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Sharon Glotzer, a computational physicist and professor of chemical engineering at the University of Michigan, uses statistical mechanics to probe how the properties of materials emerge from the dynamics of their countless constituent particles. This week, she speaks with host Steven Strogatz about how a broken oil pump changed her life, how entropy is all about choices, and how she is driven to find the simple rules that explain the universe’s complexity. This episode was produced by Dana Bialek. Read more at Quantamagazine.org. Production and original music by Story Mechanics.

Listen on Apple PodcastsSpotifyAndroidTuneInStitcherGoogle Podcasts, or your favorite podcasting app, or you can stream it from Quanta.


Sharon Glotzer: I was the only woman in the class, and none of the men would hold up their hands and go, “I don’t know that word you’re using right now.” But I didn’t care. I was like, “I’m not gonna sit here and waste my time,” so I asked, “What is a residue?” And afterward, half of them were like, “Thank you for asking.”

Steve Strogatz (narration): From Quanta Magazine, this is The Joy of x. I am Steve Strogatz. In this episode, Sharon Glotzer.

Steve Strogatz: What gave you the strength to do it?

Glotzer: I don’t know. I don’t know.

Strogatz: I mean, if you were the only woman in the class, some people in your position would have thought, “Oh geez, I’m the only woman in here, I better not look stupid in front of all the boys.”

Glotzer: If someone said something to me that was, you know, sexist or biased or something like that, my first thought wasn’t “I don’t belong here.” My first thought was, “You’re an idiot, so…”

Strogatz: That’s fantastic, great. What a good, healthy attitude.

Glotzer: Well, I think I must have gotten that from my parents, who just made me think I could do anything, and that I could be anything, and that I shouldn’t be afraid to go get it.

Strogatz: Sharon Glotzer is hard to classify. I guess you could call her a computational physicist because she uses computers to think about deep physics problems, but she’s also a materials scientist and her work has a lot of overlap with chemical engineering. In fact, all her work is driven by one quest, which is really the quest to understand complex systems made out of enormous numbers of simple parts.

She wants to know how order emerges out of chaos in systems like this. And something I found really delightful and fascinating about talking to Sharon is that her journey to asking these questions was itself full of randomness and curiosity.

Strogatz: I mean, how does someone become a scientist? What were you like as a kid? Tell me about your family.

Glotzer: Oh my God, Sharon as a little girl.

Strogatz: Yeah.

Glotzer: Like my least — no, okay.

Strogatz: Well, why not? What did your parents think of you? Were you a —?

Glotzer: Oh my gosh. Well, my parents were always very supportive of anything. I was actually born in New York City, but we moved out to L.A. when I was 5. My dad, he was working for a schmatta — he was a schmatta salesman, meaning he sold fabrics.

Strogatz: Okay.

Glotzer: Fabric swatches. Like, you know, he’d send fabrics to, like, the big houses and things.

Strogatz: So nice, a schmatta salesman.

Glotzer: Yeah.

Strogatz: So who needs whatever the plural is of schmatta? Schmattas?

Glotzer: Everybody.

Strogatz: Everyone needs fabric.

Glotzer: Everyone needs fabric, yes. I just remember, like, living with boxes of fabrics everywhere all the time.

Strogatz: Huh, that’s interesting.

Glotzer: That’s what I remember.

Strogatz: Yeah.

Glotzer: But yeah, so we lived out there — so I lived in the neighborhood where they filmed E.T., which was up on Brasilia Drive, which is a couple of streets over from us, where the kids are riding bicycles and stuff, and they’re going down these — like, there’s lots, but prepared for houses. And they’re going down and —. So we used to ride our bikes there like that, too. Ride dirt bikes off of those lots.

Strogatz: Yeah.

Glotzer: And what’s really — I remember we would make, like, little tricorders out of foil and we’d make, like, little hats and stuff, and pretend that we were astronauts on the moon. And we would go to these places and, like, search around and bring home rocks, moon rocks. I think —. So, I wanted to be an astronaut for a long time.

So, I have to admit to something. Like second grade, third grade, I borrowed a microscope from school. So, we actually lived on a golf course, and I would go down to the pond, and we would get little samples so I could, like, look at little parameciums under my microscope.

Strogatz: Sure.

Glotzer: I still have it. I never brought it back, and then it became, like, too late to bring it back, like it was too embarrassing to bring it back, and now the school doesn’t even exist anymore.

Strogatz: Okay.

Sharon Glotzer: And I’m, like — but I can’t bring myself to, like, get rid of it, because nobody would want it anymore. There are much better little microscopes that you can buy for your kids now.

Strogatz: Right, sure.

Glotzer: And so, I just decided I would just keep it because it was my first one.

Strogatz: Oh, okay. This is a very good rationalization.

Glotzer: Exactly, exactly. Then my grandmother, who had lived with us, she moved out with us from New York City, and then she got cancer. She got sick, and I decided I would start learning about cancer and the body and stuff, so I could hurry up and cure it.

Strogatz: Do you picture yourself being, how old at that point, 10 or —?

Glotzer: I was 10.

Strogatz: Yeah, you were 10, okay.

Glotzer: Yeah, 10, 9, 9, 10, yeah.

Strogatz: Uh-huh, 9 or 10, uh-huh.

Glotzer: So, then I wanted to be, you know, like a physician researcher, whatever. And I remember my mom would get calls from the teacher at school saying, “Sharon’s not going out for recess today because she is reading a book on endocrinology, and I think you need to talk with her.”

