Research scope :   complex systems / neural networks &  evolution

"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. "

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

Contents : it may take several minutes to download the numerous illustrations.

1. Keywords math

2. Abstract

3. evolution : the big picture  a synopsis with links
   
   

4. empirical observations

1. empirical observations :  astrophysics

2. empirical observations :  geophysics, geology, geoscience, meteorology

3. empirical observations :  bio-chem, biology, plant, animal, ecosystems

4. empirical observations :  economics,  social systems

5. empirical observations :  religion, sociology

6. empirical observations :  linguistics

7. empirical observations :  mechanical systems, communication systems, computer tech

8. empirical observations :  science, education, innovation

9. empirical observations :  world wide web

10. empirical observations :  brain, neural networks
    
    

11.  theoretical approaches    a synopsis with links

    Zipf's principle of least effort,
    
    Pareto efficiency Pareto frontier,
    
    Holland Gell-Mann complex adaptive systems
    
    Preferential attachment
    
    Odum's maximum power principle*
    

    “

    That theory, as it is expressed by the maximum power principle, addresses the empirical question of why systems of any type or size organize themselves into the patterns observed. Such a question assumes that physical laws govern system function. It does not assume, for example, that the system comprising economic production is driven by consumers; rather that the whole cycle of production-consumption is structured and driven by physical laws.

    
    West's min-max principle for hierarchical branching networks,
    
    The law of Maximum Entropy Production
    
    Winiwarter's first law of genesis**
    ** The complexity of a selforganized system can only increase or remain constant.
    
    Winiwarter's second law of genesis***
    *** The rank frequency distribution of any selforganized system is of the PZM Pareto-Zipf-Mandelbrot type.
    
    Winiwarter & Cempel generalized "life symptoms" ****
    **** any selforganized system can be mapped on a hierarchy of birth and death processors formally equivalent to an ANN artificial neural network of the type multilayer perceptron (feedforward with backpropagation).
    
    Winiwarter Neural Networks ...
    
    Baillon-Moreno's unified Scientometric Model

Pareto-Zipf-Mandelbrot (parabolic fractal) distributions are observed in virtually all fields of research
covering the evolution from the big bang over the evolution of man
 to the world wide web.

empirical observations : self-organized* systems/  scalefree small-world networks and power laws

Let's take the income size distribution of any country.  There are very few very rich billionaires, there are few rich millionaires, there are many middle class peope and the remaining vast majority are just plain poor. This inequality can be described by a mathematical distribution, which yields a straight line in log-log coordinates. (Pareto law).

Another example for PZM Pareto-Zipf-Mamdelbrot regularity. Let's take the city size distribution of a country and rank the citites in decreasing order of number of inhabitants. There are a few very big metropoles, there are a few big cities, there are many cities of medium size and the vast number of agglomerations are small towns. This inequality can be described by a mathematical distribution, which yields a straight line in log-log coordinates. (rank size rule).  etc... 

This asymmetric distribution is very different from the well known Gaussian bell shaped symmetric distribution. 



normal Gaussian distribution versus Pareto-Zipf distribution

for those who persist to say they are the same mathematical structures, there is a major difference even in the second and third degree of a taylor development.

Pareto-Zipf-Mandelbrot (parabolic fractal) distributions  are scalefree.




In the parabolic fractal distribution the right tail of the poor is very much longer than the short left tail of the rich.  Therefore the term longtailed. For these distributions there is no such thing calculable like a mean or average income, since there is no symmetry and a value would be different for every arbitrary cutoff point in the ranking.

-
Note that there are only two families of mathematical distributions which do not change their form after the merger or split of system distributions :
1) the Gaussian  (Gauss folded with Gauss yields Gauss).
2) the Pareto-Zipf-Mandelbrot distribution  (Pareto folded with Pareto yields Pareto). see second law of genesis/

For all the examples on this page we observe similar regularities of the Pareto-Zipf-Mandelbrot (parabolic fractal) type.

