The Power of Power Laws

Dear Fellow FISers,

I was intrigued by Pedro's post not too long ago, linking power laws as one
common factor in the work of various complexity theorists. I, too have been
fascinated by the brand new symmetry in nature, self-similarity, that lurks
beneath power laws. I believe its ubiquity quite meaningful.

In my opinion,self-similar dynamics and fractal geometry serve as a bridge
between the imaginary and real, mind and matter, unconscious and conscious.
Everywhere in nature, fractal separatrices articulate a paradoxical zone of
bounded infinity that both separates and connects nature�s edges. By
occupying the �space between� dimensions and various levels of existence,
fractal boundaries appear to exemplify reentry dynamics of Varela�s
autonomous systems. As a psychologist, I am most intrigued by fractal models
of the psyche and how these dynamics appear to occupy that seamless seam
where brain, mind and consciousness are most entangled.

Best,
Terry

>Dear colleagues,
>
>Returning to the discussion about optimization days ago, I believe it is a
>really important piece in the fis puzzle. At the beginning of this
>conference I ventured about the close relationship between three dynamic
>optimization principles that could be understood as fundamental 'pillars'
>of the info bridge: biological maximization of fitness, neurodynamic
>minimization of 'desajuste' (neural entropy), and rational maximization of
>utility-- they were respectively referred to such 'saint patrons' as
>Darwin, Ramon y Cajal, and Adam Smith.
>
>It is in this highly dynamic-functional context (more than in the strictly
>structural one), where the biggest difficulties to optimize, to satisfy
>multiple contradictory constraints, can be found. So, no wonder that the
>respective informational entities --either at the cellular, organismic or
>societal level-- have to incur in amazingly complex accounting processes in
>order to orientate in an optimized direction their ongoing
>self-construction processes and keep themselves 'alive' in the adaptive
>interaction with their environments.
>
>We can look at the above dynamism in quite different time scales. The
>largest possible one is the vast paleontological panorama of species
>adaptation (phyla or classes indeed). I mentioned days ago van Valen's Red
>Queen hypothesis, proposed in the 70's I think, nowadays well-developed
>formally by Kauffman's 'rugged landscapes' and other authors. Actually,
>Kauffman's approach incorporates the emerging non-linearity that each
>species has to confront when climbing to a 'mount fitness' that deforms and
>reacts as the species tries to move upwards (as John C noted). It does not
>mean an 'impossible task' provided that the inter-species dynamic coupling
>keeps below some moderate boundaries. Then, evolving genomes may explore
>more or less OK within the other evolving genomes and get caught into a
>co-evolving niche of co-adapted species...(a very conspicuous example:
>coevolution of flowering plants and insects)
>
>As far as I know, some of the gaps in this approach (eg, it was not leading
>very well to reasonable models of extinction) have been tackled by
>different complementary/competing approaches, partly outside the Santa Fe
>complexity groups. For instance, Self-Organized Criticality, by Per Bak and
>others. They have managed to produce co-evolution models that incorporate
>bona fide 'punctuated equilibrium' dynamics, conducing to fast periods of
>massive extinctions and intense evolutionary change followed by long
>periods of stasis, and massive extinction and evolutionary episodes again
>(classical Stephen Gould's views on macroevolution). Although SOC has
>gotten a lot of interdisciplinary clutch, perhaps the most appreciated
>theoretical approach has been built around the 'coupled map lattices'
>(Kaneko, Tsuda, Freeman) that, as far as I know, implies the least
>assumptions and has the most elegant 'dynamic systems theory' basements
>(and is leading to new fertile developments).
>
>Let me emphasize that, rather unexpectedly, power laws show up in these
>three different approaches. It is quite interesting that as a result,
>either of Boolean nets, or of differential equations, or stochastic
>dynamical systems, we find the power law as a sort of common signature for
>adaptation processes. For some authors, notoriously Per Bak, it is quite
>unclear the why and how of this generalized emergence of power laws....
>(the very laws John C and me were talking about a few days ago in the
>metabolic budget context).
>
>The Italian economist Paretto was the first author to point at such power
>laws; thereafter Zipf worked on their pervasive presence in other fields.
>And now we find them as a generalized outcome of the most interesting
>adaptive games played by informational entities somehow involved in an
>endless coupling of structural / generative / communicational processes.
>
>Why should the work of the 'invisible hand' of information blindly conduce
>to power law outcomes, irrespective of the molecular, neuronal or economic
>players? Intriguingly, the easiest way to produce a power law is by means
>of Karl's partitions (and conceptually it is not far away from Shu-Kun
>approach to 'entropy of mixing')...
>
>I would also like to relate these adaptive games to the processing and
>self-constructing limitations of the informational agents (so the need of
>specialization and the further problems of integration found in all realms:
>molecular, neuronal, social, interdisciplinary). And also to the
>considerations that John H made weeks ago in his comments to Floridi: 'Is
>the flow of information quantitatively directional?' I believe it is, and
>that the above processing march by the info agents under the guidance of
>the invisible hand towards their natural places (necessarily including
>'extinction, degradation, etc.) impinges into our own conversion
>data/meanings too. Meaning would be best understood as a byproduct of
>ontogenetic adaptation...
>
>all the best
>
>Pedro
>
>
>
>=========================================
>Pedro C. Mariju�n
>Fundaci�n CIRCE
>CPS, Univ. Zaragoza, 50018 Zaragoza, Spain
>TEL. (34) 976 762036-761863, FAX (34) 976 732078
>email: marijuan@posta.unizar.es
>=========================================

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Received on Sat Oct 26 01:44:38 2002