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Last Updated: Wednesday, 14 January, 2004, 18:12 GMT
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Patterns in Randomness
 By Michael Blastland Producer, BBC Radio 4's More or Less

 Can maths explain the occurence of "cancer clusters" near phone masts?
Campaigners have pointed the finger at phone masts for certain so-called "cancer clusters". More or Less on BBC Radio 4 has been looking at a possible mathematical explanation.

Toss a coin 30 times and how many heads or tails in a row would you typically expect?

In experiments, people seem to plump for no more than three before they think it is time for the other side.

In fact, says maths writer Rob Eastaway on BBC Radio 4's More or Less, you commonly get a run of five or even six, sometimes seven or eight.

Chaos Theory

What that seems to tell us is that even our expectations of clustering underestimate the true extent to which things do just bunch together.

 Often a cluster is perfectly ordinary; it would be a bizarre world where they did not happen

So when we see a cluster of illnesses - cancers say - near a phone mast, what do we conclude?

It is a horribly difficult problem, as we found out.

The mathematical evidence is that things will simply cluster.

When we talk of bad things happening at random, we seem often to expect that they will be evenly distributed.

But the coin-tossing example shows what a random world truly looks like.

It does not produce an even distribution at all. It also shows that our notion of a cluster as something out of the ordinary may also be misplaced.

Often a cluster is perfectly ordinary; it would be a bizarre world where they did not happen.

The perplexing thing about probability seems to be that averages of large numbers of people - or coin tosses - produce something predictable. Given a reasonable number of tosses you get about the same number of heads as tails, but within that predictability we will always get pockets of randomness.

Living in a 'cluster'

More or Less Presenter Andrew Dilnot, went to see someone whose terrible misfortune is to have cancer in a tiny village which has 17 other cases.

The maths tells us that in respect of probability, people are much like tosses of a coin: we will see occasional clusters, even of cancer.

Tell that to the residents of Wishaw near Sutton Coldfield where a huge mobile phone mast overshadowed 35 of the houses, until someone pulled it down one bonfire night.

The site is now guarded 24 hours a day and it is become a little like Greenham Common airbase, almost a shrine to protesters, one of whom is Eileen O'Conor.

"I was going through chemotherapy," she says, "when I started meeting my neighbours in the hospital.

"It was then we started looking at the mobile phone mast and now we know for certain that it is responsible."

And when we asked her if she was convinced that it was not a random cluster of the kind we would expect in a place the size of Britain, she was emphatic. "I am absolutely positive," she said.
 Just because we would expect to find clusters, it does not mean all clusters have an innocent explanation

You have to sympathise.

Her bedroom is right in line of the mast, and nothing she says, will convince her that it is not to blame for the local cancers.

Equally important, the maths of clustering does not necessarily prove her wrong.

Just because we would expect to find clusters, it does not mean all clusters have an innocent explanation.

In the film Erin Brokovich, the campaigning character played by Julia Roberts was not wrong; there was a proven local cause for the spate of illness in one neighbourhood.

There might be other objections to the fears of people in Wishaw: that we had have seen more conclusive evidence from other sites if the causal link to phone masts was established, for example.

The British Radiological Protection Board is sceptical of a local cause in cases like this, though it has been investigating.

But I wonder, even knowing the maths, how many people would be content to live there?

BBC Radio 4's More or Less was broadcast on Thursday, 15 January, 2004, at 1500 GMT.

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