Six Degrees

this is the Infinite Monkey Cage.

I'm sitting next to Professor Brian Cox of the Order of the British Empire, Fellow of the Institute of Physics, International Fellow of the Explorers Club, Professor of Particle Physics and Royal Society University Research Fellow at the University of Manchester.

But I always prefer to think of him like this.

That was Dare's Don't Need a Reason with teenage keyboardist Brian Cox.

Brian Cox, there's a song Don't Need a Reason from a physicist, a man who believed that once things might occur without reason.

It's a song that violates causality, which is built into the fabric of space-time.

I'll give you that, Robin.

Yep.

Dare are the only band ever to have broken up over scientific differences.

And next to me is Robin Inns, who will be getting in the way of scientific discussion over the next 30 minutes, but only because that's the clichéd role he's been given in order to make science more accessible to a wider audience.

Fortunately, Brian still thinks that I'm playing a character.

I'm not, I am an idiot.

But

having read up on Joseph Leibit's experiments that proved, or at least possibly proved, the illusion of free will, at least I know it's not my fault, it is predestined.

And I don't even know why I said what I just said.

A veritable comedic touring machine, Godelian in his undecidability.

Hey, very good.

Oh, that's exactly what he wanted you to do as well, Stephen Fry, you fell into his trap.

He never normally writes things like that.

He went, I'll write that because Stephen Fry's on.

This whole show's changed.

Today, we're going to be examining six degrees of separation.

Although, for some people, it's just a pub game connecting Kevin Bacon to any other actor.

The ideas behind it have ramifications for epidemiology, genetics, and mathematics.

And I am delighted to say that this is the first topic we've ever done in any of the series where Brian actually came up and went, I have no idea what this is.

Yes, ladies and gentlemen, observe the feet of clay that so often walk near a volcano.

Genuinely true.

To help us find out if it's meaningless, trivia, and therefore more appropriate to an arts program, we're joined by a panel of experts.

Meow!

The sound of Schrödinger's cat.

Or not?

It's hard to decide.

Let's not open the programme so no one will ever know.

So, as we said, due to six degrees of separation, in some ways it doesn't matter who the guests are.

For instance, we could have Cheryl Cole on.

We could actually have Cheryl Cole on.

It appears she's at a loose end at the moment.

But Cheryl Cole may not appear to be the ideal guest, but she appeared in Children in Need, hosted by Terry Wogan, who played himself in Being Human, written by Toby Whitouse, who also writes Doctor Who, which had a guest appearance from Simon Pegg, who appeared in Hot Fuzz with Stephen Merchant, who created The Office with Ricky Gervais, who appeared in The Simpsons, as did Stephen Hawking.

So, in many ways, she would be the perfect guest.

On today's panel, a man who has written books on Fermat's Last Theorem, The Big Bang and Codes, which he imaginatively titled Fermat's Last Theorem, Big Bang, and the Code Book.

Simon Singh.

An expert on computer games, which for once isn't a youth prism for being unemployed.

She knows of all things virtual, is a researcher in residence at the British Library, and formerly wrote a column for the Guardian's Technology section.

She is Alex Kratoski.

Now, in terms of connectivity, the hardest thing to do with our final guest is to drag it out to a whole six degrees, because with only one or two degrees, you can connect him directly to George Formby, Olivia Newton-John, Joseph Stalin and Dick Peabody.

Who is Dick Peabody?

Look it up on the webday.

Yeah.

Stephen Fry.

Alex.

First of all this idea of six degrees of separation.

What does that mean?

Well everybody's had this experience before where you've been in a foreign country, you start chatting with somebody in a cafe, you say to them, oh, you know, I'm from X place and I've done X, Y, and Z.

And somebody else says, oh, right, well, do you know blah?

And you, oh my god, you're joking.

Here we are in Berlin, you happen to be on holiday, and yet we both know exactly the same person.

And so this started in 1967.

This started Stanley Milgram thinking how small is the world.

And his theory and the empirical work that he did helped to establish this notion that everybody is connected or the probability that everybody is connected by six intermediaries between them.

