Sieving Through Complexity: How Transient Dynamics Emerge from the Finite Observer-Referenced Framework

Abstract: Natural systems—from biogeochemical cycles to ecological networks to stellar evolution—are transient. Their dynamics do not settle into asymptotic states but instead navigate multiple regimes over observable timescales. Yet predicting when and how systems shift between regimes remains elusive, partly because we rely on theories designed for asymptotic behavior rather than finite observations. Here, I will present a theoretical framework that inverts this problem. Rather than asking what a system's "true" dynamics are, we ask: what processes matter to a specific observer working within a finite reference frame? The framework reveals that the number of possible dynamical regimes grows exponentially with the number of underlying processes (a consequence of combinatorial state-space expansion), but observers experience only those whose processes exceed critical thresholds or tipping points, which vary across observers' contexts. I will detail the application of this framework in a case study of a classic predator-prey system: bacteria infected by lytic bacteriophages. The theoretical framework predicts sixteen distinct dynamic regimes, all of which are recovered by numerical simulations. An adaptive Boolean model based solely on observer-relevant processes accurately predicts the full system's outcomes. I will discuss how this perspective suggests a conceptual shift: tipping points are not intrinsic properties of systems independent of observation, but rather emerge from the interaction between system complexity and observer perspective. More importantly, I will illustrate how focusing on observable processes rather than system-intrinsic states yields practical tools for forecasting regime shifts in natural systems—and philosophical clarity on how complexity manifests across scales and contexts.