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

翻译人员: jiayi jiang 校对人员: Hong Li

The world is awash with divisive arguments,

这个世界充斥着引发分歧的观点，

conflict,

冲突，

fake news,

虚假新闻，

victimhood,

受害者情绪，

exploitation, prejudice, bigotry, blame, shouting

剥削， 偏见，偏执，责怪，喊叫

and minuscule attention spans.

和极短的注意力时间。

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

有时候似乎我们注定要选边站队，

be stuck in echo chambers

固执己见，

and never agree again.

再也无法与人达成共识。

It can sometimes seem like a race to the bottom,

有时候似乎我们在比惨，

where everyone is calling out somebody else's privilege

每个人都在说别人有特权，

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

然后争先恐后地怨天尤人，

in the conversation.

都说自己最惨。

How can we make sense

在这个疯狂的世界，

in a world that doesn't?

我们怎样才能做到理智？

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

我有一样工具， 可以帮助理解这个费解的世界，

a tool that you might not expect:

一样你们可能意想不到的工具：

abstract mathematics.

抽象数学。

I am a pure mathematician.

我是个纯粹的数学家。

Traditionally, pure maths is like the theory of maths,

传统意义上，纯数学更多是 研究数学理论，

where applied maths is applied to real problems like building bridges

而应用数学是解决实际问题， 比如建造大桥，

and flying planes

开飞机，

and controlling traffic flow.

控制交通流量。

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

但我打算讲一种 将纯数学作为一种思维方式

to our daily lives

直接运用到

as a way of thinking.

我们日常生活的情况。

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

我解二次方程并不是为了 方便我的日常生活，

but I do use mathematical thinking to help me understand arguments

但我确实运用数学思维来理解争论，

and to empathize with other people.

与别人产生共鸣。

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

所以纯数学可以帮助我 理解整个人类世界。

But before I talk about the entire human world,

但在谈整个人类世界之前，

I need to talk about something that you might think of

我必须和你们谈一些看起来可能

as irrelevant schools maths:

无关的学校里教的数学：

factors of numbers.

数字的因数。

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

我们先想一下30的因数。

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

如果这令你回想起数学课的糟糕回忆，

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

我深表同情，因为我也觉得数学课无聊。

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

但我很确定，接下来发生的事情

that is very different from what happened at school.

跟学校里学到的会非常不一样。

So what are the factors of 30?

那么30的因数有哪些？

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

它们是30能整除的数字。

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

你们或许还记得，我们来算一下。

有1、2、3、

It's one, two, three,

five, six,

5、6、

10, 15 and 30.

10、15和30。

It's not very interesting.

这没什么意思。

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

就是一串数字。

We can make it more interesting

我们能让它变得有趣一些，

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

想一下，这些数字中， 有哪些互为因数，

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

然后画一张像家谱图的图，

to show those relationships.

来展示这些关系。

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

30在最上方，像是曾祖父母。

Six, 10 and 15 go into 30.

6、10、15连上30。

Five goes into 10 and 15.

5连上10和15。

Two goes into six and 10.

2连上6和10。

Three goes into six and 15.

3连上6和15。

And one goes into two, three and five.

1连上2、3和5。

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

我们看到10不能被3整除，

but that this is the corners of a cube,

但这里是一个立方体的8个角，

which is, I think, a bit more interesting

我觉得这样的关系

相比于一串数字要有趣得多。

than a bunch of numbers in a straight line.

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

我们能发现更多东西。 它是分层级的。

At the bottom level is the number one,

最底层是数字1，

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

然后是 2、3、5，

and nothing goes into those except one and themselves.

这些数字能被1和它们自己整除。

You might remember this means they're prime.

你或许记得，这表示他们是质数。

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

再往上一层，是6、10和15，

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

它们都是两个质数的乘积。

So six is two times three,

6 = 2 × 3

10 is two times five,

10 = 2 × 5，

15 is three times five.