And he did an experiment, didn't he?

A very simple experiment.

Oh, it was so exceptionally beautifully, beautifully simple.

So what Milgram did was he came up with this really, really clever idea of choosing two random people and saying, right, you're going to be the recipient of a package.

And then he contacted 300 people in Nebraska and said, Just based on the people that you know, their first names, we want you to get this package to this completely random person back in Boston.

And through that, they, you know, if somebody happened to know somebody who was flying to Boston or if somebody had a cousin who lived in Boston, then they passed that package from person to person to person.

Unfortunately, while this helped to establish this idea of six degrees of separation, which has these pop culture implications with Kevin Bacon and all these other things, it was an extremely flawed study.

The methods, while they were humongously, profoundly simple, what happened was that the results were all based upon something like three packages that ended up back in Boston.

And this is out of like 300 packages that he seeded in the first place in Omaha, Nebraska.

Yet, we still have this philosophy, this theory that it's six degrees of separation.

And the idea is that the ones that actually made it had less than six steps.

That's right.

So essentially.

But all the ones that didn't

had more than six steps.

They're still being passed around the airports of Omaha, Nebraska.

And so it proved nothing.

Yeah, well, I mean, it's interesting because it's been...

Social science.

We're still working on it, and we're still working on it.

If anything, we're tenacious as social scientists.

No, but they've done this again and again and again.

And

regardless of whether it's offline or whether it's online, it seems to come up with

intermediaries.

There are tribes I visited in northern Kenya, in various remote places, who obviously have very little contact with the outside world.

And they may have met a few BBC crews, a few National Geographic crews, and some anthropologists, but that would be it.

Now, they obviously would not be as likely to be six steps away from me, say, or imagine more likely me, because I've visited those places, but from people who haven't.

So, we're talking about the West

as a sort of amorphous, you know, modern place that connects to itself, rather than the pockets of the world which are still discreet.

Well, this was very specifically to do with these populations as well.

It seems that you can choose somebody in a remote village in Kenya and get a package to you somehow because they'll be able to pass it to somebody who goes to the market who then blah, blah, blah.

And it is an average number.

That just seems to work.

Simon, is this more of a philosophical idea or is it actually, has it got science behind it?

Has it got hard science behind it?

No, I think Milgram was a genius.

Not only did he come up with this classic, wonderful experiment, but he also came up with the obedience and authority experiment and the electrocution.

So two absolutely groundbreaking experiments of the 20th century in social psychology.

So he was a very smart guy.

But but this experiment was flawed because there was one package.

So somebody in Nebraska had this package, right?

300 people across Nebraska had each had a package, and they could only pass that package on to one person.

So somehow they had to kind of predetermine the best route.

And that's a very difficult way to do it.

Whereas what we're really talking about is that somewhere out of the hundred people you know, and out of the hundred people that they know, and out of the hundred people they know, and you can see this multiplies up very quickly to millions and billions, there is a path.

It's worth exploring, actually, mathematically, this exponentiation, isn't it?

Because it's quite surprising in many ways.

You said that, let's say, you have a thousand friends, and they have a thousand friends, and they have a thousand friends.

To be fair, a lot of those are going to be quite shallow friendships.

I think you're the acquaintances.

After all, if you think you only have two parents, so if you're going backwards in time rather than across space at the same moment, which is what the six degrees of separation suggests, if you go back in time, as it were, who do you know, who you're actually related to in the past, It's a vast number of people.

And we have two parents, four grandparents, eight great-grandparents, 16, 32, 64, 128, 256, 512, 1028.

We know how that goes on.

No, we don't keep going.

You know, everyone in this audience is going, he's going to do it.

He's going to do it.

We don't know.

It's the grains of rice on the chessboard story, you know, which I'm sure you're all familiar with, that the inventor of the game of chess was said to have impressed the Emperor so much,

he said, I will give you anything as a prize for creating this great game.

And the inventor said, Well, I have my modest requirements.

Just put a grain of rice on the first square, A1, as a chess player would call it, and then two on the next one, B1, and four on the next, and then eight, and so on.

