Volume 30, Number 1 January 2001


Dynamical Modeling Of The Onset Of War By Alvin M. Saperstein. World Scientific, Singapore, New Jersey, London, Hong Kong, 1999, 148 pages, $38.

This book was written to serve two purposes. It is a review of past efforts to model arms races in general, and the onset of war specifically. Secondly it seeks to explain the role of chaos in arms races. Saperstein argues that the onset of war is generally caused by crisis instabilities in the international system. And since the transition from predictability to chaos is such an instability, a system with a tendency toward chaos is likely to break out in war.

Saperstein distinguishes between static and dynamic models of arms races. He summarizes and discusses the static models of Kaye, Legault and Lindsey--with their regions of stability and instability. However, he feels that static models are inadequate because they include nothing of the interactions between the participants in the international relations. He is somewhat more satisfied with existing dynamic models, such as those involving the Richardson equations and their extension by Lee, Zinnes and Muncaster.

However, the existing models tend to be linear coupled equations, which he says cannot represent the complex real world. He believes that non-linear equations coupling participants in international relations are required to describe the real world. And he shows that such non-linear equations can lead to chaotic behavior. One strength of this book is the clear distinction drawn between predictable and unpredictable futures. To Saperstein, chaos represents situations in which a small change in an input parameter can lead to a very different final outcome. In such situations, knowing the initial parameters with high precision still does not allow a prediction of the future outcome even with large uncertainties. He argues that such chaotic futures are likely to lead to the outbreak of war.

Dynamical Modeling is aimed at graduate students in the social sciences, students who want to understand the role of chaos in the modeling of international systems. These students indeed can benefit not only from the reviews, but also from the explanations of "crisis instability" in mathematical terms. Unfortunately the mathematics is dense; but no denser than it is in the equivalent social-science literature. The book may be even more useful for the physical scientist who is interested in understanding war in a more mathematical way. Its reviews and critiques of static models are good. Its reviews of dynamic models explore well the mathematical complexities of coupled non-linear equations with many parameters. Saperstein cites the best literature of the field.

The new modeling approach of Saperstein in this book, namely the incorporation of chaos, is aimed at both social and physical scientists. The book contains reproductions and summaries of essays on chaos previously published by Saperstein. The mathematics is formidable because of the many parameters and coupled equations. The mathematical inclinations of the physical scientists are reasonably satisfied, as the equations are solved either completely with no input of specific real-world parameters, or else are solved by iterative steps on a desk computer in very generic terms. The social scientist is likely to be reasonably satisfied because the mathematics confirms the intuitive understanding previously derived from non-quantitative analyses. Some sample conclusions from chaos theory: (1) Three nation systems seem more likely to lead to war than two-nations systems. [We should mourn the end of the Cold War?] (2) If nations fear and loathe each other less, the chance of war is reduced. (3) Democracies are less prone to war.

Perhaps the greatest contribution of this book is how Saperstein relates the social-science concept of "crisis instability" to the mathematical concept of "chaos". Each of these is characterized by the fact that a small variation in the input parameters (e.g. an assassination), can lead to enormously different outcomes (e.g. a World War).

For me what is missing are specific calculations for actual situations. I found myself wanting to know what values a "loathing" parameter might take; and what might be the value of the coupling coefficient between the building of an NMD by the United States and the resulting building of more ICBMs by China. This neglect of numbers is deliberate. Saperstein says: "... the goal is to illustrate method, and to develop insight and intuition, rather than to achieve realistic results."(p. 115) But I personally understand complex relationships best when illustrated by specific examples. When this book mentions specific real-world examples such as the instability created by deploying an NMD, it does not give actual calculations. Instead, the book refers to articles containing the details. But a book is usually an extension of shorter articles, so I had hoped to find detailed calculations and applications to justify the intuitions. I found myself agreeing with Lord Kelvin who said that he only understood something that he could put into numbers.

I recommend that you read the book, then go to some earlier Saperstein articles where he works out some detailed calculations, and then play around with the Richardson model and with the two- versus three-nations coupled non-linear equations.

There are some mistakes in the text due to insufficient proof reading. Two notable mistakes are on p. 102, where the parameter epsilon should equal zero (NOT one) to reduce the three-nation system to the two-nation system; and p. 118 where in Eq. (1) the parameters x(j) should be coupled not to x(i) but to the time derivative of x(i).

Dietrich Schroeer

Physics Department

University of North Carolina at Chapel Hill.


The Woman Who Knew Too Much: Alice Stewart (1906-) and the Secrets of Radiation by Gayle Greene, University of Michigan Press 2000, ISBN 0 472 11107 8, #19.95 <www.alicestewart.org>.

[This review first appeared in the Times Higher Education Supplement (United Kingdom), and is reprinted here by permission.]

The devastation of Hiroshima and Nagasaki in 1945 was plain to see. But the true horrors of radiation damage to thousands of survivors were concealed by the nuclear establishment and self-deluding politicians; worse, their gross underestimates became benchmarks. One of the courageous few to challenge this, from the 1970s, was the epidemiologist Alice Stewart. She had long been a thorn in the side of the medical establishment, for she uncovered the true hazards, namely childhood leukaemia or cancer, of X-raying pregnant women.

