Orders of magnitude: use semitones, not decibels

I'm going to teach you a secret. It's a secret known to few, a secret way of using parts of your brain not meant for mathematics. for mathematics. It's part of how I (sort of) do logarithms in my head. This is a nearly purposeless skill. What's the growth rate? What's the doubling time? How many orders of magnitude bigger is it? How many years at this rate until it's quintupled? All questions of ratios and scale. Scale. hmm. 'Wait', you're thinking, 'let me check the date. Indeed. But please, stay with me for the logarithms.