An unexpected tool for understanding inequality: abstract math
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0:01 - 0:07The world is awash
with divisive arguments, -
0:07 - 0:09conflict,
-
0:09 - 0:11fake news,
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0:11 - 0:12victimhood,
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0:13 - 0:19exploitation, prejudice,
bigotry, blame, shouting -
0:19 - 0:22and minuscule attention spans.
-
0:23 - 0:28It can sometimes seem
that we are doomed to take sides, -
0:28 - 0:30be stuck in echo chambers
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0:30 - 0:33and never agree again.
-
0:33 - 0:36It can sometimes seem
like a race to the bottom, -
0:36 - 0:40where everyone is calling out
somebody else's privilege -
0:40 - 0:46and vying to show that they
are the most hard-done-by person -
0:46 - 0:47in the conversation.
-
0:49 - 0:51How can we make sense
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0:51 - 0:53in a world that doesn't?
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0:56 - 1:00I have a tool for understanding
this confusing world of ours, -
1:00 - 1:03a tool that you might not expect:
-
1:04 - 1:06abstract mathematics.
-
1:07 - 1:10I am a pure mathematician.
-
1:10 - 1:14Traditionally, pure maths
is like the theory of maths, -
1:14 - 1:19where applied maths is applied
to real problems like building bridges -
1:19 - 1:21and flying planes
-
1:21 - 1:23and controlling traffic flow.
-
1:24 - 1:29But I'm going to talk about a way
that pure maths applies directly -
1:29 - 1:30to our daily lives
-
1:30 - 1:32as a way of thinking.
-
1:33 - 1:37I don't solve quadratic equations
to help me with my daily life, -
1:37 - 1:42but I do use mathematical thinking
to help me understand arguments -
1:42 - 1:45and to empathize with other people.
-
1:46 - 1:51And so pure maths helps me
with the entire human world. -
1:52 - 1:56But before I talk about
the entire human world, -
1:56 - 1:59I need to talk about something
that you might think of -
1:59 - 2:01as irrelevant schools maths:
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2:02 - 2:04factors of numbers.
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2:04 - 2:08We're going to start
by thinking about the factors of 30. -
2:08 - 2:12Now, if this makes you shudder
with bad memories of school maths lessons, -
2:12 - 2:17I sympathize, because I found
school maths lessons boring, too. -
2:17 - 2:21But I'm pretty sure we are going
to take this in a direction -
2:21 - 2:25that is very different
from what happened at school. -
2:26 - 2:27So what are the factors of 30?
-
2:27 - 2:31Well, they're the numbers that go into 30.
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2:31 - 2:33Maybe you can remember them.
We'll work them out. -
2:33 - 2:37It's one, two, three,
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2:37 - 2:39five, six,
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2:39 - 2:4210, 15 and 30.
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2:42 - 2:43It's not very interesting.
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2:44 - 2:46It's a bunch of numbers
in a straight line. -
2:47 - 2:48We can make it more interesting
-
2:48 - 2:52by thinking about which of these numbers
are also factors of each other -
2:52 - 2:55and drawing a picture,
a bit like a family tree, -
2:55 - 2:56to show those relationships.
-
2:56 - 3:00So 30 is going to be at the top
like a kind of great-grandparent. -
3:00 - 3:03Six, 10 and 15 go into 30.
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3:04 - 3:06Five goes into 10 and 15.
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3:07 - 3:10Two goes into six and 10.
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3:10 - 3:13Three goes into six and 15.
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3:13 - 3:17And one goes into two, three and five.
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3:17 - 3:21So now we see that 10
is not divisible by three, -
3:21 - 3:24but that this is the corners of a cube,
-
3:24 - 3:26which is, I think, a bit more interesting
-
3:26 - 3:28than a bunch of numbers
in a straight line. -
3:30 - 3:33We can see something more here.
There's a hierarchy going on. -
3:33 - 3:35At the bottom level is the number one,
-
3:35 - 3:37then there's the numbers
two, three and five, -
3:37 - 3:40and nothing goes into those
except one and themselves. -
3:40 - 3:42You might remember
this means they're prime. -
3:42 - 3:45At the next level up,
we have six, 10 and 15, -
3:45 - 3:49and each of those is a product
of two prime factors. -
3:49 - 3:51So six is two times three,
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3:51 - 3:5210 is two times five,
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3:52 - 3:5415 is three times five.
-
3:54 - 3:56And then at the top, we have 30,
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3:56 - 3:59which is a product
of three prime numbers -- -
3:59 - 4:01two times three times five.