And the Emperor thought, I've got away with this easily, called for a couple of bags of rice, and then hadn't got to the third row before he realized the man had asked for more rice than had ever been grown in the world ever.

That's how extraordinary numbers are when they exponentiate.

And so if we we must be related, if you've got any English blood in your veins, if that means anything, English blood,

then we're all related to certainly Henry IV,

even allowing for the quite generous amount of incest that may have gone on.

And so, these interconnections happen in the past as well as in the present.

That sounds like a wonderful advert for incest.

There was a way that quite generous amounts of incest can now be added to the party.

I think it was the composer Arnold Bach who said, In this life, you should try everything once except incest and country dancing.

Brian's embarrassed by all those years of country dancing.

That was another reason the pop band dare fell apart.

Brian, you stopped thinking country dancing.

We're meant to be a metal actor.

Simon, then, so this idea, what is so surprising then about this idea of six degrees?

Because it seems that if you do exponentiate, so quite literally, I suppose, I have a thousand friends, they have a thousand friends, and they have a thousand friends, that's a billion connections.

If those connections are random, if you could randomly pick a thousand friends from around the world, and they could randomly pick a thousand friends, that's a million, then a billion, and then a trillion.

So, in four steps, theoretically, if we had random connections with people, you could connect to everybody in the world in four steps.

Now, we are clearly not random.

You know, the network scientists talk about something called clustering.

You know, I know you, Brian, and I know Robin, and of course, Robin knows Brian.

So,

there's clustering that goes on.

And most of the friends we know, you know, often in the science communication community or and so on.

So most of the people we know are in closely knit clustered groups.

But a few of the people we know are from very odd places or very have very odd careers or odd backgrounds.

And just a smattering of randomness, just a handful.

If you increase the randomness by just 1% from a very tightly clustered group, increase the randomness by just 1%

and the path length to get into other people people around the world reduces by a factor of 10.

So, this is what Stephen, exactly what Stephen said, because we know Stephen, he knows tribes people in Kenya, and so we're connected by one step now.

Yeah, if I needed to get a package to a tribesman in Kenya, you're the first person that I'd call.

Stephen.

Well, that's the thing, Simon.

Where do we actually see the hard use of this beyond, oh, you know so-and-so, that's funny.

I think the foot-and-mouth outbreak of the 60s, 95% of the cases were within 100 kilometers of the first case.

So that's a very unconnected agricultural world.

So a virus breaks out and it's pretty much isolated within a small area.

In the recent foot and mouth outbreak, it spread right across the country because of transport of animals, because viruses and the foot and mouth could spread.

And so it's agriculture, it's epidemiology, it's the neurons in our head, they're connected.

And just like I was saying before, there's a lot of local clustering.

A lot of our neurons in our brain are clustered very locally to the ones around them.

But every so often, one neuron will zip across to the other side of the brain, or another part of the brain at least, and create this kind of randomness.

And that connectivity therefore allows connectivity throughout the entire brain.

They've studied nematodes and found exactly this pattern.

It's computer viruses,

it's everywhere.

I mean, if you're a network scientist, you just see the entire world as one network, or as a series of networks.

That can lead to paranoia, though, I would imagine, as well.

In the interest of uniting C.P.

Snow's two cultures, it's also what literature, especially since the invention of the novel, has expressly addressed.

If you think of some of the great masterpieces of literature, like Bleak House, they posit a world of apparent random vastness, which was London, an unimaginably huge city, filled with hierarchies of people who seem completely unconnected.

And in Bleak House, as you read it, you think you've got these families, who are these?

The crossing sweeper here, there's this strange man here, is actually called Nemo, there's these aristocrats, there are all these different people, and you know instinctively because it's a novel that there's going to be some solution.

Some people call it the first detective novel.

It does have a policeman in it called Inspector Bucket, and there is a crime.

But the fact is, what Dickens is suggesting is that you take a city like London and everybody is connected.

And he actually specifically uses disease.

Esther in the book gets ill through money.

And money and disease Dickens tracks as basically vectors

that transmit both good and ill in similar ways.

