A couple of weeks ago I had intense arguments with Belokurov (Cambridge) and Farr (Stony Brook) about the definition of a photometric bandpass and a photometric magnitude. And a few months ago I had long conversations with Breivik (Flatiron) about the bolometric correction. For some reason these things took over my mind today and I couldn't stop myself from starting a short pedagogical note about how magnitudes are related to spectral energy distributions. It's not trivial! Indeed, the integral isn't the integral you naively think it might be, because most photometric systems count photons (they don't integrate energy). People often say that a magnitude is negative-2.5 times the log of a flux. But that's not right! It is negative-2.5 times the log of a ratio of signals measured in two experiments.
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