
My issue with orders of magnitude is while useful, a ratio of 10 seems very large and completely arbitrary. It relates to our use of base-10 (decimal), which probably derives from our pentadactyly.
A more natural scale for orders of magnitude would be binary. This is the lowest practical ratio. An order of magnitude larger would be twice the size, 2 orders of magnitude 4 times the size.
Of course a constant multiplier, be it 2 or 10, represents a logarithmic function. Order of magnitude being logarithmic may be better modelled on the natural logarithm. Using base e (~2.71828), while difficult numerically, would mean that the scale of magnitude is ~2.7.
A thousand-fold difference is 3 orders of magnitude (decimal). It would be ~10 orders of magnitude using binary, or ~7 orders or magnitude with base-e.
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