Chaos Is Relative: A Formal Principle of Framework Dependence in Complex Systems

Scientific practice repeatedly encounters systems described as both chaotic and ordered,
producing persistent disputes across physics, neuroscience, and data science. This paper shows
that the contradiction is methodological rather than empirical. We formalize chaos and order
as properties relative to a descriptive framework and formulate the Law of Relativity of Chaos:
for any system, the appearance of chaos or regularity depends on choices of boundaries, scale,
observables, and encoding conventions, while some regularity remains unavoidable within any
fixed framework. We provide strengthened formal claims, clarify scope boundaries and edge
cases, and supply minimal computational validation on the logistic map, including entropy-rate
estimates and compression-based complexity proxies across explicit coarse-grainings. We further
state a quantitative, falsifiable scaling prediction for coarse-grained entropy in the Lorenz system,
and we demonstrate how explicit framework declaration dissolves a concrete scientific controversy
concerning whether brain dynamics are “chaotic.” The result is a unifying methodological
constraint for multiscale modeling and debate resolution in complex systems.