on optimization, again

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

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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 Fri Oct 18 14:40:30 2002