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  • The world is awash with divisive arguments,

  • conflict,

  • fake news,

  • victimhood,

  • exploitation, prejudice, bigotry, blame, shouting

  • and minuscule attention spans.

  • It can sometimes seem that we are doomed to take sides,

  • be stuck in echo chambers

  • and never agree again.

  • It can sometimes seem like a race to the bottom,

  • where everyone is calling out somebody else's privilege

  • and vying to show that they are the most hard-done-by person

  • in the conversation.

  • How can we make sense

  • in a world that doesn't?

  • I have a tool for understanding this confusing world of ours,

  • a tool that you might not expect:

  • abstract mathematics.

  • I am a pure mathematician.

  • Traditionally, pure maths is like the theory of maths,

  • where applied maths is applied to real problems like building bridges

  • and flying planes

  • and controlling traffic flow.

  • But I'm going to talk about a way that pure maths applies directly

  • to our daily lives

  • as a way of thinking.

  • I don't solve quadratic equations to help me with my daily life,

  • but I do use mathematical thinking to help me understand arguments

  • and to empathize with other people.

  • And so pure maths helps me with the entire human world.

  • But before I talk about the entire human world,

  • I need to talk about something that you might think of

  • as irrelevant schools maths:

  • factors of numbers.

  • We're going to start by thinking about the factors of 30.

  • Now, if this makes you shudder with bad memories of school maths lessons,

  • I sympathize, because I found school maths lessons boring, too.

  • But I'm pretty sure we are going to take this in a direction

  • that is very different from what happened at school.

  • So what are the factors of 30?

  • Well, they're the numbers that go into 30.

  • Maybe you can remember them. We'll work them out.

  • It's one, two, three,

  • five, six,

  • 10, 15 and 30.

  • It's not very interesting.

  • It's a bunch of numbers in a straight line.

  • We can make it more interesting

  • by thinking about which of these numbers are also factors of each other

  • and drawing a picture, a bit like a family tree,

  • to show those relationships.

  • So 30 is going to be at the top like a kind of great-grandparent.

  • Six, 10 and 15 go into 30.

  • Five goes into 10 and 15.

  • Two goes into six and 10.

  • Three goes into six and 15.

  • And one goes into two, three and five.

  • So now we see that 10 is not divisible by three,

  • but that this is the corners of a cube,

  • which is, I think, a bit more interesting

  • than a bunch of numbers in a straight line.

  • We can see something more here. There's a hierarchy going on.

  • At the bottom level is the number one,

  • then there's the numbers two, three and five,

  • and nothing goes into those except one and themselves.

  • You might remember this means they're prime.

  • At the next level up, we have six, 10 and 15,

  • and each of those is a product of two prime factors.

  • So six is two times three,

  • 10 is two times five,

  • 15 is three times five.

  • And then at the top, we have 30,

  • which is a product of three prime numbers --

  • two times three times five.

  • So I could redraw this diagram using those numbers instead.

  • We see that we've got two, three and five at the top,

  • we have pairs of numbers at the next level,

  • and we have single elements at the next level

  • and then the empty set at the bottom.

  • And each of those arrows shows losing one of your numbers in the set.

  • Now maybe it can be clear

  • that it doesn't really matter what those numbers are.

  • In fact, it doesn't matter what they are.

  • So we could replace them with something like A, B and C instead,

  • and we get the same picture.

  • So now this has become very abstract.

  • The numbers have turned into letters.

  • But there is a point to this abstraction,

  • which is that it now suddenly becomes very widely applicable,

  • because A, B and C could be anything.

  • For example, they could be three types of privilege:

  • rich, white and male.

  • So then at the next level, we have rich white people.

  • Here we have rich male people.

  • Here we have white male people.

  • Then we have rich, white and male.

  • And finally, people with none of those types of privilege.

  • And I'm going to put back in the rest of the adjectives for emphasis.

  • So here we have rich, white non-male people,

  • to remind us that there are nonbinary people we need to include.

  • Here we have rich, nonwhite male people.