Strogatz: But that’s interesting.

Glotzer: And I was like, what is wrong with this?

Strogatz: It’s interesting to me that you mentioned earlier, you said “physician researcher,” as if —. Because that’s not what people would normally say, right? The usual move is doctor-doctor, not doctor-researcher.

Glotzer: I thought that if you want to help people and cure cancer, you need to be a doctor, but I knew that you had to use, probably, microscopes. Well, I think I changed my major like seven times. So I just — you know, I think — so, I’m sure I started premed. Then I wanted to study microbiology, because I remember that was a new major at UCLA, and I thought, “Well, I have no idea what that is, but that’s got to be cool.”

And then I took my first bio course, which is like 600 people at UCLA, and you’re just memorizing all of the phyla — you know, all the different species, and I just thought, “This is gonna kill me. This is so boring, I can’t memorize stuff, I’m not good at that.”

Strogatz: Yeah.

Glotzer: And it was so, so boring, and then —. So then I was looking around, and I thought, “Oh, I’ll switch to electrical engineering.” I have no idea why I thought to do that. So, I had to take my first physics course. And that was like the first C I ever got in my life.

Strogatz: Oh, sorry to hear it.

Glotzer: And I was super pissed.

Strogatz: Yeah, yeah.

Glotzer: I was like, “You’ve got to be kidding me. Like, this is ridiculous.” So then I said, “Okay, well, I have to do physics, then.”

Strogatz: Uh-huh, good.

Glotzer: I wanted to do something that was hard.

Strogatz: Good attitude.

Glotzer: Yeah. So I switched into physics. And then I took a course from Bob Cousins, Professor Cousins on, like, particle physics. Like, you know, the upper division Intro to Particle Physics where you learn about quarks and color. And I’m like, “Quarks? You’ve got to be kidding me, this is so awesome.” So that’s what got me hooked on physics.

Strogatz: It sounds like it really was good old-fashioned, inspiring teachers and textbooks and things like that.

Glotzer: Yeah. It was, it was. I mean I was already interested in all these things. I just didn’t know, like, all the things that existed to be excited about.

Strogatz: Yeah.

Glotzer: And so, yeah, so that just opened up all these new worlds for me. It was, you know, like being a kid in a candy store, right? It’s like, oh my God, there’s so much stuff to know. This is so neat.

Strogatz: Then apparently there was some formative experience with an oil pump that maybe you could tell us about.

Glotzer: How did you hear that?

Strogatz: Well, okay, I did a little research.

Glotzer: Oh my gosh, that’s so funny.

Strogatz: But it seems like that changed your direction somewhat.

Glotzer: When I went to UCLA, I lived my first year in the dorms, and then the next year my mother made me go through sorority rush. So, I’m like, “What are you talking about?” She’s like, well, “I know you, you’re studying all the time, you’re not gonna make friends, you’re not gonna blah, blah, blah, you’re just gonna work, work, work.” Because she knew back then that I was a workaholic, which I am. And so, she said, “I just want you to just go through the experience.” I’m like, “You have got to be kidding me.” She’s like, “Nope, nope, I am not gonna pay for your housing if you don’t go.”

Strogatz: Oh boy, that’s really serious pressure.

Glotzer: I’m like, “Oh my God, fine, fine.”

Strogatz: Okay. So fine, so you rush.

Glotzer: Yeah. It was, it was ridiculous, it was ridiculous. I thought, this is like so stupid. What am I gonna have in common with these girls? I am a scientist, goddammit. Anyway, whatever. Like Hilgard Row, there’s all these sororities, and so you had to go up and down, and you’d go to visit all these houses, and it was — it was just like — I really just hated it.

Until I got to this one house, Alpha Epsilon Phi. And I felt like, “Oh my God, these are my people,” and they were, because it was, like, the Jewish sorority. I didn’t even know that existed, but it existed because decades earlier, nobody let Jews into sororities and so they made their own.

And then I met all these women that — and they’re all like really — like, they study a lot and they’re — you know, they all have big aspirations and stuff. And I thought, oh, this is so great. And so yeah. So then I went through it. I couldn’t even believe it, that I liked these women. So, I joined the sorority.

And so, the reason I’m telling you this is because at some point, maybe my junior year or something, I — this was my astronaut phase, and aerospace, like, that’s the big thing in southern California, right? All of these aerospace companies. And I decided that I wanted to work at TRW, which is now Northrop Grumman. I wanted to go, like, get a summer job at TRW, where they made satellites. And I couldn’t get past the HR, like I couldn’t get anywhere. And I remember sitting at dinner one night in the sorority house and talking to my sorority sisters about this, and one of them said, “Oh, my dad works there.” I said, “He does? Where have you been? Hook me up, girl!” And she said — I said, “What does he do?” She goes, “I don’t know, he’s in management or something. I don’t know what he does but I’ll find out.”

Strogatz: Yeah.

Glotzer: Anyway, so she finds me, like, whatever, next day, next week, and she said, “Oh, my dad wants to meet you.” So, I went in to visit him, and it turns out that he was the vice president of TRW, like the highest-ranking person for TRW, okay? And I’m like, you have got to be kidding me. I remember going home, thinking, “Are you insane? Do you know what your dad does?” She goes, “Not exactly.” I’m like, “Oh my God.”

So, yeah. So, he later became the administrator of NASA, yes.

