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← The mathematics of love

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.

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Showing Revision 33 created 02/28/2017 by Krystian Aparta.

  1. Today I want to talk to you
    about the mathematics of love.
  2. Now, I think that we can all agree
  3. that mathematicians
    are famously excellent at finding love.
  4. (Laughter)

  5. But it's not just because
    of our dashing personalities,

  6. superior conversational skills
    and excellent pencil cases.
  7. It's also because we've actually done
    an awful lot of work into the maths
  8. of how to find the perfect partner.
  9. Now, in my favorite paper
    on the subject, which is entitled,

  10. "Why I Don't Have a Girlfriend" --
  11. (Laughter)

  12. Peter Backus tries to rate
    his chances of finding love.

  13. Now, Peter's not a very greedy man.
  14. Of all of the available women in the UK,
  15. all Peter's looking for
    is somebody who lives near him,
  16. somebody in the right age range,
  17. somebody with a university degree,
  18. somebody he's likely to get on well with,
  19. somebody who's likely to be attractive,
  20. somebody who's likely
    to find him attractive.
  21. (Laughter)

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

  23. (Laughter)

  24. It's not looking very good, is it Peter?

  25. Now, just to put that into perspective,
  26. that's about 400 times fewer
    than the best estimates
  27. of how many intelligent
    extraterrestrial life forms there are.
  28. And it also gives Peter
    a 1 in 285,000 chance
  29. of bumping into any one
    of these special ladies
  30. on a given night out.
  31. I'd like to think
    that's why mathematicians
  32. don't really bother
    going on nights out anymore.
  33. The thing is that I personally
    don't subscribe

  34. to such a pessimistic view.
  35. Because I know,
    just as well as all of you do,
  36. that love doesn't really work like that.
  37. Human emotion isn't neatly ordered
    and rational and easily predictable.
  38. But I also know that that doesn't mean
  39. that mathematics hasn't got something
    that it can offer us,
  40. because, love, as with most of life,
    is full of patterns
  41. and mathematics is, ultimately,
    all about the study of patterns.
  42. Patterns from predicting the weather
    to the fluctuations in the stock market,
  43. to the movement of the planets
    or the growth of cities.
  44. And if we're being honest,
    none of those things
  45. are exactly neatly ordered
    and easily predictable, either.
  46. Because I believe that mathematics
    is so powerful that it has the potential
  47. to offer us a new way of looking
    at almost anything.
  48. Even something as mysterious as love.
  49. And so, to try to persuade you
  50. of how totally amazing, excellent
    and relevant mathematics is,
  51. I want to give you my top three
    mathematically verifiable tips for love.
  52. (Laughter)

  53. OK, so Top Tip #1:

  54. How to win at online dating.
  55. So my favorite online dating
    website is OkCupid,
  56. not least because it was started
    by a group of mathematicians.
  57. Now, because they're mathematicians,
  58. they have been collecting data
  59. on everybody who uses their site
    for almost a decade.
  60. And they've been trying
    to search for patterns
  61. in the way that we talk about ourselves
  62. and the way that we interact
    with each other
  63. on an online dating website.
  64. And they've come up with some
    seriously interesting findings.
  65. But my particular favorite
  66. is that it turns out
    that on an online dating website,
  67. how attractive you are
    does not dictate how popular you are,
  68. and actually, having people
    think that you're ugly
  69. can work to your advantage.
  70. (Laughter)

  71. Let me show you how this works.

  72. In a thankfully voluntary
    section of OkCupid,
  73. you are allowed to rate
    how attractive you think people are
  74. on a scale between one and five.
  75. Now, if we compare this score,
    the average score,
  76. to how many messages
    a selection of people receive,
  77. you can begin to get a sense
  78. of how attractiveness links to popularity
    on an online dating website.
  79. This is the graph the OkCupid guys
    have come up with.

