Sir

The US government's recent decision to enlarge its missile-defence systems, and the response of other countries in Asia which have perceived this as a threatening move, raise the question of whether a new global arms race is beginning. Mathematical models about the relationship between armaments and conflict need to be discussed openly by scientists, ideally in a structured context similar to the way in which climate-change models are discussed, to help governments make the most appropriate strategic decisions.

Lewis Fry Richardson developed a simple model of coupled differential equations to show how expenditure on armaments by antagonistic nations had grown exponentially before the First and Second World Wars. This led him to predict — in a letter beginning “As Nature has encouraged scientific workers to think about public affairs ...” (Nature 135, 830; 1935) — that there would be a second world war when the armaments of both sides became dangerously numerous. War could be avoided, he warned, only if the leaders of the arming countries took immediate and decisive action.

By 1951, Richardson had developed and refined his model, and Nature published his letter (Nature 168, 567–568; 1951) in which he asked whether the third major arms race of the twentieth century would also inevitably lead to a world war. In some respects his refined model predicted the ending of the US–Soviet cold war, though it has been argued that his equations do not strictly allow such an interpretation (see I. Sutherland, Collected Papers of Lewis Fry Richardson Vol. 2, Cambridge University Press, 1993).

Most countries reduced their stock of armaments during the 'new world order' period between 1989 and 1999, with the exception of China and India. The question now is what kind of prediction would result from conflict/armament models such as Richardson's when applied to the present situation. As things stand, the model equations tend to show great sensitivity to small variations in relative armaments at this critical stage, so much work is needed. It is to be hoped that concerned “scientific workers” and others are convinced that the present international situation is potentially serious, and that every relevant method should be applied to the prediction of events and the exploration of constructive strategies.

Political analyses are necessary, but are not a complete substitute for scientifically based quantitative and probabilistic evaluations of complex outcomes and possible remedial actions.

Nowadays, when governments are more open about their use of mathematical models for systems such as the economy, climate change and spread of disease, it could be argued that they should also be open about how they are applying mathematical models to the international strategic situation. Those models would be more effective in influencing events if they were widely applied and accepted, especially in countries where crucial political and defence decisions are now being considered.