WILLIAMSTOWN -- William Wootters has a conundrum -- a mathematical conundrum.

Wootters is a physics professor at Williams College, and on Thursday he's one of the presenters of the Williams Faculty Lecture Series. His lecture is titled: "Why Does Nature Like The Square Root of Negative One?"

Here's the conundrum: The square root of negative one is an "imaginary'"number, a number that exists, but it is not a "real" number.

"For a long time, people said there is no such thing," Wootters said.

But today, although the square root of negative one is an "imaginary" number, it is an integral part of several formulas in quantum physics, Wootters explained.

"It turns out to be really useful in mathematics and central to fundamental equations of physics," he said. "It's quite surprising that quantum mechanics depends so crucially on this ‘imaginary' number. It's extremely successful, but still a mystery."

In quantum mechanics, the square root of negative one is used to compute probabilities. That's the mystery. One would not use an imaginary number to compute, say, the probability of rolling a six on a die. Still, teachers have a hard time explaining it and students have difficulty understanding it.

Wootters' lecture, he said, will explore the square root of negative one, its role in quantum physics, and why its presence there calls out for explanation.

"We know that it works, and many people are OK with that," Wootters said. "But I'm hoping that someday we'll understand it better."

The presentation will begin at 4:15 p.m. on Feb. 21 at the Wege Auditorium in the Science Center at Williams College. For more information: www.williams.edu.

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