There's something that inspires awe, if not fear, in the sight at close quarters of a towering electricity pylon, strung with high wires, humming gently and plastered with red danger notices. Add in one of our deepest fears - cancer - and now you have two big, very scary things together. For some time there's been talk of an increased risk of cancer for children who live and play under power lines. We are all a bundle of electrical impulses - what more likely than that man-made electricity in the environment should cause something to go wrong in our own wiring?

But of course, that is not remotely scientific and the issue, which surfaced again this week, is nothing like that simple. That's part of the problem. If we had simple answers to this - power lines cause cancer or power lines don't - the whole controversy would be over. As it is, like the worries over mobile phones, this is one that will be revisited many times yet.

Leading the latest research is Sir Richard Doll, the epidemiologist most famous for establishing the link between smoking and cancer. The study he has conducted is for the government's National Radiological Protection Board. It is not new research, but a careful analysis of recent studies by other people in the UK, the US and elsewhere.

What Doll found did not merit the headlines last weekend (before his work was published). Power lines do not "cause cancer - official". In fact, the story slipped rapidly down the news agenda once Doll actually stood up to say his piece. He found what has been found before: that children around the world who are exposed over a long period to particularly high levels of electromagnetic radiation have an increased risk of falling ill with leukaemia - from a potential one in 1,400 to one in 700. Those high levels of electromagnetic radiation are more common in the US than here, and a previous study by Doll found that there was not a single existing extra childhood leukaemia case in the UK underneath the pylons.

So there's a slightly increased risk, although at the moment no increased numbers here. But even so, it doesn't have to be the power lines at fault. It could be, for instance, something common to less affluent families, who tend to be those living in their shadow.

So should we worry? Doll says not. He says he personally believes it is safe to live under power lines. But as long as there is still a small risk that can't be explained away, few families are going to feel comfortable at having to watch their children play within metres of one of these steel giants.

There's a difference here from the mobile phone issue. You don't have to risk your child frying her brain. Last year's warning from an independent inquiry that maybe children should not use mobile phones until further research has been done is the perfect excuse for living without one. But for many of the pylon-blighted families, there is no such choice.

Pylons are lethal if kids climb them and reach the wires, quite apart from their ugliness and the anxiety they now engender. Even if the risk is very slight, there must be a strong case for burying electricity cables wherever possible or moving them away from homes.

Miracle cures rule, OK? If only. The people who believe in miracle cures are usually the most desperate ones - for instance, parents who have a bright and wonderful child whose dyslexia threatens to wreck his or her life.

Then they hear of Harold Levinson, who has flown in from the US for another visit. More than 30 years ago, he came up with the theory that dyslexia was caused by a malfunction of the cerebellum. Astronauts in space have problems with word recognition because of the sudden weightlessness of the inner ear and brain, and get over it with tablets for motion sickness.

So Professor Levinson treats children with astronaut-style balance exercises, motion sickness pills and vitamin supplements. He says he has amazing results. So he may, but his work has not been independently evaluated - there have been no trials to see how well the method works, whether it works in all dyslexics or just some, and whether it has any ill-effects at all.

It would be fantastic if there were a cure for dyslexia, but parents need the evidence. Go on, professor - if it works, prove it in the customary scientific way and then maybe a lot more people can benefit.