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Thank you very much.
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So, yes, I'm Hannah Fry,
I am a mathematician,
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and today I want to talk to you
about the mathematics of love.
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Now, I think that we can all agree
-
that mathematicians
are famously excellent at finding love.
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But it's not just
because of our dashing personalities,
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superior conversational skills
and excellent pencil cases.
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It's also because we've actually done
an awful lot of work into the maths
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of how to find the perfect partner.
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Now, in my favorite paper
on the subject, which is entitled,
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"Why I Don't Have a Girlfriend" -
(Laughter) -
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Peter Backus tries to rate
his chances of finding love.
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Now, Peter's not a very greedy man.
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Of all of the available women in the U.K.,
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all Peter's looking for
is somebody who lives near him,
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somebody in the right age range,
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somebody with a university degree,
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somebody he's likely to get on well with,
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somebody who's likely to be attractive,
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somebody who's likely
to find him attractive.
-
(Laughter)
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And comes up with an estimate
of 26 women in the whole of the UK.
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It's not looking very good, is it Peter?
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Now, just to put that into perspective,
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that's about 400 times fewer
than the best estimates
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of how many intelligent
extraterrestrial life forms there are.
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And it also gives Peter
a 1 in 285,000 chance
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of bumping into any one
of these special ladies
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on a given night out.
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I'd like to think
that's why mathematicians
-
don't really bother
going on nights out anymore.
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The thing is that I personally
-
don't subscribe
to such a pessimistic view.
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Because I know,
just as well as all of you do,
-
that love doesn't really work like that.
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Human emotion isn't neatly ordered
and rational and easily predictable.
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But I also know that that doesn't mean
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that mathematics hasn't got something
that it can offer us
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because, love, as with most of life,
is full of patterns
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and mathematics is, ultimately,
all about the study of patterns.
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Patterns from predicting the weather
to the fluctuations in the stock market,
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to the movement of the planets
or the growth of cities.
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And if we're being honest,
none of those things
-
are exactly neatly ordered
and easily predictable, either.
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Because I believe that mathematics
is so powerful that it has the potential
-
to offer us a new way of looking
at almost anything.
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Even something as mysterious as love.
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And so, to try to persuade you
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of how totally amazing, excellent
and relevant mathematics is,
-
I want to give you my top three
mathematically verifiable tips for love.
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Okay, so Top Tip #1:
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How to win at online dating.
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So my favorite online dating website
is OkCupid,
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not least because it was started
by a group of mathematicians.
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Now, because they're mathematicians,
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they have been collecting data
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on everybody who uses their site
for almost a decade.
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And they've been trying
to search for patterns
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in the way that we talk about ourselves
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and the way that we interact
with each other
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on an online dating website.
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And they've come up with some
seriously interesting findings.
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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.
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Let me show you how this works.
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In a thankfully voluntary
section of OkCupid,
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you are allowed to rate
how attractive you think people are
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on a scale between 1 and 5.
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Now, if we compare this score,
the average score,
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to how many messages
a selection of people receive,
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you can begin to get a sense
-
of how attractiveness links to popularity
on an online dating website.
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This is the graph that the OkCupid guy
shave come up with.
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And the important thing to notice
is that it's not totally true
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that the more attractive you are,
the more messages you get.
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But the question arises then
of what is it about people up here
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who are so much more popular
than people down here,
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even though they have the same
score of attractiveness?
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And the reason why is that it's not just
straight forward looks that are important.
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So let me try to illustrate their
findings with an example.
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So if you take someone like
Portia de Rossi, for example,
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everybody agrees that Portia de Rossi
is a very beautiful woman.
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Nobody thinks that she's ugly,
but she's not a supermodel, either.
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If you compare Portia de Rossi
to someone like Sarah Jessica Parker,
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now, a lot of people,
myself included, I should say,
-
think that Sarah Jessica Parker
is seriously fabulous
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and possibly one
of the most beautiful creatures
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to have ever have walked
on the face of the Earth.
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But some other people,
i.e., most of the Internet,
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seem to think that she looks
a bit like a horse. (Laughter)
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Now, I think that if you ask people
how attractive they thought
-
Sarah Jessica Parker
or Portia de Rossi were,
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and you ask them to give them
a score between 1 and 5,
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I reckon that they'd average out
to have roughly the same score.
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But the way that people would vote
would be very different.
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So Portia's scores would
all be clustered around the 4
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because everybody agrees
that she's very beautiful,
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whereas Sarah Jessica Parker
completely divides opinion.
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There'd be a huge spread in her scores.
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And actually it's this spread that counts.
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It's this spread
that makes you more popular
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on an online Internet dating website.
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So what that means then
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is that if some people
think that you're attractive,
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you're actually better off
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having some other people think
that you're a massive minger.
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That's much better
than everybody just thinking
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that you're the cute girl next door.
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Now, I think this begins
makes a bit more sense
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when you think in terms of the people
who are sending these messages.
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So let's say that you think
somebody's attractive,
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but you suspect that other people
won't necessarily be that interested.
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That means there's
less competition for you
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and it's an extra incentive
for you to get in touch.
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Whereas compare that to
if you think somebody is attractive
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but you suspect that everybody
is going to think they're attractive.
