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Today I want to talk to you
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.

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(Laughter)

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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" --

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(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 UK,

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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.

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(Laughter)

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And comes up with an estimate
of 26 women in the whole of the UK.

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(Laughter)

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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

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don't really bother
going on nights out anymore.

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The thing is that I personally
don't subscribe

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to such a pessimistic view.

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Because I know,
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.

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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

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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

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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,

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I want to give you my top three
mathematically verifiable tips for love.

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(Laughter)

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OK, 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

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is that it turns out
that on an online dating website,

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how attractive you are
does not dictate how popular you are,

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and actually, having people
think that you're ugly

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can work to your advantage.

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(Laughter)

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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 one and five.

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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

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of how attractiveness links to popularity
on an online dating website.

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This is the graph the OkCupid guys
have 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
straightforward 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,

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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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(Laughter)

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seem to think that she looks
a bit like a horse.

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(Laughter)

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Now, I think that if you ask people
how attractive they thought

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Jessica Parker or Portia de Rossi were,

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

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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 four

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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
to make 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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But 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

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deliberately choosing
a very cropped photo,

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(Laughter)

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or bald men, for example,

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deliberately choosing pictures
where they're wearing hats.

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But actually this is the opposite
of what you should do

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if you want to be successful.

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You should really, instead,

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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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OK, Top Tip #2:
How to pick the perfect partner.

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So let's imagine then
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

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into longer-term happiness,

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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

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

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

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if you want to maximize your chance
of long-term happiness.

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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."

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(Laughter)

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Thanks a lot, Jane.

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What do you know about love?

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(Laughter)

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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,

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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

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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,

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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,

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you can't look ahead to see
what you could have had,

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and equally, you can't go back
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

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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,

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you should just reject everybody
as serious marriage potential.

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(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.

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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,

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that this is the best possible way

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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 appeared

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during your first 37 percent.

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Now, unfortunately,
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,

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so you have to go on
rejecting everyone and die alone.

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(Laughter)

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Probably surrounded by cats ...

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(Laughter)

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nibbling at your remains.

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OK, another risk is,
let's imagine, instead,

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that the first people that you dated
in your first 37 percent

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are just incredibly dull,
boring, terrible people.

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That's OK, because
you're in your rejection phase,

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so that's fine, you can reject them.

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But then imagine
the next person to come along

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is just marginally less boring,
dull and terrible ...

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(Laughter)

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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 ...

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(Laughter)

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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 for Hallmark to cash in on

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and really cater for this market.

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A Valentine's Day card like this.

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(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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(Laughter)

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It's actually more romantic
than I normally manage.

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(Laughter)

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OK, so this method doesn't give you
a 100 percent success rate,

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but there's no other possible
strategy that can do any better.

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And actually, in the wild,
there are certain types of fish

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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

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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,

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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

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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,

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that everybody's brains are prewired
to be just a little bit mathematical.

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OK, so that was Top Tip #2.

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Now, Top Tip #3: How to avoid divorce.

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OK, 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.

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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?

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(Laughter)

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But it's a sad fact of modern life

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that one in two marriages
in the States ends in divorce,

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with the rest of the world
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

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are not an ideal candidate
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.

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But this didn't stop a psychologist,
John Gottman, who did exactly that.

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Gottman observed hundreds of couples
having a conversation

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and recorded, well,
everything you can think of.

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So he recorded what was said
in the conversation,

00:12:30.455 --> 00:12:32.748
he recorded their skin conductivity,

00:12:32.772 --> 00:12:34.835
he recorded their facial expressions,

00:12:34.859 --> 00:12:36.850
their heart rates, their blood pressure,

00:12:36.874 --> 00:12:43.110
basically everything apart from whether
or not the wife was actually always right,

00:12:43.134 --> 00:12:46.325
which incidentally she totally is.

00:12:46.349 --> 00:12:48.998
But what Gottman and his team found

00:12:49.022 --> 00:12:52.037
was that one of the most
important predictors

00:12:52.061 --> 00:12:54.543
for whether or not a couple
is going to get divorced

00:12:54.567 --> 00:12:59.190
was how positive or negative each partner
was being in the conversation.

NOTE Paragraph

00:12:59.214 --> 00:13:01.544
Now, couples that were very low-risk

00:13:01.568 --> 00:13:05.837
scored a lot more positive points
on Gottman's scale than negative.

00:13:05.861 --> 00:13:08.402
Whereas bad relationships,

00:13:08.426 --> 00:13:11.173
by which I mean,
probably going to get divorced,

00:13:11.197 --> 00:13:15.554
they found themselves getting
into a spiral of negativity.

00:13:15.578 --> 00:13:17.838
Now just by using these very simple ideas,

00:13:17.862 --> 00:13:20.333
Gottman and his group were able to predict

00:13:20.357 --> 00:13:23.079
whether a given couple
was going to get divorced

00:13:23.103 --> 00:13:25.288
with a 90 percent accuracy.

00:13:26.005 --> 00:13:29.294
But it wasn't until he teamed up
with a mathematician, James Murray,

00:13:29.318 --> 00:13:31.209
that they really started to understand

00:13:31.233 --> 00:13:35.727
what causes these negativity spirals
and how they occur.

00:13:35.751 --> 00:13:37.284
And the results that they found,

00:13:37.308 --> 00:13:41.957
I think, are just incredibly
impressively simple and interesting.

