Emergence of a Multiplicity of Time Scales in the Modelling of Climate, Matter, Life, and Economy

This topic review communicates working experiences regarding the interaction of a multiplicity of processes. We draw on examples of climate change modelling, materials science, cell physiology, public health, and macroeconomic modelling. Recent years have witnessed astonishing advances not only in broadband temporal frequency sampling, multiscale modelling, and fast large-scale numerical simulation of complex systems, but also in the continual uncertainty of many science-based results. In accordance with the aims of this collection, in this chapter we describe and analyze properties that depend on the time scale of the measurement, structural instability, tipping points, thresholds, hysteresis, and feedback mechanisms with runaways, stabilization or delays. While paying tribute to the advances in data collection and interpretation, we point to grave disorientation in statistical sampling, the interpretation of observations, and the design of control when neglecting the presence or emergence of multiple characteristic times. To us, environmental research is the preferred field of application to demonstrate the meaning of these working experiences, mostly gained in materials science, public health, and macroeconomics.