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)
   
   a part of the input energy rate is irreversibly accumulated in an internal reservoir from birth to death of the processor.
   
   
   
   
   fractal hierarchy of birth and death processors in nature
   
   
   
   
   
   Physics, complexity and causality
   
   With this view, the higher levels in the
   hierarchy of complexity have autonomous
   causal powers that are functionally independent
   of lower-level processes. Topdown
   causation takes place as well as
   bottom-up action, with higher-level contexts
   determining the outcome of lowerlevel
   functioning, and even modifying the
   nature of lower-level constituents.
   
   George F. R. Ellis
   NATURE|Vol 435|9 June 2005
   - 
3. all processors are linked in a complex "small world"  network mappable on a multilayer perceptron network of artificial neurons*
   
    
   
   Small worlds, between perfect order and chaos;
   the first graph is completely ordered, the graph in the middle is a "small world" graph, the graph at the right is complete random.
   
   
   
   
   
    
     
                                                                       
   
   Note: when a small world network is mapped on a specific multilayer feedforward network (multilayer perceptron) the neurons of the top layer constitute virtual nodes of the binary "shortcut" links of the small world.
   
   
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, electo-magnetic, chemical, geothermal, wind, water, fire, genetic code, words, written codes, computer codes ...
   -
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. Additional ideas regarding cell assembly theory and its role in forming engrams, along the lines of the concept of auto-association, described as follows:

**  "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

"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. "

"The Universe and Life are literally mind-like. "

1) empirical observations : self-organized* systems/  scalefree small-world networks and power laws

Pareto-Zipf-Mandelbrot (parabolic fractal) distributions are observed in virtually all fields of research
covering the evolution from the big bang over the evolution of man
 to the world wide web.

- astrophysics :

star size distributions are of the PZM Pareto-Zipf-Mandelbrot type (parabolic fractal)

galaxy size distributions

 meteorite size distributions

the brain of the sun, peak gamma ray intensity distribution of solar flares 

are of the PZM Pareto-Zipf-Mandelbrot type (parabolic fractal)

- geophysics, geology :

geoscience :

field size distribution of oil reserves

- physics :

meteorology

weapon systems :

nuclear arm explosion energy size distributions

phys-chem  :

bio-chemistry :

The E.coli metabolic network is scalefree ( PZM Pareto-Zipf-Mandelbrot type, parabolic fractal) and has small-world properties


The yeast protein interaction network has a scalefree topology (Pareto-Zipf Mandelbrot distribution)
The scale-free nature of protein interaction networks is a generic feature of all organisms.

- biology 

Darwin Tree of Life

evolutionary leaps :

appearance of life, eucariotes, pluricellular, tetrapodic, homeothermic, vivipartide, primates
rank-time distribution
 

animal :

plant :

"I see trees everywhere"  Peter Winiwarter





tree stem diameter distributions 

"most citations are truncated."  Peter Winiwarter






leaf area size distribution  

"        'leaf me alone' is the most fundamental principle of plants."   Peter Winiwarter


the same scaling law is observed over 27 orders of magnitude from microbacteria to whales.

 bloodvessel

metabolic pathways


metabolic rate in animals of all size (allometric scaling distribution)

1. MINIMIZE ENERGY DISSIPATED IN THE NETWORKS
2. MAXIMISE THE SCALING OF THEIR AREA OF INTERFACE WITH THEIR RESOURCE ENVIRONMENT

heart rate of all animals follow a power law distribution

"The number of your heartbeats until your death are counted by your weight."   Peter Winiwarter





blood vascular system

- ecosystems  environment :

http://www.bordalierinstitute.com/target1.html#religion

- social systems, transportation systems :

     
         

 public transportation networks ... (Marcel Duchamp  "Network stoppages")

PZM (Pareto-Zipf-Mandelbrot, parabolic fractal) Power laws are observed for the world's 12 major metropolitan public transportation network systems





railroad networks

The world-wide airport network is a

where α = 1.0 ± 0.1 is the power-law exponent, f(u) is
a truncation function, and k× is a crossover value that
depends on the size S of the network as k× ∼ S0.4.






