In the world of modern machine learning, the convolution operator occupies the strange position: it's both trivially familiar to anyone who's read a neural network paper since 2012, and simultaneously an object whose deeper mathematical foundations are often poorly understood. In audio processing contexts, you might hear it described as a signal smoother. In convolutional nets, it aggregates information from nearby pixels and is also described as a pattern-matching filter, activating more strongly in response to specific local pixel patterns. From the surface, it's not immediately obvious how all of these different conceptual aspects of convolution are rooted to a shared mathematical reality. The process of piecing all of these interpretations together into a shared web of understanding was reminiscent of finally really looking at a mural on a building you pass every day, only to find it deep with connotations you hadn't previously seen.