And that's why I suppose people talk very excitedly about the importance of ethical trading and of buying ethical products and so on, because our very act of purchasing is doing something to someone to whom we are connected.

And we're probably not particularly religious around this table, but what you do unto the least of mine, you do unto me, is not a bad quotation, were there to be a divine being.

And if we were to act as if that were the case, we would live in a better world.

I think we instinctively know that.

We can show we're all brothers and sisters

in a Baptist ministry, say, by saying we're all brothers and sisters, or we can do it by looking at the human genome.

But in either case, it's quite clear that our connections are something that are only going to get more and more important.

And at the same time, we're living in a world where people are desperate to divide themselves from others.

There were DNA studies that were attempted in Israel where both the Palestinian Arabs and the Israelis kicked out the scientist because they didn't want to know what they knew knew was true, which is that they are very, very closely related.

Now, of course, one of the most famous examples of six degrees, we talked about it before, is the six degrees of Kevin Bacon, which in some ways is a weird thing.

So, as we were saying, in fact, if you are in any way an actor and you've actually had a career, then you should be able to link to most people within six degrees.

I think about two degrees, three degrees is rather, is about the most we've managed so far around this table.

Yeah,

if anybody can find an actor from anywhere in the world, from any era, it takes more than four steps to get to Kevin Bacon, that would be a pretty good achievement.

The first time I tried it was Barbara Windsor.

I thought, well, that's not going to be so obvious.

But Barbara Windsor turns out to have been in Alice in Wonderland with Michael Sheen, and then Michael Sheen was in Frost Nixon with Kevin Bacon.

Two steps, and you're there.

You'll be pleased to know, Brian, that Carl Sagan is also linked to Kevin Bacon.

Now, this is something we were talking about.

I'm not entirely sure.

Can we just check the rules of Kevin Bacon?

I think you actually have to have appeared.

It's an acting-based element.

In the film with Kevin Bacon, you have a Kevin Bacon number of one.

If you've been in a film with someone who has also been in a film with Kevin Bacon but not been in yourself, then it's two, and so on.

I think my Kevin Bacon number is likely to be two, because I know I've worked with lots of actors who've been in films with Kevin Bacon, so I have a Kevin Bacon number of two.

Incidentally, you should know that he himself was very annoyed by this when

he first heard, because he thought, mistakenly, it was a comment on his availability and tendency to do lots and lots of films.

It's nothing to do with that.

I think it's just the verbal pleasure that it sounds a bit like separation Kevin Bacon.

It's a sort of half-rhyme.

You could actually take any other actor.

It doesn't have to be Kevin Bacon.

He's a pretty good guy to work with because he was in Frost Nixon, he was in Sleepers, but he was also in Foot Loose and Friday the 13th.

So it's a

large range of material.

But there are other actors who are more connected.

So when you try and measure the path length, the average path length is even shorter.

And the top three, I think, are Donald Pleasance at three,

Christopher Lee at two, and Rod Steiger at one.

Rod Steiger is the most connected actor in history.

Brian does not have a Bacon number, but one of your papers does, doesn't it?

Because Brian's paper, where is it?

It's

WW Scattering at the Large Hadron Collider appeared in Sunshine behind Killian Murphy, who was in Cold Mountain with Donald Sutherland, who was in Animal House with Kevin Bacon.

And mine is a link via Kerry Armstrong, who was in Razzle Dazzle, which I appeared in and wrote wrote, and is widely available for about a pound, even though it was

quite well reviewed by the Observer, but rather snottily by The Independent.

What's also an interesting

number called the, and I'm going to mispronounce it now, but I believe you could pronounce it correctly.

Should we all try this?

I would say Erdos number.

Discharz.

Erdos.

It's a

Hungarian, anyway.

Tell us a little bit about this.

This is fascinating.

There's a wonderful biography of him called The Man Who Loved Only Numbers, I think it's called.

And I remember reading it and just falling in love with this man.

He was a remarkable mathematician, one of that great breed that Simon will know very well, the really pure mathematician

whose obsession simply was with numbers.

And he was also someone who had no interest in almost anything else.

