Maths to maintain a relationship

The path of true love never runs smooth, or so the saying goes. But is there a mathematical formula for a long and happy relationship? University College London's Hannah Fry has just published a book on the subject so she clearly believes that there is, as she explains to Chris Smith...

Chris - We're talking about the science of love in the anticipation of Valentine's Day this week. So, when it comes to maths Hannah, in the words of Tina Turner, "What's love got to do with it?" Do you like Tina Turner by the way?

Hannah - I'm an enormous fan, yes especially now. So, maths can't really help us describe the emotional side of love I suppose. It's very difficult to formulate the thrill of romance and do a set of equations. But that doesn't mean that it doesn't have an involvement because the way that we date each other, the way that we act through our love life, the way that we find partners - all has lots of patterns associated with it. those patterns, maths is uniquely placed to be able to describe and investigate them.

Chris - Tell us about some of the most important ones.

Hannah - Well, so my personal favourite is something known as the stable marriage problem which you can reformulate to look at a group of friends who are in a bar and deciding whether or not to approach people they find attractive at the party. And so it turns out, you can prove it mathematically that if you are the people who do the approaching rather than sit back and wait for suitors to come to you, you will always, always end up much better off than just being the wall flower in the corner.

Chris - You've got to sort of be in it to win it so to speak?

Hannah - Yes, exactly. It kind of make sense because if you think that - if you go out, be proactive and you go out to get what you want, you're going to end up with the best person whereas if you stand back and wait for people to come to you, you'll end up with the least bad person who approaches you.

Chris - I got a Valentine's Day card once from somebody and it had two horses having dinner and it had one of them saying, "I want a stable relationship" and the other one said, "I'll have sex anywhere". That's just me. Now, what about the wedding? Let's assume Hannah that actually, this mating and dating game does go well and your maths does enable you to meet a significant number of partners and, eventually, one of them is compatible. Where can maths fit into the wedding plans?

Hannah - Yes. So, the idea behind the book was to go through a whole story of all different phases of love. And so, the wedding planning is one of them. So for example, if you're having a terrible time deciding on your guest list for your wedding and having got married 18 months ago, I know how terrible it can be. You want to be really careful in terms of the number of people you invite because you don't want to end up overfilling your venue or equally, you don't want to end up with loads of empty spaces when you could've invited more people. Equally, sending out invitations in phases, people get offended, and so on. I mean, this is a minefield.

There is one way that you can use maths to help you decide how many people to invite. And that's by assigning a probability to each person that you expect to arrive and looking at it in those terms to adding up a score as you go down your list and then cutting off when you hit the capacity of your venue. If you do that on average, you'll end up with the right number of people coming up to your wedding.

Chris - Does this kind of rob the occasion of romance a little bit to think there's a mathematical formula behind where you are on the guest list?

Hannah - No. I think it's very practical actually. It better be to be on the guest list than be left out due to a misjudgement.

Chris - What about where you sit people though. There must be some probabilities and permutations. I mean, it was the old probability problem at school, wasn't it? you've got X number of sits around the table. How many places are there to put grandma and granddad and so on? There's an important statistics angle to this, isn't it?

Hannah - Yes. There was a paper actually that was published a few years ago. They're actually a married mathematical couple and they based the paper on their own table at their wedding. They borrowed an idea from economics where you sign a utility or a happiness score if you like between each possible pairing of guests at your wedding and then work through all the different possible table combinations so that you can end up with a quantitative assessment of how good your table plan is.

Chris - You need a computer programme to do this. I mean, is there more obsoletions than atoms in the known universe?

Hannah - Yeah, there is. Although computer programme can do it in a mere 36 hours. I mean, just ask your friendly neighbourhood mathematician for help if you get stuck. I mean, I always find that they're more than willing to help out.

Chris - The book also sort of ventures into the domain of, "Once you're married, how do you stay married?" Because that's obviously an important issue because it is a fact that about half of all marriages do founder, don't they? What does maths have to say about that?

Hannah - So, this is one of my absolutely favourite studies. It's a really incredible piece of interdisciplinary work between a psychologist and a mathematician. Psychologist (John Gottman) spent decades filming couples in conversation with each other, asking them to talk about the most contentious issue in their relationship. He and his team came up with a way to score how negative or positive each person was being in each turn in the conversation. But when Gottman teamed up with mathematician (James Murry), they were able to translate this into a mathematical model and really get to the heart of what it was that caused the spirals of negativity that end up causing divorce.

Chris - So, what do I have to do? Tell me, how do I keep my wife sweet?

Hannah - So, the key idea is something called the negativity threshold. So, that's basically how annoying one person has to be before the other  person really reacts strongly. So, I mean, you might think that good relationships are all about compromise and giving each other room to be yourself. So, relationships with a really high threshold for negativity might do well. But actually, the team found that the opposite is true. The relationship is the really low negativity threshold that do well. The ones that if something bothers them they bring it up and they deal with it immediately and they don't know anything faster so that small things never end up becoming a really big deal.

Chris - I've always said that to people that actually, if you let it sort of fester and then it boils up then it's a bit like a pressure cooker and then it suddenly goes off catastrophically, as if you have lots of little bickering. I mean, this is my philosophy.

Hannah - I know. I think you're absolutely right. the data from real life couples supports it.

Chris - I'm very pleased. I'll tell my wife. We'll go home and I'll be proactive, Hannah. I'll go ahead and have an argument tonight.

Hannah - Do more arguing.

Chris - And say, "Look! This is all of interest of a healthy relationship." Hannah Fry from University College London, thank you very much. Her book, The Mathematics of Love is out now.