The mathematics of love

Today I want to talk to you
about the mathematics of love.

Now, I think that we can all
agree that mathematicians

are famously excellent at finding love.

But it's not just because
of our dashing personalities,

superior conversational skills
and excellent pencil cases.

It's also because we've actually done
an awful lot of work into the maths

of how to find the perfect partner.

Now, in my favorite paper on
the subject, which is entitled,

"Why I Don't Have a Girlfriend" --
(Laughter) --

Peter Backus tries to rate
his chances of finding love.

Now, Peter's not a very greedy man.

Of all of the available women in the U.K.,

all Peter's looking for is
somebody who lives near him,

somebody in the right age range,

somebody with a university degree,

somebody he's likely to get on well with,

somebody who's likely to be attractive,

somebody who's likely
to find him attractive.

(Laughter)

And comes up with an
estimate of 26 women

in the whole of the UK.

It's not looking very good,
is it Peter?

Now, just to put that
into perspective,

that's about 400 times fewer
than the best estimates

of how many intelligent
extraterrestrial life forms there are.

And it also gives Peter
a 1 in 285,000 chance

of bumping into any one
of these special ladies

on a given night out.

I'd like to think that's why
mathematicians don't really bother

going on nights out anymore.

The thing is that I personally don't
subscribe to such a pessimistic view.

Because I know, just
as well as all of you do,

that love doesn't really work like that.

Human emotion isn't neatly ordered
and rational and easily predictable.

But I also know that that doesn't mean

that mathematics hasn't got
something that it can offer us

because, love, as with most of life,
is full of patterns

and mathematics is, ultimately,
all about the study of patterns.

Patterns from predicting the weather
to the fluctuations in the stock market,

to the movement of the planets
or the growth of cities.

And if we're being honest,

none of those things are exactly neatly
ordered and easily predictable, either.

Because I believe that mathematics
is so powerful that it has the potential

to offer us a new way of looking
at almost anything.

Even something as mysterious as love.

And so, to try to persuade you

of how totally amazing, excellent
and relevant mathematics is,

I want to give you my top three
mathematically verifiable tips for love.

Okay, so Top Tip #1:

How to win at online dating.

So my favorite online dating
website is OkCupid,

not least because it was started
by a group of mathematicians.

Now, because they're mathematicians,

they have been collecting data

on everybody who uses their site
for almost a decade.

And they've been trying
to search for patterns

in the way that we talk about ourselves

and the way that we
interact with each other

on an online dating website.

And they've come up with some
seriously interesting findings.

But my particular favorite

is that it turns out
that on an online dating website,

how attractive you are
does not dictate how popular you are,

and actually, having people
think that you're ugly

can work to your advantage.

Let me show you how this works.

In a thankfully voluntary
section of OkCupid,

you are allowed to rate
how attractive you think people are

on a scale between 1 and 5.

Now, if we compare this score,
the average score,

to how many messages a
selection of people receive,

you can begin to get a sense

of how attractiveness links to popularity
on an online dating website.

This is the graph that the OkCupid guys
have come up with.

And the important thing to notice
is that it's not totally true

that the more attractive you are,
the more messages you get.

But the question arises then
of what is it about people up here

who are so much more popular
than people down here,

even though they have the
same score of attractiveness?

And the reason why is that it's not just
straightforward looks that are important.

So let me try to illustrate their
findings with an example.

So if you take someone like
Portia de Rossi, for example,

everybody agrees that Portia de Rossi
is a very beautiful woman.

Nobody thinks that she's ugly,
but she's not a supermodel, either.

If you compare Portia de Rossi
to someone like Sarah Jessica Parker,

now, a lot of people,
myself included, I should say,

think that Sarah Jessica Parker
is seriously fabulous

and possibly one of the
most beautiful creatures

to have ever have walked
on the face of the Earth.

But some other people,
i.e., most of the Internet,

seem to think that she looks
a bit like a horse. (Laughter)

Now, I think that if you ask people
how attractive they thought

Sarah Jessica Parker
or Portia de Rossi were,

and you ask them to give
them a score between 1 and 5,

I reckon that they'd average out
to have roughly the same score.

But the way that people would vote
would be very different.

So Portia's scores would
all be clustered around the 4

because everybody agrees
that she's very beautiful.

whereas Sarah Jessica Parker
completely divides opinion.

There'd be a huge spread in her scores.

And actually it's this spread that counts.

It's this spread that
makes you more popular

on an online Internet dating website.

So what this means then
is that if some people

think that you're
attractive,

you're actually better off
having some other people

think that you're
a massive minger.

