0:00:00.303,0:00:04.941
Today I want to talk to you[br]about the mathematics of love.

0:00:04.941,0:00:06.681
Now, I think that we can all agree

0:00:06.681,0:00:11.597
that mathematicians[br]are famously excellent at finding love.

0:00:11.597,0:00:15.045
But it's not just[br]because of our dashing personalities,

0:00:15.045,0:00:19.544
superior conversational skills[br]and excellent pencil cases.

0:00:19.544,0:00:24.070
It's also because we've actually done[br]an awful lot of work into the maths

0:00:24.070,0:00:26.462
of how to find the perfect partner.

0:00:26.462,0:00:29.875
Now, in my favorite paper[br]on the subject, which is entitled,

0:00:29.875,0:00:33.371
"Why I Don't Have a Girlfriend" --[br](Laughter) --

0:00:33.371,0:00:37.091
Peter Backus tries to rate[br]his chances of finding love.

0:00:37.091,0:00:39.457
Now, Peter's not a very greedy man.

0:00:39.457,0:00:41.542
Of all of the available women in the U.K.,

0:00:41.542,0:00:44.955
all Peter's looking for[br]is somebody who lives near him,

0:00:44.955,0:00:46.856
somebody in the right age range,

0:00:46.856,0:00:49.666
somebody with a university degree,

0:00:49.666,0:00:51.824
somebody he's likely to get on well with,

0:00:51.824,0:00:53.900
somebody who's likely to be attractive,

0:00:53.900,0:00:56.438
somebody who's likely [br]to find him attractive.

0:00:56.438,0:00:59.441
(Laughter)

0:00:59.441,0:01:04.427
And comes up with an estimate[br]of 26 women in the whole of the UK.

0:01:05.441,0:01:07.602
It's not looking very good, [br]is it Peter?

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Now, just to put that into perspective,

0:01:09.469,0:01:12.574
that's about 400 times fewer[br]than the best estimates

0:01:12.574,0:01:16.799
of how many intelligent[br]extraterrestrial life forms there are.

0:01:16.799,0:01:21.676
And it also gives Peter[br]a 1 in 285,000 chance

0:01:21.676,0:01:23.902
of bumping into any one[br]of these special ladies

0:01:23.902,0:01:25.288
on a given night out.

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I'd like to think[br]that's why mathematicians

0:01:27.491,0:01:30.915
don't really bother[br]going on nights out anymore.

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The thing is that I personally

0:01:32.644,0:01:35.373
don't subscribe[br]to such a pessimistic view.

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Because I know,[br]just as well as all of you do,

0:01:37.602,0:01:40.194
that love doesn't really work like that.

0:01:40.194,0:01:45.304
Human emotion isn't neatly ordered[br]and rational and easily predictable.

0:01:45.304,0:01:47.711
But I also know that that doesn't mean

0:01:47.711,0:01:51.015
that mathematics hasn't got something[br]that it can offer us

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because, love, as with most of life,[br]is full of patterns

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and mathematics is, ultimately,[br]all about the study of patterns.

0:01:59.042,0:02:03.345
Patterns from predicting the weather[br]to the fluctuations in the stock market,

0:02:03.345,0:02:06.750
to the movement of the planets[br]or the growth of cities.

0:02:06.750,0:02:09.454
And if we're being honest,[br]none of those things

0:02:09.454,0:02:12.850
are exactly neatly ordered[br]and easily predictable, either.

0:02:12.850,0:02:17.877
Because I believe that mathematics[br]is so powerful that it has the potential

0:02:17.877,0:02:21.631
to offer us a new way of looking[br]at almost anything.

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Even something as mysterious as love.

0:02:25.187,0:02:26.675
And so, to try to persuade you

0:02:26.675,0:02:31.236
of how totally amazing, excellent[br]and relevant mathematics is,

0:02:31.236,0:02:39.220
I want to give you my top three[br]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 [br]website is OkCupid,

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not least because it was started[br]by a group of mathematicians.

0:02:53.574,0:02:55.343
Now, because they're mathematicians,

0:02:55.343,0:02:57.083
they have been collecting data

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on everybody who uses their site[br]for almost a decade.

