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.
At a glance
- Uses the Hairy Ball Theorem to illustrate a proposed causal model
- 10 sources in the bibliography
- 3 figures
Table of Contents
The document does not contain a table of contents or numbered chapters.
Objectives and Topics
The paper asks whether synchronicity, conventionally described as an acausal meaningful coincidence, can instead be understood through causality, computational complexity and a proposed application of the Brouwer fixed-point theorem.
- Jung’s concept of synchronicity and meaningful coincidence
- Cause-effect relationships and interacting vectors
- Cellular automata and computational irreducibility
- The Brouwer fixed-point and hairy ball theorems
- Memory, observation and the perception of meaningful events
Excerpt from the Book
Synchronicity, Causality, Complexity, and the Brouwer Fixed-Point Theorem
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.
In the case of synchronicity we have many causes and effects, including all those causes which can produce effects on memory, and dreams. The mind, in turn, is the cause of other effects on the world, including other minds. In other words, simple immediate (direct cause-effect) vectors, AB, CD, EF (instantaneous ‘world lines’) can interact with one another in the most complex ways. The word ‘immediate’ means occurring together over a ‘short’ period of time where Δt, the time magnitude of the vector, is infinitesimally small.
All of these simple immediate cause-effect relationships can be seen as the elements of a ‘rule’ defining the computations of a universal cellular automaton where these vectors interact in complex ways.
The Principle of Computational Equivalence (PCE) holds that simple rules, such as Wolfram #110, can lead to complex behavior. A multitude of interactions among these vectors as elements in a complex cellular automaton can result in unexpected causal relationships.
Summary of the Work
The paper has no chapter headings. It introduces Jung’s account of synchronicity, develops a conceptual model involving causality and computational complexity, and uses diagrams of vector whorls to discuss the proposed role of fixed-point and hairy ball theorems. It concludes by presenting synchronicity as observer-relative within the author’s proposed causal framework.
Keywords
synchronicity, causality, meaningful coincidence, Carl Jung, computational complexity, cellular automata, Wolfram #110, computational irreducibility, computational equivalence, Brouwer fixed-point theorem, hairy ball theorem, vector fields, observer relativity, memory
Frequently Asked Questions
What is the paper about?
It examines whether events described as synchronistic can be interpreted within a causal framework rather than as acausal coincidences.
What are its central topics?
The paper connects synchronicity with causality, cellular automata, computational complexity, vector fields and mathematical fixed-point arguments.
What is the primary question?
It asks how meaningful coincidences might arise from complex causal interactions that observers cannot readily trace.
What method does the author use?
The author develops a conceptual and theoretical argument using examples, mathematical analogies and diagrams. The paper does not report an empirical survey or experiment.
What does the main discussion cover?
It considers cause-effect vectors, cellular automata and computational irreducibility, then illustrates the proposed model with vector whorls and situations differing in time and place.
Which keywords characterize the paper?
Key terms include synchronicity, causality, computational irreducibility, cellular automata, the Brouwer fixed-point theorem and observer relativity.
Why does the paper discuss Wolfram #110?
The author uses it as an example of a universal cellular automaton in which simple rules can generate complex behavior.
How does the paper use the hairy ball theorem?
It presents a whorl on a sphere as an illustration for discussing the proposed convergence of causal vectors.
What role do memory and observation play?
The paper considers how memories and mental states can influence whether an observer regards a coincidence as meaningful.
- Quote paper
- MD Dr. Marshall Goldberg (Author), 2018, Synchronicity, Causality, Complexity, and the Brouwer Fixed-Point Theorem, Munich, GRIN Verlag, https://www.grin.com/document/428099
