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Hannah Fry: The mathematics of love
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Finding the right mate is no cakewalk -- but is it even mathematically likely? In a charming talk, mathematician Hannah Fry shows patterns in how we look for love, and gives her top three tips (verified by math!) for finding that special someone.
Hannah Fry - Complexity theorist
Hannah Fry researches the trends in our civilization and ways we can forecast its future. Full bio
Hannah Fry researches the trends in our civilization and ways we can forecast its future. Full bio
Double-click the English transcript below to play the video.
00:12
Today I want to talk to you
about the mathematics of love.
about the mathematics of love.
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Now, I think that we can all agree
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that mathematicians
are famously excellent at finding love.
are famously excellent at finding love.
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But it's not just
because of our dashing personalities,
because of our dashing personalities,
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superior conversational skills
and excellent pencil cases.
and excellent pencil cases.
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It's also because we've actually done
an awful lot of work into the maths
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,
on the subject, which is entitled,
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"Why I Don't Have a Girlfriend" --
(Laughter) --
(Laughter) --
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Peter Backus tries to rate
his chances of finding love.
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,
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.
to find him attractive.
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01:08
(Laughter)
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And comes up with an estimate
of 26 women in the whole of the UK.
of 26 women in the whole of the UK.
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It's not looking very good,
is it Peter?
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
than the best estimates
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of how many intelligent
extraterrestrial life forms there are.
extraterrestrial life forms there are.
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And it also gives Peter
a 1 in 285,000 chance
a 1 in 285,000 chance
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of bumping into any one
of these special ladies
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
that's why mathematicians
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don't really bother
going on nights out anymore.
going on nights out anymore.
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The thing is that I personally
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don't subscribe
to such a pessimistic view.
to such a pessimistic view.
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Because I know,
just as well as all of you do,
just as well as all of you do,
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that love doesn't really work like that.
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Human emotion isn't neatly ordered
and rational and easily predictable.
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
that it can offer us
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because, love, as with most of life,
is full of patterns
is full of patterns
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and mathematics is, ultimately,
all about the study of patterns.
all about the study of patterns.
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Patterns from predicting the weather
to the fluctuations in the stock market,
to the fluctuations in the stock market,
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to the movement of the planets
or the growth of cities.
or the growth of cities.
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And if we're being honest,
none of those things
none of those things
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are exactly neatly ordered
and easily predictable, either.
and easily predictable, either.
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Because I believe that mathematics
is so powerful that it has the potential
is so powerful that it has the potential
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to offer us a new way of looking
at almost anything.
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,
and relevant mathematics is,
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I want to give you my top three
mathematically verifiable tips for love.
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,
website is OkCupid,
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not least because it was started
by a group of mathematicians.
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.
for almost a decade.
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And they've been trying
to search for patterns
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
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.
seriously interesting findings.
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But my particular favorite
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is that it turns out
that on an online dating website,
that on an online dating website,
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how attractive you are
does not dictate how popular you are,
does not dictate how popular you are,
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and actually, having people
think that you're ugly
think that you're ugly
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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,
section of OkCupid,
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you are allowed to rate
how attractive you think people are
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,
the average score,
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to how many messages a
selection of people receive,
selection of people receive,
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you can begin to get a sense
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of how attractiveness links to popularity
on an online dating website.
on an online dating website.
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This is the graph that the OkCupid guys
have come up with.
have come up with.
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And the important thing to notice
is that it's not totally true
is that it's not totally true
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that the more attractive you are,
the more messages you get.
the more messages you get.
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But the question arises then
of what is it about people up here
of what is it about people up here
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who are so much more popular
than people down here,
than people down here,
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even though they have the
same score of attractiveness?
same score of attractiveness?
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And the reason why is that it's not just
straightforward looks that are important.
straightforward looks that are important.
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So let me try to illustrate their
findings with an example.
findings with an example.
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So if you take someone like
Portia de Rossi, for example,
Portia de Rossi, for example,
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everybody agrees that Portia de Rossi
is a very beautiful woman.
is a very beautiful woman.
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Nobody thinks that she's ugly,
but she's not a supermodel, either.
but she's not a supermodel, either.
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If you compare Portia de Rossi
to someone like Sarah Jessica Parker,
to someone like Sarah Jessica Parker,
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now, a lot of people,
myself included, I should say,
myself included, I should say,
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think that Sarah Jessica Parker
is seriously fabulous
is seriously fabulous
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and possibly one of the
most beautiful creatures
most beautiful creatures
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to have ever have walked
on the face of the Earth.
on the face of the Earth.
