Intellectual Toughness

As the author of a widely used thermal physics textbook, I get a steady stream of email from students around the world who are using the book. By far the most common type of inquiry is requests for answers to the end-of-chapter problems. Some students ask for the answer to a particular problem; others want copies of the entire solution manual.

To most of these students, my standard response is “Ask your instructor.” However, not all of them are using the book in a traditional classroom setting. Some have moved on to advanced studies or workplace settings where for various reasons they need to go back and brush up on their undergraduate thermal physics.

Of course I’m delighted that people are using the book in such diverse ways. But I’m also dismayed that, even after earning an undergraduate degree, so many scientists and engineers still believe that answers come from textbook authors.

The whole point of science is that you can figure out answers for yourself, without relying on any authority. For physics textbook problems, that usually means you have to do some sort of calculation. And how do you know if the calculation is correct? Not by consulting a teacher or solution manual or some other authority! Mathematics has its own internal logic that tells you whether it’s correct, without reference to anything external.

But what about careless errors, which everyone makes from time to time? There are endless ways to catch them without any appeal to authority. Do the calculation a different way. Compare the answer to other known facts. Ask one of your peers to check your work.

Our educational system does a lousy job teaching these skills. In our fervent desire to “cover” as much material as possible in our courses, we don’t give students time to ponder their results and root out their own mistakes. Instead, we authoritatively mark their answers right or wrong, then hurry on to the next problem.

Nor is this situation unique to the mathematical sciences. Students of biology, economics, sociology, and history must all learn to distinguish truth from falsehood without an instructor’s help. Critically examining one’s methods, and thus developing confidence in one’s answers, is fundamental to every discipline that deals in hard facts.

It’s not enough to teach facts, or even to teach specific technical skills. We somehow need to help our graduates develop the intellectual toughness to know when they’re right, so they can become leaders in their chosen fields.

Adopt-a-Weed Report, May 2012

It’s been a productive weed-pulling season in Ogden’s foothills.

Our most visible weed is dyer’s woad, with its upright stalks topped with a head of yellow during May. Ridding the foothills of this invasive plant may seem hopeless, but the Ogden Sierra Club has made a significant dent by “adopting” a 10-acre area above the 22nd Street trailhead and returning there to pull the dyer’s woad each spring. If I’ve counted correctly, this was our eighth year working in this area, and I’m delighted to report that we’ve made great progress. The plants do keep coming back, but they’re much thinner than before. This year it took only two hours for four of us to cover the entire area. (I went back for another half hour, a week later, to get the late bloomers.) In coming years we should be able to expand our adopted area to the north and/or south.

Most of Ogden’s trail users now seem to be aware of the dyer’s woad problem, and many will pause along a hike to pull a few plants. But to make real headway against this weed, our “adoption” method—spending a few hours working the same area each year—seems to be the key. I hope more groups will try it.

Meanwhile, two years ago I learned about myrtle spurge, a weed that’s still far less widespread than dyer’s woad but well established in a few dense infestations. One of those is at the 27th Street trailhead, and I personally adopted it two years ago. The strategy was to start pulling plants at the perimeter of the infestation and gradually work inward, containing and reducing the affected area.

Follow-up is also crucial with myrtle spurge, but it’s much easier because the plant grows more slowly than dyer’s woad. It’s taken me only about an hour each season to pull the small plants that are trying to come back in the areas that are already purged of mature plants. Now, after three seasons of work, the infestation is reduced to a single patch between the westernmost trail and a resident’s fence.