Outlines and shading, drawn on a page, appear to us as unambiguous, three-dimensional shapes. How that perception happens is usually considered a matter of psychology or neuroscience, but it can also be understood through mathematics.
A successful mathematical analysis can become readily applicable in other fields. Someone could apply those results to computer graphics or making microprocessors that work more like the brain or endowing robots with a more accurate means of perception.
“Science must often be expressed in mathematics for application in another field,” said Benjamin Kunsberg, a new Prager Assistant Professor of Applied Mathematics.
Kunsberg has been considering the mathematics of vision and the brain since 2008 when he was a visiting researcher at Los Alamos National Laboratory in New Mexico. In various forms the problem remained his focus throughout his master’s, doctoral, and postdoctoral studies at Yale University.
He has recently been studying how the mathematical reconstruction of shaded objects changes with small movements of the drawn object, viewer, or light source. This could reduce the unknowns when modeling the way the brain infers properties like the object’s apparent depth.
“If you just have an image, you don’t know its full 3-D structure. The problem is ambiguous,” he said. “But if you include these assumptions that the solutions you want are stable up to some amount of viewpoint or lighting changes, that eliminates some of the ambiguity.”
This is one of many topics Kunsberg has explored in a far-reaching journey both as a student and as a teacher. Math has repeatedly proven versatile, both in its utility and in how it has engaged him.
In the summer between his graduation from Johns Hopkins and enrollment at Stanford for his first master’s degree, he worked at the National Security Agency on cryptography. In his first visit to Los Alamos, as an undergraduate in 2005, he used math to model an outbreak of foot-and-mouth disease in Uruguay. Before that he worked at the National Institute of Allergy and Infectious Disease in Bethesda, Md., to help find receptor sites for the herpes simplex virus.
Throughout all those undergraduate-era projects he was also a team leader of research on the metabolism changes of crickets in microgravity. With $15,000 of competitively earned grant funding, his team put those crickets on the successor to NASA’s “Vomit Comet” (a C-130 plane flying steep parabolic loops to create zero-gravity during the dive).
“In a lot of the projects you do at college or in internships, you are just trying to get enough experience with mathematical techniques to solve a problem,” he said. “It’s a great way to become a mathematician.”
Fundamentally, Kunsberg finds math to be a fun, if consuming, endeavor.
“I find that doing math is a lot of just playing with concepts and ideas,” he said. “You and a couple of other people get into a room and you are just talking, and there’s a little bit of competition as well as teamwork as you’re trying to come up with a new insight. It’s very collegial.
“It’s good for people who easily get obsessed,” he said. “Then your work and your passion are aligned.”
He hopes to convey his excitement about mathematics to students. Doing so doesn’t happen by drilling or rote memorization but by incorporating the history of why people, like the ancient Greeks or Gauss, were so motivated to pursue their discoveries in the first place. It’s a matter of presenting math as a breathtaking human achievement.
“I think I have more fun teaching than doing research,” he said. “When you are teaching you get to show your students the highlights of the last millennium.”
For the years of the Prager appointment, Brown will be the next place Kunsberg makes his own highlights. He said he’s excited to teach and to collaborate with colleagues in a large and well-regarded Division of Applied Mathematics.
“I’m sure this department will give me plenty of opportunity for intellectual development,” he said.