WEBVTT 99:59:59.999 --> 99:59:59.999 The world is awash with divisive arguments, 99:59:59.999 --> 99:59:59.999 conflict, fake news, 99:59:59.999 --> 99:59:59.999 victimhood, 99:59:59.999 --> 99:59:59.999 exploitation, prejudice, bigotry, blame, shouting, 99:59:59.999 --> 99:59:59.999 and minuscule attention spans. 99:59:59.999 --> 99:59:59.999 It can sometimes seem 99:59:59.999 --> 99:59:59.999 that we are doomed to take sides, 99:59:59.999 --> 99:59:59.999 be stuck in echo chambers, 99:59:59.999 --> 99:59:59.999 and never agree again. 99:59:59.999 --> 99:59:59.999 It can sometimes seem like a race to the bottom, 99:59:59.999 --> 99:59:59.999 where everyone is calling out somebody else's privilege 99:59:59.999 --> 99:59:59.999 and vying to show that they 99:59:59.999 --> 99:59:59.999 are the most hard-done-by person in the conversation. 99:59:59.999 --> 99:59:59.999 How can we make sense 99:59:59.999 --> 99:59:59.999 in a world that doesn't? 99:59:59.999 --> 99:59:59.999 I have a tool for understanding this confusing world of ours, 99:59:59.999 --> 99:59:59.999 a tool that you might not expect: 99:59:59.999 --> 99:59:59.999 abstract mathematics. 99:59:59.999 --> 99:59:59.999 I am a pure mathematician. 99:59:59.999 --> 99:59:59.999 Traditionally, pure maths is like the theory of maths, 99:59:59.999 --> 99:59:59.999 where applied maths is applied to real problems like building bridges 99:59:59.999 --> 99:59:59.999 and flying planes 99:59:59.999 --> 99:59:59.999 and controlling traffic flow. 99:59:59.999 --> 99:59:59.999 But I'm going to talk about a way that pure maths applies directly 99:59:59.999 --> 99:59:59.999 to our a daily lives as a way of thinking. 99:59:59.999 --> 99:59:59.999 I don't solve quadratic equations to help me with my daily life, 99:59:59.999 --> 99:59:59.999 but I do use mathematical thinking to help me understand arguments 99:59:59.999 --> 99:59:59.999 and to empathize with other people. 99:59:59.999 --> 99:59:59.999 And so pure maths helps me with the entire human world. 99:59:59.999 --> 99:59:59.999 But before I talk about the entire human world, 99:59:59.999 --> 99:59:59.999 I need to talk about something that you might think of 99:59:59.999 --> 99:59:59.999 as irrelevant schools maths: 99:59:59.999 --> 99:59:59.999 factors of numbers. 99:59:59.999 --> 99:59:59.999 We're going to start by thinking about the factors of 30. 99:59:59.999 --> 99:59:59.999 Now, if this makes you shudder with bad memories of school maths lessons, 99:59:59.999 --> 99:59:59.999 I sympathize, 99:59:59.999 --> 99:59:59.999 because I found school maths lessons boring too. 99:59:59.999 --> 99:59:59.999 But I'm pretty sure we are going to take this in a direction 99:59:59.999 --> 99:59:59.999 that is very different from what happened at school. 99:59:59.999 --> 99:59:59.999 So what are the factors of 30? 99:59:59.999 --> 99:59:59.999 Maybe you can remember them. We'll work them out. 99:59:59.999 --> 99:59:59.999 It's one, two, three, 99:59:59.999 --> 99:59:59.999 five, six, 99:59:59.999 --> 99:59:59.999 10, 15, and 30. 99:59:59.999 --> 99:59:59.999 It's not very interesting. 99:59:59.999 --> 99:59:59.999 It's a bunch of numbers in a straight line. 99:59:59.999 --> 99:59:59.999 We can make it more interesting by thinking about which of these numbers 99:59:59.999 --> 99:59:59.999 are also factors of each other and drawing a picture, 99:59:59.999 --> 99:59:59.999 a bit like a family tree 99:59:59.999 --> 99:59:59.999 to show those relationships. 99:59:59.999 --> 99:59:59.999 So 30 is going to be at the top like a kind of great grandparent. 99:59:59.999 --> 99:59:59.999 Six, 10, and 15 go into 30. 99:59:59.999 --> 99:59:59.999 Five goes into 10 and 15. 99:59:59.999 --> 99:59:59.999 Two goes in six and 10. 99:59:59.999 --> 99:59:59.999 Three goes into six and 15. 99:59:59.999 --> 99:59:59.999 And one goes into two, three, and five. 99:59:59.999 --> 99:59:59.999 So now we see that 10 is not divisible by three, 99:59:59.999 --> 99:59:59.999 but that is this the corners of a cube, 99:59:59.999 --> 99:59:59.999 which is I think a bit more interesting 99:59:59.999 --> 99:59:59.999 than a bunch of numbers in a straight line. 99:59:59.999 --> 99:59:59.999 We can see something more here. There's a hierarchy going on. 99:59:59.999 --> 99:59:59.999 At the bottom level is the number one, 99:59:59.999 --> 99:59:59.999 then there's the numbers two, three, and five, 99:59:59.999 --> 99:59:59.999 and nothing goes into those except one and themselves. 