[Script Info] Title: [Events] Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text Dialogue: 0,0:00:01.25,0:00:06.86,Default,,0000,0000,0000,,The world is awash\Nwith divisive arguments, Dialogue: 0,0:00:06.88,0:00:08.76,Default,,0000,0000,0000,,conflict, Dialogue: 0,0:00:08.78,0:00:10.59,Default,,0000,0000,0000,,fake news, Dialogue: 0,0:00:10.62,0:00:12.20,Default,,0000,0000,0000,,victimhood, Dialogue: 0,0:00:13.15,0:00:18.85,Default,,0000,0000,0000,,exploitation, prejudice,\Nbigotry, blame, shouting Dialogue: 0,0:00:18.87,0:00:21.79,Default,,0000,0000,0000,,and minuscule attention spans. Dialogue: 0,0:00:22.86,0:00:28.05,Default,,0000,0000,0000,,It can sometimes seem\Nthat we are doomed to take sides, Dialogue: 0,0:00:28.07,0:00:30.33,Default,,0000,0000,0000,,be stuck in echo chambers Dialogue: 0,0:00:30.36,0:00:32.68,Default,,0000,0000,0000,,and never agree again. Dialogue: 0,0:00:33.34,0:00:36.34,Default,,0000,0000,0000,,It can sometimes seem\Nlike a race to the bottom, Dialogue: 0,0:00:36.37,0:00:40.38,Default,,0000,0000,0000,,where everyone is calling out\Nsomebody else's privilege Dialogue: 0,0:00:40.41,0:00:45.52,Default,,0000,0000,0000,,and vying to show that they\Nare the most hard-done-by person Dialogue: 0,0:00:45.55,0:00:47.08,Default,,0000,0000,0000,,in the conversation. Dialogue: 0,0:00:49.03,0:00:50.86,Default,,0000,0000,0000,,How can we make sense Dialogue: 0,0:00:50.89,0:00:53.29,Default,,0000,0000,0000,,in a world that doesn't? Dialogue: 0,0:00:55.60,0:01:00.36,Default,,0000,0000,0000,,I have a tool for understanding\Nthis confusing world of ours, Dialogue: 0,0:01:00.38,0:01:03.29,Default,,0000,0000,0000,,a tool that you might not expect: Dialogue: 0,0:01:04.19,0:01:05.85,Default,,0000,0000,0000,,abstract mathematics. Dialogue: 0,0:01:07.27,0:01:09.65,Default,,0000,0000,0000,,I am a pure mathematician. Dialogue: 0,0:01:10.06,0:01:14.08,Default,,0000,0000,0000,,Traditionally, pure maths\Nis like the theory of maths, Dialogue: 0,0:01:14.10,0:01:19.27,Default,,0000,0000,0000,,where applied maths is applied\Nto real problems like building bridges Dialogue: 0,0:01:19.29,0:01:20.81,Default,,0000,0000,0000,,and flying planes Dialogue: 0,0:01:20.83,0:01:23.18,Default,,0000,0000,0000,,and controlling traffic flow. Dialogue: 0,0:01:23.89,0:01:28.82,Default,,0000,0000,0000,,But I'm going to talk about a way\Nthat pure maths applies directly Dialogue: 0,0:01:28.84,0:01:30.35,Default,,0000,0000,0000,,to our daily lives Dialogue: 0,0:01:30.38,0:01:32.22,Default,,0000,0000,0000,,as a way of thinking. Dialogue: 0,0:01:32.93,0:01:37.12,Default,,0000,0000,0000,,I don't solve quadratic equations\Nto help me with my daily life, Dialogue: 0,0:01:37.14,0:01:42.28,Default,,0000,0000,0000,,but I do use mathematical thinking\Nto help me understand arguments Dialogue: 0,0:01:42.31,0:01:44.82,Default,,0000,0000,0000,,and to empathize with other people. Dialogue: 0,0:01:45.50,0:01:51.11,Default,,0000,0000,0000,,And so pure maths helps me\Nwith the entire human world. Dialogue: 0,0:01:52.43,0:01:55.54,Default,,0000,0000,0000,,But before I talk about\Nthe entire human world, Dialogue: 0,0:01:55.57,0:01:58.63,Default,,0000,0000,0000,,I need to talk about something\Nthat you might think of Dialogue: 0,0:01:58.65,0:02:01.34,Default,,0000,0000,0000,,as irrelevant schools maths: Dialogue: 0,0:02:01.97,0:02:04.05,Default,,0000,0000,0000,,factors