As “shopping week” wound down, half a dozen popular professors — and, for the first time, one undergraduate — put their best wares on display Thursday evening at Harvard Thinks Big 4, a chance to take the stage at Sanders Theatre with a screen, a microphone, and one big thought.

In 12 minutes apiece (two of them donated by President Drew Faust, who had to cancel her scheduled appearance), the panel members delved into their favorite ideas, ranging from a look at why dead Romans are so much fun to a detailed explanation of breast-feeding in mammals.

Joseph Blitzstein, professor of the practice in statistics and co-director of undergraduate studies, opened a mini-Stat 110 class by displaying columns of airplanes (“They don’t look like fighter planes, but they’re fighter planes,” he said of his art) on the overhead screen, then shooting holes into them with a pointer. The planes illustrated the work of Abraham Wald, a statistician who was asked by the British government how to protect the Royal Air Force during World War II. His answer came not in adding armor to the areas on returned planes where inspectors saw the most damage — the wings, the sides — but to something quite different, the nose.

“What we’re really interested in is the planes we didn’t see, the planes that didn’t come back. There’s some statistical thinking there” about missing data, Blitzstein said, “a whole army of Rudolph the Red-Nosed Aircraft — and they all died.”

Emma Dench also had things to say about dead people, who she said have obsessed her since she was small.

“By the time I was 7, I realized that the Romans were more intriguingly dead than the run-of-the-mill dead people you see in the churchyard,” said the professor of classics and of history. You know, Betty Smith, she’s still warm.”

Dench said the reason to study “very, very, dead people” is that they “can tell you about us.”

“They can tell us where we’ve been, where we are, and where we’re going,” she said. “In Rome we’ve got a senate, we have a capitol, and we have a Roman hero, and he is called Cincinnatus. So cutting to this country, ooh, yes, in this country we have a senate, we have a capitol, and we have Cincinnati. … We have a self-consciously multicultural society. Rome had a self-consciously multicultural society.”

With enough study, she said, “We might even find out, because we are Rome, will we fall? And the answer to that, in my considered, scholarly opinion, is I haven’t a clue.”

Doris Sommer, the Ira Jewell Williams Professor of Romance Language and Literatures, professor of African and African-American studies, and director of graduate studies in Spanish, put her emphasis on culture.

“If we want to take on the responsibility to change the world, we [must] engage with art and humanity,” she said. “Art because it involves change, and humanity because it involves a twist.”

Sommer cited the case of Antanas Mockus, a “strange, nerdy philosophy professor” who became mayor of Bogotá, Colombia, in 1995, and began making a dent in the city’s violence and graft by hiring mimes to replace corrupt traffic cops. Within a year traffic deaths had been reduced by more than half, Sommer said, and Mockus then created one public performance art position after another. In his two administrations, Bogotá’s homicide rate went down 70 percent, income increased threefold, and public works boomed.

“What we learn from Mockus and other great cultural agents is that first, without pleasure, there is no lasting cultural or political change,” Sommer said.

Shifting gears, Roberto Mangabeira Unger, the Roscoe Pound Professor of Law, put forth the proposition that “No one should ever have to do work that can be done by a machine.”

“Everything that we have learned how to repeat, we can express in a formula, in a rule, in an algorithm. And everything we can express in a rule, we can embody in a physical contraption, a machine,” he said. “The point of a machine should be to do for us what we have already learned how to repeat, so that we can preserve our supreme resource — time — to learn that which we have not learned how to repeat.”

Katie Hinde’s big idea was pretty simple: The power of breast milk is, her topic said, “Why Mammals Suck.” Calling such milk “a magic potion [that has] everything you need exactly when you need it, and … made just for you,” the assistant professor of human evolutionary biology said she wants to see more research into what milk provides, and see that translated into medical technology, government policy, and more support for nursing mothers.

Milk “has the potential to change lives,” she said.

“Staying Healthy for Fun” was the theme of the lone student speaker, Annie Ryu ’13, but her focus was serious. In a world of preventable crises, she said, “I have become a social entrepreneur, and I’ve learned to question the status quo.” Among her projects are a message service that texts reminders of medical appointments to expectant mothers in India; MyZooPets, a game that uses virtual pets to help improve children’s health; and her own pet, promoting the jackfruit, “one of the world’s underutilized crops,” to alleviate waste, poverty, and the scarcity of what she calls the world’s most delicious food.

The night’s final speaker, Michael Puett, the Walter C. Klein Professor of Chinese History and chair of the Committee on the Study of Religion, went straight for the young audience with a mea culpa: His generation, he told them, left a mess for theirs to fix.

“There was a sense in my generation that we had figured out how to organize the economic world, how to organize the political world … we really thought the basic problems had been solved,” Puett said in his talk titled “Ritual and Humanity.” “Meanwhile, all this evidence has emerged to prove this fundamentally false.”

Like Ryu, Puett urged the audience members to question what they have been taught.

“We’ve left you a foolishly complacent way of thinking,” he said. “Break out of that worldview. Do it now. … The world we’ve left you with, bad as it is, can still be saved.”

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