Recursion of Reality: Between Determinism and Chaos | Nguyen Tien Hoach

1. Introduction

Disclaimer: This is a hypothesis and a conceptual exploration rather than a definitive theory.

This article explores free will, choice, and chaos through the lens of recursion. It examines how different dimensions alter causal relationships and applies mathematical models to analyze these interactions.

• The question of whether the world is predetermined or if free will exists.
• Analysis of different models of causality.
• The connection between determinism, chaos, and multidimensionality.

2. Causal Relationships Across Dimensions

• 1D: Linear causality (A → B).
• 2D: Multiple outcomes (A → {B, C, D}).
• 3D: Influence of external factors, cyclicality (A ↔ B ↔ C, mutual influence).
• 4D+: Temporal and alternative timelines (A → B, but also D influencing B).
• The hypothesis of dimensional recursion as a model of infinity.

3. Determinism vs. Chaos

• In a linear model, the world is predetermined.

• In a multidimensional model, chaos and determinism are two sides of the same system.

• The possibility of alternative pathways for events.

• Dynamic systems theory: even in deterministic systems, chaotic effects can arise if the system is sensitive to initial conditions.

• The Lorenz equations as an example of a system where deterministic laws lead to chaotic behavior:

  $$\frac{dx}{dt} = \sigma (y - x) \frac{dy}{dt} = x (\rho - z) - y \frac{dz}{dt} = xy - \beta z$$

• The recursive approach to chaos: chaos can have a fractal structure, where order and randomness intertwine at different scales.

4. The Possibility of Free Will

• Free choice exists within a system of constraints.
• Absolute free will is impossible due to the interconnectivity of all events.
• The influence of perception on the interpretation of reality.
• Probabilistic models in quantum mechanics suggest that processes may be locally deterministic but globally probabilistic.
• A hybrid model of reality:
  • Locally, the world may follow deterministic laws.
  • Globally, chaos or stochasticity creates the appearance of randomness.
  • The recursive structure of reality forms a “fractal” model of consciousness and physical processes.

5. Conclusion

• The world can be viewed as a recursion of dimensions encompassing all possibilities.
• Our world may be either the only possible one or one of the best possible versions.
• Infinity as a self-referential system that we cannot escape.
• The more we understand, the more questions arise.
• Determinism and chaos may not be opposites but manifestations of a single recursive structure of reality.

Conclusion: The world is a complex system where predetermination and free will coexist, influencing each other.