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But some other people,
i.e., most of the Internet,
i.e., most of the Internet,
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seem to think that she looks
a bit like a horse. (Laughter)
a bit like a horse. (Laughter)
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Now, I think that if you ask people
how attractive they thought
how attractive they thought
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Sarah Jessica Parker
or Portia de Rossi were,
or Portia de Rossi were,
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and you ask them to give
them a score between 1 and 5,
them a score between 1 and 5,
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I reckon that they'd average out
to have roughly the same score.
to have roughly the same score.
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But the way that people would vote
would be very different.
would be very different.
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So Portia's scores would
all be clustered around the 4
all be clustered around the 4
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because everybody agrees
that she's very beautiful,
that she's very beautiful,
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whereas Sarah Jessica Parker
completely divides opinion.
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
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,
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.
think that you're a massive minger.
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That's much better
than everybody just thinking
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
makes a bit more sense
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when you think in terms of the people
who are sending these messages.
who are sending these messages.
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So let's say that you think
somebody's attractive,
somebody's attractive,
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but you suspect that other people
won't necessarily be that interested.
won't necessarily be that interested.
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That means there's
less competition for you
less competition for you
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and it's an extra incentive
for you to get in touch.
for you to get in touch.
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Whereas compare that
to if you think somebody is attractive
to if you think somebody is attractive
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but you suspect that everybody
is going to think they're attractive.
is going to think they're attractive.
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Well, why would you bother
humiliating yourself, let's be honest?
humiliating yourself, let's be honest?
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Here's where the really
interesting part comes.
interesting part comes.
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Because when people choose the pictures
that they use on an online dating website,
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.
will find unattractive.
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The classic example is people
who are, perhaps, a little bit overweight
who are, perhaps, a little bit overweight
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deliberately choosing
a very cropped photo,
a very cropped photo,
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or bald men, for example,
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deliberately choosing pictures
where they're wearing hats.
where they're wearing hats.
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But actually this is the opposite
of what you should do
of what you should do
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if you want to be successful.
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You should really, instead, play up to
whatever it is that makes you different,
whatever it is that makes you different,
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even if you think that some people
will find it unattractive.
will find it unattractive.
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Because the people who fancy you
are just going to fancy you anyway,
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.
well, they only play up to your advantage.
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Okay, Top Tip #2:
How to pick the perfect partner.
How to pick the perfect partner.
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So let's imagine then
that you're a roaring success
that you're a roaring success
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on the dating scene.
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But the question arises
of how do you then convert that success
of how do you then convert that success
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into longer-term happiness
and in particular,
and in particular,
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how do you decide
when is the right time to settle down?
when is the right time to settle down?
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Now generally,
it's not advisable to just cash in
it's not advisable to just cash in
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and marry the first person
who comes along
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
want to leave it too long
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if you want to maximize your
chance of long-term happiness.
chance of long-term happiness.
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As my favorite author,
Jane Austen, puts it,
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."
inspire affection again."
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(Laughter)
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Thanks a lot, Jane.
What do you know about love?
What do you know about love?
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So the question is then,
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how do you know when
is the right time to settle down
is the right time to settle down
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given all the people
that you can date in your lifetime?
that you can date in your lifetime?
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Thankfully, there's a rather delicious bit
of mathematics that we can use
of mathematics that we can use
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to help us out here, called
optimal stopping theory.
optimal stopping theory.
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So let's imagine then,
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that you start dating when you're 15
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and ideally, you'd like to be married
by the time that you're 35.
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,
date across your lifetime,
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and they'll be at varying
levels of goodness.
levels of goodness.
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Now the rules are that once
you cash in and get married,
you cash in and get married,
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you can't look ahead to see
what you could have had,
what you could have had,
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and equally, you can't go back
and change your mind.
and change your mind.
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In my experience at least,
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I find that typically people don't
much like being recalled
much like being recalled
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years after being passed up
for somebody else, or that's just me.
for somebody else, or that's just me.
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So the math says then
that what you should do
that what you should do
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in the first 37 percent
of your dating window,
of your dating window,
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you should just reject everybody
as serious marriage potential.
as serious marriage potential.
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(Laughter)
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And then, you should pick the
next person that comes along
next person that comes along
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that is better than everybody
that you've seen before.
that you've seen before.
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So here's the example.
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Now if you do this, it can be
mathematically proven, in fact,
mathematically proven, in fact,
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that this is the best possible way
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of maximizing your chances
of finding the perfect partner.
of finding the perfect partner.
