The Exchanges

Q It's really fascinating to me. Can you talk to me a little bit more about the pandemic and sort of like how you think about it through the lens of math?

A Yeah, totally. So I actually, um, in 2018, I did a big project with the BBC because we knew that a pandemic was coming. So we teamed up with some epidemiologists from the London School of Hygiene and Tropical Medicine. And the University of Cambridge to collect the best possible data so that we could be prepared for when something like this did happen. The big problem at that point, so this is, you know, a couple of years ago, the big problem was that if you want to know how an epidemic or flu-like virus will spread through a population, then you need to have really good data on how far people travel, And how often people come into contact with one another and crucially who they come into contact with the different age groups, um, the settings, they come into contact with other people and so on. And up until a couple of years ago, uh, it sounds mad to say it, but you know, given that everyone's carrying mobile phones, but up until a couple of years ago, the best possible data that we had within the UK, at least, um, for how people did that, how people moved and how people mixed with one another was a paper survey From 2006 where a thousand people said, oh yeah, I reckon, I reckon I did this. I reckon I came into, I reckon I went about that fine. I reckon I came into contact with these people. So what we did with this, with the help of the BBC, because, you know, they have such …

AI assessment note: “if you want to know how an epidemic or flu-like virus will spread through a population”

Q Do we see that sort of manifesting itself now with kids' attitudes? Because they're surrounded by algorithms and machines, and does that change how they perceive math?

A Well, yeah, but I think that, unfortunately, the math is invisible, right? Because, I mean, for this stuff to work, for a mobile phone to work, it has to be all of, I mean, the amount of math involved in getting your mobile phone, or, you know, me speaking to you now, however many thousand miles apart we are, the amount of math that's involved is, like, phenomenal. I mean, it's, it's easily PhD level stuff, but for this to work effectively, it has to be invisible. It has to be hidden completely behind the scenes. You as the user can't really be aware that any of it is there. So even though, you know, as you say, with algorithms dominating more and more of the way that we're communicating with each other, How we're accessing information, you know, what we're watching, who we're dating, everything. Even so, I think the maths is so behind the scenes that I don't think it's necessarily clear that it's, it's, it's driving so much of the change.

AI assessment note: “unfortunately, the math is invisible... it has to be hidden completely behind the scenes”

Q Can you give me examples of what comes to mind when you say that?

A Just as a silly example, a kind of more trivial example, I think that the way that some sat navs used to be designed, this is less, less true now, but certainly the way that some sat navs used to be designed was, uh, that you would just type it in and it would tell you your destination and off you went, right? Tell you where you were going and off you went. And you could, if you wanted to go in and interrogate the interface and find out exactly where the thing was sending you. But, uh, but most of all, you'd put in the address and it would just tell you where to go. And that is an example, I think of not thinking clearly about the interface between the human and the machine, because there are all sorts of stories about people, uh, just blindly following their, their sat nav. So my favorite example is there's a group of Japanese tourists in Brisbane. And this is a few years ago who wanted to go visit this very popular tourist destination on an island on Off the coast of Brisbane, got a sat nav, put it in, didn't look at the map off. They went, um, didn't realize the sat nav was essentially telling them to, uh, to drive out into the ocean. Um, and amazingly, amazingly, the story you'd think you'd think, okay, fine.

AI assessment note: “Just as a silly example, a kind of more trivial example, I think”

Q That's really interesting. So how do, how do we make a better story around mass then?

A So I think it's that for me, it's humanizing it. I think that's, that really is it for me. I think, you know, one of the, um, certainly in Britain, I think in the States too, there's this massive book called Fermat's Last Theorem, um, massive as in, in terms of its sales rather than physically big. Um, it's, uh, it was written by Simon Singh and it's, uh, you know, I read it when I was maybe 16 years old. Uh, and one of the things that really, um, I guess solidified the idea that I wanted to be a mathematician. And in it, it's just a long story of, you know, hardcore maths throughout the centuries. But what he did was he anchored all of the stories to the people that were involved. And it's, it's exactly like your race car driving, right? Like you care so much about the characters who are involved in this, this history of math. There's stories of someone like, um, like Galois is a great example of a, of a character that Simon Singh tells, um, the story of in the book. So he was French. He was about 19 years old. I think someone I'm sure will know the facts better than me and sure will contact me and correct me. But, uh, he was about 19 or 20, and he'd been having an affair with a very important person in French society, a woman who was older than he was, and her husband had found out about this affair and had challenged him to a duel. Now, of course, in, in France, this is like…

AI assessment note: “So I think it's that for me, it's humanizing it.”

Q How can we use, I don't want to say argue better, but I'll use your language. Like, how can we use math to argue better in our relationship?

