Kevin Knudson: Welcome to My Favorite Theorem, a podcast about mathematics, favorite theorems, and other random stuff that we never know what it’ll be. I’m one of your hosts, Kevin Knudson. I’m a professor of mathematics at the University of Florida. This is your other host.
Evelyn Lamb: Hi, I'm Evelyn Lamb. I'm a freelance math and science writer in Salt Lake City, Utah, where I forgot to turn on the heat when I first woke up this morning. I've got separate systems. So it is very cold in the basement here where I am recording.
KK: Well, yeah, it's cold in Florida this morning. It was, you know, in the mid-60s. It's very pleasant. I'm still in short sleeves. Our listeners can't see this, but I'm in short sleeves. Evelyn’s in a sweater. And our guest is in a jacket in his attic.
KK: So today we are happy to welcome Nira Chamberlain all the way from the UK. Can you tell everyone about yourself a little bit?
Nira Chamberlain: Yes, hello. My name is doctor Nira Chamberlain. I’m a professional mathematical modeler. I'm also the president-designate of the Institute of Mathematics and its Applications.
KK: Fantastic. So tell us about the IMA a little bit. So we have one of those here, but it's a different thing. So what is it?
NC: Right. I mean, the Institute of Mathematics and its Applications is a professional body of mathematicians, of professional mathematicians, and it's a learned society. It's been around since 1964. And it is actually to make sure that UK has a strong mathematical culture and look after the interest of mathematicians by industry, government and academia.
KK: Oh, that's great. Maybe we should have one of them here. So the IMA here is something else. It’s a mathematics institute. But maybe the US should have one of these. We have the AMS, right, the American Mathematical Society.
EL: Or SIAM might be more similar because it does applications, applied math.
KK: Yeah, maybe.
EL: Yeah, we’ve kind of got some.
NC: So we asked you on for lots of reasons. One is, you know, you're just sort of an interesting guy. Two, because you’re an applied mathematician, and we like to have applied mathematicians on as much as we can, Three you actually won something called the Great Internet Math-Off this summer, of which Evelyn was a participant.
EL: Yes. So he has been ruled—he’s not just an interesting guy, he has been officially ruled—the most interesting mathematician in the world…among people who were in the competition. The person who ran it always put this very long disclaimer asterisk, but I think Nira definitely has some claim on the title here. So, yeah. Do you want to talk a little bit about the big, Great Internet Math-Off?
NC: Yes, we have let's say an organization, a group of mathematicians that do a blog, Aperiodical, and they decided to start this competition called the big internet math-off. And it’s a as a knockout tournament, 16 mathematicians, and they put up something interesting about mathematics. It was put up on the internet, it was there for 48 hours, the general public would vote for what they found was their most favorite or most interesting, and the winner would progress to the next round, and it was four rounds all together. And if you reach to the final end, and you win it, you get the title “World's Most Interesting Mathematician.” And when I was invited, I thought, “Oh, isn't this really for those mathematicians that are pure mathematicians and those public communicators and those into puzzles? I mean, I'm a mathematical modeler, I’m in applied mathematics, so what am I really going to talk about?” And then when I saw that when I was actually introduced as the applied mathematician and everybody else was, let's say the public communicator, and here's the applied mathematician. It was almost like: then here's the villain—boo!
I thought, “Okay, there you go.” I’m thinking, “All right, what we're going to do is I'm actually going to stick to being an applied mathematician.” So three out of the four topics I actually introduced were about applied mathematics, and yes, the fourth topic was actually about the history of mathematics. And I was fortunate enough to get through each of the rounds and win the overall competition. It was very interesting and very good.
EL: Yeah, and I do wish — I think you look very interesting right now—I wish our listeners could see that you've got headphones on that make you look a little bit like a pilot, and behind you are these V-shaped beams, I guess in the attic, where I can totally imagine you, like, piloting some ship here, so you're really looking the part this morning, or this afternoon for you.
