The world is awash with divisive arguments, conflict, fake news,
这个世界充斥着引发分歧的观点，冲突，虚假新闻，
victimhood, exploitation, prejudice, bigotry, blame, shouting and minuscule attention spans.
受害者情绪，剥削，偏见，偏执，责怪，喊叫和极短的注意力时间。
It can sometimes seem that we are doomed to take sides, be stuck in echo chambers and never agree again.
有时候似乎我们注定要选边站队，固执己见，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 and vying to show that they are the most hard-done-by person in the conversation.
每个人都在说别人有特权，然后争先恐后地怨天尤人，都说自己最惨。
How can we make sense in a world that doesn't?
在这个疯狂的世界，我们怎样才能做到理智？
I have a tool for understanding this confusing world of ours, a tool that you might not expect: abstract mathematics.
我有一样工具，可以帮助理解这个费解的世界，一样你们可能意想不到的工具：抽象数学。
I am a pure mathematician. Traditionally, pure maths is like the theory of maths,
我是个纯粹的数学家。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 and flying planes and controlling traffic flow.
而应用数学是解决实际问题，比如建造大桥，开飞机，控制交通流量。
But I'm going to talk about a way that pure maths applies directly to our daily lives as a way of thinking.
但我打算讲一种将纯数学作为一种思维方式直接运用到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 and to empathize with other people.
但我确实运用数学思维来理解争论，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 as irrelevant schools maths: factors of numbers.
我必须和你们谈一些看起来可能无关的学校里教的数学：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, I sympathize,
如果这令你回想起数学课的糟糕回忆，我深表同情，
because I found school maths lessons boring, too.
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 that is very different from what happened at school.
但我很确定，接下来发生的事情跟学校里学到的会非常不一样。
So what are the factors of 30? Well, they're the numbers that go into 30.
那么30的因数有哪些？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。
It's one, two, three, five, six, 10, 15 and 30. It's not very interesting.
有1、2、3、5、6、10、15和30。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 by thinking about which of these numbers are also factors of each other
我们能让它变得有趣一些，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, to show those relationships.
然后画一张像家谱图的图，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. Five goes into 10 and 15.
6、10、15连上30。5连上10和15。
Two goes into six and 10. Three goes into six and 15. And one goes into two, three and five.
2连上6和10。3连上6和15。1连上2、3和5。
So now we see that 10 is not divisible by three, but that this is the corners of a cube,
我们看到10不能被3整除，但这里是一个立方体的8个角，
which is, I think, a bit more interesting than a bunch of numbers in a straight line.
我觉得这样的关系相比于一串数字要有趣得多。
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, then there's the numbers two, three and five,
最底层是数字1，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, and each of those is a product of two prime factors.
再往上一层，是6、10和15，它们都是两个质数的乘积。
So six is two times three, 10 is two times five, 15 is three times five.
6=2×3，10=2×5，15=3×5。
And then at the top, we have 30, which is a product of three prime numbers -- two times three times five.
最顶层的30，是三个质数的乘积，2x3x5。
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, we have pairs of numbers at the next level,
我们看到2、3、5在最顶层，成对的数字在第二层，
and we have single elements at the next level and then the empty set at the bottom.
单个的数字在下一层，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 that it doesn't really matter what those numbers are.
现在或许清楚了，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, and we get the same picture.
所以我们可以用A，B，C替代它们，也会得到同样的图。
So now this has become very abstract. The numbers have turned into letters.
这样就变得抽象了。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, because A, B and C could be anything.
因为这张图能被广泛应用了，因为A，B，C可以是任何东西。
For example, they could be three types of privilege: rich, white and male.
比如，它们可以是3种特权：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. Here we have white male people.
这里是“有钱的”“男性”。这里是“白人”“男性”。
Then we have rich, white and male. And finally, people with none of those types of privilege.
然后是“有钱的”、“白人”、“男性”。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, to remind us that there are nonbinary people we need to include.
