I'll discuss some recent work of Michael Christ which establishes smoothing for the integral of a four-fold product. In particular, I will outline some key ideas involving a reduction to the trilinear case using spicy Cauchy-Schwarz, a study of sublevel set estimates for a linear combination of measurable functions with analytic coefficients, and a musical "sharp/flat" local decomposition that helps capture oscillation. I'll try to sweep technical details under the rug and draw pictures instead whenever possible.