Judy Walker

Dr. Judy L. Walker, professor of mathematics, delivered these remarks for the graduate commencement ceremony.

The Height of Knowledge

Judy L. Walker
May 8, 2009


Chancellor Perlman, Dean Weissinger, colleagues, graduates and guests:

It is a great honor to be here today, giving the final remarks on behalf of the faculty at UNL to you -- the May 2009 graduate degree recipients. Today we celebrate this wonderful achievement of yours and I am proud to be able to officially congratulate you on behalf of my colleagues. I'm especially pleased to see so many family members here sharing this day with you.

My own dad recently came for a visit. He lives in southern Illinois, still in the house I grew up in. His current mission is to clean out the years of accumulated stuff in that house, and he arrived in Lincoln with the contents of my childhood bedroom. Four boxes and five huge plastic bags filled with pictures, letters and memorabilia, mostly from high school. As I looked through these things, I realized two things about my high school senior self: (1) I thought I knew everything. (2) I knew almost nothing.

I started thinking about how fleeting that feeling of knowing everything was – how nervous I was as a college freshman, certain that someone would discover that this small town southern Illinois girl was a fraud who didn't belong.

This feeling seems to be common: many college freshmen pretend to know everything while fearing they know nothing. (Show kids/dorm pic.) They pretend that their knowledge measures up to the top of the dorms they live in, but they fear it is the same as that of the pre-schoolers at Ruth Staples.

By the time I reached my senior year in college, I was back to thinking I knew everything. After all, I was about to complete my degree; if there was more that I needed to know then there would have been more degree requirements. Tomorrow, the undergraduate commencement ceremonies will be here at Devaney, and the graduates will be seated on the floor like you. (Show stadium pic.) They're going to feel like they're in the blimps flying above the stadium on football Saturdays.

You, as graduate degree recipients, know how fleeting the feeling of being an expert can be. You've experienced the fear of being a freshman twice, the second time being when you started graduate school. Many of you probably hit a new low while studying for your graduate exams, (Show ice cream/love pic.) certain that your knowledge no longer measured up even to the ice cream counter at the Dairy Store but was instead in the basement of Love Library.

You've also reached highs higher than undergraduate students can even imagine. . (Show Oldfather/union pic.) You found your first original research result, and realized you were the only person in the world who knew what you knew at that moment. You were on the roof of Oldfather Hall. And then, perhaps, you became worried that there were only about ten other people in the world who would want to know what you knew, and you sank to just the top of the Union, still tall, but not 12 stories.

And now, where are you? You're receiving your graduate degree. You are officially an expert in your field. You're proud of yourself. You're nervous about what comes next. And maybe you alternate between feeling that you're in the basement of Love Library or on the roof of Oldfather.

(Show graph.) Since no talk by a mathematician is complete without a graph, let's look at one. The horizontal axis is time, and the vertical axis is knowledge. Time 0 is graduation from high school, when people think they know everything --- a vertical asymptote. The sharp decrease happens as they enter college and realize that they're surrounded by people who know more than they do. Then we have a steady increase over time until college graduation. For each of you, this wasn't the end of the story -- you went on to graduate school. The low point on the graph represents when you were studying for graduate exams, and the next high point -- a local maximum -- is when you obtained your first result. The oscillatory behavior from there is how many of us feel as our time in graduate school comes to a close, certain we're becoming experts, but realizing just how much there is that we don't know.

And that's the key. Of course you know much more now than you did when you graduated from high school. But you also now realize that what you know is just a tiny fraction of all there is to know. This graph we're looking at isn't a graph of how much we know, but rather of our perception of how much we know -- it's the ratio of how much we know to how much we believe there is to know. Graduate school has, I hope, left you with more questions than answers. Although you are an expert in your field, you still want to know more. (Don’t show anything.)

I'll leave you with a story that illustrates my hope for you. I volunteer in my daughter's first grade class and the teacher recently asked me to administer spelling pre-tests. I sat down with a little boy and started reading words to him. It was amazing -- he didn't agonize over his answers; he just wrote what I said and then looked at me expectantly, waiting for the next one. I said “himself”, and he wrote “H-I-M-S-E-L-F”. But then I said “toward”, and he said, “What?” I said, “I walk toward the door.” He said “Oh” and wrote “T-O-R-D”. “Usually” had two “W”s. “Friend” was perfect. He wrote all these words with no hesitation, no shame, no nervousness. When we were done, I told him which words he spelled correctly and which ones would be on his next spelling list. He was proud of the ones he got right and eager to learn the ones he didn't.

And this is my hope for you. Take pride in what you know. Share it with others. But also be aware of what you don't know. Ask questions of others and of yourself. Don't hesitate. Don't be ashamed if you get something wrong. Don't be nervous about taking chances. Make hypotheses. Test them. If they're wrong, try again.

You are recipients of graduate degrees from the University of Nebraska. You are not in the basement of Love Library. You are not pre-schoolers at Ruth Staples. You are not even on the roof of Oldfather Hall. (Show capitol pic.) You are at the top of the Capitol Building, experts in your field and sowing your knowledge -- enlightening your peers and planting the seeds for future generations of scholars.

Congratulations.