This paper introduces Emergence Dynamics, a novel computational paradigm in which computation is represented as Emergence: a process of Evolutionary Nondeterministic State Transitions over dynamically evolving Markets, driven by interactions among Agents whose Beliefs and Measure Spaces evolve in response to Information to price an Event. I mathematically formalize those concepts and prove that Turing machines can be embedded as a degenerate special case under the emergence dynamics paradigm. I further develop a Geometric Perspective on
The paradigm is first applied to financial markets-I examine the Boundaries of the Efficient Market Hypothesis and the Black-Scholes model. I introduce the concept of Cross-Measure Arbitrage, a market mechanism arising from inconsistencies among dynamically evolving agent beliefs and pricing measure spaces. I further develop a general architecture for Perpetual Derivatives, including Event Contracts and Trustless Insurance. Besides, the paradigm might further inspire studies on AGI, hallucination, embodied AI, and beyond.
Emergence Dynamics, Continuous Measurement, Nondeterministic State Flows, Computation as Emergence, Computational Complexity, Geometrization of
I have realized that the chronological genesis of an idea carries deeper scientific value than the paper itself. Therefore, I have open-sourced all intermediary materials, including conversations (human prompts and AI responses), draft papers, images, corpora, and other materials, to serve as a rigorous empirical case study for future investigations in cognitive science, psychology, and the heuristics of scientific discovery. Visit https://github.com/theparadigmgroup/EmergenceDynamics to download these materials.
I encourage all researchers to open-source their prompts and streams of research ideas and thoughts, rather than only their final papers. The non-linear thought process is far more critical than the publication itself. In fact, some of those abandoned, mid-way discarded ideas (much like the "scratch papers" of Gauss or Newton) hold infinitely more value than the papers themselves, even if the authors fail to realize their importance at the time-largely because the true significance of these raw ideas often manifests in entirely unpredictable, seemingly unrelated fields.
Therefore, I urge the scientific community to develop platforms dedicated exclusively to open-sourcing streams of research ideas and thoughts-a conceptual equivalent to arXiv-which would also serve as a powerful deterrent against academic fraud. Modern papers, in an effort to appease peer reviewers (often rigid "experts" who excel merely at standard linear thinking), are forced to strip away the living, breathing reality of exploration-the dead ends, the walls hit, and the non-linear intuitions-and artificially package them into a cold, smooth, linear chain of causality. A paper is a "results-oriented" specimen. Conversely, a platform dedicated to open-sourcing streams of research ideas and thoughts aims to preserve, in their authentic and raw form, those genius