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4:01 - 4:06So I could redraw this diagram
using those numbers instead. -
4:06 - 4:09We see that we've got
two, three and five at the top, -
4:09 - 4:12we have pairs of numbers
at the next level, -
4:13 - 4:15and we have single elements
at the next level -
4:15 - 4:17and then the empty set at the bottom.
-
4:17 - 4:23And each of those arrows shows
losing one of your numbers in the set. -
4:23 - 4:25Now maybe it can be clear
-
4:25 - 4:28that it doesn't really matter
what those numbers are. -
4:28 - 4:30In fact, it doesn't matter what they are.
-
4:30 - 4:35So we could replace them with
something like A, B and C instead, -
4:35 - 4:36and we get the same picture.
-
4:37 - 4:39So now this has become very abstract.
-
4:40 - 4:42The numbers have turned into letters.
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4:42 - 4:46But there is a point to this abstraction,
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4:46 - 4:50which is that it now suddenly
becomes very widely applicable, -
4:50 - 4:54because A, B and C could be anything.
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4:54 - 4:59For example, they could be
three types of privilege: -
4:59 - 5:01rich, white and male.
-
5:02 - 5:06So then at the next level,
we have rich white people. -
5:06 - 5:09Here we have rich male people.
-
5:09 - 5:11Here we have white male people.
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5:11 - 5:15Then we have rich, white and male.
-
5:15 - 5:18And finally, people with none
of those types of privilege. -
5:18 - 5:22And I'm going to put back in
the rest of the adjectives for emphasis. -
5:22 - 5:25So here we have rich, white
non-male people, -
5:25 - 5:28to remind us that there are
nonbinary people we need to include. -
5:28 - 5:30Here we have rich, nonwhite male people.
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5:30 - 5:34Here we have non-rich, white male people,
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5:34 - 5:36rich, nonwhite, non-male,
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5:37 - 5:39non-rich, white, non-male
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5:39 - 5:41and non-rich, nonwhite, male.
-
5:41 - 5:44And at the bottom,
with the least privilege, -
5:44 - 5:48non-rich, nonwhite, non-male people.
-
5:48 - 5:52We have gone from a diagram
of factors of 30 -
5:52 - 5:55to a diagram of interaction
of different types of privilege. -
5:56 - 6:00And there are many things
we can learn from this diagram, I think. -
6:00 - 6:07The first is that each arrow represents
a direct loss of one type of privilege. -
6:07 - 6:12Sometimes people mistakenly think
that white privilege means -
6:12 - 6:16all white people are better off
than all nonwhite people. -
6:16 - 6:20Some people point at superrich
black sports stars and say, -
6:20 - 6:24"See? They're really rich.
White privilege doesn't exist." -
6:24 - 6:27But that's not what the theory
of white privilege says. -
6:27 - 6:32It says that if that superrich sports star
had all the same characteristics -
6:32 - 6:34but they were also white,
-
6:34 - 6:37we would expect them
to be better off in society. -
6:39 - 6:42There is something else
we can understand from this diagram -
6:42 - 6:44if we look along a row.
-
6:44 - 6:48If we look along the second-to-top row,
where people have two types of privilege, -
6:48 - 6:52we might be able to see
that they're not all particularly equal. -
6:52 - 6:58For example, rich white women
are probably much better off in society -
6:59 - 7:01than poor white men,
-
7:01 - 7:04and rich black men are probably
somewhere in between. -
7:04 - 7:07So it's really more skewed like this,
-
7:07 - 7:08and the same on the bottom level.
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7:09 - 7:11But we can actually take it further
-
7:11 - 7:15and look at the interactions
between those two middle levels. -
7:15 - 7:21Because rich, nonwhite non-men
might well be better off in society -
7:21 - 7:23than poor white men.
-
7:23 - 7:27Think about some extreme
examples, like Michelle Obama, -
7:27 - 7:29Oprah Winfrey.
-
7:29 - 7:34They're definitely better off
than poor, white, unemployed homeless men. -
7:34 - 7:37So actually, the diagram
is more skewed like this. -
7:38 - 7:40And that tension exists
-
7:40 - 7:43between the layers
of privilege in the diagram -
7:44 - 7:47and the absolute privilege
that people experience in society. -
7:47 - 7:51And this has helped me to understand
why some poor white men -
7:51 - 7:54are so angry in society at the moment.