So it wasn't that the title The Man Who Loved Only Numbers wasn't accidental, so he had no house.

He just moved from room to room of fellow mathematicians and collaborated more than any other mathematician, I think, in history.

And so there are thousands and thousands of papers in mathematics which are by Erdos and whoever else, some other name.

And so if you collaborated directly with Erdos, you have an Erdos number of one.

And if you've collaborated with someone who collaborated with someone, then it's two, and so on.

So it's the same theory, but it's within the world of mathematics.

And almost every, I mean, it's getting on now because he died some time ago, but still there must be hundreds of professors of mathematics around the United States and the rest of the world who have Erdos numbers.

There is also another number which we haven't told about yet, which is the Erdos Bacon number.

Now what exactly?

Okay so the Erdős Bacon number applies to people who are either researchers who've appeared in films.

It's a much bigger industry than you imagine.

Researchers

or actors who've written research papers.

And then you can have this combined Erdős-Bacon number.

Can I suggest that the second group

there are fewer people with the number.

Burt Reynolds' paper

on Fermat's last.

Yeah, you know, you're right, you're right.

You're really looking at mathematicians that have had bit pass.

So, for example, there's a guy I know in Columbia who is an expert in the mathematics of card shuffling called David Bayer from Columbia.

And

he's got an Erdish number of, I think, three, I think.

It's a pretty good Erdish number.

He's written a paper with somebody who's written a paper, who's written a paper with Erdish.

But he was also maths advisor to A Beautiful Mind with Russell Crowe.

And because he was maths advisor, they said, well, why don't you play a role?

And I don't know if you remember, at the end of the film, there was that Penn ceremony when Nash, played by Russell Crowe, gets a Nobel Prize, and the other professors offer him up their pens in honor.

It's a completely fictitious ceremony, never happened.

Anyway,

he was also Russell Crowe's hand double.

If you see any blackboard writing in that film, it was

because he had to write equations on a blackboard.

And there's a special, there's a beautiful way, an elegant way to write mathematics on a board.

And David Bayer knows how to do it.

So he has a speaking role.

So he was in the speaking role in A Beautiful Mind with Rance Howard, and Rance Howard was in Apollo 13 with Kevin Bacon.

So that gives him an Erdish Bacon number of four.

What I find is interesting about this subject though is that, so initially, I suppose, there's this study of Erdős numbers and

Bacon numbers.

It's completely abstract.

It's completely useless in a sense.

Well, in a sense, genuinely pure exploration of number and pattern for no reason at all.

But it does now seem, quite recently actually, to be blossoming into a very useful science.

It's also a useful way of testing

whether it's nematode brains, whether it's human brains, whether it's links on the internet.

This seems to be a universal law that you have local networks with random, spurious connections to more distant networks, and that allows communication or linkages throughout the entire system.

And you can apply that to biological systems, and you can apply that to trivial Kevin Bacon games and airdish numbers.

I think it's also really important socially, not just looking at the biological, the natural world, but also has a huge amount to do with what I'm concerned with, which is the diffusion of attitudes and behaviors, how attitudes cluster in networks, how behaviors cluster in networks.

Nicholas Christakis, who's a social scientist in the States and a network scientist, talks about how obesity clusters, health problems cluster, various sort of biological systems cluster within networks.

And this also has to do with how people are influenced within these networks.

Very interesting, because that's a if as a just a conventional scientist, I suppose you may say, well, if there's an obesity cluster there, is it to do with diet?

Is it you begin to look for a cause?

And what essentially you're saying, I could ask you, are you saying, that this kind of ordered behavior emerges as a result of the network connections between individuals.

It doesn't necessarily need a cause in the sense of them being near a fast food outlet or something like that.

Well, it can just emerge.

Yeah, and I think that there is, at the moment, there's a sort of push and pull between the hard network scientists who are very much saying, you know, all we need to do is map the network, and then that's fine.

And then we're done and we've got all the answers.

And then the social scientists who say, well, we need to figure out a little bit more.

Because

is it because everybody's around a fast food restaurant?

Is it because did they cluster because they all happen to be obese and they want to be like one another and whatever?

