sketerpot comments on Fermi Estimates - Less Wrong
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There's a free book on this sort of thing, under a Creative Commons license, called Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving. Among the fun things in it:
Chapter 1: Using dimensional analysis to quickly pull correct-ish equations out of thin air!
Chapter 2: Focusing on easy cases. It's amazing how many problems become simpler when you set some variables equal to 1, 0, or ∞.
Chapter 3: An awful lot of things look like rectangles if you squint at them hard enough. Rectangles are nice.
Chapter 4: Drawing pictures can help. Humans are good at looking at shapes.
Chapter 5: Approximate arithmetic in which all numbers are either 1, a power of 10, or "a few" -- roughly 3, which is close to the geometric mean of 1 and 10. A few times a few is ten, for small values of "is". Multiply and divide large numbers on your fingers!
... And there's some more stuff, too, and some more chapters, but that'll do for an approximate summary.