Date: Wed 14 Jul 2004 - 12:16:47 CEST
I will try to express the idea...
Originally Zipf and recently Ramon Ferrer i Cancho, Richard V. Sole (2003)
both attribute Zipf's law to the principle of "least effort".
Now let me translate your question 'how does "data to being plotted as a
power laws suggest systematicity" ?' to 'how can the principle of the least
effort relate with systematicity in terms of structure of a system ?'
Possible answer...
Systems evolve or grow, they respond to changes in their environment, they
have to optimize their structure and performance for optimal functioning
(being a structural part of other systems), or in other words systems
communicate with their environment. Something that is 'not a system' does
not 'care' about optimization of it's performance, growth, development,
adaptation, or any sort of evolution, energy saving (principle of least
efforts) or structural change simply because of the absence of any internal
organization or structure or feedback loop between the 'non-system' or
random system' and it's environment. Its history should be uniform: no
changes in structure, no development, no growth, no evolution, no function,
no communication - no need for the least effort...
As a consequence a structure of any system facing the entropy should be
organized in such a way as to oppose the II-nd law and optimize its
performance against energy losses - e.g. the principle of least effort that
is true for language also works elsewhere (any other communication). How
does it look like ?
Design features of a communication system are the result of interaction
between the constraints and demands of the job required (Hauser, M.D., 1996.
The evolution of communication). Probably differentiation of parts according
to their functioning scales is the right answer. So we have several large
elements performing some specific functions, and much larger amounts of
smaller elements that do 'finer and more precise functionality'. And it is
likely that aranging systems internals (elements, design features,
communication system) according to Zipf's law is the optimal solution. Thus
my speculative (as always :) ) conclusion would be that zipf's law is
observed in systems trying to compensate entropy related energy or
information loss. If it is 'not a system' - it will not try to optimize
anything... And it's elements will not follow the Zipf's law. The same as a
dice or a coin will not attempt to optimize themselves (and the random
result they produce) according to environmental conditions...
Best regards
Viktoras
-------Original Message-------
From: Stanley N. Salthe
Date: Sunday, July 11, 2004 12:39:01
To: fis@listas.unizar.es
Subject: RE: [Fis] probability versus power laws
We have had many interesting comments about power laws from Victoras (and
Loet) but I am afraid I have not yet seen an answer to my question, which I
repeat again:
> 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 (Victoras) construe it that the susceptibility of data to being
>plotted as a power laws suggest systematicity? What would be an Xi by i
>(rank) plot have to look like in order to falsify the hypothesis that
>power law plots suggest systematicity?
I ask this because I believe that there could be no observations of ranked
data that could falsify the hypothesis that power law "behavior" (chaotic
fluctuations) is a sign of systematicity in the source of the data. An
attempt to perturb the data will just change the slope of the log-log plot.
In my current(ly evolving) view, power law fluctuations result when
different fluctuations are partly reinforced to different degrees by energy
gradient dissipations, and would, if the system had reached equilibrium,
been random fluctuations instead. In the limit, where fluctuations are
being "used" by a system, their randomness would get converted to power law
configurations. For example, I cut up tree saplings into equal sized
pieces and weighed the dried pieces. I found the weights to make a power
law when ranked. To me this is evidence that branching in trees is
RANDOMLY initiated, but subsequent growth is driven by energy gradients.
STAN
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