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And they've been trying [br]to search for patterns

0:03:02.200,0:03:04.067
in the way that we talk about ourselves

0:03:04.067,0:03:06.184
and the way that we [br]interact with each other

0:03:06.184,0:03:07.876
on an online dating website.

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And they've come up with some[br]seriously interesting findings.

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But my particular favorite

0:03:12.447,0:03:15.827
is that it turns out[br]that on an online dating website,

0:03:15.827,0:03:21.672
how attractive you are[br]does not dictate how popular you are,

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and actually, having people[br]think that you're ugly

0:03:25.391,0:03:28.260
can work to your advantage.

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Let me show you how this works.

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In a thankfully voluntary[br]section of OkCupid,

0:03:34.565,0:03:37.565
you are allowed to rate[br]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, [br]the average score,

0:03:43.362,0:03:46.216
to how many messages a[br]selection of people receive,

0:03:46.216,0:03:47.876
you can begin to get a sense

0:03:47.876,0:03:51.854
of how attractiveness links to popularity[br]on an online dating website.

0:03:51.854,0:03:55.177
This is the graph that the OkCupid guys[br]have come up with.

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And the important thing to notice[br]is that it's not totally true

0:03:58.230,0:04:01.058
that the more attractive you are,[br]the more messages you get.

0:04:01.058,0:04:04.932
But the question arises then[br]of what is it about people up here

0:04:04.932,0:04:09.566
who are so much more popular[br]than people down here,

0:04:09.566,0:04:12.170
even though they have the[br]same score of attractiveness?

0:04:12.170,0:04:16.699
And the reason why is that it's not just [br]straightforward looks that are important.

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So let me try to illustrate their[br]findings with an example.

0:04:19.477,0:04:23.607
So if you take someone like[br]Portia de Rossi, for example,

0:04:23.607,0:04:28.279
everybody agrees that Portia de Rossi[br]is a very beautiful woman.

0:04:28.279,0:04:31.940
Nobody thinks that she's ugly,[br]but she's not a supermodel, either.

0:04:31.940,0:04:36.561
If you compare Portia de Rossi[br]to someone like Sarah Jessica Parker,

0:04:36.561,0:04:39.846
now, a lot of people, [br]myself included, I should say,

0:04:39.846,0:04:44.320
think that Sarah Jessica Parker[br]is seriously fabulous

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and possibly one of the[br]most beautiful creatures

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to have ever have walked [br]on the face of the Earth.

0:04:49.639,0:04:55.660
But some other people, [br]i.e., most of the Internet,

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seem to think that she looks [br]a bit like a horse. (Laughter)

0:05:01.838,0:05:05.098
Now, I think that if you ask people[br]how attractive they thought

0:05:05.098,0:05:07.260
Sarah Jessica Parker [br]or Portia de Rossi were,

0:05:07.260,0:05:10.213
and you ask them to give [br]them a score between 1 and 5,

0:05:10.213,0:05:13.218
I reckon that they'd average out[br]to have roughly the same score.

0:05:13.218,0:05:15.979
But the way that people would vote[br]would be very different.

0:05:15.979,0:05:18.522
So Portia's scores would[br]all be clustered around the 4

0:05:18.522,0:05:20.982
because everybody agrees [br]that she's very beautiful,

0:05:20.982,0:05:23.643
whereas Sarah Jessica Parker[br]completely divides opinion.

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There'd be a huge spread in her scores.

0:05:26.067,0:05:28.389
And actually it's this spread that counts.

0:05:28.389,0:05:30.865
It's this spread[br]that makes you more popular

0:05:30.865,0:05:33.065
on an online Internet dating website.

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So what that means then

0:05:34.236,0:05:36.735
is that if some people[br]think that you're attractive,

0:05:36.735,0:05:38.683
you're actually better off

0:05:38.683,0:05:43.935
having some other people[br]think that you're a massive minger.

0:05:43.935,0:05:46.173
That's much better[br]than everybody just thinking

0:05:46.173,0:05:47.904
that you're the cute girl next door.

0:05:47.904,0:05:50.153
Now, I think this begins [br]makes a bit more sense

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when you think in terms of the people[br]who are sending these messages.

0:05:53.387,0:05:55.738
So let's say that you think[br]somebody's attractive,

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but you suspect that other people[br]won't necessarily be that interested.