A Oh, this is my favorite, favorite one. So this is, this is some work that was done by, um, the psychologist John Gottman. He's done some amazing work with couples in long-term relationships, and he's worked out a way that he, what he essentially does is he gets couples in a room together, and he videotapes them, and he gets them to effectively, to have an argument with one another, right? So officially, they say that it's, uh, they ask them to have a A conversation about the most contentious issue in their relationship. But basically they, they lock up a couple in a room and make them have an argument. But what they've done is they've worked out a way to score everything that happens during that conversation. So every time that someone's positive, they get a positive score. Every time someone sort of laughs and, you know, gives way to the partner and, you know, but even gestures, right? So if you roll your eyes, you get a negative score. If you stonewall your partner, you get a negative, negative score, that kind of thing. Anyway, the thing that's kind of Neat about this is that it then means that you can look at a graph of how an argument evolves over time. So the really nice thing about this is that, um, John Gottman then teamed up with a mathematician called James Murray, who came up with a set of equations for how these arguments ebb and flow, the dynamics of these equation…

AI assessment note: “mathematician called James Murray, who came up with a set of equations”

Q I mean, math is such a tricky subject for students. I mean, they seem to have this very love-hate relationship with it, with most people hating it. What are some of the things that schools could do to promote better engagement with students over math?

A So it's a tough thing because, I mean, on the one hand, if you're ever going to be able to reach the most beautiful elements of the subject, if you're ever really going to be able to properly to put it to use, you can't have your working memory being swamped by remembering all of these rules and remembering these really fundamental basics of the subject. So it's slightly unfortunate that that inevitably means that when you're starting out, when you're in the early stages, It has to be dominated by essentially learning the basics of the subject. It's something that's, you know, it's difficult, it's not particularly inspiring, or, or, you know, if it's taught in a very straight fashion, it's not particularly inspiring. So in terms of what schools can do, I mean, I think for me, the, the, I've really seen a difference when, um, when teachers really put in the effort to demonstrate just how useful this stuff is. I think one of the big complaints that you get from school kids Is like, well, I'm never going to use this stuff. What's the point of it? It doesn't apply anywhere. And I think really showing just how dramatically important maths is to virtually every aspect of our modern world. I think that that's, that's something that can really make the subject come alive.

AI assessment note: “teachers really put in the effort to demonstrate just how useful this stuff is”

Q That's such an amazing and incredible story. Thanks for sharing that. Your first book, The Mathematics of Love, explain the math, um, underlying human relationships. How can applying math, math concepts to romantic situations be helpful to people?

A Well, uh, so this was, this is a, uh, it was sort of a, a kind of private joke that got terribly out of hand to that book, um, where I, I, you know, when I was sort of, um, you know, in the dating game or like, you know, designing my table plan for my wedding or like any of those things, I mean, I just like generally apply maths to everything and would just try and calculate as much as possible. I'm trying to like game it as much as possible. And so in the end, I like wrote these up into a book and it's all very tongue in cheek. But the thing is, is that while I totally believe that you cannot write down an equation for, for real romance, you can't write down an equation for that sort of, that spark of delight that you get when you meet someone and you know, you really like them. There's kind of, there's no real maths in that, but there's still loads of maths in, in lots of aspects of your love life, right? So there's maths in, you know, how many people you date before you decide to settle down. Watch. There's, there's maths in the data of what photographs work well on online dating, um, or, you know, apps or, or websites. There's loads of maths in designing your table plan for your wedding to make sure that people that don't like each other don't have to sit together instantly. Uh, my code's available if anyone wants it. Um, and there's, um, there's even actually my favorite, …

AI assessment note: “there's maths in, you know, how many people you date before you decide to settle down”

Q Do you think in a way, uh, we get to advocate ourselves from responsibility if we defer to an algorithm? So if you're a judge and you defer to an algorithm, it's not like you're going to be fired for deferring to the algorithm that everybody agreed was supposed to input or make the decision.

A Exactly that. Especially if you're, you know, especially if people vote you in, like, you know, and, and here's a way that you can absolve yourself of responsibility. I completely agree. I can, I think all of us do it. All of us do it. And that's the problem is that this is a really, really easy thing to happen. It's very easy for us to, to just, I don't know, take a cognitive shortcut and, and do what, do what the machine tells us to do, which is why you have to be so careful about thinking about this interface of thinking about the kind of mistakes that people are going to make and how you mitigate against them by, by, by designing stuff to, to, to prevent that from happening.

AI assessment note: “Exactly that... here's a way that you can absolve yourself of responsibility. I completely agree.”

Q open source? And then it, that would be sort of like stage one where, you know, you can critique and see the actual algorithm working, but stage two would be maybe it's a machine learning algorithm. And then each iteration that it runs is actually slightly different. Like, do we have to keep a copy of each algorithm, and would we be able to detect, like, how it actually worked?

A I know, I, I know. It's so hard. It's so hard because I think it's very easy, you know, that it's very easy to say there are definitely problems with algorithms that are not open source. It's very easy to say there are huge problems with transparency, but finding the, the way around it, finding the solutions is a lot harder. It's a lot harder. I mean, because I think actually I, I sort of am of the opinion that open source algorithms, uh, at least the ones that are proprietary, at least the ones that have some sort of intellectual property attached to them, I think that that is both too much and too little. So what I mean by that is I think it's too little because if you publish the code, if you publish the source code of something, the level of technical knowledge and time actually that it would take to interrogate that as an outsider, enough that you have a really good understanding of how it works, enough to be able to say, okay, you know what, to sort of sanity check it if you like. It's just fast. And I just don't think it's realistic that actually you can ask the community at large really to, uh, to be able to take on that load. But then simultaneously, I think it's by doing so by releasing, um, making everything open source, then I think that you are going to stifle innovation, right? Because I think that, that, that part of the really good thing, part of the reason why …

AI assessment note: “I think that open source algorithms... is both too much and too little.”