Strogatz: Oh, that’s funny.

Glotzer: Yes, it is, yes, it is. So, I got a job, and then TRW ended up giving me a fellowship for graduate school, and they supported me through graduate school. It was fantastic. And while I was there, the first —. So, the man who hired me, his name was Cameron Knox, he put me in a group that was doing, like, plasma physics, and they put me in a room with a bunch of filing cabinets. You would go through, pick one out and look for some signatures for some particular kind of plasma waves.

And after one day of this, I went to find Dr. Knox and I said, “This is not gonna work, this is not —.”

Strogatz: Yeah.

Glotzer: “This is not using my talents. I don’t know what they are, but I know they’re not this.” And then I got into grad school, and I was going to go to Boston, and they said you should go to Boston University and work with Bill Skocpol. So I went to BU, and then I joined his group. And he hadn’t — you know, he hadn’t built his —.  He had just got there, so the lab was empty, and my job for my first year of graduate school as a member of the Skocpol group was to design a flange for a sputtering chamber. To design, like, where do you put the holes for the electron guns, so you could sputter yttrium, barium and copper and make high TC super connectors.

So, anyway. So, we finally got the sputtering chamber put together, and I remember we were pumping it, you know, down to vacuum. And at some point, this oil pump blew up all over me.

Steve Strogatz: Well, wait a second. What happens when an oil pump blows up on you? I never had that happen to me.

Sharon Glotzer: I don’t know, there was just oil all over me. I was just, like, covered in oil. I was covered in oil.

And so, I walk out of the lab, and this lab was in the basement and the Boston University Physics Building is all open in the interior, so everything’s around the perimeter. And so, you could lean over the balcony off any floor and look straight down to the basement. And so, I’m standing there, like, in the middle of the basement, and so I could look up, like, through the skylights up above, or up to the ceiling. And so Gene Stanley is walking up the stairs, and he sees me and he says, “You look like a theorist. Come up and talk to me later.”

Strogatz: [LAUGHING]

Glotzer: And so I did, I did go up and talk to him later, and by the end of the day I had, like, decided that I was going to switch to his group. It was clear once I started learning from Gene Stanley that statistical mechanics — like, that was it for me. That was what I was born to do.

Strogatz: This oil pump moment was really big for Sharon for a couple of reasons. First, it’s how she met Gene Stanley, a renowned physicist who uses physics to understand everything, from the stock market to sexually transmitted diseases to network theory. Second, though, the little physics joke that he told her about looking like a theorist instead of an experimental physicist destined to do very hands-on work (you know, like building an oil pump), this led Sharon into the type of computational science that she does now.

And finally, this moment introduced her to the field of statistical mechanics, which has become her lifelong area. A branch of physics that deals with problems that otherwise seem completely intractable and can only be viewed statistically.

Strogatz: Can you give us a flavor of what is meant by statistical mechanics, and what appealed to you about it?

Glotzer: Mm-hmm. I thought it was amazing that you could describe — like, predict how a system would behave when that system is made up of lots of little things. Like lots of little atoms or lots of little molecules or lots of little particles. Or you know, even like, you know, objects, like, you know, birds. If you go to nonequilibrium statistical — you know, flocks of birds. That you could, without having to know what every little thing is doing, but just by looking at kind of averages and just the statistics, that you could make predictions that were right. Right.

Strogatz: Yeah.

Glotzer: Like, I mean, it’s —. People do this all the time when you, like, take a temperature of something, right? What are you taking a temperature of? Well, it’s an average. You know, you stick a little thermometer in a glass of water or something, it’s — you’re taking an average, but you don’t think of it like that. But it’s not the same as —.

Strogatz: Well, you’re saying it’s an average because it’s an average of billions and zillions of molecules banging around and —.

Glotzer: Exactly, yes.

Strogatz: Uh-huh.

Glotzer: And that you don’t have to know what each one of those billions and zillions of molecules are doing to be able to make predictions about what temperature water will freeze at or, you know, what it will do under different conditions. That kinda thing. And I just thought that’s amazing.

Strogatz: It’s one of the most miraculous parts of physics, right. It is amazing that you can —.

Glotzer: It is amazing.

Strogatz: It’s almost like you getting more out than you put in. How can you get such good answers if you don’t know what the little guys are doing?

Glotzer: Yeah, right. But when I was taking thermodynamics as an undergrad, I don’t remember appreciating that it was beyond like substances, atoms and molecules. Like, I thought, oh, that’s really cool, but I’m not sure I understood that as long as the system is ergodic — meaning that all of the different possibilities of the system could in principle be accessed by the system — then statistical mechanics doesn’t care what the objects are. It doesn’t care, right? Which is why you can apply it —

Strogatz: So interesting.

Glotzer: Apply it to nanoparticles and, you know, micron-sized particles in — you know, suspended in solution and moving around, jiggling around like little pollen grains. You could apply it to that, too. It doesn’t care, it doesn’t care what the objects are as long as a few requirements are met. And then you could say some very, very profound things.

Strogatz: Well, I feel like I want to back up, though. Because I think you’ve made a very deep point that, unless someone has thought about statistical mechanics, might be lost. So, let’s unpack it a little bit. This idea that when you have something that’s a collective, it’s made up of what we were calling billions and zillions of little entities. So traditionally in physics, we did think of them as atoms or molecules, but then you mentioned it could be birds. You know, let’s just talk about some other cases that people nowadays do. Statistical physics of money, you know. They think about the financial world using these ideas.

