Date: Wed 07 Jul 2004 - 07:55:03 CEST
Power-law frequency distributions are known to reveal self-similarity and
fractal geometry in the underlying structures (B. Mandelbrot, 1997. Fractals
and self-affinity). In other words they reveal hierachy of real-world
structures (systems) and their composition. So naturally they have to be
widely spread thus being a good proof for the theory of hierarchies too.
Truly random events (characterized by uniform distributions) can not be
plotted in this manner. What's left - 'not (so) random' events/systems with
their internal structure and rules of their emergence/growth and
functioning/communication. So 'all what is left' follows power laws just
because they are parts of a structure being composed of yet smaller
structures, etc... Thus everything with fractal-like structure in nature is
a system.
In practice data points rarely ideally fits the power law distribution (not
a big surprise) and those distributions for different kinds of systems have
different slopes. So if data points plotted as a power law distribute into
different clusters along the line of power law (axes are logarithmic), then
most likely they belong to different systems. Or if some places show
substantial gaps, this should mean that system is under-sampled and it's
structure not completely represented.
Just suggestions. I am looking for more articles on this topic for more
proof. Also going to test those assumptions some time in future :)
with my own data.
Best regards
Viktoras
-------Original Message-------
From: Stanley N. Salthe
Date: Sunday, July 04, 2004 12:26:06
To: fis@listas.unizar.es
Subject: Re: [Fis] probability versus power laws
So, given that one can find power laws EVERYWHERE in ALL KINDS of
data, material and linguistic (just as one can do statistics anywhere), how
do you construe it that the susceptibility of data to being plotted as a
power laws suggest systems? What would be a result of an Xi by i (rank)
plot have to look like in order to falsify your system hypothesis?
STAN
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