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Now unfortunately, I have to tell you that
this method does come with some risks.
this method does come with some risks.
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For instance, imagine if
your perfect partner appeared
your perfect partner appeared
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during your first 37 percent.
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Now, unfortunately,
you'd have to reject them.
you'd have to reject them.
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(Laughter)
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Now, if you're following the maths,
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I'm afraid no one else comes along
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that's better than anyone
you've seen before,
you've seen before,
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so you have to go on
rejecting everyone and die alone.
rejecting everyone and die alone.
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(Laughter)
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Probably surrounded by cats
nibbling at your remains.
nibbling at your remains.
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Okay, another risk is,
let's imagine, instead,
let's imagine, instead,
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that the first people that you dated
in your first 37 percent
in your first 37 percent
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are just incredibly dull,
boring, terrible people.
boring, terrible people.
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Now, that's okay, because
you're in your rejection phase,
you're in your rejection phase,
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so thats fine,
you can reject them.
you can reject them.
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But then imagine, the next
person to come along
person to come along
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is just marginally less boring,
dull and terrible
dull and terrible
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than everybody that you've seen before.
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Now, if you are following the maths,
I'm afraid you have to marry them
I'm afraid you have to marry them
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and end up in a relationship
which is, frankly, suboptimal.
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
an opportunity here
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for Hallmark to cash in on
and really cater for this market.
and really cater for this market.
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A Valentine's Day card like this.
(Laughter)
(Laughter)
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"My darling husband, you
are marginally less terrible
are marginally less terrible
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than the first 37 percent
of people I dated."
of people I dated."
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It's actually more romantic
than I normally manage.
than I normally manage.
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Okay, so this method doesn't give
you a 100 percent success rate,
you a 100 percent success rate,
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but there's no other possible
strategy that can do any better.
strategy that can do any better.
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And actually, in the wild,
there are certain types
there are certain types
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of fish which follow and
employ this exact strategy.
employ this exact strategy.
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So they reject every possible
suitor that turns up
suitor that turns up
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in the first 37 percent
of the mating season,
of the mating season,
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and then they pick the next fish
that comes along after that window
that comes along after that window
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that's, I don't know, bigger and burlier
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than all of the fish
that they've seen before.
that they've seen before.
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I also think that subconsciously,
humans, we do sort of do this anyway.
humans, we do sort of do this anyway.
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We give ourselves a little bit of time
to play the field,
to play the field,
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get a feel for the marketplace
or whatever when we're young.
or whatever when we're young.
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And then we only start looking seriously
at potential marriage candidates
at potential marriage candidates
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once we hit our mid-to-late 20s.
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I think this is conclusive proof,
if ever it were needed,
if ever it were needed,
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that everybody's brains are prewired
to be just a little bit mathematical.
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
that you picked your perfect partner
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and you're settling into
a lifelong relationship with them.
a lifelong relationship with them.
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Now, I like to think that everybody
would ideally like to avoid divorce,
would ideally like to avoid divorce,
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apart from, I don't know,
Piers Morgan's wife, maybe?
Piers Morgan's wife, maybe?
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But it's a sad fact of modern life
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that 1 in 2 marriages in the
States ends in divorce,
States ends in divorce,
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with the rest of the world
not being far behind.
not being far behind.
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Now, you can be forgiven, perhaps
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for thinking that the arguments
that precede a marital breakup
that precede a marital breakup
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are not an ideal candidate
for mathematical investigation.
for mathematical investigation.
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For one thing, it's very hard to know
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what you should be measuring
or what you should be quantifying.
or what you should be quantifying.
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But this didn't stop a psychologist,
John Gottman, who did exactly that.
John Gottman, who did exactly that.
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Gottman observed hundreds of couples
having a conversation
having a conversation
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and recorded, well,
everything you can think of.
everything you can think of.
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So he recorded what was said
in the conversation,
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,
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
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was that one of the
most important predictors
most important predictors
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for whether or not a couple
is going to get divorced
is going to get divorced
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was how positive or negative each
partner was being in the conversation.
partner was being in the conversation.
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Now, couples that were very low-risk
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scored a lot more positive points
on Gottman's scale than negative.
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,
going to get divorced,
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they found themselves getting
into a spiral of negativity.
into a spiral of negativity.
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Now just by using these very simple ideas,
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Gottman and his group were able to predict
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whether a given couple
was going to get divorced
was going to get divorced
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with a 90 percent accuracy.