of numbers. Dialogue: 0,0:02:04.08,0:02:07.63,Default,,0000,0000,0000,,We're going to start\Nby thinking about the factors of 30. Dialogue: 0,0:02:07.66,0:02:12.37,Default,,0000,0000,0000,,Now, if this makes you shudder\Nwith bad memories of school maths lessons, Dialogue: 0,0:02:12.40,0:02:16.100,Default,,0000,0000,0000,,I sympathize, because I found\Nschool maths lessons boring, too. Dialogue: 0,0:02:17.48,0:02:21.36,Default,,0000,0000,0000,,But I'm pretty sure we are going\Nto take this in a direction Dialogue: 0,0:02:21.39,0:02:24.83,Default,,0000,0000,0000,,that is very different\Nfrom what happened at school. Dialogue: 0,0:02:25.72,0:02:27.44,Default,,0000,0000,0000,,So what are the factors of 30? Dialogue: 0,0:02:27.47,0:02:30.69,Default,,0000,0000,0000,,Well, they're the numbers that go into 30. Dialogue: 0,0:02:30.72,0:02:33.12,Default,,0000,0000,0000,,Maybe you can remember them.\NWe'll work them out. Dialogue: 0,0:02:33.14,0:02:36.96,Default,,0000,0000,0000,,It's one, two, three, Dialogue: 0,0:02:36.98,0:02:39.07,Default,,0000,0000,0000,,five, six, Dialogue: 0,0:02:39.10,0:02:41.96,Default,,0000,0000,0000,,10, 15 and 30. Dialogue: 0,0:02:41.98,0:02:43.46,Default,,0000,0000,0000,,It's not very interesting. Dialogue: 0,0:02:43.96,0:02:46.36,Default,,0000,0000,0000,,It's a bunch of numbers\Nin a straight line. Dialogue: 0,0:02:46.83,0:02:48.35,Default,,0000,0000,0000,,We can make it more interesting Dialogue: 0,0:02:48.37,0:02:52.06,Default,,0000,0000,0000,,by thinking about which of these numbers\Nare also factors of each other Dialogue: 0,0:02:52.09,0:02:54.62,Default,,0000,0000,0000,,and drawing a picture,\Na bit like a family tree, Dialogue: 0,0:02:54.64,0:02:56.34,Default,,0000,0000,0000,,to show those relationships. Dialogue: 0,0:02:56.37,0:03:00.44,Default,,0000,0000,0000,,So 30 is going to be at the top\Nlike a kind of great-grandparent. Dialogue: 0,0:03:00.46,0:03:03.06,Default,,0000,0000,0000,,Six, 10 and 15 go into 30. Dialogue: 0,0:03:03.69,0:03:06.49,Default,,0000,0000,0000,,Five goes into 10 and 15. Dialogue: 0,0:03:06.94,0:03:09.63,Default,,0000,0000,0000,,Two goes into six and 10. Dialogue: 0,0:03:09.66,0:03:12.94,Default,,0000,0000,0000,,Three goes into six and 15. Dialogue: 0,0:03:12.97,0:03:17.15,Default,,0000,0000,0000,,And one goes into two, three and five. Dialogue: 0,0:03:17.18,0:03:20.91,Default,,0000,0000,0000,,So now we see that 10\Nis not divisible by three, Dialogue: 0,0:03:20.93,0:03:24.11,Default,,0000,0000,0000,,but that this is the corners of a cube, Dialogue: 0,0:03:24.14,0:03:26.22,Default,,0000,0000,0000,,which is, I think, a bit more interesting Dialogue: 0,0:03:26.24,0:03:28.37,Default,,0000,0000,0000,,than a bunch of numbers\Nin a straight line. Dialogue: 0,0:03:29.76,0:03:32.67,Default,,0000,0000,0000,,We can see something more here.\NThere's a hierarchy going on. Dialogue: 0,0:03:32.69,0:03:34.56,Default,,0000,0000,0000,,At the bottom level is the number one, Dialogue: 0,0:03:34.58,0:03:36.83,Default,,0000,0000,0000,,then there's the numbers\Ntwo, three and five, Dialogue: 0,0:03:36.85,0:03:39.66,Default,,0000,0000,0000,,and nothing goes into those\Nexcept one and themselves. Dialogue: 0,0:03:39.69,0:03:42.12,Default,,0000,0000,0000,,You might remember\Nthis means they're prime. Dialogue: 0,0:03:42.14,0:03:45.17,Default,,0000,0000,0000,,At the next level up,\Nwe have six, 10 and 