Civilization is building systems that reason about themselves, audit themselves, and govern themselves — without a formal science of what self-referential systems can and cannot do. That gap is not merely academic. It is costing us clarity about AI safety, interpretability, consciousness, and the foundations of physics.… Read More “Toward a New Science of Self-Referential Systems”
This article explains my paper on the
Mathematics of Self-Referential Systems, for a non-technical audience. The paper develops a comprehensive mathematical framework for understanding systems that can represent, model, or “know” themselves. While self-reference has long been seen as a source of logical paradoxes, this work argues it may be the fundamental organizing principle of reality itself—and provides specific mathematical bounds and requirements for achieving different levels of self-awareness.… Read More “A New Mathematics of Self-Reference: A Comprehensive Non-Mathematical Summary”
This article explains my paper on the
Mathematics of Self-Referential Systems.
Have you ever wondered about the deep, perhaps even unsettling, nature of a thought thinking about itself?… Read More “The Mathematical Foundations of Self-Referential Systems: From Computability to Transfinite Dynamics”