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Well, why would you bother
humiliating yourself, let's be honest?
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Here's where the really
interesting part comes.
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Because when people choose the pictures
that they use on an online dating website,
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they often try to minimize the things
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that they think some people
will find unattractive.
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The classic example is people who are,
perhaps, a little bit overweight
-
deliberately choosing
a very cropped photo,
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or bald men, for example,
-
deliberately choosing pictures
where they're wearing hats.
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But actually this is the opposite
of what you should do
-
if you want to be successful.
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You should really, instead, play up to
whatever it is that makes you different,
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even if you think that some people
will find it unattractive.
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Because the people who fancy you
are just going to fancy you anyway,
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and the unimportant losers who don't,
well, they only play up to your advantage.
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Okay, Top Tip #2:
How to pick the perfect partner.
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So let's imagine then
that you're a roaring success
-
on the dating scene.
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But the question arises of how do you then
convert that success
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into longer-term happiness
and in particular,
-
how do you decide
when is the right time to settle down?
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Now generally,
it's not advisable to just cash in
-
and marry the first person
who comes along
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and shows you any interest at all.
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But, equally, you don't really
want to leave it too long
-
if you want to maximize your chance
of long-term happiness.
-
As my favorite author,
Jane Austen, puts it,
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"An unmarried woman of seven and twenty
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can never hope to feel or inspire
affection again."
-
(Laughter)
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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?
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Thankfully, there's a rather delicious bit
of mathematics that we can use
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to help us out here, called
optimal stopping theory.
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So let's imagine then,
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that you start dating when you're 15
-
and ideally, you'd like to be married
by the time that you're 35.
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And there's a number of people
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that you could potentially
date across your lifetime,
-
and they'll be at varying levels
of goodness.
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Now the rules are that once you cash in
and get married,
-
you can't look ahead to see
what you could have had,
-
and equally, you can't go back
and change your mind.
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In my experience at least,
-
I find that typically people don't
much like being recalled
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years after being passed up
for somebody else, or that's just me.
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So the math says then
that what you should do
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in the first 37 percent
of your dating window,
-
you should just reject everybody
as serious marriage potential.
-
(Laughter)
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And then, you should pick
the next person that comes along
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that is better than everybody
that you've seen before.
-
So here's the example.
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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.
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Now unfortunately, I have to tell you that
this method does come with some risks.
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For instance, imagine if your perfect partner
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appeared during your first 37 percent.
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Now, unfortunately,
you'd have to reject them.
-
(Laughter)
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Now, if you're following the maths,
-
I'm afraid no one else comes along
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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 come along
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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 you have to marry them
-
and end up in a relationship
which is, frankly, suboptimal.
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Sorry about that.
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But I do think that there's
an opportunity here
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for Hallmark to cash in on
and really cater for this market.
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A Valentine's Day card like this.
(Laughter)
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"My darling husband,
you are marginally less terrible
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than the first 37 percent
of people I dated."
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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
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of fish which follow and
employ this exact strategy.
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So they reject every possible suitor
that turns up
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in the first 37 percent
of the mating season,
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and then they pick the next fish
that comes along after that window
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that's, I don't know, bigger and burlier
-
than all of the fish
that they've seen before.
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I also think that subconsciously,
humans, we do sort of do this anyway.
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We give ourselves a little bit of time
to play the field,
-
get a feel for the marketplace
or whatever when we're young.
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And then we only start looking seriously
at potential marriage candidates
-
once we hit our mid-to-late 20s.
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I think this is conclusive proof,
if ever it were needed,
-
that everybody's brains are prewired
to be just a little bit mathematical.
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Okay, so that was Top Tip #2.
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Now, Top Tip #3: How to avoid divorce.
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Okay, so let's imagine then
that you picked your perfect partner
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and you're settling into
a lifelong relationship with them.
-
Now, I like to think that everybody
would ideally like to avoid divorce,
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apart from, I don't know,
Piers Morgan's wife, maybe?
-
But it's a sad fact of modern life
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that 1 in 2 marriages
in the States ends in divorce,
-
with the rest of the world
not being far behind.
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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.
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But this didn't stop a psychologist,
John Gottman, who did exactly that.
-
Gottman observed hundreds of couples
having a conversation
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and recorded, well,
everything you can think of.
-
So he recorded what was said
in the conversation,
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he recorded their skin conductivity,
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he recorded their facial expressions,
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their heart rates, their blood pressure,
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basically everything apart from whether
or not the wife was actually always right,
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which incidentally she totally is.
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But 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
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scored a lot more positive points
on Gottman's scale than negative.
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Whereas bad relationships,
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by which I mean, probably
going to get divorced,
-
they found themselves
getting into a spiral of negativity.
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Now just by using these very simple ideas,
-
Gottman and his group were able to predict
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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
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I think are just incredibly
impressively simple and interesting.
-
So these equations, they predict how
the wife or husband is going to respond
-
in their 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 at this stage,
-
that 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 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 threshold.
-
Now, the negativity threshold,
-
you can think of as
how annoying the husband can be
-
before the wife starts to get
really pissed off, and vice versa.
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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 relationships
-
were ones where there was
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 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 should never
let the sun 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 their use as 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.
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Thank you.
-
(Applause)
closed TED