Glotzer: Yeah.

Strogatz: They think about — you mentioned pollen grains, so they could be — or nanoparticles. We could talk about traffic, the flow of cars on the highway.

Glotzer: Absolutely, that’s right.

Strogatz: People use statistical physics on that. So this —.

Glotzer: You could talk about bacteria.

Strogatz: Yeah. But so, what gets me —.

Glotzer: Right, colonies of bacteria.

Strogatz: Well, there is this — I feel like — a continuity in your life story that I want to see if you agree with. You mentioned biology. What was repulsive to you is that there were no principles that you could discern. You had to memorize things. Where, with statistical physics, there is this unifying way of looking at everything —

Glotzer: Yes.

Strogatz: That’s made up of billions and zillions of things. And you would like that, that’s you, that’s your — I mean, I’m putting words in your mouth.

Glotzer: Yeah.

Strogatz: Isn’t that part of —.

Glotzer: That’s interesting.

Strogatz: The fun for you?

Glotzer: Yes, absolutely.

Strogatz: Yeah, that you always had this in you.

Glotzer: Yes, finding the underlying rules that describe — like, very simple rules that explain all of this complexity is definitely what drives me. It’s definitely the way to characterize the science that I do.

Strogatz: After the break, floating tetrahedra, forbidden symmetries and how order emerges from chaos. We’ll be right back.


Strogatz: Well, so I feel like — okay, so I don’t really know your science too much. I just read a little bit, but it feels to me like if you were an artist, you would be a minimalist.

Glotzer: It’s true.

Strogatz: There is some minimalism in —. One study in particular that I — if we could talk about for a few minutes, because I think it’s so —.

Glotzer: Okay.

Strogatz: Well, I find it very beautiful. What’s this thing that you did with lots and lots of tetrahedra that I am so excited about? Of course, you have to read my mind, but —.

Glotzer: I’ll tell you, but it will sound less profound, that I didn’t have this deep inner question. Like many discoveries in science, it was serendipitous. We were doing research on nanoparticle self-assembly, which is the idea that researchers in a lab can make all sorts of nanoparticles which are, of course, made of atoms, but they might have thousands to millions of atoms in them. And they’re little particles that can be anywhere from a nanometer across to a thousand nanometers across. And you can make ’em out of gold, out of silver. There are different semiconductors, cadmium telluride, cad selenide. There’s lots of different elements that you can mix and match together and grow little, tiny crystals in solution, and then stop them from growing at some point, so you wind up with a little nanoparticle.

And those nanoparticles can have shapes because they’re growing like little crystals. Shapes like tetrahedra or dodecahedra or cubes or octahedra. Those are the more common ones.

Strogatz: So, can I picture them like little gems almost, like little jewels?

Glotzer: Yeah.

Strogatz: You know, faceted shapes?

Glotzer: Absolutely, yes.

Strogatz: Yeah.

Glotzer: That’s exactly what they are. That’s right. You could think of them as Dungeons and Dragons dice.

Strogatz: Oh yeah? So what —.

Glotzer: Yeah. Those are little polyhedral dice.

Strogatz: Oh, okay.

Glotzer: Dungeons and Dragons.

Strogatz: I see. So, I’m used to cubical dice but in Dungeons and Dragons, the dice have these other shapes.

Glotzer: Yes.

Strogatz: Okay, all right. So go on. So, you were saying these crystals then form these shapes.

Glotzer: So, we were working with tetrahedra because my colleague, the particular nanoparticles that he makes in his lab are little tetrahedra. And so, we were collaborating with him and a bunch of other people on a big Air Force project — and trying to make materials with a negative index of refraction — that would bend light backward, basically.

Strogatz: Okay.

Glotzer: And so, okay, we never got there, we didn’t succeed at doing that. But as part of this, we were doing — my group was doing computer simulations of little nano tetrahedra particles and how they would self-assemble under various conditions. And so — which means that we would, you know —. So his particles, depending on, you know, what they were made of and what he put into the solution or what kind of molecules he stuck onto the surface, these nanoparticles would self-assemble in different ways. They would line up different ways. Sometimes they would put their faces together, or they might want to put their vertices together or their edges together.

And, you know, sometimes they would want to have just a few neighbors, sometimes they would have more neighbors. And that would —. And so if you do that locally and then keep growing, you would get different kinds of structures. And we call those assemblies, self-assemblies.

So it was our job, as simulators, to model this and try to figure out how we could — tell him how to make his nanoparticles so they would self-assemble into a structure that could be useful for the project.

To do that as a simulator, you know, you have to say — you have to come up with a model, meaning you have to model all the possible forces that are in the system. And there’s a lot of kinds of forces in that system. First of all, the nanoparticles, they’re actual little objects. They can’t — they’re like — they have excluded volume interactions, meaning they can’t overlap each other. So, like literally, like, take two dice and you can’t move them through each other.

Strogatz: Yeah, right.

Glotzer: So that’s the simplest interaction. But then the particles can have Van der Waals interactions mediated by the water solvent that they’re in. The particles are charged, so they could have electrostatic interactions, coulomb interactions. Because they’re not a perfectly isotropic shape, they have little dipole moments or even higher order moments that interact in a complex way. And so, there’s a lot of different forces going on in the system that we have to be able to account for, so that we could make accurate predictions of what his particles will do under different conditions.