所以这里是“有钱的”、“白人”、“非男性”，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, rich, nonwhite, non-male, non-rich, white, non-male and non-rich, nonwhite, male.
这里是“非有钱的”、“白人”、“男性”，“有钱的”、“非白人”、“非男性”，“非有钱的”、“白人”、“非男性”，以及“非有钱的”、“非白人”、“男性”。
And at the bottom, with the least privilege, non-rich, nonwhite, non-male people.
以及在最底层，特权最少的“非有钱的”、“非白人”、“非男性”。
We have gone from a diagram of factors of 30 to a diagram of interaction of different types of privilege.
我们从一个30的因数图表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 all white people are better off than all nonwhite people.
有时候人们错误地以为，白人特权意味着所有的白人都比非白人过得更好。
Some people point at superrich black sports stars and say, "See? They're really rich. White privilege doesn't exist."
有些人指着超级有钱的黑人运动明星说，“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 but they were also white,
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，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 if we look along a row.
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 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 than poor white men,
比如，有钱的白人女性或许比贫穷的白人男性混得更好，
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, and the same on the bottom level.
所以其实这张图应该更加倾斜，最下面一层也是一样。
But we can actually take it further and look at the interactions between those two middle levels.
我们可以更仔细地看中间两层的相互关系。
Because rich, nonwhite non-men might well be better off in society than poor white men.
因为有钱的、非白人、非男性可能比贫穷的白人男性过得更好。
Think about some extreme examples, like Michelle Obama, Oprah Winfrey.
举几个极端的例子，比如米歇尔·奥巴马，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 between the layers of privilege in the diagram and the absolute privilege that people experience in society.
图表中各个层级的人在生活中体验到的特权，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 are so angry in society at the moment.
这帮助我理解了，为什么有些贫穷的白人男性在社会中如此愤怒。
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 is much more productive than just being angry at them in return.
我认为理解愤怒的根源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 and see that different people are at the top in different contexts.
这种抽象的结构还能帮我们转换情境，看看如果不同的人位于顶端，会有什么不同。
In our original diagram, rich white men were at the top,
在我们最初的图表里，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, and now the rich, white non-men are at the top.
他们集中在这个区域，现在“有钱的”、“白人”、“非男性”在顶层了。
So we could move to a whole context of women, and our three types of privilege could now be rich, white and cisgendered.
我们可以把整个情境转换到女性，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 the gender you were assigned at birth.
“本性别”是指自我认同的性别和生理性别一致。
So now we see that rich, white cis women occupy the analogous situation that rich white men did in broader society.
现在“有钱的”、“白人”、“本性别女性”与“有钱的”、“白人”、“男性”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 towards rich white women,
这让我理解了，为什么会有那么多人讨厌“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 relative to white men,
因为她们倾向于认为自己是弱势群体，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 in which we are more privileged and less privileged.
我们能利用这些抽象的结构在情境之间转换，我们有时占优势，有时占劣势。
We are all more privileged than somebody and less privileged than somebody else.
我们总会比一些人占优势，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 because of white privilege.
比白人更弱势，因为白人特权的存在。
But I also understand that I am probably among the most privileged of nonwhite people,
但是我也知道，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, I don't think I'm super rich.
说到财富，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, and that's a much better situation to be in than people who are really struggling,
但我过得也很滋润，比起在温饱线上挣扎的人，
maybe are unemployed or working at minimum wage.
那些失业的，或者拿最低工资的人，我已经过得很好了。
I perform these pivots in my head to help me understand experiences from other people's points of view,
我在脑中进行这些转换，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 and can even help us to understand and empathize with other people.
抽象数学和我们的日常生活息息相关，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 and work with them together,
我希望每个人都能尝试更多去理解他人，共同努力，
rather than competing with them and trying to show that they're wrong.
而不是相互竞争，说对方错了。
And I believe that abstract mathematical thinking can help us achieve that. Thank you.
我相信，抽象的数学思维能帮助我们实现这些。谢谢大家。