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).