Strogatz: All right. Now, let me just pause you here for one second, because I want to play with this analogy of you as the minimal artist. That if you were a photorealistic painter, at this point you would be worrying about all of those — the Van der Waals forces, the dipole interactions, the coulomb charge interactions — and they’re all there, they really are. Like, they should be captured in the picture, the way a photo realistic artist would do, and that’s one way of doing science and it’s a perfectly respectable way. There are people that do that.

Glotzer: Yes, exactly.

Strogatz: But —

Glotzer: But it’s so messy.

Strogatz: But you are a different kind of artist. You are gonna ask — okay, go ahead, it is messy.

Glotzer: So that’s exactly what. So, we said there’s all these forces, and I have no idea which ones are more important than others. I don’t know which one is contributing to this assembled structure versus that assembled structure.

Right. So like we, the community, know what, say, the functional form of the coulomb electrostatic interaction might be between two particles mediated by water. And then the experimentalist can go in the lab and make certain measurements to tell me, like, how to parameterize the model. But it still doesn’t tell me, you know, which forces are stronger than which, and which are the ones that are responsible for making the tetrahedra line up this way instead of that way.

And so at some point, I told the student, “Okay, just turn them all off. Turn off all the forces, turn them all off. It’s too complicated. And we’ll turn each one on one at a time and then we’ll learn what is the role of each force independent of all the other forces.” That’s the beauty about being a computer simulator, it’s that you can do these things that experimentalists can’t do. We can turn off the forces.

Strogatz: I want to pause. Yeah, that is a moment I want to savor, because as you say, when you’re doing this in a computer as opposed to in the lab, in reality, you can turn off forces. You can do these simplifications. And this tradition goes back to Galileo, really — I mean even earlier, but I’m thinking of Galileo with his inclined plane experiment, where he wanted to figure out the way that things roll downhill under the action of gravity. And in real life, it’s complicated because there’s friction between the ball rolling in the groove. So Galileo says he tried to make the ball perfectly round, and he made the groove perfectly straight.

And, you know, I mean, he does all these idealizations, which is like you telling the student “turn off this force and turn off that force,” because we don’t even know what happens just from the fact that the tetrahedra can’t go through each other. I mean, that’s the key thing for — I mean let’s see what that does just on its own was the question, and then later we could put the forces back in.

Glotzer: Yeah, exactly, exactly.

Strogatz: It’s very elegant.

Glotzer: And so — it’s also, like, the simplest thing —. At the time, I thought this is the simplest thing to do.

Strogatz: It is the simplest.

Glotzer: Just, it seemed very obvious to just — like, because we just start at the beginning and then figure out what’s going on. And I describe this story when I give lectures on this work because I think it’s important for students to hear about how not everything is planned, right? That you could think, like, “Oh, I’m so smart, I’m gonna come up with this brilliant idea and test it and it will work.”

Strogatz: Yeah.

Glotzer: But a lot of times it’s just an accident. You just see something, and it’s about knowing when to pay attention and when not to pay attention. And so the student, like, came to me and showed me, you know, “Okay, I ran it without any forces.” And what I expect to happen, if you turn off all the forces and then you’re just like running the simulation, that means that you’re just — the particles are like little pollen grains, they’re undergoing Brownian motion, they’re being bombarded by the molecules in the water — and so they’re just jiggling around with thermal vibration.

So I was expecting, “Okay, so he’s just gonna randomize them. He is just jumbling them up and then we’ll start turning on the forces.” So we sat down, he showed me the simulation. He says, “Okay, let’s turn on the forces,” and — but he comes to me and he says, “Okay, there is like a pattern.” And I said, “What do you mean, there’s a pattern?” He goes, “Well, I don’t know. Here, I thermalized them.” And I looked at it and there was — I couldn’t tell what the pattern was. It wasn’t like an ordered crystalline array, but there was something weird in there. And I said, “Okay, well, I thought you turned off all the forces.” He said, “I did,” and I — “No, clearly you didn’t.” “Well, I really did.” I said, “Nope, do it again.”

So, he did it again, and it came back and, no, there was something in —. Okay, there’s something weird going on. Do a bigger box, do a bigger system, do more particles. Maybe there’s something weird going on. So he did it again, and there was still this pattern inside and we couldn’t tell what it was, but I knew there was something there, and I didn’t expect there to be anything there.

Strogatz: Can you just describe the experiment in the computer a little more? So, you say there’s a box, there’s all these dice, you know, if we want to call them tetrahedral dice, I think that’s a good image. So, it’s a big box full of dice and they’re being jiggled —.

Glotzer: Right.

Strogatz: By temperature —.

Glotzer: Yeah. And you imagine that there’s no — like, it’s as though you’re in space with no gravity.

Strogatz: Okay.

Glotzer: And so, they’re just floating around, and they can like bump into each other and bump off, and they can turn around and point in any direction, and they could move up, down, left, right. And they’re just moving based on, sort of, these collisions with each other. So, they’re just — well, even if they’re not colliding, they’re jiggling, they’re jiggling like little pollen grains in water.

Strogatz: Yeah, yeah.

Glotzer: And so, right, and so they’re all in there. And let’s say you just have, like, two of them in a box, like they’re barely gonna see each other, so you put more, you put more, you put more. And at some point, you can get to a point where, like, half the box is filled with these dice and half the box is empty.

Strogatz: Okay. Yeah, yeah.