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That means there's[br]less competition for you

0:06:02.543,0:06:04.979
and it's an extra incentive[br]for you to get in touch.

0:06:04.979,0:06:07.803
Whereas compare that [br]to if you think somebody is attractive

0:06:07.803,0:06:11.060
but you suspect that everybody [br]is going to think they're attractive.

0:06:11.060,0:06:14.624
Well, why would you bother [br]humiliating yourself, let's be honest?

0:06:14.628,0:06:16.904
Here's where the really[br]interesting part comes.

0:06:16.904,0:06:21.378
Because when people choose the pictures[br]that they use on an online dating website,

0:06:21.378,0:06:23.670
they often try to minimize the things

0:06:23.670,0:06:27.160
that they think some people [br]will find unattractive.

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The classic example is people[br]who are, perhaps, a little bit overweight

0:06:31.457,0:06:34.921
deliberately choosing [br]a very cropped photo,

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or bald men, for example,

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deliberately choosing pictures[br]where they're wearing hats.

0:06:39.477,0:06:42.142
But actually this is the opposite [br]of what you should do

0:06:42.142,0:06:43.536
if you want to be successful.

0:06:43.536,0:06:48.347
You should really, instead, play up to [br]whatever it is that makes you different,

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even if you think that some people[br]will find it unattractive.

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Because the people who fancy you[br]are just going to fancy you anyway,

0:06:55.544,0:07:00.485
and the unimportant losers who don't,[br]well, they only play up to your advantage.

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Okay, Top Tip #2:[br]How to pick the perfect partner.

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So let's imagine then[br]that you're a roaring success

0:07:05.624,0:07:07.092
on the dating scene.

0:07:07.092,0:07:11.395
But the question arises [br]of how do you then convert that success

0:07:11.395,0:07:15.179
into longer-term happiness[br]and in particular,

0:07:15.186,0:07:19.437
how do you decide[br]when is the right time to settle down?

0:07:19.437,0:07:22.269
Now generally,[br]it's not advisable to just cash in

0:07:22.269,0:07:24.292
and marry the first person[br]who comes along

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and shows you any interest at all.

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

0:07:29.659,0:07:32.661
if you want to maximize your [br]chance of long-term happiness.

0:07:32.661,0:07:35.843
As my favorite author, [br]Jane Austen, puts it,

0:07:35.843,0:07:38.061
"An unmarried woman of seven and twenty

0:07:38.061,0:07:41.726
can never hope to feel or[br]inspire affection again."

0:07:41.726,0:07:43.718
(Laughter)

0:07:43.718,0:07:47.272
Thanks a lot, Jane.[br]What do you know about love?

0:07:47.836,0:07:49.391
So the question is then,

0:07:49.391,0:07:51.996
how do you know when [br]is the right time to settle down

0:07:51.996,0:07:54.675
given all the people [br]that you can date in your lifetime?

0:07:54.675,0:07:58.350
Thankfully, there's a rather delicious bit[br]of mathematics that we can use

0:07:58.350,0:08:00.874
to help us out here, called[br]optimal stopping theory.

0:08:00.874,0:08:02.774
So let's imagine then,

0:08:02.774,0:08:05.044
that you start dating when you're 15

0:08:05.044,0:08:09.128
and ideally, you'd like to be married[br]by the time that you're 35.

0:08:09.128,0:08:10.668
And there's a number of people

0:08:10.668,0:08:13.154
that you could potentially[br]date across your lifetime,

0:08:13.154,0:08:15.308
and they'll be at varying [br]levels of goodness.

0:08:15.308,0:08:18.199
Now the rules are that once [br]you cash in and get married,

0:08:18.199,0:08:20.902
you can't look ahead to see[br]what you could have had,

0:08:20.902,0:08:23.512
and equally, you can't go back[br]and change your mind.

0:08:23.512,0:08:25.082
In my experience at least,

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I find that typically people don't[br]much like being recalled

0:08:27.904,0:08:33.320
years after being passed up [br]for somebody else, or that's just me.

0:08:33.320,0:08:36.527
So the math says then[br]that what you should do

0:08:36.527,0:08:39.558
in the first 37 percent [br]of your dating window,

0:08:39.558,0:08:43.999
you should just reject everybody[br]as serious marriage potential.

