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?

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 porcia di rossi

everybody agrees that porcia di rossi

is a very beautiful woman

nobody thinks that she's ugly

but she's not a supermodel

if you compare porcia di 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 evr

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 porcia di rossi are

and you ask them to give them a score between one and five

i reckon that they would average out to the same score

but the way that people would vote

would be dry different

so porcia'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 but overweight

deliberately choosing a very cropped phto

or bald men for example

deliberatly choosing pictures

where they're wearing hats

but this is the opposite of

what you should do if

want to be succesful

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 you r 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 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 long term 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 that 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 your 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 Uunfortunately, you'd have to reject them

now, if you're following the maths

im afraid that no one else comes along

better than anyone you've seen before

so you have to go on rejecting everyone

and die along

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 to cmd along

is just marginally less boring, dull and terrible

than everybody that you've seen before.

now, if you are following the maths

im 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 exct 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 market place

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 prrof

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 divorse

okay so let's imagine then that yu

picked your 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 one in two 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 gotman,

who did exactly THAT

he observed, hotman 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 expresisons

heart rates, their blood pressure

basically everything apart

from whether or not the wife was always right

, which incidentally she totally is

but what got man found

what got man 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 got man's scale

than negative.

whereas bad relationship

as in, those that are pribably

going to get divorced,

they found themselves getting into

a spiral of negativity

now just by using these very simple ideas

gotman 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

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 that these exact

equations have also been shown t

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 divoirce

is actually mathematically equivalent to

the beginning of a 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 threshhold

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 threshhold

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 that the exact opposite is true

the best couples of 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 succesful relationship

but i think that it's quite interesting

to know that there is really

mathematical evidence to support that

you should never let the sun

go down on your anger

so those are my top three tips for how

maths can help you with

love and relaitonships

but i hope that aside form

these aside form these tips

they also give you a little bit of

insight into the power of mathematics

because for me,

equationsand 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 wokrs

to how we behave

so i hope that perhaps

for just a couple of you

a little bit of insight into

mathematics of love

can persuade you

to have a little bit more love

for mathematics

thank you

applause