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 11 21:35:21 2004
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