NC: Thank you very much indeed. I mean that’s what I call my mathematics attack room, which is the attic, and I have 200 math books behind me. And I’ve got three whiteboards in front of me, quite a number of computer screens. And I’ve got all my mathematical resources all in one place.
KK: Okay, so I just took a screenshot. So maybe with your permission, we’ll put this up somewhere.
So this is a podcast about theorems. So, Nira what is your favorite theorem?
NC: Okay, my favorite theorem is actually to do with the Lorenz equation, the Lorenz attractor. Now it was done in the 1960s by a meteorologist called Edward Lorenz. And what he wanted to do was to take a a partial differential equation, see if he could make some simplifications to it, and he came up with three nonlinear ordinary differential equations to actually look at, let's say, the convection and the movement, to see where we can actually use that to do some meteorological predictions. And then he got this set of equations, went to work solving it numerically, and then he decided, “Actually, I’d better restart my computer game because I've done something wrong.” So he went back, he restarted the computer, but he actually changed the initial conditions by a little bit. And then when he came back, he actually saw that the trajectory of the solution was different from what he had started with. When he went back and started checking, he actually saw that the initial conditions only changed by a little bit, and what was this? It was probably one of the first examples of the “butterfly effect.” The butterfly effect is saying that if, let's say, a butterfly flaps its wings, then that will prevent a hurricane going into Florida — topical.
KK: Yeah, it’s been a rough month.
NC: Yeah, or, if, let's say, another butterfly flaps its wings, then maybe another hurricane may go into Salt Lake City, for example. And this is, like I said, an example of chaotic behavior once you choose certain parameters now. The reason why I like this theorem so much is I was actually introduced to this topic when I was in my final year of my mathematics degree. And it probably was one of the introductions to the field of mathematical modeling, recognizing that when you actually model reality, mathematics is powerful, but also has its limitations. And you’re just trying to find that boundary between what can be done and what can't be done. Mathematical modeling has a part to play in that.
KK: Right. What's so interesting about meteorological modeling is that I've noticed that forecasts are really good for about two days.
KK: So with modern computing power, I mean, of course, as you pointed out, everything is so sensitive to initial conditions, that if you have good initial data, you can get a good forecast for a couple of days, but I never believe them beyond that. It's not because the models are bad. It's because the computation is so precise now that the errors can propagate, and you sort of get these problems. Do you have any sense of how we might extend those models out better, or is it just a lost cause, is it hopeless?
NC: It's probably a lost cause. I agree with you to a certain extent. But it's a case of when we're dealing with, let’s say, meteorological equations, if they have chaotic behavior, if you put down initial conditions, and it's changed, you know, it's going out and it's changing, it just shows that, yeah, we may have good predictions to begin with, but as we go on into the future, those rounding errors will come, those differences will come. And it's almost like, let's use an analogy, let's say you go to whatever computer algebra software you have, and you get π, and let’s say you square root it 10 times, and then you raise it to a power 10 times, and then if you square root it 100 times and then you raise it to a power 100 times, and if you keep on repeating that, then actually, when you come back to the figure, you're thinking, “Is this actually π?” No, it's not. And also different calculator and different computer algebra softwares, you’ll see that they will have actually their difference. It’s that point where in terms of when we're doing, predicting a weather system, because of the chaotic behavior of the actual nonlinear differential equations, coupled with those rounding errors, it is very difficult to do that long-term weather forecast. So nobody can really say to me, “By the way, in five years’ time, on the 17th of June, the weather will be this.” That’s very much a nonsense.
KK: Sure, sure. Well, I guess orbital mechanics are that way too, right? I mean, the planetary orbits. I mean, we understand them, but we also can't predict anything in some sense.
KK: Right, right. Living in Florida, I pay a lot of attention to hurricane models. And it's actually really fascinating to go to these various sites. So windy.com is a good one of these. They show the wind field over the whole planet if you want. And they'll also, when there are hurricanes, they have the separate models. So the European model actually turns out to be better than the American one a lot, which is sort of interesting because hurricanes affect us a lot more than— I mean the remnants get to the UK and all of that. But so you’re right, it's sort of interesting, the different implementations—the same equations, essentially, right, that underlie everything get built into different models. And then different computing systems have the different rounding error. And the models, they’re sort of, they're usually pretty close, but they do diverge. It's really very fascinating.
