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The world is awash
with divisive arguments,
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conflict, fake news,
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victimhood,
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exploitation, prejudice,
bigotry, blame, shouting,
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and minuscule attention spans.
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It can sometimes seem
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that we are doomed to take sides,
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be stuck in echo chambers,
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and never agree again.
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It can sometimes seem
like a race to the bottom,
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where everyone is calling out
somebody else's privilege
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and vying to show that they
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are the most hard-done-by person
in the conversation.
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How can we make sense
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in a world that doesn't?
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I have a tool for understanding
this confusing world of ours,
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a tool that you might not expect:
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abstract mathematics.
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I am a pure mathematician.
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Traditionally, pure maths
is like the theory of maths,
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where applied maths is applied
to real problems like building bridges
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and flying planes
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and controlling traffic flow.
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But I'm going to talk about a way
that pure maths applies directly
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to our a daily lives as a way of thinking.
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I don't solve quadratic equations
to help me with my daily life,
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but I do use mathematical thinking
to help me understand arguments
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and to empathize with other people.
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And so pure maths helps me
with the entire human world.
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But before I talk about
the entire human world,
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I need to talk about something
that you might think of
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as irrelevant schools maths:
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factors of numbers.
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We're going to start by thinking
about the factors of 30.
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Now, if this makes you shudder
with bad memories of school maths lessons,
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I sympathize,
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because I found school
maths lessons boring too.
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But I'm pretty sure we are going
to take this in a direction
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that is very different
from what happened at school.
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So what are the factors of 30?
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Maybe you can remember them.
We'll work them out.
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It's one, two, three,
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five, six,
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10, 15, and 30.
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It's not very interesting.
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It's a bunch of numbers
in a straight line.
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We can make it more interesting
by thinking about which of these numbers
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are also factors of each other
and drawing a picture,
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a bit like a family tree
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to show those relationships.
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So 30 is going to be at the top
like a kind of great grandparent.
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Six, 10, and 15 go into 30.
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Five goes into 10 and 15.
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Two goes in six and 10.
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Three goes into six and 15.
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And one goes into two, three, and five.
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So now we see that 10
is not divisible by three,
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but that is this the corners of a cube,
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which is I think a bit more interesting
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than a bunch of numbers
in a straight line.
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We can see something more here.
There's a hierarchy going on.
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At the bottom level is the number one,
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then there's the numbers
two, three, and five,
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and nothing goes into those
except one and themselves.
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You might remember
this means they're prime.
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At the next level up,
we have six, 10, and 15,
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and each of those is a product
of two prime factors.
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So six is two times three,
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10 is two times five,
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15 is three times five,
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and then at the top, we have 30,
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which is a product of three prime numbers,
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two times three times five.
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So I could redraw this diagram
using those numbers instead.
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So we see that we've got
two, three, and five at the top,
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we have pairs of numbers
at the next level,
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and we have single elements
at the next level,
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and then the empty set at the bottom.
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And each of those arrows shows
losing one of your numbers in the set.
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Now maybe it can be clear
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that it doesn't really matter
what those numbers are.
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In fact it doesn't matter what they are.
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So we could replace them with
something like A, B, and C instead
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and we get the same picture.
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So now this has become very abstract.
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The numbers have turned into letters.
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But there is a point to this abstraction,
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which is that it now suddenly
becomes very widely applicable,
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because A, B, and C could be anything.
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For example, they could be
three types of privilege:
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rich, white, and male.
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So then at the next level,
we have rich white people.
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Here we have rich male people.
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Here we have white male people.
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Then we have rich, white, and male.
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And finally people with
none of those types of privilege.
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And I'm going to put back in
the rest of the adjectives for emphasis.
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So here we have rich white
non-male people,
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to remind us that there are
non-binary people we need to include.
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Here we have rich non-white male people.
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Here we have non-rich white male people,
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rich non-white non-male,
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non-rich white non-male,
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and non-rich, non-white male,
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and, and at the bottom
with the least privilege,
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non-rich, not-white, non-male people.
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We have gone from a diagram
of factors of 30
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to a diagram of interaction
of different types of privilege,
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and there are many things
we can learn from this diagram, I think.
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The first is that each arrow represents
a direct loss of one type of privilege.
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Sometimes people mistakenly think
that white privilege means
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all white people are better off
than all non-white people.
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Some people point at superrich
black sports stars and say,
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"See? They're really rich.
White privilege doesn't exist."
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But that's not what the theory
of white privilege says.
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It says that if that superrich sports star
had all the same characteristics
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but they were also white,
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we would expect them
to be better off in society.