Marshall Professors Build Machine to ‘Watch’ Math Happen
Issue:Fall 2009 : Articles
Bonita Lawrence isn’t the type of professor who just lectures to a class or uses a whiteboard.
Math excites her, makes her jump and gesture to make her points. It prods her to punctuate sentences with exclamation points. The Marshall University professor doesn’t need a personal computer or graphing calculator to teach differential equations, which describe functions with one or more variables. She teaches abstract concepts through a hands-on approach.
Her teaching gadget of choice, a differential analyzer, is different. With its motor, lights, gears, wheels and rods, this machine looks like a giant Erector Set.
“What’s great about this is that students can ‘see’ different equations and the impact on variables, which represent the rates of change of the solution you are interested in,” Lawrence said. “It isn’t the same with computer simulations,” she added. Here, screwdrivers are useful. Graphing calculators, rulers, compasses or The differential analyzer runs on a motor and uses gears, rods, wheels and integrators, which are devices that perform functions involved in calculus.
Lawrence said, “The problem you would like to solve is a set of connections between the rates of change [or derivatives]. You can change the problem by changing the connections between the integrator components of the machine. The output is your solution.”
Lawrence’s husband, Dr. Clayton Brooks, is also a math professor. They have been working on the differential analyzer for several years. “It will actually make you visualize what something abstract is going to look like,” Brooks said. “You solve different equations and take a bunch of numbers and symbols and you see the graph of the solution.”
Most people can understand the basics of the machine even if they don’t know the mathematics behind it, he said. “With this they’re quite intrigued,” Lawrence said. “When people get to touch it, it really How a differential analyzer came to be built in West Virginia is a tale that started about 100 years ago and spanned two continents.
When Lawrence and Brooks visited London’s Science Museum they saw a display of a similar machine, which wasn’t working. Later, upon investigation, they discovered that Vannevar Bush and his students at the Massachusetts Institute of Technology built the first mechanical differential analyzer in the 1930s.
In 1933, at the University of Manchester in England, Professor Douglas Hartree and his research assistant, “This is the only publicly accessible differential analyzer in the country,” Lawrence noted, “and it’s at Marshall.”
She said Porter once gave her one of her favorite compliments. “Dr. Porter points out all the time that literally thousands of people walked by that thing” at the British Museum, but ‘only Bonita noticed the educational aspect,’” she said.
Lawrence said she plans to spread her excitement about the differential analyzer. She will use the machine in her differential equations course this fall and hopes to show it to engineering and science students, among
Arthur Porter, built the first differential analyzer made mostly out of Meccano. These parts allow the construction of working models and mechanical devices. Think of a grown-up version of an Erector Set. That was the machine that Lawrence and Brooks saw in London.
“From this idea, I thought, ‘Well, let’s study the machine,’” Lawrence said she told students after her trip. “I didn’t know there wasn’t a working machine.” Her students found out that Tim Robinson, a retired electronics engineer, has a working differential analyzer at his house in California. He built it in a room originally built for a pool table.
“When I discovered that there wasn’t one” on public display, she said, “I just decided ‘What the heck, let’s go ahead and build one.’ ”
Lawrence found out that Porter, who worked on the analyzer in England, lives in North Carolina.
“Before I could call Porter he called and left a message for me.”
Lawrence and Brooks traveled to Porter’s home and learned about his experiences building one of the first differential analyzers. Porter, now 99, and Robinson served as mentors on the project.
Lawrence, Brooks and their students actually built two machines. The smaller, more portable trial version named Lizzie will be taken to the Czech Republic soon for a conference. The larger model that is ensconced on the third floor of Smith Hall is named Art, after Porter.
“This is the only publicly accessible differential analyzer in the country,” Lawrence noted, “and it’s at Marshall.”
She said Porter once gave her one of her favorite compliments. “Dr. Porter points out all the time that literally thousands of people walked by that thing” at the British Museum, but ‘only Bonita noticed the educational aspect,’ ” she said.
Lawrence said she plans to spread her excitement about the differential analyzer. She will use the machine in her differential equations course this fall and hopes to show it to engineering and science students, among others, as well. She said that eventually she wants high school students to visit. “We need to let their minds sort of create, wonder, see what they can do,” Lawrence said.
“I don’t know everything that can be done on this and I’m happy about that because I want to see what these bright minds coming in and seeing things and saying what they see and what they can come up with.” They’ll have “a completely different perspective on calculus and differential equations.”
Lawrence said she once explained to a group of engineering students why she built the differential analyzer. “This is the most beautiful, physical interpretation (of an equation) that I’ve ever seen,” she said.
She then asked the students why she might build it and one student answered, “Because it’s awesome, Dr. Lawrence!” “He was way up in the class of about 100 students. I said give me a spiritual high five.”
Brooks noted that other people could be more skeptical. “People ask why in the world are you building a 1930s computer that was obsolete in at most the 1960s? Well, there’s an indication that there’s a benefit to it,” he said.
His wife chimed in. “And it’s cool!”
This article originally appeared in the Charleston Daily Mail and is reprinted with permission.