15 = 3 × 5。

And then at the top, we have 30,

最顶层的30，

which is a product of three prime numbers --

是三个质数的乘积，

two times three times five.

2 x 3 x 5。

So I could redraw this diagram using those numbers instead.

所以我可以重新画这个图， 用数字来替代。

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

我们看到2、3、5在最顶层，

we have pairs of numbers at the next level,

成对的数字在第二层，

and we have single elements at the next level

单个的数字在下一层

and then the empty set at the bottom.

最底层是空集。

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

每个箭头表示在集合中少一个数字。

Now maybe it can be clear

现在或许清楚了，

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

这些数字是多少并不重要。

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

实际上，它们是什么都不重要。

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

所以我们可以用A, B, C替代它们，

and we get the same picture.

也会得到同样的图。

So now this has become very abstract.

这样就变得抽象了。

The numbers have turned into letters.

数字变成了字母。

But there is a point to this abstraction,

但这个抽象化是有意义的，

which is that it now suddenly becomes very widely applicable,

因为这张图能被广泛应用了，

because A, B and C could be anything.

因为A，B，C可以是任何东西。

For example, they could be three types of privilege:

比如，它们可以是3种特权：

rich, white and male.

有钱的，白人，男性。

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

所以下一层，我们得到“有钱的”“白人”。

Here we have rich male people.

这里是“有钱的”“男性”。

Here we have white male people.

这里是“白人”“男性”。

Then we have rich, white and male.

然后是“有钱的”、“白人”、“男性”。

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

最后，是没有任何特权的人。

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

我把剩下的形容词补上，用来强调。

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

所以这里是“有钱的”、“白人”、“非男性”，

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

别忘了还有人既不是男性也不是女性，

Here we have rich, nonwhite male people.

这里是“有钱的”、“非白人”、“男性”，

Here we have non-rich, white male people,

这里是“非有钱的”、“白人”、“男性”，

rich, nonwhite, non-male,

“有钱的”、“非白人”、“非男性”，

non-rich, white, non-male

“非有钱的”、“白人”、“非男性”，

and non-rich, nonwhite, male.

以及“非有钱的”、“非白人”、“男性”，

And at the bottom, with the least privilege,

以及在最底层，特权最少的

non-rich, nonwhite, non-male people.

“非有钱的”、“非白人”、“非男性”。

We have gone from a diagram of factors of 30

我们从一个30的因数图表

to a diagram of interaction of different types of privilege.

到了一个不同特权的交叉图表。

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

我们能从这张图表中学到很多。

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

首先，每个箭头表示失去一种特权。

Sometimes people mistakenly think that white privilege means

有时候人们错误地以为， 白人特权意味着

all white people are better off than all nonwhite people.

所有的白人都比非白人过得更好。

Some people point at superrich black sports stars and say,

有些人指着超级有钱的 黑人运动明星说，

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

“看到没？他们超有钱， 白人特权不存在。”

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

但是这不是白人特权的内涵。

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

白人特权是指，如果其他特征 跟那个超有钱的运动明星一样，

but they were also white,

同时还是白人，

we would expect them to be better off in society.

我们会认为他们在社会上混得更好。

There is something else we can understand from this diagram

我们从这张图表中还能学到更多

如果我们沿着一个箭头看。

if we look along a row.

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

沿最顶层到第二层的箭头看， 拥有两种特权的人，

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

他们并不是特别平等。

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

比如，有钱的白人女性 或许比贫穷的白人男性

than poor white men,

混得更好，

and rich black men are probably somewhere in between.

而有钱的黑人男性或许介于两者之间。

So it's really more skewed like this,

所以其实这张图应该更加倾斜，

and the same on the bottom level.

最下面一层也是一样。

But we can actually take it further

我们可以更仔细地

and look at the interactions between those two middle levels.

看中间两层的相互关系。

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

因为有钱的、非白人、非男性 可能比贫穷的白人男性

than poor white men.