15, Dialogue: 0,0:03:45.20,0:03:48.71,Default,,0000,0000,0000,,and each of those is a product\Nof two prime factors. Dialogue: 0,0:03:48.73,0:03:50.67,Default,,0000,0000,0000,,So six is two times three, Dialogue: 0,0:03:50.70,0:03:52.37,Default,,0000,0000,0000,,10 is two times five, Dialogue: 0,0:03:52.39,0:03:54.35,Default,,0000,0000,0000,,15 is three times five. Dialogue: 0,0:03:54.38,0:03:56.34,Default,,0000,0000,0000,,And then at the top, we have 30, Dialogue: 0,0:03:56.36,0:03:58.86,Default,,0000,0000,0000,,which is a product\Nof three prime numbers -- Dialogue: 0,0:03:58.88,0:04:00.94,Default,,0000,0000,0000,,two times three times five. Dialogue: 0,0:04:00.96,0:04:05.58,Default,,0000,0000,0000,,So I could redraw this diagram\Nusing those numbers instead. Dialogue: 0,0:04:06.34,0:04:09.40,Default,,0000,0000,0000,,We see that we've got\Ntwo, three and five at the top, Dialogue: 0,0:04:09.43,0:04:12.50,Default,,0000,0000,0000,,we have pairs of numbers\Nat the next level, Dialogue: 0,0:04:12.52,0:04:14.91,Default,,0000,0000,0000,,and we have single elements\Nat the next level Dialogue: 0,0:04:14.93,0:04:16.85,Default,,0000,0000,0000,,and then the empty set at the bottom. Dialogue: 0,0:04:17.27,0:04:22.65,Default,,0000,0000,0000,,And each of those arrows shows\Nlosing one of your numbers in the set. Dialogue: 0,0:04:22.67,0:04:25.29,Default,,0000,0000,0000,,Now maybe it can be clear Dialogue: 0,0:04:25.32,0:04:28.17,Default,,0000,0000,0000,,that it doesn't really matter\Nwhat those numbers are. Dialogue: 0,0:04:28.20,0:04:30.16,Default,,0000,0000,0000,,In fact, it doesn't matter what they are. Dialogue: 0,0:04:30.18,0:04:34.58,Default,,0000,0000,0000,,So we could replace them with\Nsomething like A, B and C instead, Dialogue: 0,0:04:34.60,0:04:36.34,Default,,0000,0000,0000,,and we get the same picture. Dialogue: 0,0:04:37.02,0:04:39.14,Default,,0000,0000,0000,,So now this has become very abstract. Dialogue: 0,0:04:39.63,0:04:41.61,Default,,0000,0000,0000,,The numbers have turned into letters. Dialogue: 0,0:04:42.09,0:04:45.57,Default,,0000,0000,0000,,But there is a point to this abstraction, Dialogue: 0,0:04:45.59,0:04:50.18,Default,,0000,0000,0000,,which is that it now suddenly\Nbecomes very widely applicable, Dialogue: 0,0:04:50.20,0:04:53.88,Default,,0000,0000,0000,,because A, B and C could be anything. Dialogue: 0,0:04:54.29,0:04:58.61,Default,,0000,0000,0000,,For example, they could be\Nthree types of privilege: Dialogue: 0,0:04:58.63,0:05:01.33,Default,,0000,0000,0000,,rich, white and male. Dialogue: 0,0:05:02.39,0:05:05.58,Default,,0000,0000,0000,,So then at the next level,\Nwe have rich white people. Dialogue: 0,0:05:06.37,0:05:08.85,Default,,0000,0000,0000,,Here we have rich male people. Dialogue: 0,0:05:08.87,0:05:10.92,Default,,0000,0000,0000,,Here we have white male people. Dialogue: 0,0:05:10.95,0:05:14.56,Default,,0000,0000,0000,,Then we have rich, white and male. Dialogue: 0,0:05:15.21,0:05:18.34,Default,,0000,0000,0000,,And finally, people with none\Nof those types of privilege. Dialogue: 0,0:05:18.36,0:05:21.63,Default,,0000,0000,0000,,And I'm going to put back in\Nthe rest of the adjectives for emphasis. Dialogue: 0,0:05:21.66,0:05:24.69,Default,,0000,0000,0000,,So here we have rich, white\Nnon-male people, Dialogue: 0,0:05:24.71,0:05:27.76,Default,,0000,0000,0000,,to remind us that there are\Nnonbinary people we