Like her mother, she was a pioneer doctor, qualifying in a female medical school. This followed a dazzling intellectual life at Cambridge in the 1920s: her circle included Cartier-Bresson, Redgrave, Lowry, Bronowski, Trevelyan, Alistair Cooke, Anthony Blunt, Kathleen Raine. She heard Virginia Woolf’s talk which became ‘A room of one’s own’. William Empson was her first and last love. Cambridge expelled him (after he had written ‘Seven Types of Ambiguity’, in two weeks) when his landlord reported finding ‘various birth control mechanisms’ in his room. They married other people--Empson went to Japan and China, she married Ludovick Stewart--coming together again after 30 years.

Ludovick’s appointment to Harrow school helped her career. She became a registrar at the Royal Free (where her parents met in 1901) and sharpened her diagnostic skills. She became a consultant at the Garrett Anderson Hospital in 1939, evacuating to St Albans with the war; Ludovick went to Bletchley Park, decoding, and their careers diverged. She moved into social medicine at the Nuffield Hospital in Oxford: with two children, she avoided call-up, and received help with child care. "The war enabled me to leap over barriers that would otherwise have blocked my way as a woman", she says, "It tells you what women could do if society would change its attitude."

She studied health risks of industrial chemicals in factories doing war work. With 40 undergraduate volunteers filling shells with TNT she showed that the risks of anaemia and liver disease were dose-related. The students’ blood counts recovered! As incentive, she set them in prize essays, published as Impressions of Factory Life. She co-founded, in 1946, the British Journal of Industrial Medicine. She studied pneumoconiosis among coal miners in Wales, working with their Communist leader, Arthur Horner. As ever, risks were downplayed. Miners dying at 55 were recorded as "succumbed to old age"; a miner who died of drink at 82, she reckoned, was an excellent advertisement for drink.

In 1943 John Ryle founded an Institute of Social Medicine in Oxford and appointed Stewart as his assistant. They were appalled by disparities in infant mortality at top and bottom of the social scale. After he died in 1950 Alice was made head of a Social Medicine Unit, as a reader (and fellow of Lady Margaret Hall), with no resources. She raised money to hire an assistant and a statistician, systematized the records, and began to study leukaemia.

Her Oxford Survey work was rich in detail which, with her insight, uncovered vital correlations. Exposure of either parent to ionising radiation correlated with childhood leukaemia, often recorded as "cot death." She fought to establish that there is no "safe" or threshold dose. Nowadays we recognise the hazards to cells in division, and so to the fetus--a single hit can cause mutation. X-raying of pregnant women stopped, and X-ray viewers disappeared from the shoe-shops.

Richard Doll was appointed Regius Professor in 1969 (Doll and Hill had linked smoking with lung cancer). Doll had little time for Alice Stewart, and research funding was difficult. When she retired in 1974 she and George Kneale, her genius statistician, moved with their Oxford Survey to Birmingham University, which appointed her Professor when she was nearly 90.

Invited to the US in the 1970s she could see workers at Hanford or Oak Ridge, producing nuclear weapons, dying of radiation-induced cancers. Safety standards were low, high exposures concealed, injury disputed, compensation was mean, and whistle-blowers were blacklisted. Gradually, her conclusions were confirmed by other scientists. When she was 80, she was awarded $2 million to study nuclear workers’ records from the US weapons complex.

Her evidence of the hazards of parental exposure to radiation around nuclear installations is still disputed. She showed supposedly safe levels to be too high; lowering them would open the floodgates to claims. A 1982 study by the National Cancer Institute, commissioned by Congress, estimated that Western Americans received doses of radioiodine in atom bomb fallout 100 times greater than those estimated in 1959, 10 times greater than at Chernobyl, leading perhaps to 10-75 thousand thyroid cancers, most as yet undiagnosed.

Her Lancet article in 1970 on "Gene-Selection Theory of Cancer Causation" quotes from an Empson poem: "How small a chink lets in so dire a foe." Slowly, surely, international researchers demolish what she calls "the gold standard," the long-standing, meretricious interpretation of A-bomb data. "Truth is the daughter of time," she says.

Gayle Greene’s book is well referenced, while betraying its American origin. It’s a good story, much of it in Alice Stewart’s own spirited words. Photographs show her family and friends, and her progress from a charming young woman to a lively indomitable ninety (plus)-year-old.

Nuclear weaponry has done more damage than Hiroshima, Nagasaki and nuclear testing. The killing of Lumumba, support of Mobutu and Kabila, and much of the subsequent tragedy of sub-Sarahan Africa, can be traced to "safeguarding" Congolese uranium. What will Sellafield do with its 60 tonnes of plutonium, half-life 24 millennia? The Barents Sea is described as "Chernobyl in slow motion"--what are those nuclear submarines doing? We need more whistle blowers like Alice Stewart.

Dr Joan Mason,

12 Hills Avenue

Cambridge CB1 7XA, U.K.