The maths of coincidence

David Spiegelhalter discusses why seemingly unlikely events occur all the time- although not often to him!
03 November 2014

Interview with 

David Spiegelhalter, University of Cambridge


Have you ever thought about an old friend, only to have them call that same day? What about singing a song just before it comes on the radio? These spooky coincidences are surprisingly common when you look for them, but can be explained by simply psychology and maths, according to David Speigelhalter of Cambridge University. He explained to Chris Smith and the live audience why creepy coincidences aren't as creepy as we might think...

David -  I'm interested in strange things that happen to people, that people say, "Whoa!  Fancy that!" and remember some of these things - the stories I've got.  People will remember for the rest of their lives some of the strange things that happen.

Chris -  Well, like what?

David -  We collect them.  We've got a website at Cambridge Coincidences and we've got thousands of them.  Some of the most popular ones, and you could tell how old some of these are, how long they've remembered them, because they're about public telephone boxes.  I think we got four now where someone's walking on the street, an old red public telephone box, it rings as they're going past it,  "Oh!  I might as well answer it."  They answer it and it's for them.  Well, I wonder if anything strange has happened tonight.  I mean, there's about 70 people in the audience.  I've actually asked you to write down your birthdays so I've got them.  Now I wonder, would it be strange if two people in the room had the same birthday?  Is that strange?

Chris -  Hands up - this audience if you would be surprised if someone in this room had the same birthday as you.  This is a sceptical audience.  So, about 5 or 6.

David -  What happens if two people in the room walked in with the same birthday and happen to sit very close to each other?  Would that be quite cool?  Come on you miserable lot, that would be cool!.  Okay, stand up if you were born on the 27th of March.  Quite a long way.

Chris -  So, we have one lady and one man and they're on the opposite side of the auditorium.

David -  Yes, sit down.  Okay, stand up if you were born on the 6th of February.  Opposite sides of the room.  This is terrible.

Chris -  It's a good hit rate so far.

David -  Yeah.  Stand up if you're born on October the 6th.  Not bad, but 6 or 7 feet away from each other.  That's not bad.

Chris -  We should point out, each time we're getting about two people standing up.  Each time, you've had a pair of people sharing those birthdates.

David -  Yeah, I'm not choosing these dates at random.  So, the sort of stories some people report to us, the classic coincidence.  I don't know anyone has had this when they meet a stranger and suddenly they find this connection with the stranger.  They went to the same school.  They know somebody in common is a usual thing.  I was just looking through the ones people have sent in just in the last week, somebody meeting somebody and finding out that they lived in the same house.  The other one is finding a connection with the one you know and then again, finding this very strange connection.  We've had one, a beautiful one, a married couple who discovered they were both born in the same bed.  They got married, yeah.  They found they were both born in the same little village in Germany which only got one little hospital and one little bed where all the babies were born.  Another one, people have just sent in a married couple who discovered that they'd both been in a hospital as children at both exactly the same time.  There's these wonderful strange ones where there's a picture of the husband when he's a boy sitting on the beach and there's his wife, just walking along behind on the beach.

Chris -  But isn't the whole point of every single one of these examples is notable because it's exceptional, whereas all of the other benign things that happen in people's lives that don't have these bizarre coincidences attached to them, people just ignore?

David -  Exactly.  There's so many million things that happen to us all the time.  There's inevitably going to be some strange things that happen.  For example, who's born on the 2nd of September?  Not bad, about 6 feet, okay.  How about on 10th of January?  Miles away, that's useless.  You all deliberately sort of - there's this powerful force.  It's making people sit at opposite ends of the room if  they've got the same birthday.  But cool, there's a lot of people in here with the same birthday.

Chris -  David, isn't it a coincidence that none of the people with the same birthday are sitting together?