Glotzer: And that you imagine that — right, okay. So, at some point — and so, he was working at this, we call it density or packing fraction — that was up around 50 percent. So, when you’re doing this simulation, you’re randomly grabbing these particles and translating them, moving them side to side or rotating them a teeny, teeny bit every single timestep until you’re doing bazillions of these little moves.

So, then we started looking at it. We couldn’t figure out what was going on. The student went and calculated all the usual kinds of things, functions that you would calculate on something to see if it has structure to it somehow. And none of it showed anything, it just looked like a disordered jumble of things.

Strogatz: But you’re saying —.

Glotzer: Like the way that —. Mm-hmm.

Strogatz: To your eye it looked like — when you looked at it visually, you thought there was something there.

Glotzer: Yeah, it was clear.

Strogatz: But you say the statistical measures weren’t showing it.

Glotzer: Right.

Strogatz: Usual numbers weren’t showing it.

Glotzer: That’s right.

Strogatz: Uh-huh.

Glotzer: Exactly, exactly. And so I couldn’t figure out what to look at — and I couldn’t — I wasn’t able to, like, guess what it would be. And so, I asked the student to make all of them translucent, like see-through but colored, like different colors. And then we would rotate it around, because I thought, well, if there’s some kind of order, then at some point these dice should line up, and then we should see these bold, black lines for their edges. And then maybe that would help us figure out what’s going on.

Strogatz: Great idea.

Glotzer: And so, then we found this image, when we turned it around enough, that where you could see these, like, wheels — circles with tetrahedra arranged in all of these circles, and circles around circles around circles. That it was like —.

Strogatz: Ooh.

Glotzer: It still — I didn’t know what it was, but it was — and it —. So that image, by the way, later became the BBC News image of the week. The week of December 14th, 2009.

Strogatz: Yeah?

Glotzer: Like I had no idea and there it was —.

Strogatz: Wow, mazel tov.

Glotzer: The BBC image. I know, right? Like usually it’s like some weird bird or something, you know.

Strogatz: I want to see this image. I mean, it’s — I’m visualizing, I don’t know, something that I’m picturing, sort of like a stained-glass window, I expect, in 3D.

Glotzer: Yes, that’s what I call it, that’s what I call it.

Strogatz: Really?

Glotzer: The stained-glass image, the stained-glass image.

Strogatz: ’Cause you said you colored them this pretty translucent, I’m guessing, lots of nice pastel-y colors or something.

Glotzer: Yeah, it looks like stained glass.

Strogatz: What are these wheels? What the heck are the wheels?

Glotzer: Right. So, I knew about quasicrystals, which are crystals that have no repeat unit, right? So, if you think of, like, an ice crystal, ice has the crystal structure of hexagonal ice, where there’s a repeat unit. Sodium chloride has a very simple crystal structure, where you can take a couple of atoms and then you just repeat in, you know, all directions: you know, left and right, up and down. And you can recreate the crystal from just knowledge of a little piece of the crystal. It’s a repeat unit, like a tiling has a repeat unit.

Strogatz: Mm-hmm, sure.

Glotzer: Quasicrystals don’t have that, but they do have what are called Bragg peaks. They scatter, they scatter x-rays, and they look like crystals from the way they scatter, but they have what used to be called “forbidden symmetries.”

Strogatz: Quasicrystals are mysterious. They were not something that people learned about in traditional solid state physics, so many of us are not very familiar with them, and Sharon herself was not particularly familiar with them when she happened to create one accidentally. If she had these tetrahedral dice in a box, in a computer simulation, and started jiggling them, they spontaneously ordered into a quasicrystal and she recognized that there was some kind of order there. Wheels within wheels, but she didn’t know what she was seeing. And it was only after she started to learn the terminology and the concepts of quasicrystals that she realized she had accidentally, spontaneously created one in the computer.

Glotzer: And here is another serendipitous thing that happens. It’s that right at that time, I got an e-mail from a senior professor in Germany, who wrote to me and said, “I have a very, very bright Ph.D. student who would like to come and do a postdoc, and he’s an expert in quasicrystals,” which I was not.

Strogatz: Yeah.

Glotzer: And so, like just out of the blue, right? Just sometimes, just like the stars align and weird stuff happens.

Strogatz: Yeah.

Glotzer: And like it’s so berserk. So I thought, okay, this is a sign, and so I said absolutely, yes. And Dr. Michael Engel showed up on my doorstep at some point a short time later. But even before he came, we started sending him this data and saying, you know, “Help us figure out what this is,” and he did. And then, you know, we ended up working together for the next five years, publishing on all these kinds of things. It’s known — it has been known by, I don’t know, seven people, that hard, spherical particles will spontaneously order into a simple crystal structure —.

Strogatz: Yeah.

Glotzer: With no forces. Just by doing what we did, but with spheres. We know that rods — if you take little rodlike particles, and you do the same kind of simulations that we did, they would also order into what’s called a nematic liquid crystal, where the rods all tend to point in the same direction. And this has been known since 1949, and the — 1958, the very first computer simulation paper ever was published, and it was on hard spherical particles spontaneously transforming from a fluid to a crystal.

Strogatz: I wanted to ask about an analogy and see if it’s on track or not, which was that I saw something on Twitter a couple days ago that I thought might be close to what you just mentioned. When you talked about rods and jiggling of rods, this was a Twitter video of someone showing a box of nails. Like, if you went to the hardware store and bought a box of nails —.

Glotzer: I should have had it as a demo.