  80. And the important thing to notice
    is that it's not totally true
  81. that the more attractive you are,
    the more messages you get.
  82. But the question arises then
    of what is it about people up here
  83. who are so much more popular
    than people down here,
  84. even though they have the same
    score of attractiveness?
  85. And the reason why is that it's not just
    straightforward looks that are important.
  86. So let me try to illustrate
    their findings with an example.
  87. So if you take someone like
    Portia de Rossi, for example,
  88. everybody agrees that Portia de Rossi
    is a very beautiful woman.
  89. Nobody thinks that she's ugly,
    but she's not a supermodel, either.
  90. If you compare Portia de Rossi
    to someone like Sarah Jessica Parker,
  91. now, a lot of people,
    myself included, I should say,
  92. think that Sarah Jessica Parker
    is seriously fabulous
  93. and possibly one
    of the most beautiful creatures
  94. to have ever have walked
    on the face of the Earth.
  95. But some other people,
    i.e., most of the Internet ...
  96. (Laughter)

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

  98. (Laughter)

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

  100. Jessica Parker or Portia de Rossi were,
  101. and you ask them to give
    them a score between one and five
  102. I reckon that they'd average out
    to have roughly the same score.
  103. But the way that people would vote
    would be very different.
  104. So Portia's scores would
    all be clustered around the four
  105. because everybody agrees
    that she's very beautiful,
  106. whereas Sarah Jessica Parker
    completely divides opinion.
  107. There'd be a huge spread in her scores.
  108. And actually it's this spread that counts.
  109. It's this spread
    that makes you more popular
  110. on an online Internet dating website.
  111. So what that means then
  112. is that if some people
    think that you're attractive,
  113. you're actually better off
  114. having some other people
    think that you're a massive minger.
  115. That's much better
    than everybody just thinking
  116. that you're the cute girl next door.
  117. Now, I think this begins
    to make a bit more sense

  118. when you think in terms of the people
    who are sending these messages.
  119. So let's say that you think
    somebody's attractive,
  120. but you suspect that other people
    won't necessarily be that interested.
  121. That means there's
    less competition for you
  122. and it's an extra incentive
    for you to get in touch.
  123. Whereas compare that
    to if you think somebody is attractive
  124. but you suspect that everybody
    is going to think they're attractive.
  125. Well, why would you bother
    humiliating yourself, let's be honest?
  126. But here's where the really
    interesting part comes.
  127. Because when people choose the pictures
    that they use on an online dating website,
  128. they often try to minimize the things
  129. that they think some people
    will find unattractive.
  130. The classic example is people
    who are, perhaps, a little bit overweight
  131. deliberately choosing
    a very cropped photo,
  132. (Laughter)

  133. or bald men, for example,

  134. deliberately choosing pictures
    where they're wearing hats.
  135. But actually this is the opposite
    of what you should do
  136. if you want to be successful.
  137. You should really, instead,
  138. play up to whatever it is
    that makes you different,
  139. even if you think that some people
    will find it unattractive.
  140. Because the people who fancy you
    are just going to fancy you anyway,
  141. and the unimportant losers who don't,
    well, they only play up to your advantage.
  142. OK, Top Tip #2:
    How to pick the perfect partner.

  143. So let's imagine then
    that you're a roaring success
  144. on the dating scene.
  145. But the question arises
    of how do you then convert that success
  146. into longer-term happiness,
  147. and in particular, how do you decide
    when is the right time to settle down?
  148. Now generally,
    it's not advisable to just cash in
  149. and marry the first person who comes along
    and shows you any interest at all.
  150. But, equally, you don't really
    want to leave it too long
  151. if you want to maximize your chance
    of long-term happiness.
  152. As my favorite author,
    Jane Austen, puts it,
  153. "An unmarried woman of seven and twenty
  154. can never hope to feel
    or inspire affection again."
  155. (Laughter)

  156. Thanks a lot, Jane.

  157. What do you know about love?
  158. (Laughter)

  159. So the question is then,

  160. how do you know when
    is the right time to settle down,
  161. given all the people
    that you can date in your lifetime?
  162. Thankfully, there's a rather delicious bit
    of mathematics that we can use
  163. to help us out here,
    called optimal stopping theory.
  164. So let's imagine, then,
  165. that you start dating when you're 15
  166. and ideally, you'd like to be married
    by the time that you're 35.
  167. And there's a number of people
  168. that you could potentially
    date across your lifetime,
  169. and they'll be at varying
    levels of goodness.
  170. Now the rules are that once
    you cash in and get married,
  171. you can't look ahead to see
    what you could have had,
  172. and equally, you can't go back
    and change your mind.
  173. In my experience at least,
  174. I find that typically people
    don't much like being recalled
  175. years after being passed up
    for somebody else, or that's just me.
  176. So the math says then
    that what you should do

