Mathematics and War

International Scientific Meeting,
Karlskrona (Sweden), August 29-31, 2002

Draft, August 12, 2002

Maurice de Gosson (Mathematician, Karlskrona, Sweden), Reiner Braun (Director, Dortmund, Germany), Stig Andur Pedersen (Philosopher, Roskilde, Denmark).

Akira Asada (Mathematician, Osaka, Japan), Wolfgang Coy (Computer Scientist, Humboldt University, Berlin, Germany), Sergei Demidov (Mathematics Historian, Moscow University, Russia), Tinne Hoff Kjeldsen (Mathematics Historian, Roskilde, Denmark), Matthias Kreck (Mathematician, Heidelberg, Germany), Lee Lorch (Mathematician, Toronto, Canada), Armin Tenner (Physicist, Amsterdam, Netherlands), Paola Valero (Researcher on Mathematics Education, Bogota, Colombia, p.t. Aalborg, Denmark).

Mathematics has for centuries been stimulated, financed and credited by military purposes. Some mathematical thoughts and mathematical technology have also been vital in war. During World War II mathematical work by the Anti-Hitler coalition was part of an aspiration to serve humanity and not help destroy it. At present, it is not an easy task to view the bellicose potentials of mathematics in a proper perspective.

At the conference, we will present historical evidence and recent changes in the interaction between mathematics and the military. We will discuss the new mathematically enhanced development of military technology which seems to have changed the very character of modern warfare.

Speakers will include historians of mathematics, science and engineering, historians of war, military analysts, and philosophers.

(1) Military traces in the history of mathematics and in present day mathematics. (2) Changes in the character of warfare under the influence of mathematical theory and mathematically supported technology. (3) Ethical and social aspects of the interaction between mathematics and the military. Mathematics and arms control and disarmament.

There will be invited lectures and ample time for discussions opened by invited comments by respondents. The lectures, major points of the discussion, and introductory material to the subject will be published afterwards.

The Meeting is open subject to registration (see below). It is supported by the Blekinge Institute of Technology (BTH), the Danish Network for History and Philosophy of Mathematics (MATHNET), and the International Network of Engineers and Scientists for Global Responsibility (INES) .

The meeting will be held at the Karlskrona Campus Annebo of the University of Karlskrona-Ronneby in the scenic historical military port and now IT centre Karlskrona (South-East of Sweden). It is at 3 hours distance by train from Copenhagen Airport. Click here for more information on the location. You can also have a look at the weather forecast and the train schedule Copenhagen-Karlskrona. Official conference hotel is Hotel Conrad . Low-rate student accommodation will be available.

Please register via email to cdg@ihn.bth.se or via ordinary mail to

Blekinge Institute of Technology
Department of Mathematics
att. Charlyne de Gosson
S-37179 Karlskrona
Sweden
Fax: +46 455 38 54 07

A registration form can be found here in HTML or WORD format.

Please notify in your registration if you want us to book accommodation at Hotel Conrad or student accommodation.

The registration fee is SKR 500.

Wednesday, August 28

20:30, Welcome Cocktail at Hotel Conrad

Thursday, August 29

9:00, Opening. Welcome by Maurice de Gosson

Greetings by ...
Greetings by Claes Jogreus (Prefect)

1. Co-development of Mathematics and the Means of War? Perspectives from Mathematics
9:30-10:10,

Roger Godement (Mathematician, Bourbaki Group, Paris),
Science and Military - A Short History of the Topic in the 20th Century

This talk will be an attempt at explaining connections between the military, science and technology in the 20th century. It will mostly deal with the United States since the 1930s and a few selected fields upon which the military influence has been particularly heavy, with "revolutionary" consequences, good or bad, for the evolution of civilian society everywhere.