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But it wasn't until he teamed up
with a mathematician, James Murray,
with a mathematician, James Murray,
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that they really started to understand
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what causes these negativity spirals
and how they occur.
and how they occur.
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And the results that they found
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I think are just incredibly
impressively simple and interesting.
impressively simple and interesting.
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So these equations, they predict how
the wife or husband is going to respond
the wife or husband is going to respond
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in their next turn of the conversation,
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how positive or negative
they're going to be.
they're going to be.
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And these equations, they depend on
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the mood of the person
when they're on their own,
when they're on their own,
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the mood of the person when
they're with their partner,
they're with their partner,
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but most importantly, they depend on
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how much the husband and wife
influence one another.
influence one another.
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Now, I think it's important
to point out at this stage,
to point out at this stage,
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that these exact equations
have also been shown
have also been shown
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to be perfectly able at describing
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what happens between two
countries in an arms race.
countries in an arms race.
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(Laughter)
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So that -- an arguing couple
spiraling into negativity
spiraling into negativity
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and teetering on the brink of divorce --
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is actually mathematically equivalent to
the beginning of a nuclear war.
the beginning of a nuclear war.
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(Laughter)
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But the really important term
in this equation
in this equation
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is the influence that people
have on one another,
have on one another,
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14:47
and in particular, something called
the negativity threshold.
the negativity threshold.
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Now, the negativity threshold,
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you can think of as
how annoying the husband can be
how annoying the husband can be
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before the wife starts to get
really pissed off, and vice versa.
really pissed off, and vice versa.
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Now, I always thought that good marriages
were about compromise and understanding
were about compromise and understanding
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and allowing the person to
have the space to be themselves.
have the space to be themselves.
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So I would have thought that perhaps
the most successful relationships
the most successful relationships
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were ones where there was
a really high negativity threshold.
a really high negativity threshold.
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15:16
Where couples let things go
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15:17
and only brought things up if
they really were a big deal.
they really were a big deal.
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15:20
But actually, the mathematics
and subsequent findings by the team
and subsequent findings by the team
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have shown the exact opposite is true.
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The best couples,
or the most successful couples,
or the most successful couples,
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15:29
are the ones with a really low
negativity threshold.
negativity threshold.
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These are the couples that don't
let anything go unnoticed
let anything go unnoticed
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and allow each other
some room to complain.
some room to complain.
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15:40
These are the couples that are continually
trying to repair their own relationship,
trying to repair their own relationship,
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that have a much more positive
outlook on their marriage.
outlook on their marriage.
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Couples that don't let things go
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15:50
and couples that don't let trivial things
end up being a really big deal.
end up being a really big deal.
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15:56
Now of course, it takes bit more than
just a low negativity threshold
just a low negativity threshold
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and not compromising to
have a successful relationship.
have a successful relationship.
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16:06
But I think that it's quite interesting
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to know that there is really
mathematical evidence
mathematical evidence
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to say that you should never
let the sun go down on your anger.
let the sun go down on your anger.
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So those are my top three tips
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of how maths can help you
with love and relationships.
with love and relationships.
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But I hope
that aside from their use as tips,
that aside from their use as tips,
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they also give you a little bit of insight
into the power of mathematics.
into the power of mathematics.
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Because for me, equations
and symbols aren't just a thing.
and symbols aren't just a thing.
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They're a voice that speaks out
about the incredible richness of nature
about the incredible richness of nature
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and the startling simplicity
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in the patterns that twist and turn
and warp and evolve all around us,
and warp and evolve all around us,
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16:41
from how the world works to how we behave.
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So I hope that perhaps,
for just a couple of you,
for just a couple of you,
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a little bit of insight into
the mathematics of love
the mathematics of love
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can persuade you to have
a little bit more love for mathematics.
a little bit more love for mathematics.
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Thank you.
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(Applause)
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ABOUT THE SPEAKER
Hannah Fry - Complexity theoristHannah Fry researches the trends in our civilization and ways we can forecast its future.
Why you should listen
Hannah Fry completed her PhD in fluid dynamics in early 2011 with an emphasis on how liquid droplets move. Then, after working as an aerodynamicist in the motorsport industry, she began work on an interdisciplinary project in complexity sciences at University College London. Hannah’s current research focusses on discovering new connections between mathematically described systems and human interaction at the largest scale.
Fry is the author of the TED Book, The Mathematics of Love: Patterns, Proofs, and the Search for the Ultimate Equation.
Hannah Fry | Speaker | TED.com