By the Numbers

Professor shows us how to work out the probabilities


(As published in the Calgary Herald, November 19, 2005.)

The dream of Jeffrey Rosenthal, a University of Toronto professor, is for his fellow citizens to acquire a "probability perspective."

Hence his new book, Struck by Lightning: The Curious World of Probabilities (HarperCollins, 264 pages, $34.95), a mild-mannered professor's attempt at bringing math to the masses.

"This book doesn't require any mathematics background," Rosenthal says. "A lot of people are scared -- if a book's got something to do with math they won't even dream of picking it up. But probability theory has a lot of relevance to everyday life and understanding the world around us."

Struck by Lightning is a short, entertaining and highly readable guidebook to learning how to incorporate probability theory into everyday life. Rosenthal creates a breezy mix of direct yet simple mathematical tools for decision making along with explanations for things the non-mathematically minded have always wanted to know, but were unsure how to ask. There is a chapter on why casinos always come out on top (including tips for playing card games), a chapter on how to understand opinion polls (what exactly does "accurate 19 times out of 20" mean?) and throughout the book there are numerous examples of how common fears can be put into manageable perspective.

Rosenthal writes about his topic with such clarity and warmth that even the fiercest math-phobe will feel welcome. He believes "probability and randomness apply to just about everything. That is, anything where you don't know for sure exactly what's going to happen next that's probability and that's randomness. I'm not going to say that if you understand probability then you understand everything or that you always know what to do next, but I do think that it always helps."

For instance, in the case of wanting to ask someone out on a date, but being unsure whether to go through with it, Rosenthal recommends assigning a number value, known as a utility function, to potential outcomes. The eventuality that the person you want to ask out accepts could be assigned a value of +1,000, while the value of that same person declining could be given a value of -50 (because really, there's nothing to lose). The odds of that person accepting the invitation could be figured at, say, 10 per cent.

All of this is subjective and up to you, depending on the available information and your intuition. To figure out whether it's worth making the call, Rosenthal writes in the book, "Well, 10 per cent of the time you would score +1,000 (if the person agrees to go out with you), which works out to +100. And 90 per cent of the time you would score -50 (if that person rejects you), which works out to -45. You conclude that making the call has an average utility of +100 -45, which equals +55, a net positive. So, on average, you stand to gain from making the call."

It appears, in grasping this, that at long last there is a concrete way to wrestle indecision.

"If you're feeling uncertain," Rosenthal explains, "it can be useful to sit down and ask yourself what the possible outcomes and probabilities are. To me, it can be helpful and a comfort that there's some way to approach such problems. It's not that mathematics will solve your problem for you, but it will at least provide a context for it."

Rosenthal has led a life of math. He was born in Scarborough, Ont., in 1967, into a family that was somehow involved with math. "My parents were both math teachers, my grandfather taught high school math and my uncle was an accountant. Unlike most families it was not at all strange to want to study math; in fact, it would have been stranger not to."

By his early 20s, Rosenthal was already a graduate student at Harvard. "I was in a rush to get established -- I got my PhD at 24 and tenure at 29. Partially it was because I never took time off to study something else, or take a year in Europe to find myself. I thought I'd get tenure then find myself."

If probability theory can be applied in some way to just about everything -- from lottery tickets, to e-mail spam, to dating -- doesn't it take some of the magic out of life? Rosenthal says no. "It doesn't to me. For me, the more you understand something, the more magical it is." Nor should a probability perspective, as Rosenthal calls it, supplant intuition. "I still have intuition and gut feelings. I try as much as I can to quantify things, but you can't always. There are times when I have a gut feeling about something I can't explain in probability terms, but I still respect it because somewhere deep underneath it must be reflecting some knowledge I have. Probability is related, it's a more precise gut feeling."

Beyond its everyday applications, Rosenthal also believes that a greater understanding of basic probability can help dismantle the current culture of fear.

"It seems that people's fear of things is not very accurately related to the probability of them happening," Rosenthal explains. "From the SARS panic that didn't actually kill so many people to homicides -- newspapers tell us how scared we should all be when in reality only a small fraction of people die by homicide."

Rosenthal also points to the 2001 terrorist attacks in New York, Pennsylvania and Washington, D.C. "There's a lot to be concerned about with terrorists, but at the same time it is possible to put the numbers in perspective. The 9-11 attacks were so horrific that sales of anxiety medicines shot way up. Well, more Americans died in automobile accidents that same month as died in the 9-11 attacks. That's not in any way to minimize the attacks, but to put it in perspective. Just like we don't all get fearful and take anxiety medicines because we hear that there were so many car accidents in a given month, we should maybe also not overreact when it comes to terrorism."

In the end, Rosenthal hopes readers will get something useful out of his book. "If people say that it was fun to read, then I'll consider that a victory. But I also hope more substantially that people can take away from the book that it's worth thinking about things in a more precise way -- especially things involving uncertainty and randomness. Just a little bit of an understanding of probability can go a long towards understanding how a lot of things work."

Using Rosenthal's own utility functions, I'd assign Struck by Lightning an entertainment value of +70, a math cringe factor of only -25 and a helpfulness rating of +90. All in all, the probability of it being successful is very good.

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