Quantitative Limits of Internal Observer Knowledge: A Simulation-Based Framework

This paper introduces a quantitative framework for measuring the epistemic limits of an internal observer embedded within a simulated world. We define a knowability coefficient η ∈ [0,1] that measures how well an internal observer can recover engine parameters from coarse-grained observations alone.

We test five engines of distinct physical classes: cellular automaton (Game of Life), lattice Boltzmann fluid, discrete wave equation, Ising spin system, and agent-based model (Boids).

Main results:
- Theorem 1 (proven analytically): absolute scale parameters satisfy η(dx) = η(dt) = 0 for any local engine. Absolute units are operationally unknowable to any internal observer.
- Regularity T2: η_total < 1 for all engines tested (bounded knowability).
- Regularity T3: η peaks near critical points (shown for Ising model at T/T_c = 1).
- Regularity T4: η > 0 only when the observer's model class matches the engine's continuum limit.

The central finding is that limits of physical knowledge are structural rather than technological: certain parameters are operationally underdetermined for internal observers regardless of measurement quality.

Keywords: internal observer, coarse-graining, knowability, epistemic limits, computational epistemology, simulation, information theory.