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 a 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?
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 in 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 is this 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.
So 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 non-binary people we need to include.
Here we have rich non-white male people.
Here we have non-rich white male people,
rich non-white non-male,
non-rich white non-male,
and non-rich, non-white male,
and, and at the bottom with the least privilege,
non-rich, not-white, 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 non-white 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.