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.
Table of Contents
1. Synchronicity, Causality, Complexity, and the Brouwer Fixed-Point Theorem
Objectives and Themes
The primary objective of this work is to challenge the conventional view of synchronicity as an acausal phenomenon by proposing that it is instead a deterministic, causal process. The author posits that what appear to be acausal, meaningful coincidences are actually complex causal interactions within a closed system, governed by specific mathematical and computational principles.
- The re-evaluation of synchronicity through the Axiom of Causality (AOC).
- The application of universal cellular automata (e.g., Wolfram #110) to model complex causal chains.
- The role of the Principle of Computational Irreducibility (PCI) in rendering causal chains non-calculable.
- The geometric interpretation of synchronicity as a confluence of vectors via the Brouwer Fixed-Point Theorem (BFPT).
- The observer-relative nature of meaning in synchronistic events.
Excerpt from the Book
The Axiom of Causality (AOC)
The Axiom of Causality (AOC) implies that all effects have causes, and all causes have effects. Every ‘cause-effect’ pair or vector arises from an antecedent cause and, in turn, produces an immediately subsequent effect which is also a cause. There are no causes without effects or effects without causes; the system is closed—every vector comes from a vector and goes to a vector. It is proposed that these vectors can interact with one another in very complex ways which can be modeled by a universal cellular automaton such as Wolfram #110. Moreover, because the system is ‘closed’ these vectors can be represented as a vector field on the N-1 surface of an N-dimensional closed surface (e.g. a sphere)—the Brouwer Fixed-Point Theorem (BFPT).
In a universal cellular automaton such as Wolfram #110, the Principle of Computational Irreducibility (PCI) teaches that no ‘shortcut’ equation can tell us the state of the cellular automaton at some future time merely by ‘plugging in’ a value (TFUTURE). Instead, one must ‘run’ the cellular automaton to see its future state. The cellular automaton is deterministic, but a priori indeterminable. Furthermore, for a given ‘state’ of the cellular automaton, it is not generally possible to trace the pathway by which that state was reached, even though it was reached deterministically. To do so would violate the PCI.
Summary of Chapters
1. Synchronicity, Causality, Complexity, and the Brouwer Fixed-Point Theorem: This chapter introduces the core thesis that synchronicity is not an acausal phenomenon, but a deterministic consequence of causality within a closed system, illustrated through topology and computational theory.
Keywords
Synchronicity, Axiom of Causality, Brouwer Fixed-Point Theorem, Cellular Automaton, Principle of Computational Irreducibility, Complex Systems, Determinism, Hairy Ball Theorem, Vector Fields, Observer-Relativity, Meaningful Coincidence, Causality, Computational Equivalence, Topology, Superdeterminism
Frequently Asked Questions
What is the fundamental premise of this paper regarding synchronicity?
The paper argues that synchronicity is not an acausal principle as originally defined by Carl Jung, but rather a result of complex causal chains that appear acausal due to our inability to calculate them.
What are the primary theoretical pillars used to explain synchronicity?
The explanation relies on the Axiom of Causality, the Principle of Computational Irreducibility, the Brouwer Fixed-Point Theorem, and the modeling capabilities of universal cellular automata.
What is the significance of the Brouwer Fixed-Point Theorem in this context?
It is used to demonstrate that within a closed system, causal vectors necessarily converge to form a "whorl" or region of confluence, which a conscious observer may perceive as a synchronistic event.
How does the Principle of Computational Irreducibility (PCI) affect our understanding of causality?
The PCI asserts that there are no "shortcuts" to determine future states of complex deterministic systems; therefore, we cannot trace the complex causal chains leading to a synchronistic event, making them appear acausal.
What role does the "observer" play in the perception of synchronicity?
Synchronicity is described as observer-relative; it only exists if a conscious mind can assign "meaning" to the coincidence of events based on their personal memories or internal states.
What methodology does the author use to reach these conclusions?
The author uses a theoretical and analytical approach, drawing on established principles from mathematics, topology, and computer science to propose a new interpretation of Jungian concepts.
How does the "Hairy Ball Theorem" relate to the author's argument?
The Hairy Ball Theorem serves as an intuitive, visual example of the Brouwer Fixed-Point Theorem, illustrating how vectors on a closed surface must inevitably form a whorl.
Does the author suggest that human minds are excluded from this system?
No, the author explicitly includes "minds," along with memories and dreams, as part of the causal world, suggesting they interact with other causal vectors through various communication channels.
What is the implication of viewing the universe as a "superdeterministic cellular automaton"?
If the universe is such an automaton, then quantum mechanics is merely a tool for calculation, and the underlying reality is deterministic, rendering the notion of true acausality obsolete.
Why does the author use the example of a "golden scarab"?
The author references Jung's famous case study to illustrate how a specific synchronistic event can "break the ice" of rational resistance, serving as a catalyst that requires an observer to attribute meaning to the confluence of events.
- Arbeit zitieren
- MD Dr. Marshall Goldberg (Autor:in), 2018, Synchronicity, Causality, Complexity, and the Brouwer Fixed-Point Theorem, München, GRIN Verlag, https://www.grin.com/document/428099
