By Michael Blastland
Producer, BBC Radio 4's More or Less
How well are you connected?
Could we really all be "connected" to each other?
Not necessarily to the rich and famous, but how well are we all connected to each other?
One of the most famous claims is that anyone can reach anyone else through a chain of acquaintances no more than six people long.
This idea, known as "six degrees of separation", is a measure of our social networks.
The phrase was coined by an American academic, Stanley Milgram, after experiments in which he asked people to pass a letter only to others they knew by name. The aim was to get it, eventually, to a named person they did not know living in another city.
The average number of times it was passed on, he said, was six. Hence, the six degrees of separation.
It is a seductive idea.
Films have been made about it, there are parlour games based on it and mathematics has begun to propose theories for why it should be true. But is it?
Judith Kleinfeld, a professor psychology at Alaska Fairbanks University, went back to Milgram's original research notes and found something surprising.
It turned out, she told us, that 95% of the letters sent out had failed to reach the target.
Not only did they fail to get there in six steps, they failed to get there at all.
Milgram was a giant figure in his world of research, but here was evidence that the claim he was famously associated with was not supported by his experiments.
"I was shocked. I was horrified," she said.
And when she looked for other studies, none of those matched up to the claim either.
In the most recent, two years ago, only 3% of letters reached their target.
"If 95 or 97 letters out of 100 never reached their target, would you say it was proof of six degrees of separation? So why do we want to believe this?"
"The pleasing idea that we live in a 'small world' where people are connected by 'six degrees of separation' may be the academic equivalent of an urban myth," she says.
Now Professor Kleinfeld argues that what is more important is not the number of links, but the quality.
Even if you were able to say you could get to the Queen in three steps, it would tell you little about how well you are really connected with her.
We like the idea of six degrees of separation, she says, because it makes the world feel more intimate. But there are barriers - like race and class - she argues, that can sometimes make separation real and deep.
Of course, just because a letter fails to reach its target does not mean that it could not have done it in six steps by some other route. But that is a reasonable hope, not a fact.
The belief that it has been proved that we live in a world of six degrees of separation does not seem to be true.
BBC Radio 4's More or Less was broadcast on Thursday, 13 July, 2006 at 1500 BST.