That's much better than
everybody just thinking

that you're the cute
girl next door.

Now I think that this
makes a bit more sense

when you think in terms
of the people

who are sending
these messages.

So let's say that you think
somebody's attractive,

but you suspect that
other people

won't necessarily be
that interested.

That means there's
less competition for you

and it's an extras incentive
for you to get in touch.

Whereas compare
that to if you think

somebody is attractive
but you suspect

that everybody is going
to think they're attractive.

Well, why would you
bother humiliating yourself,

let's be honest?

Here's where the really
interesting part comes.

Because when people
choose the pictures

that they use on an online
dating website,

they often try to
minimize the things

that they think some people
will find unattractive.

The classic example is people
who are, perhaps, a little bit overweight

deliberately choosing
a very cropped photo.

or bald men, for example,

deliberatly choosing pictures
where they're wearing hats.

But this is the opposite of
what you should do

if you want to
be successful.

You should really, instead, play
up to whatever it is

that makes you different.

Even if you think that
some people

will find you unattractive.

Because the people
who fancy you

are just going to
fancy you anyway,

and the unimportant
losers who don't

well, they only play out
to your advantage.

Okay, Top Tip #2: How to pick
the perfect partner.

So let's imagine then that
you're a roaring success

on the dating scene.

But the question arises of
how do you then convert

that success into
longer-term happiness

and in particular,

how do you decide when is the
right time to settle down?

Now generally, it's not
advisable to just cash in

and marry the first person
who comes along

and shows you any
interest at all.

But, equally, you don't really
want to leave it too long

if you want to maximize your
chances of longterm happiness.

As my favorite author,
Jane Austen, puts it,

"An unmarried woman
of seven and twenty

can never hope to feel or
inspire affection again."

(Laughter).

Thanks a lot, Jane.

What do you know
about love?

So the question is then,

how do you know when
is the right time

to settle down given
all the people

that you can date
in your lifetime?

Thankfully, there's a
rather delicious bit

of mathematics that
that we can use

to help us out here called
Optimal Stopping Theorum.

So lets imagine then,

that you start
dating when you're 15

and ideally, you'd like
to be married

by the time that you're 35.

And there's a
number of people

that you could potentially
date across your lifetime,

and they'll be at kind of varying
levels of goodness.

Now the rules are
that once you cash in

and get married,

you can't look ahead and see
what you could have had,

and equally, you can't go back
and change your mind.

In my experience at least,

I find that typically people don't
much like being recalled

years after being
passed up

for somebody else,
or that's just me.

So the math says then
that what you should do

in the first 37 percent
of your dating window,

you should just
reject everybody

as serious marriage potential.

(Laughter).

And then, you should pick the
next person that comes along

that is better than everybody
that you've seen before.

So here's the example.

Now if you do this, it can be
mathematically proven, in fact,

that this is the best
possible way of

maximizing your chances of
finding the perfect partner.

Now, unfortunately, I have
to tell you that this method

does come with some risks.

For instance, imagine if
your perfect partner

appeared during your
first 37 percent.

Now, unfortunately,
you'd have to reject them.

(Laughter).

Now, if you're
following the maths,

I'm afraid no one
else comes along

that's better than anyone
you've seen before,

so you have to go
on rejecting everyone

and die alone.

(Laughter).

Probably surrounded by cats
nibbling at your remains.

Okay, another risk is,
let's imagine, instead,

that the first people
that you dated

in your first 37 percent

are just incredibly dull,
boring, terrible people.

Now, that's okay, because
you're in your rejection phase,

so thats fine,
you can reject them.

But then imagine, the next
person to comes along

is just marginally less boring,
dull and terrible

than everybody that
you've seen before.

Now, if you are following
the maths,

I'm afraid that you have
to marry them

and end up in a relationship
which is, frankly, suboptimal.

Sorry about that.

But I do think that there's
an opportunity here

for Hallmark to cash in on
and really cater for this market.

A Valentine's Day
card like this:

"My darling husband, you
are marginally less terrible

than the first 37 percent
of people I dated."

It's actually more romantic
than I normally manage.

Okay, so this method doesn't give
you a 100 percent success rate,

but there's no other possible
strategy that can do any better.

And actually, in the wild,
there are certain types

of fish which follow and
employ this exact strategy.

So they reject every possible
suitor that turns up

in the first 37 percent
of the mating season,

and then they
pick the next fish

that comes along after
that window

that's, I don't know,
bigger and burlier

than all the fish that
they've seen before.

I also think that
subconsciously,

humans, we do sort
of do this anyway.

