How people think

Partly because I was curious about what might happen next, I arranged a visit with the math student advisor to discuss, among other things, college algebra.

I had no idea when I set it up, I would get to enjoy one of my most inspiring hours in months.

But first, another math quote:

"You better cut the pizza in four pieces because I'm not hungry enough to eat six." -- Yogi Berra. I wonder whether Yogi even saw a tenth of the quotes attributed to him.

My UA Math Advisor

My appointment was at 11:30 a.m. in the Math Building with advisor Marcy DeWeese.

I don't think I was intimidated or anything, but once I found the elevator, I kept pushing the wrong button to call it. I finally found the right one and pushed it. But then I noticed the stairs and took them to the second floor.

I knocked on the door of room 202, Marcy's office. She opened it a crack and said she'd be with me in a minute. She was with another student.

As I sat outside her door I noticed a flier on a wall featuring a very attractive woman and the headline read, "Math Doesn't Suck." Well, good to know. Turns out it was promoting a book called, Math Doesn't Suck: How to Survive Middle School Math Without Losing Your Mind or Breaking a Nail , by Dancia McKellar. I checked the book's Amazon ranking, and it's up there. Not bad for a 320 page book about math.

In just a couple of minutes a petite and energetic 50 year old with tons of energy and a great smile welcomed me in to her office. I liked her immediately. We talked about marathons (she's done more than 10), El Tour de Tucson (she did the 85 mile version last year), and about the UA advisor's we knew in common.

Then we talked about math degrees. There is a lot to it and a lot that I really don't want to bother with -- things outside of math that they make the undergraduates take so they can be well rounded. Marcy told me that she imagined that many of my general studies courses from nearly 40 years ago might count. OK, we'll face that problem when I'm well into my 60s if I pass a couple of classes. Meanwhile, she told me, the next class I need to take is math 112, college algebra. Check.

But, more important, Marcy told me about a current student who I might be interested in knowing. a 50-year-old MD was pursuing a math degree. I can't wait to talk to him about sanity. Since Marcy is not allowed to give me his name or contact info, I gave her mine and asked her to pass it along to that doctor and invite him to call or email me. I hope he does.

I got up, thanked Marcy, and stepped outside her door. And, that's when fate (not that I believe in that) stepped in.

One of the professors I most admire in the whole university is Bill Velez. He is a math professor who I've never had but have assigned stories about and have photographed. He has been on the top of the list of people I have wanted to talk to about my own math adventure and about my book idea. Of course, I haven't done it yet.

So, as soon as I'm out of Marcy's door and turn to look for the stairs, I notice Bill walking around the corner. I immediately went up to him and reminded him who I was and told him how I've been meaning to eamil. We chatted for a moment and after he asked what I was up to, I told him I was taking intermediate algebra through Pima College and was hoping to take college algebra through the UA next semester.

That conversation really didn't go anywhere except that he invited me to set up a time when we could talk. But he told me they were having a pizza lunch right then with math students and a professor from UC Irvine. Would I like to join in? Sure!

Professor Donald Saari

He had Santa Claus eyes and a white beard, but it was short. He didn't say Ho! Ho! Ho!, but his demeanor did. When I walked in, he was going around the informal lounge asking the fifteen or students about themselves and their interests in math. He engaged every student and encouraged their thinking.

When I walked in the room, I had no idea that the speaker was a big time, internationally respected (and possibly revered) mathematician. Donald G. Saari is now a professor at the University of California, Irvine and director of their Institute for Mathematical Behavioral Sciences. He is a member of the National Academy of Sciences, has written and published 10 books and more than 160 articles, and is a Guggenheim fellow. And, for more than 20 years, during his tenure at Northwestern University, he served as Santa Claus at department Christmas parties.

One girl said she was taking micro-economics but didn't care for it. Professor Saari asked why. She explained that she could do the math easily enough but she thought there was a disconnect between what models predict and real life. The prof jumped on the thought and said she was so right. He agreed. But that's why math was so important.

When he came to me I explained a lot of what I've already written about here but also added how much I enjoy being exposed to people who are not part of my regular world, people who look at the world in ways that I may not even yet imagine, you know, unusual people. He smiled and glanced around at the math students and said, "I think he just called all of us strange." They all laughed.

Then he asked me, "How do you tell the difference between a an introverted and an extroverted mathematician?" I knew the answer but wasn't quick enough to get it out correctly. So, bailing me out, he said, when you're having a conversation, "the extrovert looks at your shoes instead of his."

I asked him, what has become a regular question when I'm around scientists or mathematicians, "Is there a term to describe when people trust their assumptions and the math is correct, and therefore they believe their conclusion, but the real world conclusion is absurd on its face?"

