Institute Output
Kolmogorov Complexity vs. Computational Irreducibility: Understanding the Distinction
James K. Wiles
Kolmogorov complexity and computational irreducibility describe two kinds of limits on simplification, but they apply in different ways. Kolmogorov complexity measures the shortest possible description of an object, such as a string. Computational irreducibility refers to processes that cannot be predicted or accelerated. This paper introduces each concept, explains their theoretical distinction, and illustrates the difference using simple examples.
Observer Theory and the Ruliad: An Extension to the Wolfram Model
Sam A. Senchal
This paper introduces a rigorous category-theoretic extension to Observer Theory within Wolfram's Ruliad framework, demonstrating how observers and observes like us sample and integrate information across hierarchical domains, addressing consciousness, causation, and the transition from discrete computational processes to continuous perceived reality.