  177. in the first 37 percent
    of your dating window,
  178. you should just reject everybody
    as serious marriage potential.
  179. (Laughter)

  180. And then, you should pick
    the next person that comes along

  181. that is better than everybody
    that you've seen before.
  182. So here's the example.
  183. Now if you do this, it can be
    mathematically proven, in fact,
  184. that this is the best possible way
  185. of maximizing your chances
    of finding the perfect partner.
  186. Now unfortunately, I have to tell you that
    this method does come with some risks.
  187. For instance, imagine
    if your perfect partner appeared
  188. during your first 37 percent.
  189. Now, unfortunately,
    you'd have to reject them.
  190. (Laughter)

  191. Now, if you're following the maths,

  192. I'm afraid no one else comes along
  193. that's better than anyone
    you've seen before,
  194. so you have to go on
    rejecting everyone and die alone.
  195. (Laughter)

  196. Probably surrounded by cats ...

  197. (Laughter)

  198. nibbling at your remains.

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

  200. that the first people that you dated
    in your first 37 percent
  201. are just incredibly dull,
    boring, terrible people.
  202. That's OK, because
    you're in your rejection phase,
  203. so that's fine, you can reject them.
  204. But then imagine
    the next person to come along
  205. is just marginally less boring,
    dull and terrible ...
  206. (Laughter)

  207. than everybody that you've seen before.

  208. Now, if you are following the maths,
    I'm afraid you have to marry them ...
  209. (Laughter)

  210. and end up in a relationship
    which is, frankly, suboptimal.

  211. Sorry about that.
  212. But I do think that there's an opportunity
    here for Hallmark to cash in on
  213. and really cater for this market.
  214. A Valentine's Day card like this.
  215. (Laughter)

  216. "My darling husband,
    you are marginally less terrible

  217. than the first 37 percent
    of people I dated."
  218. (Laughter)

  219. It's actually more romantic
    than I normally manage.

  220. (Laughter)

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

  222. but there's no other possible
    strategy that can do any better.
  223. And actually, in the wild,
    there are certain types of fish
  224. which follow and employ
    this exact strategy.
  225. So they reject every possible
    suitor that turns up
  226. in the first 37 percent
    of the mating season,
  227. and then they pick the next fish
    that comes along after that window
  228. that's, I don't know, bigger and burlier
  229. than all of the fish
    that they've seen before.
  230. I also think that subconsciously,
    humans, we do sort of do this anyway.
  231. We give ourselves a little bit of time
    to play the field,
  232. get a feel for the marketplace
    or whatever when we're young.
  233. And then we only start looking seriously
    at potential marriage candidates
  234. once we hit our mid-to-late 20s.
  235. I think this is conclusive proof,
    if ever it were needed,
  236. that everybody's brains are prewired
    to be just a little bit mathematical.
  237. OK, so that was Top Tip #2.

  238. Now, Top Tip #3: How to avoid divorce.
  239. OK, so let's imagine then
    that you picked your perfect partner
  240. and you're settling into
    a lifelong relationship with them.
  241. Now, I like to think that everybody
    would ideally like to avoid divorce,
  242. apart from, I don't know,
    Piers Morgan's wife, maybe?
  243. (Laughter)

