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Re: [Phys-l] Benford's Law.



On 11/15/2010 5:58 PM, brian whatcott wrote:
A recent New Scientist article explored the numeric parameters
describing numerous natural structures.
Specifically, the leading digit of such parameters has a rather high
probability of being "1". This is a 'law' ascribed to Benford.
You might easily suppose that the numerals 1 to 9 have an equal
opportunity to take the first position. They do not.

A reader's note followed up with a plausible reason why this should be:

For an observation concerning something that tends to a power law,
the logarithmic spacing between adjacent digits is unequal.
The space between 1 and 2 on a log scale is a factor of two,
the space between 8 and 9 is a factor of 0.13
[John Burns, Oxford]

Brian W
There was an interesting snippet in the wiki: the Benford law can be found
using parameters given in many different units of measure such as
meters/yards/feet/inches etc., so the effect is evidently scale-invariant
- and this shows that a log scale is a natural candidate - in order to provide
this scale-invariant effect.

Brian W