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Stanford Professor Discusses Math Modeling

FullTextImage/img/@altDr. Keith Devlin discusses mathematical modeling in a talk earlier today at VMI. -- VMI Photo by Kevin Remington.

LEXINGTON, Va., Nov. 5, 2012 – A mathematical model of the modern battlefield is like a child’s building block – a deceptively simple structure that can be used to facilitate a myriad of designs, noted mathematician and author Dr. Keith Devlin told an audience of cadets, faculty, and interested community members in a talk at VMI Monday morning.

Devlin, who is a professor of mathematics at Stanford University and director of the university’s Center for the Study of Language and Information, came to VMI as part of the H.B. Johnson Jr. ’26 Distinguished Lecture Series. The subject of his talk, “A Mathematical View of the Modern Battlefield,” grew out of the work he’s done at Stanford on situation theory, a field of mathematics developed by Devlin and others in the 1980s as part of an effort to create a mathematical model of language usage.

At the start of his talk, Devlin gave a brief snapshot of mathematical history. Ancient Sumerians invented numbers so they could have banking and commerce, Devlin explained, and other ancient peoples invented geometry and trigonometry so they could construct buildings and navigate the seas. Probability arose in the 17th century, as people began to understand that they could predict the outcome of random events, and today, situation theory has come along to explain the modeling of multi-agent operations such as warfare.

“All branches of mathematics came out of efforts to understand the world,” said Devlin, who is known as “the math guy” on National Public Radio. “All math, even the most esoteric math, can trace its way back to the real world.”

Devlin then shared with his audience the factors that must be taken into consideration when constructing a mathematical model of the battlefield. The list includes terrain; people; weapons and equipment; vehicles, both manned and unmanned; supplies; information and computer technology; and information about people, weapons, and vehicles.

“All of this stuff needs to be modeled,” said Devlin. “The killing may be local, but the battlefield is global.”

To give his audience an idea of how situation theory can be applied to the battlefield, Devlin showed a graph of a rectangular structure similar to a building block, in which a clue (smoke) leads to an inference being made (fire). When hundreds or thousands of these rectangular blocks are layered together, the result is a model of the battlefield that is both mathematical and reflective of the real world.

Devlin closed his remarks with a reiteration of his message that doing math is a process of making observations and drawing conclusions. “[Situation theory] is no different from what Archimedes was doing 2,000 years ago, modeling the world.”

–Mary Price