‘Ping” goes Louise Henry’s computer, and the 31-year-old business executive from Wimbledon dashes to her desk in anticipation. There in her in-box is a fresh message from her new best friend Juanita, a museum worker who lives in Vancouver, on the west coast of Canada.

As Louise rattles out a perky update for Juanita on life in southwest London she is, though she might not know it, helping to spread an extraordinary social trend that is sweeping the globe.

From London to Sydney, New York to Singapore, close friends may now not live on the same continent, let alone in the same city. They form their friendships through a series of hugely popular new social networking websites.

These have taken an arcane 20th-century social theory about the relationships that connect everyone on the planet and have put it into practice with the aid of 21st-century technology.

But is the internet — a huge force for shaping our existence — fostering a world in increasingly perfect harmony, or just leading millions of people to form pointless and superficial friendships with people they have never met? Once upon a time there were penpals. Now there is friendster.com, which already has more than 1.5m members even though its American-created website is still in its “beta” start-up phase. A British service, everyonesconnected.com, has 50,000 members, with hundreds more signing up every day.

Friendsters and everyonesconnected are based on the “small world hypothesis” developed by an American sociologist, Stanley Milgram, in the 1960s. His idea was that everyone was connected to everyone else by no more than six “degrees” of separation.

This is best explained by a game called Six Degrees of Kevin Bacon, named after the actor. He can be linked to any other actor by a chain of six or fewer actors who have appeared in films together.

The most frequently cited example is John Wayne, who appeared in The Longest Day with Robert Wagner — who, in turn, was in Wild Things with Kevin Bacon. So Wayne and Bacon, though vastly different characters (and one of them dead), are connected by only two degrees.

Science magazine reported last week that a team from Columbia University in New York had tested the Milgram theory. They asked computer users to track down a stranger by e-mailing acquaintances they might have in common. So Bruce in Eastbourne was asked to find Olga in Siberia.

Bruce did it through his Uncle David in Uganda, who he knew had computer penpals across Russia — a wild goose chase completed in a mere four steps.

The potential for making connections on the internet is obviously vast — but so is the potential for mischief and dishonesty. What the websites do is to put the discipline of a social structure onto networking by only accepting members who are vouched for by existing “real-life” friends.

Once members have been accepted, it is through the friends of these friends that they rapidly find other people with whom they have immediate rapport — or, as one online enthusiast put it: “Click to the clique: that person you’d love to meet may only be just a few clicks away.”

Friendsters and everyonesconnected encourage people to put their entire social networks on the internet and then plug them into others.

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