00:13:41.981 --> 00:13:46.544
So these equations predict how the wife
or husband is going to respond

00:13:46.568 --> 00:13:48.456
in their next turn of the conversation,

00:13:48.480 --> 00:13:50.613
how positive or negative
they're going to be.

00:13:50.637 --> 00:13:52.022
And these equations depend on

00:13:52.046 --> 00:13:54.352
the mood of the person
when they're on their own,

00:13:54.376 --> 00:13:56.990
the mood of the person when
they're with their partner,

00:13:57.014 --> 00:13:58.739
but most importantly, they depend on

00:13:58.763 --> 00:14:01.795
how much the husband and wife
influence one another.

NOTE Paragraph

00:14:02.115 --> 00:14:04.722
Now, I think it's important
to point out at this stage,

00:14:04.746 --> 00:14:08.255
that these exact equations
have also been shown

00:14:08.279 --> 00:14:10.474
to be perfectly able at describing

00:14:10.498 --> 00:14:14.232
what happens between two countries
in an arms race.

NOTE Paragraph

00:14:15.010 --> 00:14:18.098
(Laughter)

NOTE Paragraph

00:14:18.300 --> 00:14:21.881
So that an arguing couple
spiraling into negativity

00:14:21.905 --> 00:14:23.810
and teetering on the brink of divorce

00:14:23.834 --> 00:14:28.083
is actually mathematically equivalent
to the beginning of a nuclear war.

NOTE Paragraph

00:14:28.107 --> 00:14:30.997
(Laughter)

NOTE Paragraph

00:14:31.021 --> 00:14:33.334
But the really important term
in this equation

00:14:33.358 --> 00:14:35.853
is the influence that people
have on one another,

00:14:35.877 --> 00:14:39.134
and in particular, something called
"the negativity threshold."

00:14:39.158 --> 00:14:40.890
Now, the negativity threshold,

00:14:40.914 --> 00:14:45.541
you can think of as
how annoying the husband can be

00:14:45.565 --> 00:14:49.828
before the wife starts to get
really pissed off, and vice versa.

00:14:49.852 --> 00:14:54.384
Now, I always thought that good marriages
were about compromise and understanding

00:14:54.408 --> 00:14:57.170
and allowing the person
to have the space to be themselves.

00:14:57.194 --> 00:15:00.547
So I would have thought that perhaps
the most successful relationships

00:15:00.571 --> 00:15:03.851
were ones where there was
a really high negativity threshold.

00:15:03.875 --> 00:15:05.668
Where couples let things go

00:15:05.692 --> 00:15:08.463
and only brought things up
if they really were a big deal.

00:15:08.487 --> 00:15:12.738
But actually, the mathematics
and subsequent findings by the team

00:15:12.762 --> 00:15:15.294
have shown the exact opposite is true.

00:15:15.799 --> 00:15:18.108
The best couples,
or the most successful couples,

00:15:18.132 --> 00:15:21.495
are the ones with a really low
negativity threshold.

00:15:21.519 --> 00:15:25.153
These are the couples
that don't let anything go unnoticed

00:15:25.177 --> 00:15:28.375
and allow each other
some room to complain.

00:15:28.399 --> 00:15:33.633
These are the couples that are continually
trying to repair their own relationship,

00:15:33.657 --> 00:15:36.400
that have a much more positive
outlook on their marriage.

00:15:36.424 --> 00:15:38.492
Couples that don't let things go

00:15:38.516 --> 00:15:43.396
and couples that don't let trivial things
end up being a really big deal.

NOTE Paragraph

00:15:44.426 --> 00:15:49.684
Now of course, it takes a bit more
than just a low negativity threshold

00:15:49.708 --> 00:15:54.076
and not compromising
to have a successful relationship.

00:15:54.100 --> 00:15:56.626
But I think that it's quite interesting

00:15:56.650 --> 00:15:59.004
to know that there is really
mathematical evidence

00:15:59.028 --> 00:16:02.456
to say that you should never
let the sun go down on your anger.

NOTE Paragraph

00:16:02.480 --> 00:16:04.164
So those are my top three tips

00:16:04.188 --> 00:16:07.359
of how maths can help you
with love and relationships.

00:16:07.383 --> 00:16:09.778
But I hope, that aside from
their use as tips,

00:16:09.802 --> 00:16:13.904
they also give you a little bit of insight
into the power of mathematics.

00:16:13.928 --> 00:16:18.269
Because for me, equations
and symbols aren't just a thing.

00:16:18.684 --> 00:16:23.095
They're a voice that speaks out
about the incredible richness of nature

00:16:23.119 --> 00:16:24.905
and the startling simplicity

00:16:24.929 --> 00:16:29.742
in the patterns that twist and turn
and warp and evolve all around us,

00:16:29.766 --> 00:16:32.346
from how the world works to how we behave.

00:16:32.370 --> 00:16:34.680
So I hope that perhaps,
for just a couple of you,

00:16:34.704 --> 00:16:37.189
a little bit of insight
into the mathematics of love

00:16:37.213 --> 00:16:40.510
can persuade you to have
a little bit more love for mathematics.

NOTE Paragraph

00:16:40.534 --> 00:16:41.733
Thank you.

NOTE Paragraph

00:16:41.757 --> 00:16:48.757
(Applause)