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(Laughter)

0:08:45.513,0:08:49.319
And then, you should pick the [br]next person that comes along

0:08:49.319,0:08:52.154
that is better than everybody [br]that you've seen before.

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So here's the example.

0:08:53.476,0:08:56.308
Now if you do this, it can be[br]mathematically proven, in fact,

0:08:56.308,0:08:58.975
that this is the best possible way

0:08:58.975,0:09:03.437
of maximizing your chances [br]of finding the perfect partner.

0:09:03.437,0:09:07.909
Now unfortunately, I have to tell you that[br]this method does come with some risks.

0:09:08.382,0:09:13.072
For instance, imagine if [br]your perfect partner appeared

0:09:13.072,0:09:16.226
during your first 37 percent.

0:09:16.226,0:09:18.939
Now, unfortunately, [br]you'd have to reject them.

0:09:18.939,0:09:21.652
(Laughter)

0:09:21.652,0:09:23.997
Now, if you're following the maths,

0:09:23.997,0:09:25.663
I'm afraid no one else comes along

0:09:25.663,0:09:27.790
that's better than anyone[br]you've seen before,

0:09:27.790,0:09:32.093
so you have to go on [br]rejecting everyone and die alone.

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(Laughter)

0:09:34.736,0:09:39.617
Probably surrounded by cats[br]nibbling at your remains.

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Okay, another risk is, [br]let's imagine, instead,

0:09:43.422,0:09:46.667
that the first people that you dated[br]in your first 37 percent

0:09:46.667,0:09:50.507
are just incredibly dull,[br]boring, terrible people.

0:09:50.507,0:09:53.232
Now, that's okay, because [br]you're in your rejection phase,

0:09:53.232,0:09:55.073
so thats fine, [br]you can reject them.

0:09:55.073,0:09:58.541
But then imagine, the next[br]person to come along

0:09:58.541,0:10:02.879
is just marginally less boring, [br]dull and terrible

0:10:02.879,0:10:04.761
than everybody that you've seen before.

0:10:04.761,0:10:08.963
Now, if you are following the maths,[br]I'm afraid you have to marry them

0:10:08.963,0:10:12.376
and end up in a relationship[br]which is, frankly, suboptimal.

0:10:12.376,0:10:13.459
Sorry about that.

0:10:13.459,0:10:15.659
But I do think that there's[br]an opportunity here

0:10:15.659,0:10:18.809
for Hallmark to cash in on[br]and really cater for this market.

0:10:18.809,0:10:20.899
A Valentine's Day card like this.[br](Laughter)

0:10:20.899,0:10:24.924
"My darling husband, you[br]are marginally less terrible

0:10:24.924,0:10:27.969
than the first 37 percent[br]of people I dated."

0:10:27.969,0:10:33.456
It's actually more romantic[br]than I normally manage.

0:10:33.456,0:10:38.138
Okay, so this method doesn't give[br]you a 100 percent success rate,

0:10:38.138,0:10:41.441
but there's no other possible[br]strategy that can do any better.

0:10:41.441,0:10:44.104
And actually, in the wild,[br]there are certain types

0:10:44.104,0:10:47.817
of fish which follow and[br]employ this exact strategy.

0:10:47.817,0:10:50.456
So they reject every possible [br]suitor that turns up

0:10:50.456,0:10:53.413
in the first 37 percent [br]of the mating season,

0:10:53.413,0:10:56.944
and then they pick the next fish[br]that comes along after that window

0:10:56.944,0:10:59.000
that's, I don't know, bigger and burlier

0:10:59.000,0:11:01.518
than all of the fish [br]that they've seen before.

0:11:01.518,0:11:06.196
I also think that subconsciously,[br]humans, we do sort of do this anyway.

0:11:06.196,0:11:09.613
We give ourselves a little bit of time[br]to play the field,

0:11:09.613,0:11:13.115
get a feel for the marketplace [br]or whatever when we're young.

0:11:13.115,0:11:18.023
And then we only start looking seriously[br]at potential marriage candidates

0:11:18.023,0:11:19.913
once we hit our mid-to-late 20s.

0:11:19.913,0:11:22.716
I think this is conclusive proof,[br]if ever it were needed,

0:11:22.716,0:11:27.222
that everybody's brains are prewired [br]to be just a little bit mathematical.