We give ourselves
a little bit of time

to play the field,

get a feel for the
marketplace or whatever,

when we're young.

And then we only start
looking, seriously,

at potential marriage
candidates

once we hit our
mid-to-late 20's.

I think this is
conclusive proof,

if ever it were needed,

that everybody's brains
are prewired to be

just a little bit mathematical.

Okay, so that was Top Tip #2.

Now, Top tip #3:
How to avoid divorce.

Okay, so let's imagine then that you
picked the perfect partner

and you're settling into a
lifelong relationship with them.

Now, I like to think
that everybody

would ideally
like to avoid divorce,

apart from, I don't know,
Piers Morgan's wife, maybe?

But it's a sad fact
of modern life

that 1 in 2 marriages in the
States end in divorce,

with the rest of the world
not being far behind.

Now, you can be forgiven, perhaps

for thinking that the arguments
that precede a marital breakup

are not an ideal candidate
for mathematical investigation.

For one thing, it's very
hard to know

what you should be measuring
or what you should be quantifying.

But this didn't stop a
psychologist, John Gottman,

who did exactly that.

He observed, Gottman observed,

hundreds of couples
having a conversation

and recorded well, everything
you could think of.

So he recorded what was said
in the conversation,

he recorded their
skin conductivity,

he recorded their
facial expressions,

their heart rates,
their blood pressure,

basically everything apart from whether
or not the wife was always right,

which incidentally she totally is.

But what Gottman found, what
Gottman and his team found ,

was that one of the
most important predictors

for whether or not a couple
is going to get divorced

was how positive or negative

each partner was being
in the conversation.

Now couples that were
very low risk

scored a lot more positive points
on Gottman's scale than negative.

Whereas bad relationships,

by which I mean, probably
going to get divorced,

they found themselves getting
into a spiral of negativity.

Now just by using these
very simple ideas,

Gottman and his group
were able to predict

whether a given couple
was going to get divorced

with a 90 percent accuracy.

But it wasn't until
he teamed up

with a mathematician
James Murray

that they really started to
understand what causes

these negativity spirals
and how they occur.

And the results that they found,

I think are just incredibly,
impressively, simple and interesting.

So these equations,
they predict

how the wife or husband
is going to respond

in the next turn
of the conversation,

how positive or negative
they're going to be.

And these equations,
they depend on

the mood of the person
when they're on their own,

the mood of the person when
they're with their partner.

But most importantly,
they depend on

how much the husband and wife
influence one another.

Now I think it's important
to point out that at this stage,

these exact equations have
also been shown

to be perfectly able
at describing

what happens between two
countries in an arms race.

(Laughter).

So that an arguing couple,

spiraling into negativity,

and teetering on the
brink of divorce,

is actually mathematically equivalent to
the beginning of nuclear war.

(Laughter).

But the really important term
in this equation

is the influence that people
have on one another,

and in particular,

something called the
Negativity Threshhold.

Now the Negativity Threshold,

you can think of as
how annoying

the husband can be
before the wife

starts to get really pissed of,
and vice versa.

Now I always thought
that good marriages

were about compromise
and understanding

and allowing the person to
have the space to be themselves.

So I would have thought
that perhaps

the most successful
successful relationships

are the ones where there is a
really high Negativity Threshold.

Where couples let things go

and only brought things up if
they really were a big deal.

But actually, the mathematics
and subsequent findings

by the team have shown the
exact opposite is true.

The best couples or
the most successful couples

are the ones are the ones

with a really low
Negativity Threshold.

These are the couples that don't
let anything go unnoticed

and allow each other some
room to complain.

These are the couples that are
continually trying to repair

their own relationship,

that have a much more positive
outlook on their marriage.

Couples that don't let things go

and couples that don't let
trivial things end up being

a really big deal.

Now of course, it takes bit more than
just a low Negativity Threshold

and not compromising to
have a successful relationship

But I think that
it's quite interesting

to know that there is really
mathematical evidence

to say that you
that you should

never let you should go
down on your anger.

So those are my Top Three tips

of how maths can help you
with love and relationships.

But I hope that aside
from these tips,

they also give you
a little bit of insight

into the power
of mathematics.

Because for me,

equations and symbols
aren't just a thing,

They're a voice
that speaks out

about the incredible
richness of nature

and the startling simplicity
in the patterns

that twist and turn,

and warp and evolve
all around us.

From how the world works,

to how we behave.

So I hope that perhaps,

for just a couple of you,

a little bit of insight into
the mathematics of love

can persuade you to have

a little bit more
love for mathematics.

Thank you.

(Applause).