10:10-10:30, Comments and Discussion, Chair Maurice de Gosson
10:30-10:45, Coffee Break
10:45-11:25,

Reinhard Siegmund-Schultze (Mathematics Historian, Agder University College, Norway),
Military Work of Mathematicians, 1914-1945: an Attempt at an International Perspective

Talk aims at tracing sources and discussing problems concerning the involvement of those participants in the multi-faceted relation of "mathematics and military/war" who considered themselves mathematicians. This includes the discussion of meeting places and ways of communication between mathematicians and the military (research councils, institutes, societies, journals), ideological positions of mathematicians as precondition for and generated by military work, and, not least, exemplary consideration of some epistemic transfer processes between mathematics and military applications.
Due to uneven historical sources the main emphasis is on comparisons between American, British and German work. Considerably less emphasis has to be given to France, Italy, Japan, and the Soviet Union, although it can be assumed that particularly Russian work in the field was well developed and effective in the war. Throughout the talk the problems of the establishment of "applied mathematics" as an academic subject and of internationalization of mathematics in the period considered (including migration and secrecy regulations) will be discussed as points of view of primary historical importance.

11:25-12:05,

Elisabeth Rakus-Andersson (Mathematician, Blekinge Institute of Technology, Karlskrona, Sweden),
The Brains Behind the Enigma Code Breaking Before World War II

The German Enigma encoding machine and the contributions of famous cryptologists who broke it, are still topics which fascinate both scientists and the general public. After the monarchy of Kaiser Wilhelm II fell, the Weimar Republic came into being, and the idea of equipping the armed forces with encoding machine already found realisation in 1926. The German encoding machine, called Enigma, alarmed the general staffs of neighbouring countries, especially Poland and France. This work intends to describe the efforts of outstanding cryptoanalysts who solved the mystery of Enigma during the 30’s before the beginning of the war. Full reconstruction of the wiring and first deciphering results were already delivered to the British codebreakers at Bletchley Park by The Polish Cipher Bureau in August 1939. The military impact of the early studies of Enigma code breaking accomplished in Poland and the later investigations made by British cryptologists will be discussed.

12:05-12:30, Comments and Discussion
12:30-14:00, Lunch
14:00-14:40,

Kathleen Williams (Military Historian, CUNY, New York)
Improbable Warriors: Mathematicians Grace Hopper and Mina Rees in World War II

The vast expansion of the US Navy in World War II and its increasing reliance on quickly emerging new technologies owed its success, in part, to the previously overlooked work of women. Much of this work was at the level of technician and mechanic, but there were also numbers of women with advanced educational and professional qualifications who held responsible positions during the war and who made high-level contributions in technical fields. While naval historians are increasingly interested in World War II technology, and historians in general are taking more account of the historical roles of women, no one is looking at these exceptional women who voluntarily set aside their professional lives to serve their country.
My talk focuses on the war work of two of these women: mathematicians Grace Murray Hopper (1906-1992) and Mina Spiegel Rees (1902-1997). Both were college professors until war service intervened. One joined the navy and the other remained a civilian but between 1943 and 1945 each held positions from which they influenced the U.S. Navy’s ability to wage a modern, science-dependent war. With a Ph.D. in mathematics from Yale University, Hopper taught at Vassar College in New York before joining the navy at the age of thirty-six. In June 1944, newly commissioned Lieutenant Hopper was sent to Harvard University's Computation Project, which had been taken over by the Bureau of Ships for the duration of the war. At Harvard the navy introduced Hopper to the emerging world of computing, pushing her into the new field which was to absorb the rest of her life. With no time for training she learned on the job how to program Harvard professor Howard Aiken’s Mark I computer, the first functional, large-scale, automatically sequenced, general-purpose, digital computer to be produced in America, and one of the few computers ready early enough to play a significant role in the war. The Mark I ran around the clock, churning out essential data for all sorts of ordnance projects, making complex calculations for navy guns, acoustic and magnetic mines, self-propelled rockets, and the atomic bomb. In addition to being one of only three programmers for the Mark I, and writing its first manual of operations, Hopper was instrumental in the development of its successors, the Mark II and the Mark III which were used by the navy after the war.
At the age of forty-one, Mina Rees, a Hunter College mathematician, was plucked from her quiet academic environment to help administer an unprecedented government-sponsored effort to organize scientific research for war. From 1943 to 1946, as Technical Aide to the Applied Mathematics Panel of the National Defense Research Committee, she oversaw contracts for navy and, to a lesser extent, for other military and civilian scientific projects involving extensive mathematical calculations. As assistant to Warren Weaver, the panel’s head, Rees was responsible for identifying significant projects and persuading suitable mathematicians to work on them, in the process directing funding involving millions of dollars of government money. Years later, Rees was recognized for her role in "deploying and sustaining" her country's mathematicians in the war effort.