0:11:27.616,0:11:29.477
Okay, so that was Top Tip #2.

0:11:29.477,0:11:32.730
Now, Top Tip #3: How to avoid divorce.

0:11:32.730,0:11:35.868
Okay, so let's imagine then[br]that you picked your perfect partner

0:11:35.868,0:11:40.645
and you're settling into[br]a lifelong relationship with them.

0:11:40.645,0:11:44.719
Now, I like to think that everybody[br]would ideally like to avoid divorce,

0:11:44.719,0:11:49.085
apart from, I don't know, [br]Piers Morgan's wife, maybe?

0:11:50.185,0:11:52.475
But it's a sad fact of modern life

0:11:52.475,0:11:56.284
that 1 in 2 marriages in the[br]States ends in divorce,

0:11:56.284,0:11:59.585
with the rest of the world[br]not being far behind.

0:11:59.585,0:12:01.684
Now, you can be forgiven, perhaps

0:12:01.684,0:12:05.344
for thinking that the arguments[br]that precede a marital breakup

0:12:05.344,0:12:08.877
are not an ideal candidate[br]for mathematical investigation.

0:12:08.877,0:12:10.777
For one thing, it's very hard to know

0:12:10.777,0:12:13.834
what you should be measuring [br]or what you should be quantifying.

0:12:13.834,0:12:20.407
But this didn't stop a psychologist,[br]John Gottman, who did exactly that.

0:12:20.407,0:12:25.602
Gottman observed hundreds of couples[br]having a conversation

0:12:25.602,0:12:28.064
and recorded, well, [br]everything you can think of.

0:12:28.064,0:12:30.551
So he recorded what was said [br]in the conversation,

0:12:30.551,0:12:32.614
he recorded their skin conductivity,

0:12:32.614,0:12:34.534
he recorded their facial expressions,

0:12:34.534,0:12:36.874
their heart rates, their blood pressure,

0:12:36.874,0:12:43.324
basically everything apart from whether[br]or not the wife was actually always right,

0:12:43.324,0:12:46.348
which incidentally she totally is.

0:12:46.348,0:12:49.268
But what Gottman and his team found

0:12:49.268,0:12:51.772
was that one of the[br]most important predictors

0:12:51.772,0:12:53.922
for whether or not a couple[br]is going to get divorced

0:12:53.922,0:12:59.022
was how positive or negative each [br]partner was being in the conversation.

0:12:59.022,0:13:01.634
Now, couples that were very low-risk

0:13:01.634,0:13:05.861
scored a lot more positive points[br]on Gottman's scale than negative.

0:13:05.861,0:13:08.001
Whereas bad relationships,

0:13:08.001,0:13:10.793
by which I mean, probably[br]going to get divorced,

0:13:10.793,0:13:15.405
they found themselves getting [br]into a spiral of negativity.

0:13:15.405,0:13:17.758
Now just by using these very simple ideas,

0:13:17.758,0:13:20.260
Gottman and his group were able to predict

0:13:20.260,0:13:23.103
whether a given couple[br]was going to get divorced

0:13:23.103,0:13:25.758
with a 90 percent accuracy.

0:13:25.758,0:13:29.152
But it wasn't until he teamed up[br]with a mathematician, James Murray,

0:13:29.152,0:13:31.291
that they really started to understand

0:13:31.291,0:13:35.601
what causes these negativity spirals [br]and how they occur.

0:13:35.601,0:13:37.308
And the results that they found

0:13:37.308,0:13:41.667
I think are just incredibly[br]impressively simple and interesting.

0:13:41.667,0:13:46.005
So these equations, they predict how [br]the wife or husband is going to respond

0:13:46.005,0:13:47.971
in their next turn of the conversation,

0:13:47.971,0:13:50.099
how positive or negative[br]they're going to be.

0:13:50.099,0:13:51.896
And these equations, they depend on

0:13:51.896,0:13:54.242
the mood of the person [br]when they're on their own,

0:13:54.242,0:13:56.856
the mood of the person when[br]they're with their partner,

0:13:56.856,0:13:58.845
but most importantly, they depend on

0:13:58.845,0:14:01.824
how much the husband and wife[br]influence one another.

