## Scale free numbers begin with 1 (typically)

From: "andrew cooke" <andrew@...>

Date: Sun, 29 Jan 2006 13:46:07 -0300 (CLST)

Think about a log scale.  Maybe a third of the scale is between 1 and 2.
I presume that's what's behind this -
http://www.boingboing.net/2006/01/28/numbers_begin_with_1.html

Andrew

### Benford's Law

From: "andrew cooke" <andrew@...>

Date: Sun, 29 Jan 2006 13:49:18 -0300 (CLST)

Hmm.  It's more than that.  Good article here -
http://mathworld.wolfram.com/BenfordsLaw.html

### More on Benford

From: andrew cooke <andrew@...>

Date: Sun, 2 Aug 2015 01:23:51 -0300

Three reasons are given in
https://web.williams.edu/Mathematics/sjmiller/public_html/ntprob14/handouts/benford/BenfordBook10.pdf

1 - Uniformly distributed in log

2 - Central limit of mantissa when many numbers multiplied together

3 - Scale invariant

I am not sure 1 and 3 are different.  But 2 is interesting.

One implication of 2 is that such numbers are derived from other numbers.

Now consider physical constants.  If these are fundamental, then they are not
the product of other numbers (this seems to me to be a defintion of
"fundamental").

So, do fundamental physical constants follow Benford's law?

Andrew

http://www.amazon.com/Benfords-Law-Applications-Steven-Miller/dp/0691147612
http://www.amazon.com/s?field-keywords=benford%27s+law