
MR. WILCZEK: …sometimes it’s useful to think of it one way, sometimes it’s useful to think of it another way. Both can be informative in different circumstances, but it’s very difficult — in fact, impossible — to apply them both at once.
MS. TIPPETT: To apply them both at the same time.
MR. WILCZEK: And I think that’s the essence of complementarity, that you have to view the world in different ways to do it justice, and the different ways can each be very rich, can each be internally consistent, can each have its own language and rules, but they may be mutually incompatible. And to do full justice to reality, you have to take both of them into account.
MS. TIPPETT: Somewhere you say, “Complementarity is both a feature of physical reality and a lesson in wisdom.” And I think just what you just said about reality is equally true of — and I know you have to be careful to do too much of this stretching these things, but it’s equally true of the human condition.
MR. WILCZEK: Oh, very much so. [laughs] Oh, I think so. When people ask me what my religion is, I say I’m a complementarian.
MS. TIPPETT: [laughs] That’s right.
MR. WILCZEK: I believe that it’s really interesting and really fun and really informative, and the right thing to do, to be able to look at things in different ways and appreciate their different ways of looking at things that each have their own validity. And they may conflict if you try to apply them both at once, but OK, that’s fine. You apply one at a time [laughs] and try to appreciate both.
MS. TIPPETT: And in terms of this — I have spoken with physicists who will say: Of course, they take their daily perceptions seriously on some level; they understand that, essentially, what we perceive to be reality is full of illusion, and including the perception that we have freedom and choice. But you also present this as another piece of complementarity — two things that, in fact, are true, but hard to speak about in the same moment — that you, as a human being, are nothing but a collection of particles and light; and you are a thinking, feeling human being. [laughs]
MR. WILCZEK: Yes. I think those are both true. [laughs] And they are different ways of organizing our experience of the world, and each one tells us important things. Each one can be very useful in certain applications. But they’re very difficult to apply simultaneously, because they’re just from different worlds.
.. “All colors are one thing.” This is what we learned: “All colors are one thing, seen in different states of motion. And that is science’s brilliantly poetic answer to Keats’ complaint that science unweaves a rainbow.”
.. I’m saying that by understanding the world better that you gain a new perspective on what you are and a different feeling about your place in reality that’s more realistic; also, richer. And there’s good news, and there’s bad news, but in any case… [laughs]
MS. TIPPETT: Right, it’s challenging.
MR. WILCZEK: …it’s something you can — by understanding it deeply, you can certainly enrich your experience of the life you’re given.
MS. TIPPETT: You also cite somewhere what you say is, for you, one of the most beautiful passages in literature, from the 20th-century physicist, Hermann…
MR. WILCZEK: Hermann Weyl, yes.
MS. TIPPETT: …Weyl on spacetime. He’s talking about spacetime from a “God’s-eye view”: “The objective world simply is, it does not happen. Only to the gaze of my consciousness, crawling along the lifeline of my body does a section of this world come to life as a fleeting image in space which continually changes in time.” That’s a very — it’s almost a mystical image. That the world is, it does not happen, is quite a remarkable thing to try to take in.
MR. WILCZEK: Yes, but it’s really, I think, very much what the theory of relativity suggests. It’s really basic, to think of spacetime as a whole, because there are relationships between things that happen in different parts of space and at different times that are significant in forming the laws and the regularities of the world that are very, very difficult and awkward to express if you carve the world into time slices, as we experience…
MS. TIPPETT: Right — past, present, future.
MR. WILCZEK: …and regard them as separate and unrelated, or as snapshots, each a thing in itself.
Relativity teaches us to think of spacetime as a whole and that it’s very unnatural to divide them. So it leads, I think, very much to the worldview that Hermann Weyl was alluding to there, that the world — that is, spacetime — it simply is. It does not happen. It already encompasses all times.
.. “I know not how I appear to the world, but to myself I appear like a boy on a beach who came upon some particularly beautiful pebbles, while the great ocean of the unknown lay before me.”
So he realized that he understood some things very well, and he understood what it meant to really understand something, but part of that is realizing that you don’t understand a lot of things. And there’s a profound humility that comes from really understanding something, because then you understand what it means to really understand something. [laughs] And you realize how much is missing that is different.
MS. TIPPETT: [laughs] And you feel that way as a physicist at this juncture in physics, which is so far from what Newton could have imagined, also.
MR. WILCZEK: Yes. We’ve done very, very well. Physics is pretty good. [laughs] Physics, we’ve attained a high level, although there are certainly big holes in our understanding. But when it comes to the mind, when it comes to understanding society, our understanding is much, much less satisfactory and, I’m fully aware of that.
You know, I was interviewing a researcher at Columbia University. Her name is Xiaodong Lin, and she’s done a lot of work looking at trying to get children interested in science. And she finds something really fascinating that speaks to exactly what you just talked about, which is the traditional way we have of teaching science is to tell people, you know, there was this great physicist, Albert Einstein. And he was the greatest genius the world has ever known, and he came up with theories that, even today, many people struggle to understand. So that’s the classic way we tell science stories.
And what she found was that instead of doing that, if you tell a story which says something along the lines of, you know, there was a time when Einstein was working on a problem, and he got so stuck that he couldn’t figure out the math. And he needed help to figure out the math, and he reached out to somebody else, saying, I can’t figure out the math to this. Can you please help me? When you tell stories that involve struggle and obstacles and failures about scientists, not only does this hold people’s attention, but kids are now able to say, I could see myself being a scientist because I need help with math. I turn to somebody else to get help for math. And this idea that the obstacle, in some ways, is what makes the story the story is, I think, what you mean by the middle.
.. Because when I left the science show, I realized that the reason that the show worked was because we had a real connection between us. It wasn’t an ordinary interview. I never went in with a set of questions – not after the beginning. I went in just being curious and really good and ignorant. It’s good to be ignorant as long as you’re curious – not so good if you’re not curious. So I would be willing to reveal my ignorance to them, so they knew where I was in my understanding of their work. And then if I didn’t understand what they were saying, I’d grab them by the lapels and shake them. Tell me again. What do you – so they forgot about the camera. They forgot about the lectures they had given on this. They were just trying to make me understand it. And I realized that what I was doing was relating to them, and they were relating to me in the same way two actors do when they let each other in to their field of consciousness.
So I thought the best way to train people to do that is through improvisation training. And I tried it out with a group of engineers. And after three hours, they were so much better talking about their work.
.. And what this – what the improvising work does is it actually builds up your empathy. You get very good at being able to figure out what the other person is going through emotionally.
So now, this cab driver pulls over. He says, where are you going? And I start to get crazy mad. Where am I going? You’ve got to take me no matter where I’m going. But instead of that, I think, wait a minute. It’s the day – it’s the time of day when he’s switching shifts. He’s got to give the cab to somebody else. I understand why he’s saying it. And it helped me accept it.
.. And I’ve noticed that the more empathy I have, the less annoying other people are.