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"The discovery of the Universe is the discovery of our Brain"

Peter Winiwarter

"I think the next century (21st) will be the century of complexity."

 Stephen Hawking

note: computer simulation of the evolution of complex systems/networks with neural networks (universal mappers) is a young paradigme, which does not fit in any University or "classical" research department.
Let's wait for the retirement of pure reductionist scientists and see for the arrival of a new generation of  transdisciplinary holistic and open  system approaches  like
the Santa Fe Institute  ,
and the   evo devo universe commmunity

"New paradigms in science spread not because the tenants of the old paradigme are convinced by the new ideas, but because the tenants of the old paradigme die." 

Max Planck 
on Quantum physics vs. classical physics.


"We are all agreed that your theory is crazy. The question which divides us is whether it is crazy enough to have a chance of being correct. My own feeling is that is not crazy enough. "

Niels Bohr on Pauli's theory of elementary particles
from Arne A. Wyller's The Planetary Mind



"Life and mind have a common abstract pattern or set of basic organizational properties. The functional properties characteristic of mind are an enriched version of the functional properties that are fundamental to life in general. Mind is literally life-like. "

                                             Godfrey-Smith, P. (1996). Complexity and the Function of Mind in Nature. Cambridge: Cambridge University Press.

"Mind is literally life-like. The Universe and Life are literally mind-like. "

                                             Peter Winiwarter (2008). Network Nature.

"Playing with networks is fun"

                                             Sergej Dorogovtsev

Summary:  Complex Systems, Neural Networks & Cosmic Evolution

The Intelligence of Networks & the Networks of Intelligence, 

the universe : a fractal hierarchy of intelligent neural networks

all networks of evolution from the big bang to the world wide web revealing Pareto-Zipf-Mandelbrot (parabolic fractal) powerlaws are:

  1. energy/information transformation systems


  2. built of basic energy/information transformation processors that are born and run to  death in an irreversible way (birth and death processors).


  3. all processors are linked in a complex "small world" network mappable on a multilayer perceptron network of artificial neurons.


  4. it's the global field generated by all processors that "drives" the process of evolution based on energy optimization specific to the level of evolution :
    GUT, gravitation, strong nuclear, weak nuclear, elmag, chemical, geothermal, wind, water, fire, genetic code, spoken words, written codes, computer codes, Web services ...


  5. ritualization : repetitive use of pathways, Hebb's rule*  ( cells that fire together wire together) and the Pareto frontier (You can't make many people better of without making many people worse of)
     hardwire the networks information flow into "engrams"**, like timetables hardwire a railroad, or air transportation network.

*Hebbian theory has been the primary basis for the conventional view that when analyzed from a holistic level, engrams are neuronal nets or neural networks
**  "If the inputs to a system cause the same pattern of activity to occur repeatedly, the set of active elements constituting that pattern will become increasingly strongly interassociated. That is, each element will tend to turn on every other element and (with negative weights) to turn off the elements that do not form part of the pattern. To put it another way, the pattern as a whole will become 'auto-associated'. We may call a learned (auto-associated) pattern an engram." (Op cit, p44;) Gordon Allport

Lotka said,"The principle of natural selection reveals itself as capable of yielding information which the first and second laws of thermodynamics are not competent to furnish. The two fundamental laws of thermodynamics are, of course, insufficient to determine the course of events in a physical system. They tell us that certain things cannot happen, but they do not tell us what does happen."

1) First law of genesis : the complexity of a self-organized system/network can only increase or remain constant
    (irreversibility of evolution, the arrow of internal system time).


2) Second law of genesis: for self-organized systems/networks we observe element/symptom size distributions of the longtailed Pareto-Zipf-Mandelbrot (PZM) type
(parabolic fractal 'generalized life symptoms').

3) Like Gaussian probability distributions,  longtailed  Pareto-Zipf distributions are
stable under stochastic addition
(mergers and splits of systems/networks); Gauss + Gauss yields Gauss; Pareto-Zipf + Pareto-Zipf yields Pareto-Zipf .
4) Self-organized systems/networks can be mapped on a hierarchy of binary threshold automata (birth & death processors) modelled by a Neural Network of the type multilayer feed forward topology "learning" through gradient descent backpropagation of errors through consecutive "runs" - cycles of energy information transformation (multilayer perceptron).
(energy information equivalence)

5) Self-organized systems/networks have memory *.
(galaxies, ecosystems, world economy, world wide web) : the memory consists of the global system topology of the network , local weights and connection strengths of all processors.

* ability to store, retain, and subsequently retrieve information

6) Self-organized systems/networks are learning *.
Hebb's rule reinforces memory through consecutive runs of energy / information transformation cycles.

* ability to improve the  facility to store, retain, and subsequently retrieve perceived information (memory)

7) Self-organized systems/networks are intelligent  *.

global error minimization on the system level ( total system "cost" of  web) through consecutive runs of energy / information transformation through the system hierachy.

* ability to optimize learning as a function of a goal (maximum or minimum principle)

8) Evolution is Self-organization of networks of matter and mind
from astrophysical to linguistic and computer networks of the world wide web 

following the same seven conceptual categories in conceptual space


In short, the properties of artificial neural networks of the multilayer perceptron type are common to all systems / networks for which we observe PZM (Pareto-Zipf-Mandelbrot, parabolic fractal) distributions:
  1. selforganized systems / small world networks / the universe(s) have memory  
    (engrams :  topology of tree structure, hypercycle structure)
  2. selforganized systems / small world networks / the universe(s) are learning  
    (Hebb's rule, Pareto frontier)
  3. selforganized systems / small world networks / the universe(s) are intelligent
    (global energy/information optimization)


the universe: a hierarchy of neural networks

Network Nature has memory

Network Nature is learning

Network Nature is intelligent