NC: Yeah, I mean, over in the United Kingdom, we had an interesting case in 1987 where the French meteorology office says, “By the way, people in the north of France, they should be aware that there's going to be a hurricane approaching.” While the British meteorologic office was saying, “Oh, there's no way that there's going to be a hurricane. There's no hurricane. Our model says there’s going to be no hurricane.” So the French are saying there’s going to be a hurricane. The British say there’s not going to be a hurricane. And guess what? The French were right and a hurricane hit the United Kingdom.
And because of that what they did is that now the Met Office, which is the main weather place in Britain, what they've done is they put quite a number of boats out in the Atlantic to measure, to come up with a much more accurate measure of the weather system so that they can actually feed their models, and they also use more powerful models because he equation itself remains the same, it’s the information that actually goes into it which is which is the difference, yeah? So in terms of what you said in the American models, it's all dependent on who you get the measurements from because you may not get exactly the measurement from the same boat. You may get it from a different boat, from different boats in a different location, different people. This is where you come to that human factor. Some people will say, “Oh, round it to this significant figure,” while someone else will say, “Round it to that significant figure,” and guess what? All of that actually affects your final results.
EL: Yeah, that matters.
KK: So do you do this kind of modeling yourself, or are you in other applications?
NC: Oh, I'm very much in other applications. I mean, I'm still very much a a mathematical modeler. I mean, my research now is to do with—to minimize the probability of artificial intelligence takeover. That’s what my current research I'm doing at Loughborough University.
EL: Well that, you know, the robots will have you first in the line or something in the robot uprising.
NC: Well, we talk about robots, but this is quite interesting. When we're talking about, let's say, artificial intelligence takeover, everybody thinks about the Hollywood Terminator matrix, I Robot, you know, robots marching down the street. But there are different types of AI takeovers, and some of them are much more subtle than that. For instance, one scenario is, let's say for instance, you have a company, and they decide to really upgrade their artificial intelligence, their machine learning, to a certain sense it's more advanced than their competition is. And by doing so, they actually put all their competitors out of business. And so what you have is you have this one company almost running the world economy. Now the question is, would that company make decisions (based on its AI), would they make decisions that are conducive with social cohesion? And you can't put your hand on your heart and say, “Absolutely, yes, because a machine, it’s largely, like, 1-0, it doesn't really care about the consequences of social cohesion. So henceforth, we can actually to a model of that, saying could we ever get to a situation where one company actually dominates all different industrial sectors and ends up, let’s say, running the world economy? And if that's the case, what can what strategies can we actually implement to try and minimize that risk?
EL: It sounds not entirely hypothetical.
KK: No, no. Well, you know, of course the conspiracy theorists types in the US would have you believe that this already exists, right? The Deep State and the Illuminati run everything, right?
EL: But getting back to the Lorenz system and everything, you were saying that this is one of the earliest examples of mathematical modeling you saw. Was it one of the things that inspired you to go that direction when you got your PhD?
NC: Yes, so I was doing that as part of my final year mathematics degree, and I thought, well, this whole idea that, you know, here’s applied mathematics, using mathematics in the real world, saying that there are problems that some people say it's impossible, you can't use mathematics. And you're just trying to push the boundaries of mathematics and say, “This is how we actually model reality.” It was one of the things that actually did inspire me, so Edward Lorenz actually inspire me, just saying, wait a minute, applied mathematics is not necessarily about: here’s a problem, here’s an equation, put the numbers in the right places, and here's a solution. It's about gaining that insight into the real world, learning more about the world around you learning more about the universe around you through through mathematics. And that's what inspired me.
KK: And it's very imprecise, but that's sort of what makes it intriguing, right? I mean, you have to come up with simplifying assumptions to even build a model, and then how much information can we extract from that?