need to include. Dialogue: 0,0:05:27.78,0:05:30.44,Default,,0000,0000,0000,,Here we have rich, nonwhite male people. Dialogue: 0,0:05:30.46,0:05:33.76,Default,,0000,0000,0000,,Here we have non-rich, white male people, Dialogue: 0,0:05:33.78,0:05:36.48,Default,,0000,0000,0000,,rich, nonwhite, non-male, Dialogue: 0,0:05:36.51,0:05:39.06,Default,,0000,0000,0000,,non-rich, white, non-male Dialogue: 0,0:05:39.08,0:05:41.42,Default,,0000,0000,0000,,and non-rich, nonwhite, male. Dialogue: 0,0:05:41.44,0:05:43.64,Default,,0000,0000,0000,,And at the bottom,\Nwith the least privilege, Dialogue: 0,0:05:43.66,0:05:47.71,Default,,0000,0000,0000,,non-rich, nonwhite, non-male people. Dialogue: 0,0:05:47.73,0:05:51.54,Default,,0000,0000,0000,,We have gone from a diagram\Nof factors of 30 Dialogue: 0,0:05:51.57,0:05:55.50,Default,,0000,0000,0000,,to a diagram of interaction\Nof different types of privilege. Dialogue: 0,0:05:56.07,0:05:59.69,Default,,0000,0000,0000,,And there are many things\Nwe can learn from this diagram, I think. Dialogue: 0,0:05:59.71,0:06:06.52,Default,,0000,0000,0000,,The first is that each arrow represents\Na direct loss of one type of privilege. Dialogue: 0,0:06:07.33,0:06:11.81,Default,,0000,0000,0000,,Sometimes people mistakenly think\Nthat white privilege means Dialogue: 0,0:06:11.84,0:06:16.39,Default,,0000,0000,0000,,all white people are better off\Nthan all nonwhite people. Dialogue: 0,0:06:16.41,0:06:20.12,Default,,0000,0000,0000,,Some people point at superrich\Nblack sports stars and say, Dialogue: 0,0:06:20.15,0:06:23.60,Default,,0000,0000,0000,,"See? They're really rich.\NWhite privilege doesn't exist." Dialogue: 0,0:06:24.12,0:06:27.14,Default,,0000,0000,0000,,But that's not what the theory\Nof white privilege says. Dialogue: 0,0:06:27.17,0:06:32.41,Default,,0000,0000,0000,,It says that if that superrich sports star\Nhad all the same characteristics Dialogue: 0,0:06:32.43,0:06:33.91,Default,,0000,0000,0000,,but they were also white, Dialogue: 0,0:06:33.93,0:06:37.36,Default,,0000,0000,0000,,we would expect them\Nto be better off in society. Dialogue: 0,0:06:39.30,0:06:42.09,Default,,0000,0000,0000,,There is something else\Nwe can understand from this diagram Dialogue: 0,0:06:42.11,0:06:44.10,Default,,0000,0000,0000,,if we look along a row. Dialogue: 0,0:06:44.12,0:06:48.40,Default,,0000,0000,0000,,If we look along the second-to-top row,\Nwhere people have two types of privilege, Dialogue: 0,0:06:48.43,0:06:52.38,Default,,0000,0000,0000,,we might be able to see\Nthat they're not all particularly equal. Dialogue: 0,0:06:52.41,0:06:58.48,Default,,0000,0000,0000,,For example, rich white women\Nare probably much better off in society Dialogue: 0,0:06:58.51,0:07:00.70,Default,,0000,0000,0000,,than poor white men, Dialogue: 0,0:07:00.73,0:07:03.73,Default,,0000,0000,0000,,and rich black men are probably\Nsomewhere in between. Dialogue: 0,0:07:03.76,0:07:06.54,Default,,0000,0000,0000,,So it's really more skewed like this, Dialogue: 0,0:07:06.56,0:07:08.49,Default,,0000,0000,0000,,and the same on the bottom level. Dialogue: 0,0:07:08.99,0:07:11.08,Default,,0000,0000,0000,,But we can actually take it further Dialogue: 0,0:07:11.10,0:07:14.68,Default,,0000,0000,0000,,and look at the interactions\Nbetween those two middle levels, Dialogue: 0,0:07:15.08,0:07:21.01,Default,,0000,0000,0000,,because rich, nonwhite non-men\Nmight