Hello and welcome to more or less on the BBC World Service, with a program where no number

is to niche nor statistic to specific, and I'm Tim Halfard. Here at Morales HQ we do love

numbers, but we also love books. Sometimes books about numbers come along and we're so ecstatic

that we just pop with delight. One such book is The Ten Equations that rule the world by

David Sumpter, professor of Applied Mathematics at the University of Uppsala, Sweden.

I've been talking to David about one of those ten equations to rule them all, the reward

equation. It's a mathematical formula that weighs up the gains from certain activities.

David Sumpter thinks we could be more deliberate about the way we use it,

but it also emerges naturally, as David found out when he studied a group of ants.

When one ant finds food, it will go back to the nest and behind it it will leave a

phoemone trail, this chemical trail. And essentially it's assigning a score by doing this,

it's saying that this is somewhere that you should be. And when the other ants find that trail,

they'll follow it and they'll also find the reward, the food at the end of it. And then if they

think it's good, they'll leave the trail too, so you get a collective decision about what are the

best things to go for and what are the least good things to go for. When the food runs out,

ants stop leaving the phoemones so the trail fades, signaling to other ants, not to bother going

there. But how does this connect to a mathematical equation? Exchange phoemones for numbers.

The equation describes the evaporation of the trail. So every time step, you have one variable,

a number which describes how good something is, and that decays, it gets smaller and smaller and

smaller. I think it sounds a bit abstract, so I think maybe I could give it in a more human

perspective of how we would do this, if you're watching Netflix, for example. And often we watch

the first episode in a series. And my suggestion is you give that episode a score. Let's say we give it

...