Problems happen, and knowing where not to look for the answer streamlines our search for solutions. Finding a last-minute date to take to a movie might mean narrowing down our logistical scope to the nearest quad, our preferences to the female variety, her preferences to martial arts films, and our realistic self-assessment to include anyone likely to say yes, given our current haircut.
For David Nassar ’07, the process of finding the best solution to a problem by defining its parameters was the driving focus of his fall semester Operations Research course, with mathematics professor Todd Feil. It’s the mathematics of optimization, and according to Nassar, “finding the correct constraints is the hard part. After that, the solution is never very far behind.”
Operations research professionals help businesses design more efficient scheduling and routing by trimming time and labor, often saving companies millions of dollars. Feil showed his students that optimization mathematics can also apply to art, essentially by having them analyze a computer program that arranges dominoes in the form of a given image. Nasser was intrigued by the graphic possibilities of mosaics, and by the mathematical challenge of defining the constraints in a visual problem. So when Joan Krone’s Intro to Computer Science class was assigned a self-designed programming project, Nasser knew he had to give it a try.
Using both black and white dice, and Leonardo daVinci’s Mona Lisa as his sample image, Nassar devised a similar optimization program to the domino problem he had studied, and found his major constraint to be the limited number of grayscale values he had to work with (12 values total, counting the six sides each of the black and the white dice).
The results were so intriguing to Todd Feil that he encouraged Nassar to create a real model with playing dice mounted into a wooden frame. The grid of 2,050 carefully arranged dice now hangs on the second floor of Olin Hall, creating a likeness of remarkable subtlety. Nassar smiles more broadly than his subject: “From the far end of the hall, people just see a picture of the Mona Lisa.”