Use of mathematics during the Vietnam War

SUMMARY: Because of the importance of cryptography in World War II and the emergence of game theory in the 1950s, mathematics was heavily involved in the Vietnam War.

The Vietnam War, a conflict transpiring in Vietnam, Cambodia, and Laos from 1955 to 1975, involved the Communist forces of North Vietnam, the Viet Cong, the Khmer Rouge, the Pathet Lao, the People’s Republic of China, the Soviet Union, and North Korea, against the anti-Communist forces of South Vietnam, the United States, South Korea, Australia, the Philippines, New Zealand, Thailand, the Khmer Republic, Laos, and the Republic of China. Most American involvement was concentrated from 1963 to 1973, with the last U.S. troops leaving with the fall of Saigon in 1975. It eventually resulted in a Communist victory, with U.S. forces and their allies withdrawing, Communist parties taking control of Laos and Cambodia, and South Vietnam unified with the North under Communist rule.

Quantifying War

A timeless question regarding military operations is whether they are quantifiable into mathematical models that are programmed to ensure successful outcomes. This question cuts to the issue of whether military leadership is an art or a science. The former suggests military leadership is a process of grooming an individual for command, with a key aspect being the accumulation of sufficient experience that will render sound judgment in battle. The latter option aligns with a fascination that battlefield success is manufacturable. Under this system of belief, the tangibles of war are identified and replicated, and warfare is programmed for success. Under this scenario, military leadership is not of the highest priority, but rather adherence to algorithms engineered for victory.

Time-honored principles of warfare have been in circulation since at least the time of Sun Tzu, a Chinese military strategist (544–496 BCE), whose theories of warfare continue to resonate into the twenty-first century. Another oft-quoted person was Carl von Clausewitz, whose treatise On War is another timeless handbook on the nature of warfare. These two authors fundamentally differ from others such as Antoine-Henri Jomini. Jomini studied the campaigns of Napoleon in depth. From his observations, Jomini published what were essentially templates on how to position forces for success. Jomini essentially performed systems analysis in the nineteenth century, a practice employed one hundred years later by US Secretary of Defense Robert McNamara (1916–2009) which led the United States to its debacle in the Vietnam War. 

Mathematicians and the War

Mathematicians fell on both sides of the disagreement regarding the Vietnam War. Some served in the war effort, such as William Corson, an economist with an undergraduate degree in mathematics who later wrote the book The Betrayal. Grace Murray Hopper returned to active duty in 1967 because of an increased demand for naval computer systems. Others engaged in war-related research. Warren Henry helped develop the hovercraft for nighttime fighting during the 1960s while working at Lockheed Space and Missile Company and this was used in the war.

In 1966 and 1970, mathematicians at the International Congress of Mathematicians appealed to their colleagues to avoid war-related work. Mathematicians around the world organized or participated in protests, including Alexander Grothendieck in France and Steven Smale in the United States. Mathematicians in Japan at the University of Kyushu in South Japan organized “demonstrations of the 10” against the war on the 10th, 20th, and 30th of the month. Funding originally designated for teacher development during the New Math movement was instead directed to the war. Some have asserted that this diversion of funds was one of the main reasons that the educational movement failed. Mathematics played a role in the war in a number of ways, including war strategy, precision weapons, airplane computers, cryptography, and a statistically flawed 1969 draft drawing. Statisticians and others have used statistical techniques to study the long-term effects of Agent Orange on soldiers. Decision theory has been used to model the war. Systems analysis and game theory may have contributed to U.S. involvement and defeat, such as in the decisions of Secretary of Defense Robert McNamara.

Game Theory

One of the key political leaders of the American forces during the Vietnam War was McNamara, a student of game theory, who served as the secretary of defense from 1961 to 1968—the period corresponding with the nation’s first serious engagement with the war and its major expansions and escalations. McNamara was also responsible for the policy of Mutually Assured Destruction (MAD), a nuclear policy grounded in game theory. It said that the best deterrent to full-scale use of nuclear weapons was for opposing sides to each possess sufficient firepower to completely destroy the other so that neither side dares attack, knowing it cannot survive the counterattack. A chilling take on foreign policy, history may be on McNamara’s side with the Cold War. The escalating war in Vietnam is another story. From a game theory perspective, those escalations make perfect sense. Consider that fact that North Vietnam had the options to escalate or to negotiate a peace. The United States also had those options as well as the option to pull out. The only way for the United States to gain a military advantage—and potential victory—was to escalate, with the worst possible outcome of such escalation being a stalemate. Despite increased desertion and plummeting morale, as well as growing anti-war sentiment at home, McNamara continued to escalate the engagement because it was the most promising option he was trained to see.

This was later used as an example of “escalation of commitment,” a phenomenon identified in Barry Straw’s 1976 paper “Knee Deep in the Big Muddy: A Study of Escalating Commitment to a Chosen Course of Action,” wherein cumulative prior investment becomes the motive to continue to escalate one’s investment even when rational thought says it is the wrong choice. That initial error of judgment becomes the motive to continue, to stay committed to the course of action, in order to justify it. The more one continues, the greater error one must admit to if one disengages, which is why psychologists sometimes refer to this phenomenon as the “commitment bias,” a natural tendency to want to believe that one has been making the right choices and to ignore evidence to the contrary.

Bibliography

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Bosse, Michael. “The NCTM Standards in Light of the New Math Movement: A Warning!” The Journal of Mathematical Behavior, vol. 14, no. 2, 1995.

Bunge, Mario. “A Decision Theoretic Model of the American War in Vietnam.” Theory and Decision, vol. 3, no. 4, 1973.

Cavanaugh, Matt. "Uncontrollable War: Why We Can't Accurately Predict or Adequately Prepare for Violent Conflict." Modern War Institute at West Point, 6 Jan. 2017, mwi.westpoint.edu/uncontrollable-war-cant-accurately-predict-adequately-prepare-violent-conflict. Accessed 2 Oct. 2024.

Johnson, Bill, et al. "A Scientific Approach to War? Antoine-Henri Jomini." Great Strategists from War Room, 5 Sept. 2019, warroom.armywarcollege.edu/special-series/great-strategists/scientific-approach-to-war-jomini/. Accessed 2 Oct. 2019.

Livieratos, Cole. "From Complicated to Complex: The Changing Contex of War." Modern War Institute at West Point, 14 June 2022, mwi.westpoint.edu/from-complicated-to-complex-the-changing-context-of-war. Accessed 2 Oct. 2024.

Starr, Norton. “Nonrandom Risk: The 1970 Draft Lottery.” Journal of Statistics Education, vol. 5, no. 2, 1997.