Foundational Concepts
The Arche framework builds on several foundational ideas from mathematics, philosophy, and systems theory:
- •Identity and Sufficient Reason: Leibniz's principle that nothing occurs without a reason, grounded in the identity of the whole.
- •Dual-Aspect Monism: The philosophical position that reality has two irreducible aspects (interior and exterior) that are not separate substances.
- •Fourier Analysis: The mathematical insight that any signal can be decomposed into pure frequencies and recomposed from them.
- •Autopoiesis: Maturana and Varela's theory of self-organizing systems that maintain themselves through closure.
- •Complexity Science: The study of how order emerges from simple rules through networks, motifs, and phase transitions.
Related Frameworks
Integral Theory (Ken Wilber)
ARTOK's domains map to Integral's four quadrants (interior-individual, exterior-individual, interior-collective, exterior-collective) and developmental stages. The frameworks are complementary and can be used together.
Universal Theory of Knowledge (UTOK)
ARTOK's progression through domains corresponds to UTOK's planes (matter, life, mind, culture). Both frameworks provide complementary perspectives on how knowledge is organized.
Systems Theory & Cybernetics
ARTOK's concepts of closure, feedback, and self-organization align with systems theory. The framework provides mathematical precision to systems thinking.
Key Diagrams & Visualizations
The following diagrams help visualize core concepts of the Arche framework:
- •Zero-Infinity Duality: How perfect balance (zero) and inexhaustible recursion (infinity) are complementary aspects of identity.
- •Dual-Aspect Monism: Frequency and spacetime as two faces of one reality, related by holomorphic projection.
- •Archeon Composition: How Archeons combine through superposition, composition, modulation, and reflection.
- •Emergence Landscape: How closure gradients create attractors that pull systems toward stability.
- •Harmony Gradient: How value emerges from the fit of parts within wholes across scales.