well be better off in society Dialogue: 0,0:07:21.04,0:07:23.13,Default,,0000,0000,0000,,than poor white men. Dialogue: 0,0:07:23.15,0:07:27.06,Default,,0000,0000,0000,,Think about some extreme\Nexamples, like Michelle Obama, Dialogue: 0,0:07:27.08,0:07:28.50,Default,,0000,0000,0000,,Oprah Winfrey. Dialogue: 0,0:07:28.53,0:07:33.54,Default,,0000,0000,0000,,They're definitely better off\Nthan poor, white, unemployed homeless men. Dialogue: 0,0:07:34.16,0:07:36.94,Default,,0000,0000,0000,,So actually, the diagram\Nis more skewed like this. Dialogue: 0,0:07:37.52,0:07:40.22,Default,,0000,0000,0000,,And that tension exists Dialogue: 0,0:07:40.25,0:07:43.48,Default,,0000,0000,0000,,between the layers\Nof privilege in the diagram Dialogue: 0,0:07:43.51,0:07:47.17,Default,,0000,0000,0000,,and the absolute privilege\Nthat people experience in society. Dialogue: 0,0:07:47.20,0:07:50.87,Default,,0000,0000,0000,,And this has helped me to understand\Nwhy some poor white men Dialogue: 0,0:07:50.90,0:07:54.30,Default,,0000,0000,0000,,are so angry in society at the moment, Dialogue: 0,0:07:54.33,0:07:58.76,Default,,0000,0000,0000,,because they are considered to be high up\Nin this cuboid of privilege, Dialogue: 0,0:07:58.78,0:08:03.56,Default,,0000,0000,0000,,but in terms of absolute privilege,\Nthey don't actually feel the effect of it. Dialogue: 0,0:08:03.59,0:08:07.03,Default,,0000,0000,0000,,And I believe that understanding\Nthe root of that anger Dialogue: 0,0:08:07.06,0:08:11.34,Default,,0000,0000,0000,,is much more productive\Nthan just being angry at them in return. Dialogue: 0,0:08:13.29,0:08:17.84,Default,,0000,0000,0000,,Seeing these abstract structures\Ncan also help us switch contexts Dialogue: 0,0:08:17.86,0:08:21.51,Default,,0000,0000,0000,,and see that different people\Nare at the top in different contexts. Dialogue: 0,0:08:21.53,0:08:23.31,Default,,0000,0000,0000,,In our original diagram, Dialogue: 0,0:08:23.34,0:08:25.34,Default,,0000,0000,0000,,rich white men were at the top, Dialogue: 0,0:08:25.36,0:08:29.07,Default,,0000,0000,0000,,but if we restricted\Nour attention to non-men, Dialogue: 0,0:08:29.09,0:08:30.78,Default,,0000,0000,0000,,we would see that they are here, Dialogue: 0,0:08:30.80,0:08:33.54,Default,,0000,0000,0000,,and now the rich, white\Nnon-men are at the top. Dialogue: 0,0:08:33.56,0:08:36.40,Default,,0000,0000,0000,,So we could move to\Na whole context of women, Dialogue: 0,0:08:36.43,0:08:41.57,Default,,0000,0000,0000,,and our three types of privilege\Ncould now be rich, white and cisgendered. Dialogue: 0,0:08:41.60,0:08:45.30,Default,,0000,0000,0000,,Remember that "cisgendered" means\Nthat your gender identity does match Dialogue: 0,0:08:45.32,0:08:47.29,Default,,0000,0000,0000,,the gender you were assigned at birth. Dialogue: 0,0:08:48.02,0:08:54.03,Default,,0000,0000,0000,,So now we see that rich, white cis women\Noccupy the analogous situation Dialogue: 0,0:08:54.06,0:08:57.23,Default,,0000,0000,0000,,that rich white men did\Nin broader society, Dialogue: 0,0:08:57.26,0:09:00.68,Default,,0000,0000,0000,,and this has helped me understand\Nwhy there is so much anger Dialogue: 0,0:09:00.71,0:09:02.36,Default,,0000,0000,0000,,towards rich white women, Dialogue: 0,0:09:02.38,0:09:05.91,Default,,0000,0000,0000,,especially in some parts\Nof the feminist movement at the moment, Dialogue: 