0:14:01.824,0:14:04.532
Now, I think it's important [br]to point out at this stage,

0:14:04.532,0:14:07.852
that these exact equations [br]have also been shown

0:14:07.852,0:14:10.498
to be perfectly able at describing

0:14:10.498,0:14:14.256
what happens between two[br]countries in an arms race.

0:14:14.256,0:14:16.394
(Laughter)

0:14:18.194,0:14:21.905
So that -- an arguing couple[br]spiraling into negativity

0:14:21.905,0:14:23.819
and teetering on the brink of divorce --

0:14:23.819,0:14:28.107
is actually mathematically equivalent to[br]the beginning of a nuclear war.

0:14:28.107,0:14:30.606
(Laughter)

0:14:30.606,0:14:33.159
But the really important term[br]in this equation

0:14:33.159,0:14:35.877
is the influence that people[br]have on one another,

0:14:35.877,0:14:38.900
and in particular, something called [br]the negativity threshhold.

0:14:38.900,0:14:40.579
Now, the negativity threshold,

0:14:40.579,0:14:45.072
you can think of as[br]how annoying the husband can be

0:14:45.072,0:14:49.254
before the wife starts to get [br]really pissed off, and vice versa.

0:14:49.254,0:14:54.408
Now, I always thought that good marriages[br]were about compromise and understanding

0:14:54.408,0:14:57.261
and allowing the person to [br]have the space to be themselves.

0:14:57.261,0:15:00.558
So I would have thought that perhaps[br]the most successful relationships

0:15:00.558,0:15:04.024
were ones where there was[br]a really high negativity threshold.

0:15:04.024,0:15:05.692
Where couples let things go[br]

0:15:05.692,0:15:08.487
and only brought things up if [br]they really were a big deal.

0:15:08.487,0:15:12.023
But actually, the mathematics[br]and subsequent findings by the team

0:15:12.023,0:15:15.318
have shown the exact opposite is true.

0:15:15.318,0:15:17.707
The best couples,[br]or the most successful couples,

0:15:17.707,0:15:21.519
are the ones with a really low [br]negativity threshold.

0:15:21.519,0:15:25.378
These are the couples that don't[br]let anything go unnoticed

0:15:25.378,0:15:28.399
and allow each other [br]some room to complain.

0:15:28.399,0:15:33.733
These are the couples that are continually[br]trying to repair their own relationship,

0:15:33.733,0:15:36.418
that have a much more positive[br]outlook on their marriage.

0:15:36.418,0:15:38.516
Couples that don't let things go

0:15:38.516,0:15:44.426
and couples that don't let trivial things[br]end up being a really big deal.

0:15:44.426,0:15:50.023
Now of course, it takes bit more than [br]just a low negativity threshold

0:15:50.023,0:15:54.162
and not compromising to[br]have a successful relationship.

0:15:54.162,0:15:56.650
But I think that it's quite interesting

0:15:56.650,0:15:59.053
to know that there is really[br]mathematical evidence

0:15:59.053,0:16:02.480
to say that you should never[br]let the sun go down on your anger.

0:16:02.480,0:16:04.188
So those are my top three tips

0:16:04.188,0:16:07.383
of how maths can help you[br]with love and relationships.

0:16:07.383,0:16:09.826
But I hope that [br]aside from the useless tips,

0:16:09.826,0:16:13.678
I also give you a little bit of insight[br]into the power of mathematics.

0:16:13.678,0:16:18.293
Because for me, equations [br]and symbols aren't just a thing.

0:16:18.293,0:16:23.119
They're a voice that speaks out[br]about the incredible richness of nature

0:16:23.119,0:16:24.929
and the startling simplicity

0:16:24.929,0:16:29.384
in the patterns that twist and turn[br]and warp and evolve all around us,

0:16:29.384,0:16:32.187
from how the world works to how we behave.

0:16:32.187,0:16:34.485
So I hope that perhaps,[br]for just a couple of you,

0:16:34.485,0:16:36.926
a little bit of insight into[br]the mathematics of love

0:16:36.926,0:16:40.134
can persuade you to have [br]a little bit more love for mathematics.

0:16:40.134,0:16:41.521
Thank you.

0:16:41.521,0:16:43.815
(Applause)