Klir Foundations of Mathematical System Dynamics

The Fundamental Theory of Causal Recursion and Its Application to Social Science and Economics
1. Auflage 2017
ISBN: 978-1-4832-8697-6
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band Volume 2, 343 Seiten, Web PDF

Reihe: IFSR International Series on Systems Science and Engineering

This book is a foundational study of causality as conceived in the mathematical sciences. It is shown that modern mathematical dynamics involves a formulation of the fundamental concept of causality, and an exhaustive classification of causal systems. Among them are the 'self-steering' and 'self-regulating' systems, which together form the class of purposive systems, on whose specific properties the book then focuses. These properties are the mathematical-dynamical foundations of the behavioural and social sciences. This is the definitive book on causality and purposive processes by the originator of the mathematical concept of self-steering.

Autoren/Hrsg.

Klir, George J.

Inhaltsverzeichnis

1;Front Cover;1
2;Foundations of Mathematical System Dynamics: The Fundamental Theory of Causal

Recursion and its Application to

Social Science and Economics;4
3;Copyright Page;5
4;Table of Contents;6
5;Preface;12
6;Part 1: Fundamental Dynamics: The General Theory of Causal Recursion;14
6.1;CHAPTER 1. Causal Recursion in Theoretical Physics;16
6.1.1;1.1 Causal Relation, Causal Law, and Causal Recursion;16
6.1.2;1.2. Causal Recursion in Classical Physics: the Hamiltonian Formalism;17
6.1.3;1.3 Causal Recursion in Quantum Physics: the Unitary Timetranslations in a Hubert Space of States;20
6.1.4;1.4 The Molecular State-description: a Third Level of Causal Recursion;21
6.1.5;1.5 Conservative and Dissipative Systems;23
6.2;CHAPTER 2. Causal Recursion in Mathematical Dynamics;26
6.2.1;2.1. Causal Recursion in Dynamical Systems Generally;26
6.2.2;2.2 Dynamical Systems With Nilpotent Causal Recursion;31
6.2.3;2.3. Dynamical Systems with Full Causal Recursion;35
6.2.4;2.4. Self-organization vs Rigid-structured Dynamical Systems;37
6.2.5;2.5 Causality, Determinism, and Indeterminism;40
6.3;CHAPTER 3. The Systematics of Goal-directed Systems;42
6.3.1;3.1. General properties of the goals of self-regulating systems;42
6.3.2;3.2. Self-regulating equilibrium systems;43
6.3.3;3.3. Periodically pulsating self-regulating systems;46
6.3.4;3.4. Almost periodically pulsating self-regulating systems;48
6.3.5;3.5. Irregularly ('chaotically') pulsating self-regulating systems;49
6.3.6;3.6. Self-steering systems;51
6.3.7;3.7. The Ashby-Lange effect;54
6.3.8;3.8. Systems that are steerable from outside;55
6.3.9;3.9. Finite systems and Turing machines;59
6.4;CHAPTER 4. The Modes of Asymptotic Approach of Goals;63
6.4.1;4.1. Causal Suction: The Ideal Type;63
6.4.2;4.2. The Generalization of Causal Suction to ç Dimensions and to Nonlinear Causal Recursions in an Equilibrium System;65
6.4.3;4.3. The Generalization of Causal Suction t o Nonequilibrium Goals;71
6.4.4;4.4. Causal Torsion;72
6.4.5;4.5. Causal Vortex;76
6.4.6;4.6. The Approach of a Goal Through Rapid Vibrations;79
6.4.7;4.7. The Degeneracies of Causal Suction, Torsion, and Vortex, and of Rapid Vibrations, into Satellites and Comets;84
6.4.8;4.8. The General Connection Between Linear Difference and Differential Equations;91
6.5;CHAPTER 5. The Variety of Dynamical Systems Generated by a Single Nonlinear Map (An Example);95
6.5.1;5.1. The Séparatrices and Regions;96
6.5.2;5.2. The Special Points;100
6.5.3;5.3. Structural Stability and Instability;102
6.5.4;5.4. Hopf Bifurcation: an Algorithm for the Detection of its Existence;104
7;Part 2: Simple Applications: Causal Recursion in Population Dynamics and Economic Growth Theory;108
7.1;CHAPTER 6. Verhulstian Ecosystems and the Feigenbaum Bifurcations of their Equilibrium States;110
7.1.1;6.1. The Verhulst Axioms;110
7.1.2;6.2. The Preliminary (Local) Stability Analysis;111
7.1.3;6.3. Verhulstian Ecosystems as Self-regulating Equilibrium Systems: a Small or Medium Total Biomass;114
7.1.4;6.4 Verhulstian Ecosystems as Periodically Pulsating Self-regulating Systems of Period 2: a Large Total Biomass but a Small Death Rate;123
7.1.5;6.5. The Feigenbaum Bifurcations and their Interruptions in Verhulstian Ecosystems in the General Case: a Large Death Rate and Total Biomass;127
7.2;CHAPTER 7. The Role of Self-regulation in Biological Evolution and in Different Ecologies;132
7.2.1;7.1. The Survival of the Fittest;132
7.2.2;7.2. The Coexistence of Different Species;133
7.2.3;7.3. General Remarks on Self-regulation in Competitive Ecology;136
7.2.4;7.4. On Self-regulation in Predator-Prey Ecology;139
7.3;CHAPTER 8. The Conditions of Self-steering of Economic Development;142
7.3.1;8.1. A Heuristic Model of Self-steering and Selforganization of Economic Development in the Very Long Run: the Generalized Steinmann-Komlos Model;142
7.3.2;8.2. A Down-to-earth Approach to Economic Growth: the Dynamic Input-Output Model;151
7.3.3;8.3. The Condition of Self-steering to the Golden Age Path in the Solow-Swan and Related Mainstream Models;162
