Coming Of Age

Never Stop Learning 

On the first day of my final semester in graduate school, my major professor, Dr. James Gassaway, assigned a single research project: a physics problem to investigate, model, and simulate during my last class with him. 

He described this project as a graduation gift, or perhaps that's how I came to think of it in retrospect. 

I couldn't know then it'd change my view of our world for the rest of my life. 

After all, I'd nearly completed graduate school. How tough could it be? 

The problem appeared straightforward to describe, or so I believed. It had to do with predicting the resistance of a semiconductor, silicon, as it varies with temperature. Resistance, a material's opposition to the flow of electricity, is an electrical property that can be measured, and in silicon, it changes dramatically across a wide range of temperatures. 

Its temperature could be controlled from one extreme to another inside an environmental chamber: red-hot and molten at one end, brittle and liquid-nitrogen cold at the other. How tough could it be? 

Measuring the resistance turned out to be the easy part: many people had already done it, across the entire temperature range my professor wanted. Reinventing the wheel is a cardinal sin in engineering circles, so I built on the work of those who came before me and turned to the real assignment: explaining what they'd found. 

That's where it stopped being easy. 

My resulting resistance-versus-temperature graph looked less like a line or a parabola than a high-altitude photograph of the Mississippi River, snaking across the page in loops, bends, and troublesome twists no simple equation could follow. A graph like that demands an explanation: a mathematical model that predicts every twist and turn, not just the general shape. 

It offered little comfort, but I wasn't alone. A host of capable people, far more experienced than I was, had stared at the same twists and turns and come away just as baffled. This seemingly simple material had quietly defeated the experts. 

No one could model or predict its resistance as the temperature climbed and fell. Not really. Not with confidence. 

Faced with that, our engineering community did what it always does when a problem refuses to yield: we cut it down to size. Smaller ranges of temperature create smaller, easier-to-explain changes in resistance, easier to model, simulate, and predict. 

But here is what mattered more than the slicing itself. The mathematics inside each slice wasn't built on understanding. It was conjecture, an educated guess, shaped to fit a curve we'd already measured, dressed up and handed back to us as theory. Since no established theory could explain why the resistance behaved as it did, we invented an explanation that behaved the same way on paper and called it a law of physics. 

The conjecture wasn't compelling. But it was revealing. When we don't understand something, we make up an explanation, wrap it in mathematics, and present it as science. That, too, may be the best any of us can do. 

When the true complexity of the world defeats our understanding, we carve it into smaller pieces and explain each piece with a guess dressed as theory. Left unquestioned, that guess hardens into fact, and we mistake fiction for a law of physics. 

The last lesson Dr. Gassaway taught me before I left the university was built on this project, and on a single figure he drew on the board. It's shown at the top of this article. 

Fifty-one years later, it still excites my imagination and fills my heart with joy. 

His figure shows that the number of problems we can solve is tiny compared to the number we can only describe. Gray shows problems we can describe but cannot yet solve. The small circle at the center shows the problems we can both describe and solve. By contrast, the number of problems we can describe is infinitesimal when compared to those whose complexity defies description. Red shows the problems we cannot describe or solve at all, a world stretching in every direction farther than any of us will travel in a lifetime. 

That red world was never meant as a warning. It's an invitation, an ocean of keenly interesting problems waiting for someone patient enough to look closely, measure carefully, and admit what they don't yet understand. 

I've spent a career inside that innermost gold circle, learning to solve problems I once could not, turning what I could describe and model into solved problems. Every one of those small victories reminded me of how much larger the red world remained. 

Some PhD students spend their careers inside that gray ring. Few step into the red world, but when they do, their work stands apart. 

Dr. Gassaway didn't hand me an answer that first day of my final semester. He handed me something better: a durable sense of wonder at how much is still out there to learn, and a career's worth of purpose in trying to close even a little of that distance. 

I hope to pass that same gift forward, the way he passed it to me. Never stop learning. To this day, awe and wonder about this red world live in my soul; excitement and anticipation live there too. I love chasing adventures never before imagined, let alone described. The red world's problems are calling. They're calling for you.