  • Here we have non-rich, white male people,

  • rich, nonwhite, non-male,

  • non-rich, white, non-male

  • and non-rich, nonwhite, male.

  • And at the bottom, with the least privilege,

  • non-rich, nonwhite, non-male people.

  • We have gone from a diagram of factors of 30

  • to a diagram of interaction of different types of privilege.

  • And there are many things we can learn from this diagram, I think.

  • The first is that each arrow represents a direct loss of one type of privilege.

  • Sometimes people mistakenly think that white privilege means

  • all white people are better off than all nonwhite people.

  • Some people point at superrich black sports stars and say,

  • \"See? They're really rich. White privilege doesn't exist.\"

  • But that's not what the theory of white privilege says.

  • It says that if that superrich sports star had all the same characteristics

  • but they were also white,

  • we would expect them to be better off in society.

  • There is something else we can understand from this diagram

  • if we look along a row.

  • If we look along the second-to-top row, where people have two types of privilege,

  • we might be able to see that they're not all particularly equal.

  • For example, rich white women are probably much better off in society

  • than poor white men,

  • and rich black men are probably somewhere in between.

  • So it's really more skewed like this,

  • and the same on the bottom level.

  • But we can actually take it further

  • and look at the interactions between those two middle levels.

  • Because rich, nonwhite non-men might well be better off in society

  • than poor white men.

  • Think about some extreme examples, like Michelle Obama,

  • Oprah Winfrey.

  • They're definitely better off than poor, white, unemployed homeless men.

  • So actually, the diagram is more skewed like this.

  • And that tension exists

  • between the layers of privilege in the diagram

  • and the absolute privilege that people experience in society.

  • And this has helped me to understand why some poor white men

  • are so angry in society at the moment.

  • Because they are considered to be high up in this cuboid of privilege,

  • but in terms of absolute privilege, they don't actually feel the effect of it.

  • And I believe that understanding the root of that anger

  • is much more productive than just being angry at them in return.

  • Seeing these abstract structures can also help us switch contexts

  • and see that different people are at the top in different contexts.

  • In our original diagram,

  • rich white men were at the top,

  • but if we restricted our attention to non-men,

  • we would see that they are here,

  • and now the rich, white non-men are at the top.

  • So we could move to a whole context of women,

  • and our three types of privilege could now be rich, white and cisgendered.

  • Remember that \"cisgendered\" means that your gender identity does match

  • the gender you were assigned at birth.

  • So now we see that rich, white cis women occupy the analogous situation

  • that rich white men did in broader society.

  • And this has helped me understand why there is so much anger

  • towards rich white women,

  • especially in some parts of the feminist movement at the moment,

  • because perhaps they're prone to seeing themselves as underprivileged

  • relative to white men,

  • and they forget how overprivileged they are relative to nonwhite women.

  • We can all use these abstract structures to help us pivot between situations

  • in which we are more privileged and less privileged.

  • We are all more privileged than somebody

  • and less privileged than somebody else.

  • For example, I know and I feel that as an Asian person,

  • I am less privileged than white people

  • because of white privilege.

  • But I also understand

  • that I am probably among the most privileged of nonwhite people,

  • and this helps me pivot between those two contexts.

  • And in terms of wealth,

  • I don't think I'm super rich.

  • I'm not as rich as the kind of people who don't have to work.

  • But I am doing fine,

  • and that's a much better situation to be in

  • than people who are really struggling,

  • maybe are unemployed or working at minimum wage.

  • I perform these pivots in my head

  • to help me understand experiences from other people's points of view,

  • which brings me to this possibly surprising conclusion:

  • that abstract mathematics is highly relevant to our daily lives

  • and can even help us to understand and empathize with other people.

  • My wish is that everybody would try to understand other people more

  • and work with them together,

  • rather than competing with them

  • and trying to show that they're wrong.

  • And I believe that abstract mathematical thinking

  • can help us achieve that.

  • Thank you.

  • (Applause)

The world is awash with divisive arguments,

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【TED】An unexpected tool for understanding inequality: abstract math | Eugenia Cheng

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    林宜悉   に公開 2019 年 04 月 09 日
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