Strogatz: Okay. Do you want to describe it to us?

Glotzer: It was great. So yeah, they had, like, just a little box, like the size of a shoe box, and they had a bunch of long nails that maybe looked like two-and-a-half inch-long nails. And they were all mixed up, completely randomly jumbled. And then they just were, like, shaking the box just back and forth very gently, very gently, back and forth, back — like the way you’d pan for gold, because I know we all have that experience of that! Pan for gold. But you just shake it back and forth, back and forth, and slowly but surely the rods all started lining up in one direction.

Strogatz: A lot of people thought it was fake. People were saying, “Oh, sure, it’s fake, it’s a hoax, it’s the movie run backwards. It started lined up and then they shook it and it made it random.”

Glotzer: Oh yeah?

Strogatz: You’re laughing because that’s absurd to you.

Glotzer: Yeah. Yeah, that’s — but no, I could see why you would think that. But no, I mean because the shaking back and forth is a way of what we call thermalizing the system. It’s giving them a little bit of energy to, like, move around and explore. I mean, it’s not the same thing as if you had rods, and they were really floating in a liquid and they were really sampling all the different ways that they could arrange and line up, but it’s a kind of approximation of that.

Strogatz: Yeah, different because of the action of gravity in the case of the nails, but not in your simulation?

Glotzer: Yeah. I don’t think the gravity is so important but just, you know, to really be a statistical mechanical system, like a system that really follows the laws of statistical thermodynamics. But this was what this was trying to approximate.

And so, the nails line up because there are more ways of them arranging in the box if they line up than if they’re all pointing every which way, which gets them, like, jammed up.

Well, it’s also true that if you took a box, a big box of baseballs, and you just threw the baseballs in, forget about the ridges of the baseballs, but you just throw the baseballs in a box and they’re all in there randomly. And if you do the same thing but probably you have to, like, shake it a little bit more, then they will all arrange into an ordered pattern that’s just like the pattern of, you know, the way grapefruits are stacked in a market.

Strogatz: I mean, that’s such a deep thing. This is — I’m glad we’re getting to this, that you’re talking about, with the jiggling of baseballs or of the nails or, in your case, in the computer with the tetrahedra, that what we think of —

Glotzer: Yes, same thing.

Strogatz: As a disordering — yeah. I mean normally, you think of jiggling, you know, as you shake something up to make it random, and you shake stuff up and make it ordered.

Glotzer: Yes. It’s very counterintuitive. Now, technically, this system is more disordered when it’s ordered, but by disordered we mean something different than positionally, spatially ordered, right? So, we look at it and we see going from something that’s spatially disordered to spatially ordered and we think, “Well, that’s backwards.” But actually, it’s doing that because there are more ways of arranging the rods or the tetrahedra or the little hard spheres, baseballs, if they are in an ordered arrangement. There are just — there are more ways of placing them if they’re ordered.

Strogatz: So, the word that you used in one interview I read was “options.”

Glotzer: Yeah, it’s all about options. Entropy is about — and so, it’s doing this because of entropy, which is counterintuitive because people think of entropy as meaning disordered.

The best way to think about it is that entropy is about options. It’s the number of options, the number of ways you have of doing something. And so, if things are pointing every which way, then they can get stuck and you don’t have very many ways of reordering them, of organizing them. But if they’re ordered, then they could move a little bit one way or the other, but it still looks like a crystal, it still looks like an ordered thing.

Strogatz: Entropy is one of the biggest concepts in all of physics. It’s the idea that if you leave things alone, just leave them to their own devices, they will tend to get more random over time, more disorganized. Like, if you just leave your room alone and you never clean it, it’s gonna become a mess. You have to put in energy to make things organized, at least that’s our intuition. That’s what everybody tends to think, and you know, that’s why what Sharon discovered is so mind blowing, so really surprising and counterintuitive.

She found that this drive toward randomness can sometimes actually lead to spontaneous order. That order can sometimes emerge from chaos. And she has this unique, sophisticated way of looking at entropy, that really entropy is all about options. Left to their own devices, things will explore their options as much as possible and sometimes will create spontaneous order.

Strogatz: We’ve sort of taken for granted that you use computers, but you haven’t told us how you got into that, or why do you like —? Like, what do computers offer you? Or, I don’t know…

Glotzer: Computers allow you to set up experiments, computer experiments, right? So just like, when we can study nanoparticles and turn on and off forces, it’s a way of doing the most controlled experiment possible, because the computer will only do exactly what you tell it and nothing else, right? And so, you have ultimate control over setting things up.

And I think that I like that, but I also just really loved writing code, and I didn’t know that. I had no experience with computers, really at all, until I got to grad school. And then the summer after my first year, when I joined Gene’s group —. So, Boston University was one of the first places to have a Center for Computational Science, and we were partners with a company called Thinking Machines.

Strogatz: I remember them.

Glotzer: Which —.

Strogatz: Yeah.

Glotzer: Right. And they came — Danny Hillis’ company. They came out with this big parallel computer, and Boston University was what we called a beta test site, so we got this big parallel computer with 65,636 chips — cores — in it. And so instead of, like, a regular — like, regular computers at the time had a single CPU, central processing unit, and you would program it and it would carry out all the instructions serially, one after another after another after another after another.

