The Mathematics of War

During the Desert Storm, the Gulf war, it was possible to read in the newspapers words such as: “In mathematical terms, war is becoming more and more electronically controlled and, as a result, it is moving away from the battlefield. Then, when war comes down to earth, it becomes bloody, it loses its mathematical asceticism.” Reading the newspapers in those days, one had the impression that modern warfare is based on mathematics, as if it were not men but computers that decided where to carry out “surgical operations”. By contrast, the volume published a few years before the Gulf war conceived as a didactic unit to be used in schools with a guide for the teacher with the title La matematica della guerra (The Mathematics of War) published by Gruppo Abele in Turin begins with the words: “Mathematics, like any other discipline, lends itself to building several paths towards education for peace.” The volume, written by a group of teachers belonging to an anti-violence organisation forming part of the “education for peace” project, highlights the power or ambiguitiy of mathematical models used to simulate war or conflict situations and demonstrates that in some cases the use of mathematics leads to a better understanding of the situation, but in other cases, the mathematical model itself can lead to conclusions which are either wrong or morally unacceptable. Kurzreferat: Mathematik des Krieges. Während des Golfkriegs konnte man folgendes in den Zeitungen lesen: “Kriege werden – mathematisch gesprochen – mehr und mehr elektronisch kontrolliert. Das bedeutet, sie werden vom Schlachtfeld entfernt. Wenn der Krieg dann aber wieder ‘zur Erde zurückkehrt’, wird er blutig, er verliert seine mathematische Reinheit”. Die Zeitungen zu jener Zeit erweckten den Eindruck, modernes Kriegswesen sei auf Mathematik gegründet, als ob nicht Menschen, sondern Computer für die Ausführung “chirurgischer Operationen” verantwortlich seien. Ein anderes Bild hingegen vermittelt eine Lehrerhandreichung La matematica della guerra (Mathematik des Krieges), die einige Jahre vor dem Golfkrieg von der Turiner Gruppe Abele entwickelt wurde. Sie beginnt mit den Worten: “Wie jede andere Disziplin kann auch die Mathematik mehrere Wege zu einer Erziehung zum Frieden bauen”. Der Band beleuchtet die Macht bzw. manchmal auch die Zweifelhaftigkeit mathematischer Modelle zur Simulation von Kriegsund Konfliktsituationen und zeigt, daß der Gebrauch der Mathematik in manchen Fällen zu einem besseren Verständnis der Situation beitragen, in anderen Fällen jedoch das mathematische Modell selbst zu falschen oder moralisch nicht vertretbaren Schlüssen führen kann. ZDM-Classification: A40, M90 “This American war is taking place according to a pact of non-interference between political and military powers. The Pentagon has taken over the visual images and the supply of information remembering how important these factors were during the Vietnam war. And it releases the material drop by drop. In mathematical terms, war is becoming more and more electronically controlled and, as a result, it is moving away from the battlefield – in other words, it keeps troops, photographers, TV operators and journalists at a distance from the enemy. Then, when war comes down to earth, it becomes bloody, it loses its mathematical asceticism, and the feasibility of live broadcasting becomes impracticable for those involved.” These are the words of Bernardo Valli in La Repubblica newspaper on February Q G , 1991. Similar articles were written by many other journalists at the time of the Gulf war. “Bombing with surgical precision, following the fine ray of a laser, with sophisticated technology, with the circumspection and precision of science,” wrote Lidia Ravera in L’Unità on January WK , 1991. The idea is that war is based on high technology, that war is aseptic. This is the most terrible kind of war because everything seems to be based on a high-tech game, almost mathematical in its precision: a mathematical war. These words in Italian newspapers made me think of the final paragraphs of Oriana Fallaci’s novel Insciallah [2] which I had read in August 1990 when Iraq invaded Kuwait. My curiosity was kindled by the fact that several reviewers had suggested mathematics as a possible key to understanding the book. I was interested in trying to understand this popular writer’s attitude towards mathematics. In particular, I remembered Insciallah because mathematics in the book becomes a sort of evil Deus ex machina in the account of Italian soldiers sent to Lebanon a few years ago as a peace-keeping force. Even though the author emphasises the fact that mathematics alone cannot solve any of life’s problems, the theme of the book evolves around a framework involving a mathematical equation that expresses the eternal struggle between Life and Death. “The plot is interwoven with destiny which reason denies and which is confirmed by external forces beyond our control, beyond our freewill. The many people involved include the key person who seeks Life’s formula in order to fight against Death whose formula has been revealed. The dilemma, never mentioned but always present, finally explodes with the question: is Chaos really destructive – Chaos which according to the equation consumes Life; does Death really defeat Life?” From the book’s epilogue: a motorboat packed with explosive material sets out to sink an Italian ship laden with troops. We don’t know what happens because the ending is left in suspense. One can’t say that mathematics makes a good impression in the book: it doesn’t answer any of the major questions posed by the author; it’s an unreliable science in which the truth of a statement and its opposite are equivalent; its only purpose seems to be for doing calculations that lead to destruction and death. Reading the newspapers at the time of the Gulf war, one found the same points of view put forward in different forms and with more precision. I don’t believe that mathematics needs to be defended. However, it seems worth recalling another little book that I had bought in the same month of August 1990 while on holiday by the sea. It wasn’t, strictly speaking, a book but rather a slim volume conceived as a didactic unit to be used in schools with a guide for the teacher. The title is La matematica della guerra (The Mathematics of War, [3]) published by Gruppo Abele in Turin and written by a group of teachers belonging to an anti-violence organisaAntonio Drago, professor of the history of physics, Naples