过得更好。

Think about some extreme examples, like Michelle Obama,

举几个极端的例子，比如米歇尔·奥巴马

Oprah Winfrey.

奥普拉·温弗瑞。

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

她们绝对比贫穷的、失业的、 无家可归的白人男性过得好。

So actually, the diagram is more skewed like this.

所以这张图更像是这样倾斜。

And that tension exists

图表中各个层级的人

between the layers of privilege in the diagram

在生活中体验到的特权，

and the absolute privilege that people experience in society.

与在图表中所处的位置存在差异。

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

这帮助我理解了， 为什么有些贫穷的白人男性

are so angry in society at the moment.

在社会中如此愤怒。

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

因为他们被认为处于特权阶级的上层，

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

而现实生活中，他们这种 享有特权的感受并不明显。

And I believe that understanding the root of that anger

我认为理解愤怒的根源

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

比反过来对他们感到愤怒 更有实际帮助。

Seeing these abstract structures can also help us switch contexts

这种抽象的结构 还能帮我们转换情境,

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

看看如果不同的人 位于顶端，会有什么不同。

In our original diagram,

在我们最初的图表里，

rich white men were at the top,

有钱的白人男性在顶层，

but if we restricted our attention to non-men,

但如果我们只看非男性，

we would see that they are here,

他们集中在这个区域，

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

现在“有钱的”、“白人”、 “非男性”在顶层了。

So we could move to a whole context of women,

我们可以把整个情境转换到女性，

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

那么我们的三种特权变成了 “有钱的”、“白人“、“本性别”。

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

“本性别”是指自我认同的性别

the gender you were assigned at birth.

和生理性别一致。

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

现在“有钱的”、“白人”、“本性别女性” 与“有钱的”、“白人”、“男性”

that rich white men did in broader society.

在更宽泛的社会中拥有了类似的地位。

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

这让我理解了，为什么会有那么多人

towards rich white women,

讨厌“有钱的”、“白人”、“女性”，

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

尤其在最近的很多女权主义活动中，

because perhaps they're prone to seeing themselves as underprivileged

因为她们倾向于认为自己是弱势群体，

relative to white men,

如果跟白人男性比的话，

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

但她们忘记了，跟非白人女性相比， 自己享受了多少特权。

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

我们能利用这些抽象的结构 在情境之间转换

in which we are more privileged and less privileged.

我们有时占优势，有时占劣势。

We are all more privileged than somebody

我们总会比一些人占优势，

and less privileged than somebody else.

也总会比另一些人更吃亏。

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

比如，我知道并且感觉到 作为一个亚洲人，

I am less privileged than white people

比白人更弱势，

because of white privilege.

因为白人特权的存在。

But I also understand

但是我也知道，

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

我可能是非白人人群中最有特权的，

and this helps me pivot between those two contexts.

这能让我在不同情境下转换。

And in terms of wealth,

说到财富，

I don't think I'm super rich.

我不觉得自己超级有钱。

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

我比不上那些甚至不需要工作的人。

But I am doing fine,

但我过得也很滋润，

and that's a much better situation to be in

比起在温饱线上挣扎的人，

than people who are really struggling,

那些失业的，或者拿最低工资的人，

maybe are unemployed or working at minimum wage.

我已经过得很好了。

I perform these pivots in my head

我在脑中进行这些转换

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

来帮助我理解别人的处境，

which brings me to this possibly surprising conclusion:

这让我得出了一个意外的结论：

that abstract mathematics is highly relevant to our daily lives

抽象数学和我们的日常生活息息相关

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

甚至能帮我们理解他人并产生共情。

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

我希望每个人都能 尝试更多去理解他人，

and work with them together,

共同努力，

rather than competing with them

而不是相互竞争，

and trying to show that they're wrong.

说对方错了。

And I believe that abstract mathematical thinking

我相信，抽象的数学思维

can help us achieve that.

能帮助我们实现这些。

Thank you.

谢谢大家。

(Applause)

（掌声）