Danny Hillis’ idea was, “Well, what if we had, you know, thousands of them in parallel and each one of them took a piece of the problem and did all the instructions in parallel, and then brought all the partial solutions together at the end, couldn’t you do things so much faster?” And so that’s called parallel computing, and that was, like, big that year. And so, the very first computer I ever learned how to program had 65,536 processors in it.

Strogatz: We used to call it the Connection Machine, right.

Glotzer: Yes, it is the Connection Machine, CM2. In fact, I have a chip they gave me when I graduated. By then, we were working on the Connection Machine CM5, and they gave me a little computer chip that had —. So, if you wrote really good code and sometimes you could find compiler errors, or you could even find, like, chip errors… And so this was a chip that I found was bad, and they gave it to me, and my mom made it into a necklace for me.

Strogatz: Oh, I like it, I like it.

Glotzer: I know. In fact, I wore it this last — at the last American Physical Society meeting, I got an award for computational physics. It’s like this big award for computational physics called the Rahman Award, and I wore it. I wore that chip. So that’s — I got into computer programming that summer. And it was like the first time I found something where you don’t look at your watch. You know that thing where you’re so engrossed in something —.

Strogatz: They call it flow, right, that’s the feeling of flow.

Glotzer: You’re so … in the zone.

Strogatz: In the zone or — yeah, flow.

Glotzer: I call it — yeah.

Strogatz: So, a guy wrote a book about this.

Glotzer: I never heard it —.

Strogatz: Mihaly Csikszentmihalyi wrote a book called Flow. And the feeling of flow is when you’re so engrossed in a creative or whatever that you —.

Glotzer: Yes.

Strogatz: The time loses meaning, you’re just flowing.

Glotzer: Yes.

Strogatz: You’re in the zone.

Glotzer: Exactly. Oh, I never heard it called flow. I’m in the zone.

Strogatz: Oh, you’re gonna like this book, yeah, Flow.

Glotzer: Oh cool, okay, yeah. So that was the thing where I would — you know, you would start at like 3:00 in the afternoon, and all of the sudden it’s like 1:00 in the morning, and you didn’t even realize that —.

Strogatz: Wow.

Glotzer: You know, you didn’t eat dinner and you didn’t know what time it is because you’re — I was so into it. And it was something I found that I was good at. I was really good at designing and writing code.

Strogatz: I see.

Glotzer: And debugging was, like, one of the great joys of my life, where you knew you had a bug, you knew you had a bug, you knew that you did it, you created it and now you have to find it, like a total detective story.

Strogatz: You know, after talking to Sharon I felt like I had my own theory, a theory of Sharon. Her scientific journey has been driven by curiosity and chance and randomness and accidents. It’s been all about a meandering, an exploring, wandering and it sort of seems perfect, actually, because the scientist that she is today is someone who studies the power of chance and the power of systems to wander and explore their own possibilities. I think we all have something to learn from her openness about letting accidents work for you. Not everything has to be planned. Sometimes marvelous results can come from chance alone.

Strogatz: So, having discovered the quasicrystalline order in the simulations, why do we care? Why is that interesting or important? What’s the punchline of that?

Glotzer: We care because we care about how order arises in the world, and where complexity comes from. How do systems, how do — whether it’s, you know, gems and minerals, or ice in the freezer, or all of the different complex organelles in the cells in your body — how do they start from nothing and then become something that’s so complicated and so intricate?

Where are those instructions, right? How does something on its own figure out how to go from an amorphous blob into something with exquisite order to it?

Strogatz: Ah, exquisite, yes.

Glotzer: And I want to understand those rules, those underlying rules, and to understand how complicated are those rules, or are they really simple? And for me, the idea that you could have no forces, no complexity whatsoever, just the shape of a particle and some jiggling and end up with things that are so complicated to describe is extraordinary. And it doesn’t mean that that’s how everything forms, of course, but it shows you that that’s kind of the minimal model of emergence of order.

Strogatz: Yep, magnificent. We’ve heard in debate — or, is it debate? Or — I don’t know, in parliamentary procedure, they talk about Robert’s Rules of Orders. I think we just heard Sharon’s Rules of Order.

Glotzer: [LAUGHS]

Strogatz: You know, really.

Glotzer: Yeah, they’re not nearly as strict as Robert’s Rules.

Strogatz: But there’s something very inspiring. And I mean, for me, almost like quasi-religious that from such humble beginnings, banging around at random, that order, spectacular order can emerge. It’s just very — it’s exciting what nature can do with so little and you’re discovering that.

Glotzer: That’s exactly how I see it.

Strogatz: Yeah.

Glotzer: Yes. It’s very exciting.

Strogatz: Next time on The Joy of x, mathematician Federico Ardila and I discuss a couple of crossroads. His branch of math, combinatorics, where algebra meets geometry, and his brand of teaching which he infuses with his own special rhythm.

Federico Ardila: I play some more kind of improvised forms of music, where you are supposed to just kind of set some initial conditions and then you just start improvising, like jazz or like a lot of kind of music from the African diaspora.

Strogatz: The Joy of x is a podcast project of Quanta Magazine. We’re produced by Story Mechanics. Our producers are Dana Bialek and Camille Peterson. Our music is composed by Yuri Weber and Charles Michelet. Ellen Horne is our executive producer. From Quanta, our editorial advisors are Thomas Lin and John Rennie. Our sound engineers are Charles Michelet and at the Cornell University Broadcast Studio, Glen Palmer and Bertrand Odom-Reed, who I like to call Bert.

I’m Steve Strogatz. Thanks for listening.



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