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New.  below at bottom of page the table of content of the forthcoming Book Neural Network Nature

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graph of the World Wide Web


medieval woodcut

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

Peter Winiwarter


The universe :  a fractal hierarchy of intelligent neural networks from Clusters of galaxies to the World Wide Web

© 2008, 2009 Peter WINIWARTER 20


"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). Neural Network Nature.


hyperbolicFractal physics target1

Create your own universe: interactive applet hyperbolic fractal VISUALIZE click here

binarySwitchingNetwork    binary birth and death processor ( lit unlit) network VISUALIZE click here  VIZUALIZE

Neural Network C.elegans
Neural Network C.elegans


Physics, complexity and causality

"Although the laws of physics explain much of the world around us, we still do not have a realistic
description of causality in truly complex hierarchical structures."
George F. R. Ellis

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

Peter Winiwarter


 below the table of content of the forthcoming Book

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Table of Content


Fractal hierarchies of 'Perceptrons' fom Clusters of Galaxies to the World Wide Web

Introduction 5

Hierarchy Theory 8

What is a Hierarchy? Wikipedia 8

Hierarchy of Holons (1968 Koestler) 12

Living Systems (1978 Miller) 17

Compositional hierarchy vs. Subsumption hierarchy (2002 Salthe) 21

Operator hierarchy (1999 Jagers op Akkerhuis) 28

Network hierarchy (2002 Barabási) 29

Levels of evolutionary hierarchy (2008 Winiwarter) 32

A Summary of Principles of Hierarchy Theory 38

Power laws and the laws of Power 41

Common 3-level hierarchical structure 41

A short history of discovery across the disciplines 44

Pareto-Zipf-Mandelbrot (PZM) and parabolic fractal distributions 51

Illustrated regularities of the Pareto-Zipf-Mandelbrot type
Data Source: Google Images 55

Astrophysics, Nuclear networks 55

Geophysics (Gaia), Tectonic networks 62

Biophysics, Biochemistry : protein and metabolic networks 72

Biology Phylogeny: procariotes, eucariotes, genetic networks 75

Biology Ontogeny: trophic ecosystems, trophic networks 77

Social networks: the small world of scalefree networks 85

Technology networks: from stone tools to the internet 94

What do all these illustrated regularities have in common? 101

Self-similarity and the beauty of Fractals 104

fractals, Wikipedia 104

History 107

Generating fractals 109

Classification of fractals 109

Fractals in nature 110

Fractal dynamics and scale-free thinking 112

Networks everywhere 114

Networks, Wikipedia 114

The origins: the seven bridges of Königsberg 119

The random Networks of Erdős and Rényi 121

The small Worlds of Watts and Strogatz, the six degrees of separation 123

Barabási's scalefree networks from cells to the Internet 126

The mysteries of Artificial Neural Networks 134

Theoretical attempts to explain the PZM regularities: Birth and Death processors and Artificial Neural Networks 143

Self-organized critically, Wikipedia 143

West's MinMax priciple for scaling laws 145

Holistic Extremum principle (Mandelbrot, Winiwarter) 147

Pareto Pareto = Pareto , stability under addition ( Roehner, Winiwarter) 148

Birth and Death processor, the basic interaction unit 148

Artificial Neuron equivalent to birth and death processor 150

Networks of Birth and Death processors and Artificial Neural Networks 152

Trophic Web and Features of multilayer Perceptron (case study of lake Constance) 156

Future evolution: is the singularity near? 159

Increase in complexity, the first law of genesis (Winiwarter) 159

PZM power laws, the second law of genesis (Winiwarter) 159

Ritualization : the Self-Organization process of symbolic information 160

The singularity is near (Kurzweil) 164

Conclusions 170

Bibliography 174

> 10.000 citations :  "The fractal revolution" 174

1.000 - 10.000 citations  :  "The network revolution" 174

500 - 1.000 citations  "the EVOLUTION of Networks" 176

100 - 500 citations : "Evolving hierarchical systems" 178

15 - 100 citations : "The languages of Nature" 180

< 15 citations : "The Extended Mind"  The Emergence of Language, the Human Mind, and Culture 182

List of publications by Peter Winiwarter relevant to this book : 184

About the author, from Wikipedia, the free encyclopedia 186

Acknowledgments 188

Back cover Neural Network Nature 189

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