7.3.4;8.4. Criticism of Neoclassical Growth Theory from the Point of V i ew of Mathematical Dynamics;168
8;Part 3: Complex Applications: The Self-steering and Selfregulation of Human Societies as Wholes;176
8.1;CHAPTER 9. The Concept of a Self-steering Actor;178
8.1.1;9.1. Human Acts as Tools of Interaction between Consciousness and the World of Objects;178
8.1.2;9.2. Mathematical Representation of Acts;180
8.1.3;9.3. The Theorem on Dual Causality;183
8.1.4;9.4. Self-steering Actors;186
8.2;CHAPTER 10. Self-regulating Actors and Actorhierarchies;190
8.2.1;10.1 Subjective and Objective Complexity;190
8.2.2;10.2. Survival through Self-regulation: Ashby's Law;191
8.2.3;10.3. The Improvement of Self-regulation by Actor- Hierarchies;195
8.3;CHAPTER 11. The Law of Requisite Hierarchy;198
8.3.1;11.1. Human Society as a Complex Self-regulating and Self-organizing Actor-Hierarchy;198
8.3.2;11.2. The Law of Requisite Hierarchy for Undeveloped Economic Systems;200
8.3.3;11.3. The Law of Requisite Hierarchy for Developing Economic Systems;202
8.4;CHAPTER 12. The Cybernetic Concepts of Social Development and U nderdevelopment;204
8.4.1;12.1. Human Society as a Collective of Self-steering Actors;204
8.4.2;12.2. The Limits of Toleration of Self-Steering in Human Society;205
8.4.3;12.3. The Concept of Underdevelopment;208
8.4.4;12.4. The Concept of Social Development;210
8.5;CHAPTER 13. The Governability of Human Society;212
8.5.1;13.1. The Crises of Governability as Crises of Selfsteering;212
8.5.2;13.2. The Freedom of Action of Two Opposite Political Forces as the Condition of Governability of Developing Society;217
8.5.3;13.3. Full-scale Social Revolution as a Loss of Governability of Society;219
9;Part 4: Historical Illustrations of Se/fsteering in Different Types of Human Societies;224
9.1;CHAPTER 14. The Birth of the Western-style Society of Relaxed Hierarchy;226
9.1.1;14.1. The Origin of East-West Differences: Economic Development in Western and Eastern Europe since the Twelfth Century;226
9.1.2;14.2. Western-European Feudalism and its Relaxed Hierarchy of Power;228
9.1.3;14.3. The Germ of Western Democracy: the Local Power of the Middle Class in Medieval England;233
9.2;CHAPTER 15. Underdevelopment as Illustrated by Russian Social History from the Ninth to the Nineteenth Centuries;240
9.2.1;15.1. The Backwardness of the Russian Economy and the Defeat of the Norman Power;240
9.2.2;15.2. The Continual Growth of Centralized Power in Russia;242
9.2.3;15.3. The Development from Absolute towards Totalitarian Power;246
9.3;CHAPTER 16. The Gradual Breakthrough of Modern Western Society in England from the Fourteenth to the Nineteenth Centuries;253
9.3.1;16.1. The End of English Feudalism and the Rise of Independent Farmers and City Bourgeoisie;253
9.3.2;16.2. The Short-lived Threat of Full Revolution: Cromwell's Time and a Temporary Drop of Selfsteering (Human Freedom) in English Society;256
9.3.3;16.3. The Rapid Increase of Self-steering: The Emergence of Two-party Parliamentarism, Industrial Revolution, and the Anglo-Saxon Freedom of Speech;259
9.4;CHAPTER 17. The Full-scale Social Revolutions and Their After-effects on the European Continent;264
9.4.1;17.1. Delayed Social Development in France and the Instability Following the Great Revolution;264
9.4.2;17.2. Revolution Passes Eastward;267
9.4.3;17.3. The Dominating Developmental Trends in the Contemporary World and the Birth of the European 'Grey Zone';270
10;Part 5: The Problem of the Origin: The Self-steering and Steered - from-outside Layers of Consciousness?;274
10.1;CHAPTER 18. The Self-steering and Steeringfrom- outside of Man;276
10.1.1;18.1. The Mathematical Concepts of a priori and a posteriori Subjective Probability;276
10.1.2;18.2. The Filter Theorem;281
10.1.3;18.3. A Discussion of the First Condition of the Filter Theorem: Empirical and Inductive Knowledge;283
10.1.4;18.4. A Discussion of the Second Condition of the Filter Theorem: The Filter in Human Consciousness;286
10.1.5;18.5. On the Mechanisms of the Formation of a priori Knowledge;287
10.1.6;18.6. The Anthropological Evidence for the Two-layer Theory and the Conditioning Hypothesis: A Survey of the Main Points;291
10.2;CHAPTER 19. The Primitive Mind: Anthropological Evidence for the Two-layer Theory and the Conditioning Hypothesis Scrutinized*;295
10.2.1;19.1. The Two Layers of the Primitive Mind: The Sacred and the Profane;295
10.2.2;19.2. The Nature of Magic and the Conditioning of Myths;297
10.2.3;19.3. The Crucial Test of the Collective Conditioning of a priori Truths;304
11;Scientific References;317
12;APPENDIX: Why Mathematical Foundations Are Important in Science;321
12.1;1. Introduction;321
12.2;2. The Inflation of Various Models and Paradigms;321
12.3;3. The Testimony of the Accumulation of Fundamental Scientific Knowledge: Reality is Mathematical;324
12.4;4. Where and how Ultra-empiricism got it Wrong;328
12.5;5. Repercussions of Ultra-empiricism in Philosophy and in the 'Soft' Sciences;334
12.6;6. Conclusions;340
13;Index;342