Mary Cartwright, Radar & Chaos Theory
If you increase the rate of water flow to a rotating waterwheel, the wheel goes faster. But at a certain point, its behavior becomes unpredictable. It speeds up and slows down without warning. Or even changes direction. Chaos theory is the mathematics behind this phenomenon. Mary Cartwright is a pioneer of chaos theory. A memo from the British Government sparked her work.
With the threat of war looming in 1938, the British Government issued a math challenge. Though unstated, the military was testing the first radar systems and they were acting erratically. The government blamed the manufacturer.
Mary Cartwright, a professor at Girton College in Cambridge, got the memo. She was working on a similar math problem and partnered with professor JE Littlewood at Trinity College. Cartwright and Littlewood discovered that radar is like a waterwheel, its acts naturally with a certain unpredictability. The manufacturers weren’t to blame; the equation was.
The military decided to operate the radar within a predictable range—they kept the water flowing at a rate that didn’t generate as many erroneous signals.
It worked.
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Cartwright and Littlewood’s observations formed the foundation of chaos theory. It took 20 years to be recognized. Her original work was published shortly after the war ended. This is how real mathematical originality works, according to Freeman Dyson, who recalls:
"When I heard Cartwright lecture in 1942, I could see the beauty of her work but I could not see its importance. I said to myself, 'This is a lovely piece of work. Too bad it is only a practical wartime problem and not real mathematics.' I did not say, 'This is the birth of a new field of mathematics.' I shared the tastes and prejudices of my contemporaries."
While researching radar analytics (below), I grew to appreciate Dame Mary Cartwright’s work. Chaos theory aids understanding of the earth’s weather system, swinging pendulums, water flow, and even the stock market. It seems appropriate to celebrate her inspirational story during women’s history month.
