In the late 1800s, mathematicians fantasized about a machine that could answer any math question at all. But Steve Strogatz explains—by way of Sesame Street and a thought experiment involving a conflicted barber—that their dreams were dashed by a scrawny little German guy. Then, theoretical physicist Janna Levin at Barnard tells us how Kurt Godel's maddeningly loopy theorem revealed the limits of math, and the infinite depths of our ignorance.

And for our final loop, we talk with author Melanie Thernstrom who has been living with pain every day for fifteen years. Neuroscientist Sean Mackey explains that she is caught in a crossfire of signals between her body and her brain. Sean showed Melanie how to enter that loop and ultimately take control of her pain—for a while.