0,0:09:05.93,0:09:09.59,Default,,0000,0000,0000,,because perhaps they're prone\Nto seeing themselves as underprivileged Dialogue: 0,0:09:09.61,0:09:11.43,Default,,0000,0000,0000,,relative to white men, Dialogue: 0,0:09:11.45,0:09:16.56,Default,,0000,0000,0000,,and they forget how overprivileged\Nthey are relative to nonwhite women. Dialogue: 0,0:09:18.55,0:09:23.99,Default,,0000,0000,0000,,We can all use these abstract structures\Nto help us pivot between situations Dialogue: 0,0:09:24.02,0:09:26.61,Default,,0000,0000,0000,,in which we are more privileged\Nand less privileged. Dialogue: 0,0:09:26.63,0:09:29.16,Default,,0000,0000,0000,,We are all more privileged than somebody Dialogue: 0,0:09:29.18,0:09:31.62,Default,,0000,0000,0000,,and less privileged than somebody else. Dialogue: 0,0:09:32.74,0:09:37.52,Default,,0000,0000,0000,,For example, I know and I feel\Nthat as an Asian person, Dialogue: 0,0:09:37.55,0:09:40.28,Default,,0000,0000,0000,,I am less privileged than white people Dialogue: 0,0:09:40.30,0:09:41.78,Default,,0000,0000,0000,,because of white privilege. Dialogue: 0,0:09:41.80,0:09:43.45,Default,,0000,0000,0000,,But I also understand Dialogue: 0,0:09:43.47,0:09:47.60,Default,,0000,0000,0000,,that I am probably among\Nthe most privileged of nonwhite people, Dialogue: 0,0:09:47.62,0:09:50.74,Default,,0000,0000,0000,,and this helps me pivot\Nbetween those two contexts. Dialogue: 0,0:09:51.60,0:09:53.29,Default,,0000,0000,0000,,And in terms of wealth, Dialogue: 0,0:09:53.31,0:09:55.16,Default,,0000,0000,0000,,I don't think I'm superrich. Dialogue: 0,0:09:55.18,0:09:58.22,Default,,0000,0000,0000,,I'm not as rich as the kind of people\Nwho don't have to work, Dialogue: 0,0:09:58.25,0:09:59.80,Default,,0000,0000,0000,,but I am doing fine, Dialogue: 0,0:09:59.82,0:10:01.98,Default,,0000,0000,0000,,and that's a much better\Nsituation to be in Dialogue: 0,0:10:01.100,0:10:03.81,Default,,0000,0000,0000,,than people who are really struggling, Dialogue: 0,0:10:03.83,0:10:06.90,Default,,0000,0000,0000,,maybe are unemployed\Nor working at minimum wage. Dialogue: 0,0:10:08.57,0:10:11.99,Default,,0000,0000,0000,,I perform these pivots in my head Dialogue: 0,0:10:12.02,0:10:17.26,Default,,0000,0000,0000,,to help me understand experiences\Nfrom other people's points of view, Dialogue: 0,0:10:18.41,0:10:22.40,Default,,0000,0000,0000,,which brings me to this\Npossibly surprising conclusion: Dialogue: 0,0:10:23.24,0:10:30.08,Default,,0000,0000,0000,,that abstract mathematics\Nis highly relevant to our daily lives Dialogue: 0,0:10:30.10,0:10:36.82,Default,,0000,0000,0000,,and can even help us to understand\Nand empathize with other people. Dialogue: 0,0:10:38.58,0:10:44.22,Default,,0000,0000,0000,,My wish is that everybody would try\Nto understand other people more Dialogue: 0,0:10:44.25,0:10:46.16,Default,,0000,0000,0000,,and work with them together, Dialogue: 0,0:10:46.19,0:10:48.21,Default,,0000,0000,0000,,rather than competing with them Dialogue: 0,0:10:48.23,0:10:50.84,Default,,0000,0000,0000,,and trying to show that they're wrong. Dialogue: 0,0:10:52.03,0:10:56.60,Default,,0000,0000,0000,,And I believe that abstract\Nmathematical thinking Dialogue: 0,0:10:56.62,0:10:58.70,Default,,0000,0000,0000,,can help us achieve that. Dialogue: 0,0:11:00.26,0:11:01.47,Default,,0000,0000,0000,,Thank you. Dialogue: 0,0:11:01.49,0:11:05.65,Default,,0000,0000,0000,,(Applause)