The mathematics of love

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

I think we can all agree
that mathematicians

are famously excellent
at finding love.

But it's not just because
of our dashing personalities

our superior conversational skills,
our our excellent pencil cases,

It's also because we've done
a lot of work into the maths

of how to find the perfect partner.

In my favorite paper on the subject,
which is entitled,

"Why I Don't Have a Girlfriend",
Peter Backus tries to rate

his chances at finding love.

Now, peter is not a
very greedy man.

Of all of the available
women in the UK,

all that 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 attractive,

somebody who is 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
extra-terrestrial 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 night out.

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

going on nights out anymore.

The thing is is that I personally

don't subscribe to
such a pessimistic view.

I know, just as well
as you do,

that love doesn't
really work like that

human emotion
isn't neatly ordered,

rational, or easily predictable.

But I also know that that doesn't
mean that mathematics

doesn't have something
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 of
the stock market,

to the movement
of the planets,

or the growth of cities.

If we're being honest, none
of those things are neatly ordered

Or easily predictable, either.

Because I believe
that mathematics

is so powerful that
is 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, 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 OkayCupid,

not least because it was

started by a group
of mathematicians.

Now because they're
mathematicians,

they have been collecting
data on everyone

whose been using 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 online dating websites.

And they've come up with
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.

Okay, in a thankfully
voluntary section,

you are allowed to rate
how attractive people are

between 1 and 5.

And if we compare this score,
this 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 online dating.

So this is a graph
that the online

OkayCupid 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 straight-forward looks

that are important.

So let me try to illustrate
their findings

with an example.

If you take someone
like Portia de Rossi,

everybody agrees
that Portia de Rossi

is a very beautiful woman.

Nobody thinks
that she's ugly,

but she's not a supermodel.

If you compare
Portia de Rossi

to someone like
Sarah Jessica Parker,

now, a lot of people,
myself included,

think that Sarah Jessica Parker
is seriously fabulous

and possibly one of the
most beautiful creatures

to have ever have walked
the face of the earth.

But, some other people,
e.i. 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 Sarah Jessica Parker
or Portia de Rossi are,

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

I reckon that they would
average out to the same score.

But the way that people would vote

would be very different.

So Portia's scores would
all be clustered around

the four because everybody
agrees that she's very beautiful.

whereas Sarah Jessica Parker
divides opinion.

There a huge spread
in her scores.

And actually it's this
spread that counts.

It's this spread that
makes you more popular

on online internet
dating websites.

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 thinking

that you're the cute
girl next door.

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 that there is
less competition for you

and that there's
an extra 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?

Here's where the really
interesting part comes.

People choose the pictures that
they use on an online, dating website,

they often try to
minimize the things

that they think people
will find unattractive.

The classic example is that people
who are 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

on the first person who comes along
and shows you any interest at all.

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

if you want to maximize your
chances of longterm happiness.

As my favorite author,
Jane Austen put it,

"An unmarried woman
of seven and twenty

can never hope to feel or
inspire affection again."

(Laughter).

Thanks, Jane.

So the question is then,

how do you know when
is the right time

to settle down given
all the people

you can date in
your lifetime?

Thankfully, there is a
rather delicious bit

of mathematics that
we can use to

help us out here.

So lets imagine then,

that you start
dating when you're 15

and ideally, you'd like to be
married by the time you're 35.

The 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 when 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 people don't typically
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 reject everybody
as serious marriage potential.

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

who is better than everyone
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.

Now, if you're
following the maths,

I'm afraid that if no one
else comes along

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, terrible people.

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

so you can reject them.

But, then imagine that the
next person who 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
that 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 to this market.

with a valentines 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 that follow
this exact strategy.

So they reject every possible
suitor that turns up in

in the first 37 percent
of the mating season,

then they
pick the next fish

who comes along after
that window who is,

i don't know, bigger and burlier
than all the fish that they've seen.

I also think that
subconsciously,

humans, we sort of
do this anyway.

We give ourselves enough
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

when 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.

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 like to avoid divorce
from Piers Morgan's wife, maybe?

But it's a sad fact
in modern life

that 1 in 2 marriages
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, it's very
hard to know

what you should be measuring
and 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 skin conductivity,

he recorded their facial expressions,

heart rates, their blood pressure

basically everything apart from whether
or ont 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

is how positive or negative each
partner was being in the conversation.

Now couples that were
very low risk

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

Whereas bad relationship,

as in, those that are 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 caused

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
to describe

what happens between two
countries in an arms race.

(Laughter).

So that an arguing couple,

spiraling into negativity,

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

are 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 relationships

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

Where couples let things go

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

But actually, the mathematics
and subsequent findings

by the team have shown the
exact opposite to be 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.

They 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 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 support that you
that you should

never let you should go
down on your anger.

So those are my top three tips

for 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 are 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
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).