14:40-15:00, Comments and Discussion, Chair Matthias Lesch, Cologne
15:00-15:15, Coffee Break
15:15-15:55,

Tinne Hoff Kjeldsen (Mathematics Historian, Roskilde University, Denmark)
War as the Midwife of Mathematical Disciplines

In this talk I will focus on the significance of the Second World War for the rise and establishment of new disciplines in applied mathematics as well as for the renewed interest and growth in some related subjects in pure mathematics. The mathematical topics involved are mathematical programming, operations research, game theory, the theory of convexity, and the theory of systems of linear inequalities. Connections and interactions between different branches of mathematics on the one hand and between different kinds of driving forces in the development of mathematics on the other hand will be discussed. Special emphasis will be devoted to the significance of the interplay between practical problem solving and basic research in mathematics proper as a consequence of World War II and the post-war organization of science support in the USA.

15:55-16:35,

Revaz Valerianovich Gamkrelidze (Mathematician, Steklov Institute of Mathematics, Russian Academy of Sciences)
The Discovery of the Maximum Principle in Control Theory

Discovery of the Maximum Principle for the needs of optimal control and the subsequent development of optimization methods give a classical example of a mathematical theory, which initially emerged as an effective device for solving a purely engineering problem not amenable by existing mathematical methods, and eventually developed into a mathematical theory of major significance.
The Maximum Principle was discovered by L.S. Pontryagin in 1955 in an attempt to find a solution of a highly specific optimization problem related to the manoeuvres of an aircraft, formulated to him by two Air Force engineers.
I intend to briefly describe the history of this discovery, of which I was a witness and partially, together with Professor V. Boltyansky, a participant. We were both Prof. Pontryagins former post-graduates and at that time his young collaborators.

16:35-16:55, Comments and Discussion

18:00, Mayor's Reception, Town Hall


19:00, Public Lecture, Karlskrona Naval Museum

Philip J. Davis (Mathematician, Brown University, Providence, R.I., U.S.A.),
Mickey Flies the Stealth: War and Entertainment

The link between war and entertainment is probably as old as warfare itself. The speaker will describe some ancient war "games" and then move to the present scene where computer graphics and mathematical software have been playing a major role.




Friday, August 30
2. Co-development of Mathematics and the Means of War? Perspectives from the Military

9:00-9:40,

Svend Bergstein (Lieutenant Colonel (ret.), Copenhagen),
War Cannot Be Calculated

The Austrian philosopher Karl Popper in 1945 criticized the method of the social sciences. He stated that a strategist's attempt to foresee the outcome of a battle is not a scientific prediction but a historical prophecy.
Odd hundred years earlier, a reflective and experienced Prussian officer, Carl von Clausewitz, drafted a momentous book: "On War". Here he argued that war is an act of human intercourse. This makes war an object for social science. Clausewitz was in line with Popper: Though we may be able to estimate the outcome of a single battle, we have to realize that it is only an estimate and not a prognosis. Thus – when we go to war, we venture into a fog of uncertainty.
War is a continuum ranging from political ambitions to mere technology. In order to be able to analyze war at all, Clausewitz made a distinction between war as a political tool, a phenomenon in itself, and warfare, the appliance of organized violence "within" the war. The upper level of warfare is normally referred to as the art of war.
One of Clausewitz´s conclusions was "…thus we see, how the absolutes, the so-called mathematical, from the very beginning, finds no foothold anywhere in the estimates of the art of war…". My ambition is to verify this particular conclusion.

