# Predicting the unpredictable

#### Mathematics can help us make sense of the complex and sometimes destructive forces of nature

*by Peigi McGillivray*

Remember when your mom told you to do your math because you’d need it when you grew up?

For centuries, people who listened to their mothers and did their math—such as Dr. Florin Diacu, a University of Victoria mathematician—have used mathematical models to try to explain and predict complex and destructive natural phenomena, including asteroid collisions, earthquakes, tsunamis, volcanoes, hurricanes, pandemics and climate change.

Mathematical modellers use real-world data to create representations of complex systems and phenomena. They then conduct experiments on the models to deepen understanding and make predictions—such as when and where asteroids might hit the Earth, how tectonic plates move, and what factors influence hurricanes.

“Some of these phenomena are easier to model than others,” says Diacu, whose research focuses on the mechanics of celestial bodies such as planets, stars, asteroids and comets. He’s particularly interested in the stability of our solar system, the shape of the universe, and how collisions of celestial bodies occur.

“All of these things deepen our understanding of how celestial bodies move so that we can make better predictions.”

The forces that guide asteroids and comets are already well known, so mathematicians can create very accurate models that tell them exactly when a collision with Earth will occur. “Knowing this gives us a chance to deflect or destroy these bodies before they do any damage,” he says.

In case you’re wondering, there’s no indication an asteroid will collide with the Earth anytime soon, although modelling predicts a couple of close encounters in about 30 years. “A few years before they arrive, we’ll know for sure how close they’ll come,” says Diacu.

Unfortunately, not all catastrophes are as easy to predict as those in space, even with mathematical modelling. “Climate change, for instance, is highly unstable and complex with many, many factors to account for,” says Diacu “It’s difficult to create accurate mathematical models for climate change but the estimates we have are very good.”

Earthquakes present the same problem. “With earthquakes, we can talk about probabilities, but not predictions,” says Diacu. “We know there are periods when they are more likely, but that’s like knowing accidents are more likely to happen during rush hour. It’s still hard to predict exactly when or where one will occur.”

Diacu’s most recent book, the highly readable Megadisasters: Predicting the Next Catastrophe, looks at a wide range of large-scale disasters—including earthquakes, tsunamis, hurricanes and climate change—and describes the scientific and mathematical struggle to understand and predict these complex events over the centuries.

“As technology has improved, we have become better equipped to create the models we need to understand chaotic systems,” says Diacu. “The work we do today stands firmly on a foundation of mathematical models created by countless scientists and mathematicians around the world over the centuries.”

Diacu is also a gifted and popular teacher who brings his wide-ranging interests into the classroom to inspire graduate and undergraduate mathematicians.

“Students at UVic are looking into some of the most complex and sophisticated mathematical problems around,” says Diacu. “They’re doing important work that will deepen our understanding of the real world.”

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- Florin Diacu is the author of three popular science books: Celestial Encounters, a history of ideas in the field of chaos theory; The Lost Millennium, an exploration of the history of chronology; and Megadisasters: Predicting the Next Catastrophe, a history of the struggle to understand the destructive forces of nature.
- Statistics show that Vancouver Island has regular periods when earthquakes are more prevalent —once every 14 months for about two weeks at a time—although most are so minor we don’t feel them. There is currently no explanation for this pattern. Mathematical modelling predicts that an earthquake of magnitude 9.0 or greater will occur in this region, but can’t tell us when or where it will strike.
- Mathematics can also help predict individual “disasters,” such as whether you’ll lose when you gamble at the casino (hint: you’ll win only about 47 per cent of the time, so the longer you play, the more likely you are to lose).
- UVic researchers were awarded more than $104 million in outside research grants and contracts in 2008/09—more than double the research support of five years ago.