RE: [Fis] probability versus power laws

Replying to Victoras:

> 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".
     SS: So, do you mean the physical principle of least action?

>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,
     SS: Not by least effort! They strive mightily to 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)
     SS: I would like to hear this principle stated in words explicitly.
In general there is no "energy saving" in natural systems. They dissipate
energy gradents as fast as possible.

>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).
     SS: I disagree wth this supposed "least effort" Least action would
have nothing to do with it. It is the smallest integral over velocty, mass
and path length. From that you cannot derive energy efficiency.

>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.
     SS: Well, how can that explain the power functions of earthquake
magnitudes?

>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...
     SS: Is a fault line a system?

>And it's elements will not follow the Zipf's law. The same as a dice or a
>coinwill not attempt to optimize themselves (and the random result they
>produce) according to environmental conditions... Best regards Viktoras
    SS But, again, how will you tell by looking at ranked magnitudes only
whether or not the population of data come from a system?

STAN

   -------Original Message------- From:
<mailto:ssalthe@binghamton.edu>Stanley N. Salthe Date: Sunday, July 11,
2004 12:39:01 To: <mailto:fis@listas.unizar.es>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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Received on Sun Jul 18 21:01:21 2004