  244. But it's a sad fact of modern life

  245. that one in two marriages
    in the States ends in divorce,
  246. with the rest of the world
    not being far behind.
  247. Now, you can be forgiven, perhaps
  248. for thinking that the arguments
    that precede a marital breakup
  249. are not an ideal candidate
    for mathematical investigation.
  250. For one thing, it's very hard to know
  251. what you should be measuring
    or what you should be quantifying.
  252. But this didn't stop a psychologist,
    John Gottman, who did exactly that.
  253. Gottman observed hundreds of couples
    having a conversation
  254. and recorded, well,
    everything you can think of.
  255. So he recorded what was said
    in the conversation,
  256. he recorded their skin conductivity,
  257. he recorded their facial expressions,
  258. their heart rates, their blood pressure,
  259. basically everything apart from whether
    or not the wife was actually always right,
  260. which incidentally she totally is.
  261. But what Gottman and his team found
  262. was that one of the most
    important predictors
  263. for whether or not a couple
    is going to get divorced
  264. was how positive or negative each partner
    was being in the conversation.
  265. Now, couples that were very low-risk

  266. scored a lot more positive points
    on Gottman's scale than negative.
  267. Whereas bad relationships,
  268. by which I mean,
    probably going to get divorced,
  269. they found themselves getting
    into a spiral of negativity.
  270. Now just by using these very simple ideas,
  271. Gottman and his group were able to predict
  272. whether a given couple
    was going to get divorced
  273. with a 90 percent accuracy.
  274. But it wasn't until he teamed up
    with a mathematician, James Murray,
  275. that they really started to understand
  276. what causes these negativity spirals
    and how they occur.
  277. And the results that they found,
  278. I think, are just incredibly
    impressively simple and interesting.
  279. So these equations predict how the wife
    or husband is going to respond
  280. in their next turn of the conversation,
  281. how positive or negative
    they're going to be.
  282. And these equations depend on
  283. the mood of the person
    when they're on their own,
  284. the mood of the person when
    they're with their partner,
  285. but most importantly, they depend on
  286. how much the husband and wife
    influence one another.
  287. Now, I think it's important
    to point out at this stage,

  288. that these exact equations
    have also been shown
  289. to be perfectly able at describing
  290. what happens between two countries
    in an arms race.
  291. (Laughter)

  292. So that an arguing couple
    spiraling into negativity

  293. and teetering on the brink of divorce
  294. is actually mathematically equivalent
    to the beginning of a nuclear war.
  295. (Laughter)

  296. But the really important term
    in this equation

  297. is the influence that people
    have on one another,
  298. and in particular, something called
    "the negativity threshold."
  299. Now, the negativity threshold,
  300. you can think of as
    how annoying the husband can be
  301. before the wife starts to get
    really pissed off, and vice versa.
  302. Now, I always thought that good marriages
    were about compromise and understanding
  303. and allowing the person
    to have the space to be themselves.
  304. So I would have thought that perhaps
    the most successful relationships
  305. were ones where there was
    a really high negativity threshold.
  306. Where couples let things go
  307. and only brought things up
    if they really were a big deal.
  308. But actually, the mathematics
    and subsequent findings by the team
  309. have shown the exact opposite is true.
  310. The best couples,
    or the most successful couples,
  311. are the ones with a really low
    negativity threshold.
  312. These are the couples
    that don't let anything go unnoticed
  313. and allow each other
    some room to complain.
  314. These are the couples that are continually
    trying to repair their own relationship,
  315. that have a much more positive
    outlook on their marriage.
  316. Couples that don't let things go
  317. and couples that don't let trivial things
    end up being a really big deal.
  318. Now of course, it takes a bit more
    than just a low negativity threshold

  319. and not compromising
    to have a successful relationship.
  320. But I think that it's quite interesting
  321. to know that there is really
    mathematical evidence
  322. to say that you should never
    let the sun go down on your anger.
  323. So those are my top three tips

  324. of how maths can help you
    with love and relationships.
  325. But I hope, that aside from
    their use as tips,
  326. they also give you a little bit of insight
    into the power of mathematics.
  327. Because for me, equations
    and symbols aren't just a thing.
  328. They're a voice that speaks out
    about the incredible richness of nature
  329. and the startling simplicity
  330. in the patterns that twist and turn
    and warp and evolve all around us,
  331. from how the world works to how we behave.
  332. So I hope that perhaps,
    for just a couple of you,
  333. a little bit of insight
    into the mathematics of love
  334. can persuade you to have
    a little bit more love for mathematics.
  335. Thank you.

  336. (Applause)