I AM THE SON of a teacher of mathematics and a professor of measurement. When I was a boy it was quite normal to come down to breakfast to find an animated discussion taking place about the fact that a centimetre isn’t a proper SI unit of measurement, or to eat my cornflakes while someone provided a top of the head estimate of the number of 330ml cans that ought, theoretically, to be able to fit into a refrigerator of a given volume.

Maybe I am worrying about nothing, but it has recently occurred to me that perhaps this sort of discussion wasn’t quite as common around other people’s family breakfast tables as I had always presumed.

Anyway, my siblings emerged from these morning discussions as impressive mathematicians. I was left merely with a tendency to believe that every social or political issue that I encounter has a mathematical dimension.

I tell you all this to explain my attitude to a recent newspaper debate, the one that began after the police uncovered an apparent terrorist plot to blow up aircraft on their way to the United States.

The Government’s reaction to the arrests provoked two sorts of articles. The first kind advanced the view that the Government was overreacting to the threat from terrorists. This argument was, naturally, put most lucidly by Matthew Parris on these pages. He argued that, in the end, the terrorists “can never amount to more than a big, bloody nuisance” and that we should treat them as nothing more. The alternative view, set out in The Times by Mary Ann Sieghart among others, is that this attitude is complacent, as the necessity for arrests conclusively demonstrated.

My view? Let’s do the maths.

In a powerful paper for the libertarian American think-tank the Cato Institute, Professor John Mueller provides strong support for the Parris argument. He points out that “in almost all years, the total number of people worldwide who die at the hands of international terrorists anywhere in the world is not much more than the number who drown in bathtubs in the United States”. He adds that even including the September 11 attacks, the number of Americans killed by terrorists since records on this were kept is about the same as those killed by lightning, accident-causing deer or severe allergic reaction to peanuts.

To this evidence he adds the research carried out at the University of Michigan that suggests that an American’s chance of being killed in one non-stop airline flight is about one in 13 million. Apparently there “would have to be one set of September 11 crashes a month for the risks to balance out” between travelling by plane and by car.

Mueller’s conclusion is that “assessed in broad but reasonable context, terrorism generally does not do much damage” and “the costs of terrorism very often are the result of hasty, ill-considered and overwrought reactions”. Both the expense of over-the-top anti-terror measures and the damaging impact of panic on liberal institutions are greater than the cost of the terrorism itself.

This argument is too strong simply to be ignored. Nor can it be refuted by pointing to the possible danger posed by a single alleged plot. Even if such a plot had been successful, Professor Mueller’s argument would stand: the chances of a British or US citizen being killed by a terrorist are tiny and the risk of it happening is far smaller than other risks that we regard as reasonably tolerable — being killed on the road, for instance. He is, no doubt about it, quite right.

But while I think he makes an open and shut case against panic, when it comes to the need for a vigorous policy to combat terrorism Professor Mueller’s maths is less convincing.

First, the probability of an event is not really the thing you should be worrying about. In his excellent book Fooled by Randomness, the mathematician and Wall Street trader Nassim Nicholas Taleb discusses what he calls the issue of asymmetry. He explains (rather impatiently since he regards the issue as obvious) that you may believe, say, that financial markets will probably go up, while you behave, sensibly, as if they will go down. The reason? Because you think it very likely that they will go up a little, but, in the unlikely event that they go down, you think they will go down a great deal.

“How could people miss such a point?” he complains. “Why do they confuse probability and expectation, that is probability and probability times the payoff?” The probability of, say, a nuclear terrorist attack might be tiny but the consequences, the “payoff” as it were, would be huge. It is expectation, not probability, that should determine policy towards terrorism.

The second problem with Mueller’s paper is simple: the low incidence of terrorist outrages occurred when there was already a firm policy in place to prevent it. His argument, the “bloody nuisance” argument, depends on the idea that, without additional measures domestically and internationally, the number of terrorist incidents is unlikely to rise greatly.

There is, however, lots of evidence that crime doesn’t work like that. Instead of falling gently or rising gently in response to policy measures, crime behaves like a contagious disease. Potential offenders catch the idea of offending from each other. And just like a disease that starts with only a few people and becomes an epidemic, once it reaches a tipping point the amount of criminal behaviour explodes.

If successful suicide bombings became even slightly more common, can we really be confident that other fundamentalists would not copy that behaviour? We already know that ordinary suicides increase when there are front-page stories about people killing themselves. And if there were such an increase, might it escalate as one group copies another?

So Matthew Parris is right but also wrong. Without minimising the horrendous suffering of individuals, terrorism might well be little more than a “big bloody nuisance”. But should we treat it as if that was all it was? Absolutely not.

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