Frank Hartman shared this amazing article on Benford's law,
something that might be applicable because of its ubiquity,
to the collection of seemingly random information that leads
to prediction of all kinds of patterns.
I am positively sold on the use of patterns to indicate
trends and cycles which is why KeelyNet has many diverse
files, all seeking correlations that will lead to a
hypothesis that will lead to an experiment to prove or
disprove it, and modify or discard in favor of a better
hypothesis.
http://www.newscientist.com/ns/19990710/thepowerof.html
...the digits making up the shop's sales figures should have
followed a mathematical rule discovered accidentally over
100 years ago. Known as Benford's law, it is a rule obeyed
by a stunning variety of phenomena, from stock market prices
to census data to the heat capacities of chemicals. Even a
ragbag of figures extracted from newspapers will obey the
law's demands that around 30 per cent of the numbers will
start with a 1, 18 per cent with a 2, right down to just 4.6
per cent starting with a 9.
The obvious explanation was perplexing. For some reason,
people did more calculations involving numbers starting with
1 than 8 and 9. Newcomb came up with a little formula that
matched the pattern of use pretty well: nature seems to have
a penchant for arranging numbers so that the proportion
beginning with the digit D is equal to log10 of 1 + (1/D)
But in 1938, a physicist with the General Electric Company
in the US, Frank Benford, rediscovered the effect and came
up with the same law as Newcomb. But Benford went much
further. Using more than 20 000 numbers culled from
everything from listings of the drainage areas of rivers to
numbers appearing in old magazine articles, Benford showed
that they all followed the same basic law: around 30 per
cent began with the digit 1, 18 per cent with 2 and so on.
Hill's theorem, published in 1996, seems finally to explain
the astonishing ubiquity of Benford's law. For while numbers
describing some phenomena are under the control of a single
distribution such as the bell curve, many more--describing
everything from census data to stock market prices--are
dictated by a random mix of all kinds of distributions. If
Hill's theorem is correct, this means that the digits of
these data should follow Benford's law.
And, as Benford's own monumental study and many others have
showed, they really do.
---
Jerry Wayne Decker - jdecker@keelynet.com
http://www.keelynet.com
from an Art to a Science
Voice : (214)324-8741 - FAX : (214)324-3501
KeelyNet - PO BOX 870716
Mesquite - Republic of Texas - 75187
-------------------------------------------------------------
To leave this list, email <listserver@keelynet.com>
with the body text: leave Interact
list archives and on line subscription forms are at
http://keelynet.com/interact/
-------------------------------------------------------------