Attention Conservation Notice: Over 5000 words about math that I don’t particularly understand, written mostly to clarify my thoughts. A reader familiar with the topic (roughly, spectral or harmonic theory on graphs and manifolds) will find little here new except possibly misconceptions, while a reader not familiar with the topic will find minimal motivation and poorly explained jargon. The ideal reader is a pedant or troll who can tell me why I’m wrong about everything.