The world is awash with divisive arguments. Conflict, fake news, victimhood
Exploitation, prejudice, bigotry, blame, shouting, and miniscule 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 math is like the theory of math where
applied math 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 math applies directly to our 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 math 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 school math: 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 math lessons, I sympathize, because I found school math lessons
boring too. But I'm pretty sure we're going to take this in a direction that is very different from what happened at school.
So what are the factors of 30? Well, they are the numbers that go into 30. Maybe you
can remember them. We'll work them out: it's 1, 2, 3, 5, 6, 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. 6, 10, and 15 go
into 30, 5 goes into 10 and 15. 2 goes into 6 and 10. 3 goes into 6 and 15 and 1
goes into 2, 3, and 5. So now we see that this is 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 2, 3, and 5. And nothing goes into those
except one and themselves. You might remember this means they're prime. At the next
level up we have 6, 10, and 15, and each of those is a product of two prime factors.
So 6 is 2 multiplied by 3, 10 is 2 multiplied by 5, 15 is 3 multiplied by 5. And
then at the top we have 30, which is a product of three prime numbers: two multiplied
by three multiplied by 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 does not 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. Now 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 at the bottom with the least privileged: non-rich, non-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 super rich 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 super rich sports
star had all the same characteristics, but they were also white, we would expect them to be better off in society.
There is something else we can understand from this diagram. If we look along a row,
if we look along the second row from the top, where people have two types of privilege,
we might be able to see that they're not all particularly equal. For example, rich
white women are probably much better off in society than poor white men. And rich
black men are probably somewhere in between. So it's really more skewed like this.
And the same on the bottom level. But we can actually take it further and look at
the interaction between those two middle levels. Because rich, non-white non-men
might well be better off in society than poor white men. Think about some extreme
examples like Michelle Obama, Oprah Winfrey, they're definitely better off than poor,
white, unemployed homeless men. So actually, the diagram is more skewed like this,
and that tension exists between the layers of privilege in the diagram at the absolute
privilege that people experience in society. And this has helped me to understand
why some poor white men are so angry in society at the moment, because they are considered
to be high up in this cuboid of privilege. But in terms of absolute privilege, they
don't actually feel the effect of it. And I believe that understanding the root of
that anger is much more productive than just being angry at them in return.
Seeing these abstract structures can also help us switch contexts and see that different
people are at the top in different contexts. In our original diagram, rich white
men were at the top, but if we restricted our attention to non-men, we would see
that now the rich, white non-men are at the top. So we could move to a whole context
of women and our three types of privilege could now be rich, white, and cisgendered.
Remember that cisgendered means that your gender identity matches the gender you
were assigned at birth. So now we see that rich, white cis women occupy the analogous
situation that rich, white men did in broader society. And this has helped me understand
why there is so much anger towards rich white women, especially in some parts of
the feminist movement at the moment, because perhaps they're prone to seeing themselves
as underprivileged relative to white men and they forget how over privileged they are relative to non-white women.
We can all use these abstract structures to help us pivot between situations in which
we are more privileged and less privileged. We are all more privileged than somebody and less privileged than somebody else.
For example, I know and I feel that as an Asian person, I am less privileged than
white people because of white privilege, but I also understand that I am probably
among the most privileged of non-white people. And this helps me pivot between those
two contexts. And in terms of wealth, I don't think I'm super rich. I'm not as rich
as the kind of people who don't have to work, but I am doing fine. And that's a much
better situation to be in than people who are really struggling, maybe are unemployed or working at minimum wage.
I perform these pivots in my head to help me understand experiences from other people's points of view.
Which brings me to this possibly surprising conclusion that abstract mathematics is
highly relevant to our daily lives and can even help us to understand and empathize with other people.
My wish is that everybody would try to understand other people more, and work with
them together rather than competing with them and trying to show that they're wrong.
And I believe that abstract mathematical thinking can help us achieve that.
Thank you.