power grid distribution lines

- economics , income systems :

            

firm size distributions 

- religion 

 

social network of person or goddess





Jesus network shows a

  

sociology :

are of the PZM Pareto-Zipf-Mandelbrot type (parabolic fractal)

  

- linguistics :

- mechanical systems :

- communication systems :

distribution of telephone calls received

distribution of numbers of bestselling books

- computer tech :

computer evolution (Apple) written on a Mac Mini runnung under Windows Vista Pro


software development

- world wide web:

local view
hyperbolic view

- scientometrics,

  research and publications :

Journal of Theoretical Biology : Scaling properties of childhood ...

 co-citation graph of 394 articles
"the DNA/RNA and proteins of research papers"

education :

innovation : 

innovation size distribution

- Brain, neural networks :    

   

• an artificial neuron of an artificial neural network (ANN) is a binary threshold outomaton with two possible states 1 (fires) or 0 (otherwise)

• a birth and death processor is a binary threshold automaton with two possible states  1 (dead) or 0 (alive otherwise).

• The squashing function death in a trophic web is equivalent to the firing of a neuron in an ANN.

metaphysics :

We share the world view of Heinz von Förster, the world (what we call "reality") is a construction of our mind. (constrained by the form of our conceptual containers, see Semiotica article on the periodic system of system concepts).

Science is the collective construction of world views based on majority consensus.

What's beyond is called metaphysics and as Kant said, "metaphysics is like a dark ocean without shore and without light-tower." (better not talk about it)

We cannot say anything about it except believe systems.

However Kant also said, "if you drive metaphysics out of the front door, it will enter through the back window."

That's why we started and ended this illustrated scientific walk through evolution from the big bang to the world wide web by a metaphysical slide.

2) theoretical approaches

"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

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

Baillon-Moreno's  Structure and dynamics of scientific networks:

For income distributions, city-size distributions and word frequencies we observe long-tailed distribution power laws of the PARETO-ZIPF-MANDELBROT (parabolic fractal) type. In fact on all levels of evolution from the big bang to the world wide web - for properties of units belonging to the same astrophysical, geological, biological, ecological, urban, social, linguistic, economic, mechanical machinery or computer system - we observe similar regularities referred to as Pareto law, Zipfs law or rank-size law. We give a short historical overview over the discovery of these empirical regularities. Then we review a variety of theoretical tentatives, none of which can explain that similar regularities are observed in such an incredible wide range of scientific research areas.

Finally, departing from a very specific model - describing tribo-vibro-acoustic processes in machines - we propose a generalized theoretical framework in terms of energy transformation with limited internal energy dissipation capacity, which is applicable to all fields.

The proposed model unifies a large variety of concepts and applies a coherent terminology to fields, which have at first sight nothing in common. For the observed generalized life symptoms, theoretical predictions can be compared with past and future empirical observations.

What is most important is the model's inference power: from the observations of a set of units at a given moment of life-time (a snapshot of the system), one can predict the average behaviour of a single unit over its entire life-time.

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)
   -  birth and death of star

1. all processors are linked in a complex "small world" network mappable on a multilayer perceptron network of artificial neurons
   
   
2. 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, electo-magnetic, chemical, geothermal, wind, water, fire, genetic code, words, written codes, computer codes ...
   -
3. ritualization (repetitive use of pathways, Hebb's rule http://en.wikipedia.org/wiki/Hebb%27s_rule) hardwires the networks information flow, like timetables hardwire a railroad, or air transportation network.

Gordon Allport posits additional ideas regarding cell assembly theory and its role in forming engrams, along the lines of the concept of auto-association, described as follows:

"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;)

1. selforganized systems / small world  networks  / the universe have memory  
   (engrams :  tree structure, hypercycle structure)
   
2. selforganized systems / small world networks / the universe  are learning  
   (Hebb's rule, Pareto frontier)
   
3. selforganized systems / small world networks / the universe are intelligent
   (global energy/information optimization)