Preliminary White Paper: Toward an Information Dynamics Framework
The limitations inherent within formal systems, as illuminated by Gödel’s incompleteness theorems, suggest a fundamental constraint in our ability to fully capture the nature of reality through traditional mathematical frameworks. This constraint, when extrapolated to physical phenomena, manifests as “singularities” - points where our current understanding breaks down. To address this, we propose a shift in perspective, moving away from static, axiomatic models toward a dynamic, information-centric approach. This preliminary white paper outlines the foundational principles of an “Information Dynamics” framework, designed to address these limitations by treating existence as a continuous process of “eternal resolution-transitions.”
At the heart of this framework lies the concept of “existence” as a dynamic system, not a static entity. We posit that existence is fundamentally composed of “resolution states,” each representing a specific configuration of information. These states are not fixed, but rather undergo continuous “transitions,” where one resolution state transforms into another. This transition is driven by changes in information, which represents the difference between successive resolution states.
Mathematically, we can conceptualize this as a system where the collection of all possible resolution states forms the domain of our system. The transition is then defined as a function that maps one resolution state to another, using the change in information as a parameter. Thus, a subsequent resolution state is generated by applying the transition function to a preceding state, and the information change. Existence, then, is defined as the iterative application of this transition function over a sequence of resolution states.
Crucially, within this framework, “time” is not treated as an external parameter, but as an emergent property of the resolution-transition process. Time is defined as a measure of the cumulative transitions, reflecting the progression of information unfolding within the system. This leads to the definition of time as the sum of the magnitudes of each transition.
Several key axioms underpin this framework: first, the “eternal transition” axiom, asserting that the transition function is always defined, ensuring a continuous flow of information. Second, the “information conservation” axiom, stating that the total information within a closed system remains constant, though it may undergo transformations. Third, the “emergent time” axiom, establishing time as a product of the resolution-transition process.
This initial formulation lays the groundwork for further development. Future research will focus on formalizing concepts such as information fields, resolution operators, and probabilistic transitions. By shifting our focus to the dynamic interplay of information, we aim to create a mathematical language capable of describing the complexities of existence, resolving the singularities that arise from static, axiomatic models.