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Cute tidbit... [Jan. 4th, 2017|09:34 pm]
I found this on Benford's law:

I reckon you could find low initial digits in some scientific data, and you might think it's really amazing... but the point of the law is that when reporting things, the first digit is the most significant, and a lot of times, people want a measurement that tends to make that important at 1. So if a Watt is a decently meaningful amount of power, then it's no surprise if you find that 1, or 10, or 100 Watts will be more likely to be meaningful than 5, or 50. If 5 Watts was a common, useful quantity, then the measurement probably would have been divided by 5 to make 1 (new) Watt a useful quantity.

Now: it would be kinda curious if it turned out that the number of miles (exactly) between the center of the sun and the center of other stars followed Benford's law for miles, or even for light years (since the 365 days of light's travel is arbitrary - I mean, forced by the length of a year, but "a year" on another planet could be vastly different.)

Heh. Though this reminds me of a story idea I had that I never did anything with. An earth scientist, shortly after the earth joins the league of planets comes with stunning news - delivered humbly, or perhaps boastfully depending on the story - about how the earth is actually the perfect center of the known universe. And everyone laughs... because there's always some measurement for any planet that joins the league that puts them in the perfect center, and a new planet's scientists always "discover" it shortly after they get their map of inhabited systems.

[User Picture]From: redbird
2017-01-05 01:28 pm (UTC)
The interesting thing, imho, is that Benford's law applies in some cases where there are no units of measurement, like Fibonacci numbers or things that are being counted rather than measured in any arbitrary unit, like the populations of different places. Changing from base 10 to base 16, or something weird like base 7, affects the shape of the curve, but for counted things you'd still get more 1's as first digits than 6's.

I first met Benford's law as a hint for taking multiple-choice math tests: if you have no idea of the right answer, pick the one with the lowest initial digit, because the test-makers will tend to put in more wrong answers that start with higher digits so the set of choices "looks right" to them. (This is like the forensic accounting application mentioned in the Wikipedia article.)

(Also, your link is broken: I think the problem is with the apostrophe.)
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[User Picture]From: johnpalmer
2017-01-28 07:29 am (UTC)
Thanks, I think I've got the link fixed.

You're right, it's odd that things like Fibonacci numbers have this property, or that populations seem to follow it, but I still have this sense (rightly or wrongly) that it's because "1" is important. (And I'm fully aware that sometimes these intuition-based guesses are wildly off!)
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