Re: [Fis] probability versus power laws

Dear FIS colleagues,

As argued here recently, a number of theoretical threads may conduce to
power laws. Malcolm was citing a particular work by Ricard Vicent Solé
(Spanish scientist who leads the most creative interdisciplinary group in
the country, he is also in the Santa Fe Institute). His web page
http://complex.upf.es/~ricard/ contains quite many of the applied research
fields where power laws are caught 'into action': networks dynamics,
genomic and proteomic networks, protein modular evolution, languages
evolution, technological graphs, electronic circuits, ecological dynamics,
catastrophic shifts in ecosystems, development and morphogenetic gene
networks, neural networks topology, etc.

In my opinion, Per Bak has been one of the leading parties attempting to go
beyond power laws as mere 'signatures of complexity'. His
Self-Organized-Criticality doctrine (particularly in the 1996 book How
Nature Works) is often reflected and cited in Ricard's own papers... My
only addition in this posting to his (and Ricard's) views would be about
the importance of distinguishing between the contexts where power laws may
appear, as otherwise we easily get caught into a deluge of advanced
formalisms. I have made some rough explorations based on the three info
categories presented long ago in this list --structural, generative,
communicational-- and found that the discussion on power laws gets some
further interesting nuances towards coherence. In the communicational case
for instance, there is already a classical optimization thesis ('info
compression') by Horace Barlow on neural coding in sensory varieties that
connects power laws with my previous message on sentic forms--I tried to
apply some of this stuff not just to music, but to the 'melodies' behind
sounds of laughter (plosives). See my past contribution about laughter with
Jose Antonio Bea in http://www.mdpi.net/fis2002/

Rather than in magnitudes of physical structures, it is particularly in the
'internal dynamics' of generative classes of info, or properly
'infostructures' (eg, DNA evolutionary tinkering, repositories of
scientific knowledge itself) where the discussion on power laws becomes
really interesting and dense...

all the best

Pedro

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Received on Thu Jul 15 13:57:52 2004