NC: That’s one of the key things about mathematical modeling. I mean, you're looking at the world. The world is complex, full of uncertainty, and it’s messy. And you are making some simplifying assumptions, but the key thing is: do you make simplifying assumptions to an extent that it actually corrupts and compromises your solution, or do you make simplifying assumptions that say, “Actually, this gives me insight into how the world actually works.”? And recognizing which factors do you include, which factors do you exclude, and bring a model that is what I call useful.
KK: Right. That’s the art, right?
NC: Yeah, that's the art. That's the art of mathematical modeling.
KK: So another thing we do on this podcast is we ask our guests to pair their theorem with something. So what pairs well with the Lorenz equation?
NC: I chose to pair it with the Jamaican dish called ackee yam and saltfish[16:48] . Now the reason why is with ackee yam and saltfish, if you cook it right, it is delicious, but if you cook it wrong, the Ackee turns out to be poisonous and that’s a bit like the Lorenz equation.
KK: What is ackee? I don't think I know what this is.
NC: Okay. Ackee is actually a vegetable, but if you actually were to look at it, it looks like scrambled egg, but it's actually a vegetable. It's like a yellow vegetable.
NC: And yam, it’s like an overgrown, very hard potato. It’s looks like a very overgrown, hard potato.
KK: Sure, yeah.
NC: And saltfish is just a Jamican saying for cod. Even though you could really say ackee yam and cod, they don't call it cod, they call it saltfish.
KK: Okay. All right. So I've never heard ackee.
EL: Yeah, me neither.
KK: I mean, I knew that yams, so in the United States, most people will call sweet potatoes yams, they’ll use those two words interchangeably. But of course, yams are distinct, and I think they can be poisonous if you don't cook them right, right? Or some varieties can. But so ackee is something separate from the yam.
EL: Also poisonous if you don't cook it right.
KK: So can you actually access this in England, or do you have to go to Jamaica to get this?
NC: Yes, we can access this this in England because in England we have a large West Indian diaspora community.
KK: Sure, right.
NC: And also we do get lots of variety of foods from different countries around the world. So we can, it's relatively easy to to access ackee yam. And also we’ve got quite a number of Caribbean restaurants, so definitely there they are going to cook it right.
KK: So it's interesting, we have a Caribbean restaurant here in town in Gainesville, which of course we're not as far away as you are, but they don't try to poison us. The food is delicious. EL: That you know of.
KK: Well that's right. I love eating there. The food is really spectacular. But this is interesting.
EL: And is this a family recipe? Do you have roots in in the West Indies, or…
NC: Yes, my parents were from from Jamaica. I still have relatives in Jamaica, and my wife’s descent is Jamaican. Now and again we do have that Caribbean meal. I thought, “Well, what shall I say as a food? I thought, “Well, should I go for the British fish and chips?” I thought, “No, let's go for ackee yam and saltfish.”
KK: Sure, well and actually I think your jacket looks like a Jamaican-influenced thing, right? With the black, green, and yellow, right?
NC: Yes, absolutely. And that's because it's quite cold in the in the attic. This is the same style of jacket as the Jamaican bobsled team, so I decided to wear it, as it’s quite cold up here.
EL: Yeah, Cool Runnings, the movie about that, was an integral part of my childhood. My brother and sister and I watched that movie a lot. So I’m curious about this ackee vegetable, like how sensitive are we talking for the dependence on initial conditions, the dependence on cooking this correctly to be safe? Is it pretty good, or do you have to be pretty careful?
NC: You have to be pretty good, you have to be pretty careful. As long as you follow the instructions you’re okay, but in this case, if you don't cook it long enough, you don't cook it at a high enough temperature, whatever you do, please do not eat it cold, do not eat it raw.
KK: Like actually it might kill you, or it just makes you really sick?
NC: It will make you really sick. I haven't heard— well let’s put it this way, I do not wish to carry out the experiments to see what would happen.
KK: Well this has been great fun. I've learned a lot.
KK: Thanks for joining us, Nira.
NC: Thank you very much indeed for inviting me.