-
7:54 - 7:59Because they are considered to be high up
in this cuboid of privilege, -
7:59 - 8:04but in terms of absolute privilege,
they don't actually feel the effect of it. -
8:04 - 8:07And I believe that understanding
the root of that anger -
8:07 - 8:11is much more productive
than just being angry at them in return. -
8:13 - 8:18Seeing these abstract structures
can also help us switch contexts -
8:18 - 8:22and see that different people
are at the top in different contexts. -
8:22 - 8:23In our original diagram,
-
8:23 - 8:25rich white men were at the top,
-
8:25 - 8:29but if we restricted
our attention to non-men, -
8:29 - 8:31we would see that they are here,
-
8:31 - 8:34and now the rich, white
non-men are at the top. -
8:34 - 8:36So we could move to
a whole context of women, -
8:36 - 8:42and our three types of privilege
could now be rich, white and cisgendered. -
8:42 - 8:45Remember that "cisgendered" means
that your gender identity does match -
8:45 - 8:47the gender you were assigned at birth.
-
8:48 - 8:54So now we see that rich, white cis women
occupy the analogous situation -
8:54 - 8:57that rich white men did
in broader society. -
8:57 - 9:01And this has helped me understand
why there is so much anger -
9:01 - 9:02towards rich white women,
-
9:02 - 9:06especially in some parts
of the feminist movement at the moment, -
9:06 - 9:10because perhaps they're prone
to seeing themselves as underprivileged -
9:10 - 9:11relative to white men,
-
9:11 - 9:17and they forget how overprivileged
they are relative to nonwhite women. -
9:19 - 9:24We can all use these abstract structures
to help us pivot between situations -
9:24 - 9:27in which we are more privileged
and less privileged. -
9:27 - 9:29We are all more privileged than somebody
-
9:29 - 9:32and less privileged than somebody else.
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9:33 - 9:38For example, I know and I feel
that as an Asian person, -
9:38 - 9:40I am less privileged than white people
-
9:40 - 9:42because of white privilege.
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9:42 - 9:43But I also understand
-
9:43 - 9:48that I am probably among
the most privileged of nonwhite people, -
9:48 - 9:51and this helps me pivot
between those two contexts. -
9:52 - 9:53And in terms of wealth,
-
9:53 - 9:55I don't think I'm super rich.
-
9:55 - 9:58I'm not as rich as the kind of people
who don't have to work. -
9:58 - 10:00But I am doing fine,
-
10:00 - 10:02and that's a much better
situation to be in -
10:02 - 10:04than people who are really struggling,
-
10:04 - 10:07maybe are unemployed
or working at minimum wage. -
10:09 - 10:12I perform these pivots in my head
-
10:12 - 10:17to help me understand experiences
from other people's points of view, -
10:18 - 10:22which brings me to this
possibly surprising conclusion: -
10:23 - 10:30that abstract mathematics
is highly relevant to our daily lives -
10:30 - 10:37and can even help us to understand
and empathize with other people. -
10:39 - 10:44My wish is that everybody would try
to understand other people more -
10:44 - 10:46and work with them together,
-
10:46 - 10:48rather than competing with them
-
10:48 - 10:51and trying to show that they're wrong.
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10:52 - 10:57And I believe that abstract
mathematical thinking -
10:57 - 10:59can help us achieve that.
-
11:00 - 11:01Thank you.
-
11:01 - 11:06(Applause)
- Title:
- An unexpected tool for understanding inequality: abstract math
- Speaker:
- Eugenia Cheng
- Description:
-
How do we make sense of a world that doesn't? By looking in unexpected places, says mathematician Eugenia Cheng. She explains how applying concepts from abstract mathematics to daily life can lead us to a deeper understanding of things like the root of anger and the function of privilege. Learn more about how this surprising tool can help us to empathize with each other.
- Video Language:
- English
- Team:
- closed TED
- Project:
- TEDTalks
- Duration:
- 11:19
Brian Greene edited English subtitles for An unexpected tool for understanding inequality: abstract math | ||
Brian Greene approved English subtitles for An unexpected tool for understanding inequality: abstract math | ||
Brian Greene edited English subtitles for An unexpected tool for understanding inequality: abstract math | ||
Camille Martínez accepted English subtitles for An unexpected tool for understanding inequality: abstract math | ||
Camille Martínez edited English subtitles for An unexpected tool for understanding inequality: abstract math | ||
Camille Martínez edited English subtitles for An unexpected tool for understanding inequality: abstract math | ||
Joseph Geni edited English subtitles for An unexpected tool for understanding inequality: abstract math | ||
Joseph Geni edited English subtitles for An unexpected tool for understanding inequality: abstract math |