I wasn't quite going to go there.

Thank you very much for

waiting for that.

Stephen, social networking, you're famous now for being at the centre, a giant node, I was going to say.

You have, what, over almost three million followers on Twitter.

I mean, with so many millions of followers, do you find that you communicate?

Do you think you influence those people?

Is it just

reading it?

It's

become a very awesome responsibility to some extent.

It's a very short space of time.

I've grown from having, as everyone who starts on Twitter, and I happen to start on Twitter as Twitter started with a few hundred.

It never occurred to me that this would be a big deal.

And then suddenly the numbers got bigger, the requests that started coming in from charities and good causes for me to retweet this and retweet that got enormous.

So one felt one had a social responsibility.

And now, for me, the whole point of being Twitter is that it's me.

It's not a corporate thing.

It has no, I'm not a public service, I'm not a broadcasting station.

I can sometimes be drunk or annoyed and tweet something stupid and I'll might apologise, put my hand up.

But as far as the wider world is, I mean I've noticed over uh two years after Twitter became something of a phenomenon, I I would get these requests to address businesses uh with hideous titles like How to Harness Your Twitter Potential.

And and I just wanted to vomit all over them because it it it struck me that it ignored the one point of Twitter, which is bizarrely small as the tweet is, 140 characters, um people can read bullshit in it straight away.

And they know when they're being preached to, they know when they're being sold to.

And in the end, all this social science is fascinating as science, but it's hardly pure science because it's really all about politics and money.

The people who really want to plug into this kind of science are politicians who want to know how to persuade us to vote one way and people who want to persuade us how to buy one way.

And there has to be a countervailing, open nature to this science which tells us what's going on and allows us to retain our free will.

And while we may be part of migratory patterns or any other kind of pattern, we also have within us the ability to say, No, I'm not going to be one of those.

I shall not do this because I know I'm being pushed by someone who thinks they understand how the human works.

Inside, there's the individual human heart and the individual human brain, and it's better than any system that can devise

an ideology around it.

See, that's what I always like about your tweet.

So, I never know whether it's going to be something about a charity or whether it's about the fact you've got diarrhea in Algeria.

And I think it's a lovely mix.

Oh, I should give five pounds for that.

Oh, poor Stephen.

So, we have now reached the end because at this point of the show, it's actually an in-belt system I have of cosmological vertigo, which is the information you get so much that I actually get kind of a sense of nausea about the size of the universe.

I could use a watch, but instead I prefer a system of nausea and cosmological vertigo.

So, thanks to all our guests, Simon Singh, Alex Kratoski, and Stephen Fry.

And just one last thing I'd like to know from all of you.

Did you want to be an astronaut?

I go through each of you.

Yes.

Hell yeah.

I'm the only person who's vomited with an astronaut, I think.

I was at university with an astronaut.

It was very extraordinary.

You can cut this out because we're finishing, but

I was at one of the initiation ceremonies in the same year as me, there was this guy who was a really nice guy, and he seemed rather modest.

I thought,

and in a very drunken way, having had the initiation cocktails and everything else, and thrown up several times.

I asked him what he was going to do in life, and he said, Oh, I'm going to be an astronaut.

I said, Yeah, seriously, what are you going to do?

He said, No, I'm going to be an astronaut.

I said, What?

Are you serious?

He said, Yeah,

I'm going to be an astronaut.

And I said, Okay.

And sure enough, he was the first Britain.

And I think he is the European who's been longest in space, Mike Folds.

Brilliant.

So, your astronaut number is an astronaut number of one.

That's brilliant.

That is genuinely what next week's show is.

We're going to be so you want to be an astronaut.

So that brings us to the end of the show.

Yeah, if you have any complaints, anything you've heard on the show, please send them to slash dev slash null at bbc.co.uk.

That's a Unix joke for geeks.

I'd just like to say that we, as usual, always get people actually complaining that because we talk about monkey cages,

we may well be suggesting that vivisection is a good thing.

I'd like to make clear, very not, it is an infinite monkey cage and therefore roomy.

Goodbye.