9:40-10:00, Comments and Discussion, Chair Stig Andur Pedersen, Roskilde

10:00-10:40,

Svend Clausen (Cing., Danish Defence Research Establishment, Copenhagen),
Warfare Can Be Calculated

The practical need for and some general limitations of combat modelling will be mentioned.
Two traditional deterministic Lanchester laws will be presented, discussed (especially with regard to hidden assumptions) and criticised (traditionel Lanchester laws are quite often used far outside their field of validity). This goes for

  • the linear Lanchester law (for combat with limited detection capability) and
  • the square Lanchester law (for combat with limited kill capability).
  • These deterministic Lanchester laws will be compared to similar stochastic Lanchester laws to illustrate general problems with determining the average combat outcome.
    The basics of an existing and unique Danish combat model, Defence Dynamics will be explained and discussed. Defence Dynamics is a deterministic model, which based on Markovian processes integrates the above mentioned linear and the square Lanchester law. Defence Dynamics intends to determine the average combat outcome. Furthermore Defence Dynamics includes a large number of more realistic features and is able to represent a broad spectrum of combat from two weapon systems fighting each other to a full scale triservice war. Defence Dynamics has been used for a number of practical purposes, for example Danish long term planning.

    10:40-11:00, Comments and Discussion
    11:00-11:15, Coffee Break
    11:15-11:55,

    Helge Löfstedt (Military Analyst, Swedish Defence Research Establishment, Stockholm),
    Duels of Systems and Forces

    My presentation will start with a presentation of the vital changes in warfare during the last decades. Mass armies are no more common tools for warfare. The big war has turned unusual, while limited (and controlled) use of military forces for political purpose still is in use. However the ability to maneuver and fight with weapons still remains a basic military skill and modeling of combat remains important for understanding war. A formulation of a basic problem for single weapon systems will be given and the effect of technology development are discussed in that context. Further comments will be given on problems in information processing in modern weapons and in Command, Control, Communication and Intelligence, where the technological changes are expected to be revolutionary. A short comment will also be given on transforming single weapons data to force characteristics, which is important for connecting analyses on low level with those on high level. I will also give some comments on Operations Other Than War and Asymmetric War - which are new challenges for military analysts as well as officers. Finally a critique will be given on the state of the art in military modeling.

    11:55-12:15, Comments and Discussion
    12:15-13:15, Lunch
    13:15-13:55,

    Elmar Schmähling (Rear Admiral (ret.), Berlin, Germany),
    Less or More Exposed Non-Combatants and Civilian Objects Under "Surgical Strikes"?

    In my contribution I will elaborate on facts, perceptions and allegations with regard to so called surgical strikes. What are the technical changes in modern weaponry? What are the professional and psychological approaches towards high tech arms? Political, legal, military and humanitarian aspects of the use of military force will be addressed in connection with "humanitarian intervention" and "fight against terrorism" before the background of NATO's aggression against Yugoslavia and war in Afghanistan.

    13:55-14:15, Comments and Discussion, Chair John Perram, Odense

    14:15-14:45,

    Ralf Bendrath (Political Scientist, Research Group Information Society and Security Policy, Berlin, Germany)
    Cyberwarfare: Fiction, Facts and the Future of Arms Control

    The presentation will give a real-world based assessment of the developments in cyberwar, i.e. war in, on, and against data networks. Do we have to fear cyberterrorism or rather a new digital arms race between states. Finally, some implications on how to deal with arms control in this field will be discussed.

    14:45-15:00, Comments and Discussion, Chair John Perram, Odense
    16:00, Guided Tour of the Naval Museum


    Saturday, August 31
    3. Co-development of Mathematics and the Means of War? Ethical Issues

    9:00-9:40,

    Finn Aaserud (Historian of Science, Niels Bohr Archive, Copenhagen),
    Niels Bohr's Political Crusade During World War II

    Niels Bohr's "Open Letter to the United Nations", published in 1950 and pleading for an "open world" between nations, is well known. It is also well known that Bohr took part in the Manhatten Project during World War II. My paper will describe in some detail how Bohr's idea of an open world not only matured during his war-time exile, but even constituted the basis for a veritable crusade on Bohr's part in the course of the war to convince the statesmen of the necessity to think differently in the post-nuclear bomb era. How and why did Bohr come to these ideas? Why were they so important to him? How did his crusade relate to his simultaneous participation in the Manhattan project? What means did he use during war-time to convince the statesmen? How successful were his efforts? What general lessons, if any, can be drawn on the basis of Bohr's crusade with regard to the political role of the scientist, particularly in a war situation? These are some of the questions to be taken up in the course of the talk.