Without skipping a beat he said, "Yes. Wishful thinking!"

But then, more seriously he said, "If the model doesn't match the reality, you look at the data. You look at the assumptions."

Earlier in the week, while I was still deciding whether or not to take another math class, I was thinking more about the math experience generally. I certainly wasn't spending all this time just to learn some mechanics with numbers or even what buttons to push on a calculator to solve a complicated looking equation. What I was really curious about was how mathematicians see the world, or how I could look at the world or a situation the way a mathematician would. How mathematicians think.

I know how to look at the world as a journalist and as a photographer. During high school and my first two years of college, I could look at the world through the eyes of a poet and a play write. Most of my motivation for getting an MBA was to figure out how business people think. I figured it out, but don't do it. And when I went through my Ph.D. program and wrote my dissertation, the biggest challenge for me was to see the world through academic eyes. I don't think I ever quite got it. Besides those, I imagine there are lots of filters or points of view with which people make sense of the world. Scary ones such as religious lenses. Slightly less scary ones such as a political or economic take on everything. But for some reason, I couldn't even begin to put together a way to describe how I thought a mathematician would make sense of day to day living, relationships, or being happy and making other people happy, much less the world at large.

Then, coming back to my own little adventure with the abstract and The Minimalist Math Book, I wondered whether there might be something more valuable than knowing the difference between the mean and the median that journalists could learn from mathematicians. Could math provide any new ways to ask questions? To structure narratives? To make sense of a larger story? Or a smaller story? Of course, I didn't know, but I was curious.

So you might understand my internal Wow!" reaction when Professor Saari, with complete passion and conviction, tempered by a smile his happy light blue Santa eyes, said, "Mathematics is a way of thinking. It's a way of living."

That's when said, "damn" and told myself never go anywhere without my tape recorder again.

But I did have my fountain pen and notebook.

Professor Saari went on to assert that mathematics is the only academic discipline where we can predict what might happen six or seven levels ahead of what other people are looking at. And, he said, mathematicians can do that in any discipline. You can land in a field, look at their equations the describe their observations, and discuss it at the most sophisticated levels, he said.

That's kinda like what reporters do, except we figure out how to ask good questions and then try to translate the answers.

During the conversation I told Professor Saari that when I talk to my journalism students, I always tell them that in approaching a feature story, there is never one right answer. There might be a hundred right answers. Same with photography. There are a thousand ways to photograph a face. I said, one of the things that intrigued me about math was the idea that there was just one right answer. But, I said, that's probably not true. Would he talk about that?

He jumped all over my remark.

What I think I heard him say was that for problems where you have an equation on a blackboard, sure, there is likely one right answer. And nearly anyone who knows the mechanics can get there.

However, when you are taking a mathematical approach to big problems, problems that exist in the real world, the exciting thing about math is how many ways it offers to examine questions, in fact, even to find questions.

"Every time you look at something in a different way, you will have new results."

He said "taking a fresh approach" is one of the strongest things a mathematician does. "If you don't, all you do is end up modifying standard approaches."

He told a couple of stories about how he encourages his graduate students to find new questions and new solutions.

He said he doesn't allow his graduate students to immediately read academic papers through from beginning to end. He allows them to read the introduction or an abstract that simply describes the problem. Then he asks his grad students to come up with their own ways to solve that problem and to come up with new questions that solving the problem might pose. Then, finally, they can read the whole paper. Saari's concern was, that once students read a paper by an "academic expert" they would be stuck thinking about the problem only in the terms that the researcher defined. He said that encourages students to find their own way to approach a problem.

That describes part of the reason I don't use a textbook in my feature writing class. Most of the books I've examined, prescribe one formula about how to write a feature story. That formula often works for a whole lot of people, but for lots of others, it doesn't.

I was surprised at how frequently he used phrases to describe things I've tried to suggest to my own student.

He advocated: Simple problems, simple solutions.

I've always used the phrase: Simple but elegant.

He said when one of his graduate students is stuck, he makes them try to explain the problem in terms that a 9th grader could understand. To illustrate, he asked several students in the room to explain the calculus term, "limits" in simple terms. They couldn't. Professor Saari could. "Limit - using information to predict what will happen."

Then he asked about the term, "continuity." Same result. The students couldn't answer in simple English. Saari could. "Continuity -- if what you predict would happen, happens."

During the entire hour my book was in the back of my mind. Was I thinking too narrowly? Was it worth putting together a book that at least two other people have already written and published that basically gives recipes to journalists about how to perform some basic numerical mechanics? Could I include that useful stuff, but also more.

Professor Saari concluded his visit by saying, as a mathematician, "The goal is not to solve difficult problems. It's to influence the way people think."