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> I was hoping "roughly speaking an order of magnitude" would go down to 3.

I'd call that half a order of magnitude, considering log₁₀(3) is around 0.477. So you're off by more than a factor of two.




You know, I considered saying that the "roughly" buys me a factor of two in log space. I didn't want to be that person, but I'm glad you were ;).


It's surprisingly non-trivial to pin down exactly what the 'correct' scale[0] for a given measurement is. I do agree about "roughly" generally being up to a factor of two in the appropriate scale[1], although I'm the sort who thinks a 19% increase (or 16% decrease) should be called a quarter of a factor of two.

0: Uniform, linear and logarithmic are obvious candidates, but depending on the domain you can end up with some really wierd scales (eg floating-point ULPs, which can look logarithmic or linear, but aren't either).

1: hence > So you're off by more than a factor of two.




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