    9:40-10:00, Comments and Discussion, Chair Heinrich Wefelscheid, Duisburg
    10:00-10:40,

    Andrew Hodges (Mathematician, Oxford, Great Britain),
    Military Use of Mathematics During and After World War II: the Case of Alan Turing

    Alan M. Turing (1912-1954) was the chief scientific figure in the British communications war, personally responsible for the reading of Atlantic U-boat signals. As a result of this experience, he emerged in 1945 able to design a digital computer in the modern sense, as a practical version of the Universal Turing machine he had described as pure mathematics in 1936. In one sense, therefore, the war greatly accelerated the application of mathematical ideas. Yet Turing's chief mathematical collaborator, M. H. A. Newman, gave an entirely different assessment, presenting in entirely negative terms the loss to science caused by the war having interrupted Turing's career. This paper will examine both viewpoints, tracing the positive and negative influences of the war in Turing's theories of computation and artificial intelligence.

    10:40-11:00, Comments and Discussion
    11:00-11:15, Coffee Break
    11:15-11:55,

    Jesper Ryberg (Philosopher, Roskilde University, Denmark),
    Military Research and Moral Responsibility

    The purpose of this paper is to discuss the personal moral responsibility of scientists contributing to military research. A number of arguments defending the view that scientists do not carry any responsibility (or only a marginal responsibility) for the way in which their work is used are evaluated. It is argued that none of the arguments are convincing. Furthermore, some of the difficulties related to the ascription of moral responsibility to scientists are considered.

    11:55-12:15, Comments and Discussion
    12:15-14:00, Lunch
    14:00-14:40,

    Ib Martin Jarvad (International Lawyer, Roskilde University, Denmark),
    Mathematical Thinking and the Law of War

    I shall address: 1. The revolution in the 17th century of the military, the state, and the rules of war and peace. 2. The application of mathematics to the art of warfare, political science and to law. 3. The 17th century’s conception of natural law as the science of really existing moral phenomena like physics as the science of real physical phenomena. 4. The Law of War and Peace by Grotius was the establishment of a new moral legal order on a new secular basis. Therefore the mathematical method explicitly subscribed to by Grotius meant something different from axiomatic deductive reasoning. 5. Examination of his forensic method of argument in persuasion and his historical theory of the relations of moral phenomena with phases of socioeconomic development. 6. The Grotian regime of the present and the role of military in it.

    14:40-15:00, Comments and Discussion, Chair Matthias Kreck, Heidelberg
    15:00-15:40,

    Jürgen Scheffran (Physicist, Institute for Climate Impact Research, Potsdam, Germany),
    Calculated Security? Mathematical Modelling of Conflict and Cooperation in Social Systems

    Since the pioneering work by L.F. Richardson on modelling the arms race between the World Wars, it was hoped that mathematics can contribute to conflict resolution. In this talk I shall discuss whether and how mathematical modelling might be used to analyse and resolve conflicts as well as to understand the evolution of cooperation and the formation of coalitions in social systems. It is a key question to what extent mathematics can identify conditions for the instability of social interaction, potentially leading to an escalation towards violent conflict, arms race and war. Examples will be given where mathematics was able to provide a mechanism to stabilize interactions via communication and negotiation, disarmament and verification, confidence-building and common security concepts. Another question is to what extent "dynamic games" are appropriate or inappropriate to study the relationship between conflict and cooperation in international security policy (e.g. missile defense and nuclear disarmament) as well as conflicts between environmental and economic systems (energy and climate change, fishery conflicts, sustainable resource economics).

    15:40-15:50, Comments and Discussion
    15:50-16:30, Closing Remarks by Bernhelm Booss-Bavnbek (Mathematician, Roskilde University, Denmark) and Open Discussion.

    Send an electronic message to Charlyne de Gosson at cdg@ihn.bth.se. You may download our poster, and our folder front page , back page in PDF format or poster and folder front page , back page in PS format.


    Back to Department of Mathematics and Physics at Roskilde University

    Rel. 5.2; Date August 12, 2002. Please send suggestions, criticism and contributions to cdg@ihn.bth.se or Booss@ruc.dk