99:59:59.999 --> 99:59:59.999 You might remember this means they're prime. 99:59:59.999 --> 99:59:59.999 At the next level up, we have six, 10, and 15, 99:59:59.999 --> 99:59:59.999 and each of those is a product of two prime factors. 99:59:59.999 --> 99:59:59.999 So six is two times three, 99:59:59.999 --> 99:59:59.999 10 is two times five, 99:59:59.999 --> 99:59:59.999 15 is three times five, 99:59:59.999 --> 99:59:59.999 and then at the top, we have 30, 99:59:59.999 --> 99:59:59.999 which is a product of three prime numbers, 99:59:59.999 --> 99:59:59.999 two times three times five. 99:59:59.999 --> 99:59:59.999 So I could redraw this diagram using those numbers instead. 99:59:59.999 --> 99:59:59.999 So we see that we've got two, three, and five at the top, 99:59:59.999 --> 99:59:59.999 we have pairs of numbers at the next level, 99:59:59.999 --> 99:59:59.999 and we have single elements at the next level, 99:59:59.999 --> 99:59:59.999 and then the empty set at the bottom. 99:59:59.999 --> 99:59:59.999 And each of those arrows shows losing one of your numbers in the set. 99:59:59.999 --> 99:59:59.999 Now maybe it can be clear 99:59:59.999 --> 99:59:59.999 that it doesn't really matter what those numbers are. 99:59:59.999 --> 99:59:59.999 In fact it doesn't matter what they are. 99:59:59.999 --> 99:59:59.999 So we could replace them with something like A, B, and C instead 99:59:59.999 --> 99:59:59.999 and we get the same picture. 99:59:59.999 --> 99:59:59.999 So now this has become very abstract. 99:59:59.999 --> 99:59:59.999 The numbers have turned into letters. 99:59:59.999 --> 99:59:59.999 But there is a point to this abstraction, 99:59:59.999 --> 99:59:59.999 which is that it now suddenly becomes very widely applicable, 99:59:59.999 --> 99:59:59.999 because A, B, and C could be anything. 99:59:59.999 --> 99:59:59.999 For example, they could be three types of privilege: 99:59:59.999 --> 99:59:59.999 rich, white, and male. 99:59:59.999 --> 99:59:59.999 So then at the next level, we have rich white people. 99:59:59.999 --> 99:59:59.999 Here we have rich male people. 99:59:59.999 --> 99:59:59.999 Here we have white male people. 99:59:59.999 --> 99:59:59.999 Then we have rich, white, and male. 99:59:59.999 --> 99:59:59.999 And finally people with none of those types of privilege. 99:59:59.999 --> 99:59:59.999 And I'm going to put back in the rest of the adjectives for emphasis. 99:59:59.999 --> 99:59:59.999 So here we have rich white non-male people, 99:59:59.999 --> 99:59:59.999 to remind us that there are non-binary people we need to include. 99:59:59.999 --> 99:59:59.999 Here we have rich non-white male people. 99:59:59.999 --> 99:59:59.999 Here we have non-rich white male people, 99:59:59.999 --> 99:59:59.999 rich non-white non-male, 99:59:59.999 --> 99:59:59.999 non-rich white non-male, 99:59:59.999 --> 99:59:59.999 and non-rich, non-white male, 99:59:59.999 --> 99:59:59.999 and, and at the bottom with the least privilege, 99:59:59.999 --> 99:59:59.999 non-rich, not-white, non-male people. 99:59:59.999 --> 99:59:59.999 We have gone from a diagram of factors of 30 99:59:59.999 --> 99:59:59.999 to a diagram of interaction of different types of privilege, 99:59:59.999 --> 99:59:59.999 and there are many things we can learn from this diagram, I think. 99:59:59.999 --> 99:59:59.999 The first is that each arrow represents a direct loss of one type of privilege. 99:59:59.999 --> 99:59:59.999 Sometimes people mistakenly think that white privilege means 99:59:59.999 --> 99:59:59.999 all white people are better off than all non-white people. 99:59:59.999 --> 99:59:59.999 Some people point at superrich black sports stars and say, 99:59:59.999 --> 99:59:59.999 "See? They're really rich. White privilege doesn't exist." 99:59:59.999 --> 99:59:59.999 But that's not what the theory of white privilege says. 99:59:59.999 --> 99:59:59.999 It says that if that superrich sports star had all the same characteristics 99:59:59.999 --> 99:59:59.999 but they were also white, 99:59:59.999 --> 99:59:59.999 we would expect them to be better off in society.