Synchronicity, Causality, Complexity, and the Brouwer Fixed-Point Theorem

Scientific Essay , 2018 , 8 Pages

Psychology - General

Synchronicity--'an acausal connecting principle' as proposed by Carl Jung may be shown to be bound by the axiom of causality (AOC) if one takes into account three factors: the principle of computational equivalence (PCE); the principle of computational irreducibility (PCI); and the Brouwer fixed-point theorem (BFPT).

Direct causal relationships presented as elements in a universal cellular automaton can result in a deterministic yet a priori indeterminate result in which the outcome of computation is bound by the PCI. This means that the circuitous computational pathway by which events are related causally cannot be determined.

Moreover, if these direct causal relationships are represented as vectors on the surface of a sphere, then according to the Brouwer fixed-point theorem they will meet at a fixed point or in a 'whorl'. If at least one of the vectors represents a conscious agent, then the confluence of vectors in the whorl may be seen as an acausal coincidence. However, the vectors ARE causally related in the past (AOC), but--because of the PCI--may seem to be acaually related due to their convergence within the same patch of space and time in the whorl.

Inhaltsverzeichnis (Table of Contents)

• Synchronicity, Causality, Complexity, and the Brouwer Fixed-Point Theorem
• The Axiom of Causality
• The Principle of Computational Irreducibility
• The Brouwer Fixed-Point Theorem
• Synchronicity Explained
• Observer Specific
• Causality and Memory
• Conclusion

Zielsetzung und Themenschwerpunkte (Objectives and Key Themes)

This paper aims to provide a new interpretation of synchronicity, arguing that it is not an acausal phenomenon, but rather a complex result of causal interactions within a deterministic system. It explores the concept of synchronicity as an emergent phenomenon that arises from the intricate interplay of causal events within a universal cellular automaton.

• The relationship between synchronicity and the Axiom of Causality (AOC)
• The role of the Principle of Computational Irreducibility (PCI) in explaining synchronicity
• The application of the Brouwer Fixed-Point Theorem (BFPT) to understand synchronicity
• The implications of synchronicity for the understanding of causal relationships and the nature of reality
• The observer-specific nature of synchronicity

Zusammenfassung der Kapitel (Chapter Summaries)

• Synchronicity, Causality, Complexity, and the Brouwer Fixed-Point Theorem: This chapter introduces the concept of synchronicity, its historical context, and the author's proposed alternative interpretation of the phenomenon.
• The Axiom of Causality: This chapter explores the Axiom of Causality and its implications for understanding causal relationships.
• The Principle of Computational Irreducibility: This chapter discusses the Principle of Computational Irreducibility and its relevance to understanding the complexity of causal systems.
• The Brouwer Fixed-Point Theorem: This chapter introduces the Brouwer Fixed-Point Theorem and its connection to the Axiom of Causality, arguing that it provides a framework for understanding synchronicity as a consequence of causal interactions within a closed system.
• Synchronicity Explained: This chapter presents the author's explanation of synchronicity as an emergent phenomenon arising from complex causal interactions within a universal cellular automaton.
• Observer Specific: This chapter explores the observer-specific nature of synchronicity, highlighting the role of individual perception and interpretation in shaping the experience of synchronistic events.
• Causality and Memory: This chapter examines the role of memory and the human mind in shaping perceptions of synchronicity, emphasizing that synchronistic events are often influenced by the memories and experiences of the observer.

Schlüsselwörter (Keywords)

This paper focuses on the concepts of synchronicity, causality, complexity, the Axiom of Causality, the Principle of Computational Irreducibility, the Brouwer Fixed-Point Theorem, and universal cellular automata. It explores the relationship between these concepts and the nature of reality, with a particular focus on the implications of synchronicity for understanding causal relationships.

• Author: MD Dr. Marshall Goldberg (Author)
• Publication Year: 2018
• Pages: 8
• Catalog Number: V428099
• ISBN (eBook): 9783668719897
• ISBN (Book): 9783668719903
• Language: English
• Tags: synchronicity; causality; complexity; cellular automata; principle of computational irreducibility; Brouwer fixed-point theorem; archetypes; collective unconscious; precognition.