David -  Wait, I haven't finished yet.  We'll see.  The other ones I love are where people rediscover objects.  It was lovely, someone sent one in recently where they had carefully stencilled on a lovely picture on their chest of drawers.  And then they've given it to a friend and the friend had gone away a couple of hundred miles, and years later, this woman had moved to this new town and she got a friend next door who invited her into her room and there was the chest of drawers - complete stranger, at that.  So, when these things happen to people, they go, "Whoa!  That's really cool."  People in the past have invented theories why these things happen.  A guy called Kammerer had this theory of seriality.  It was a sort force that caused these strange things to happen more than they should and Jung had this idea of synchronicity.  This is definitely to do with premonitions as well that we could feel things happening before they did.  We banned premonitions from our website.  I don't let them go in there.  I'd only accept premonitions if people told me them before the event happened.  Afterwards, it's cheating.  Okay, 7th of March.  They're not sitting next to each other.  Pretty good, but not quite there.  We'll see.  So yeah, those are sort of things, and then there's numbers.  There's people, the pin number keeps on cropping up, same pin numbers, someone wrote in and said, "There's the same pin number from my child's primary school and the bike lock at work."  But these things happen.  The other thing is, we get a lot of people writing to us saying, "These things keep on happening to me.  It's really actually quite disturbing.  These things happen to me all the time.  I keep noticing these connections between everything."  I'm afraid - I do believe they do happen to some people more than others.  I really do.  They never happen to me.  Coincidences never happen to me.  I once had someone phone me up when I was on the train about a story about a bacon sandwich while I was eating a bacon sandwich.  But that's the only time that's happened to me.  It was so obvious, I couldn't miss it.  Now the point is, now why don't they happen to me?  I'm the sort of person who goes around, staring at the ground.  I never notice what's going on around me and I never speak to anybody at all.  I'm miserable.  I could sit next to someone in the train for hundreds of miles and not utter a word.  So, these things never happen to me.  But if you're the sort of person who sits next to someone in the train and starts talking to them, or you're the sort of person who actually notices what's going on around you, and then notices, "I saw that person earlier in the day," then that's who they happen to.  The coincidences happen. So we have people, they happen to them all the time because they notice things and they talk to people.  I could sit next to my long lost twin I was separated from at birth and I would never know because I'd just get up without speaking to them.  So, who knows how many things I've not noticed?  So, what I'm amazed at is not how many coincidences there are but how few there are.  I'm afraid I failed rather on the sitting next to each other.  Got quite close, but there were 6 pairs or 7 pairs of people that shared birthdays in this room, which I think is quite a good coincidence.

Chris -  Any questions for David on the science and study of coincidence?

Anne -  Anne from Canada.  I'm just wondering how you go about saying this.  Are you using numbers and statistics and probability to study how coincidence happen or...?

David -  Yeah, I'm a statistician.  I work in the math department here.  So, where possible, we try to do the maths.  So, the people sharing birthdays, I can work out exactly what the chances of various pairings in this thing is.  I know that if there's 23 people in a room, there's a 51% chance to them sharing the same birthday and so on, and so on.  So, I can do all these calculations and sometimes on the pin codes, you can do the maths.  Does anyone share birthday with their parent, same birthday as their mom and dad or anything like that?

Anne -  Anyone got a birthday this year?

David -  Anyone got a birthday shared with a brother or sister?  Who isn't a twin.  I don't care.  That doesn't count.  That's cheating.  Because we've got I think 5 examples of people with us, 3 siblings, all with the same day, but born in different years.  So, they were all born on each other's birthday.  The chance of that happening, we know is 135,000 to 1, which is rare.  It's extremely unusual for it to happen, except that it happens every year in this country because there's 160,000 third children born every year in this country.  And just by chance, there'll be one - you can expect one to match, have an older brother and sister born on the same day as well.  So, they come up in the news.  If you Google '3 births in the same day' they'll come up all time and the Daily Mail always gets the odds wrong.  It says it's 48 million to 1, which it isn't.

Chris -  Ladies and gentlemen, David Spiegelhalter.


(Callum) -  Callum from (Stratum).  Are you destined for each coincidence?  So, if you keep crossing paths with someone else, is it destined for you to always meet with them or mix with them?

David -  Whoah!  That's a big question.  That's quite a tricky one really, because you're really talking about almost predestination, is everything we do actually sort of pre-decided and we don't have to choose ourselves, there's no randomness and no freewill, which is a reasonable argument that some people have got.  The fact that we don't know what's going to happen it's just because we don't know, it is pre-decided, we just don't know what it is.  I don't have a too strong opinion on that at all.  What I say is that the fact that we don't know means that it might as well be random because we don't know, and we don't want to know.  Who would like to know what they're going to get for Christmas?  Yes.  All the kids want to know what they're going to get for Christmas.  Come on.  Live with uncertainty.  But the grownups don't, no, look at this.  Adults are quite happy about it.  Let's say, if I were a great all powerful being that could tell the future and I could tell you how long you're going to live.  Who would like to know?  Yes, look at these kids.  They want to know.  Why do you want to know?  I would say, the young people are the ones who want to know.  Why do you want to know?

Sophie -  Sophie from Blenheim.  I want to know because then if you're going to live a really long life then you could plan it.  But then if you weren't, then you could think, well, what's the most important thing I need to get done in my life and do that first.

Chris - Run up a big bill on the credit card.

David -  Exactly, well done.  If you knew you could plan it - so, that's a very sensible thing to do but most people - notice that as you get older, you're actually prepared to embrace a little bit more uncertainty in life and you quite like it.  So, I think that's a really interesting age profile in that.  But unfortunately, I'm not an all-powerful, all-knowing being, so I can't tell you.


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