The Law of Scale Independence

ABSTRACT Geography and geosciences deal with phenomena that span spatial scales from the molecular to the planetary, and temporal scales from instantaneous to billions of years. A strong reductionist tradition in geosciences and spatial sciences tempts us to seek to apply similar representations and process-based explanations across these vast-scale ranges, usually from a bottom-up perspective. However, the law of scale independence (LSI) states that for any phenomenon that exists across a sufficiently large range of scales, there exists a scale separation distance at which the scales are independent with respect to system dynamics and explanation. The LSI is evaluated here from five independent perspectives: geographic intuition, dynamical systems theory, Kolmogorov entropy, hierarchy theory, and algebraic graph theory. All of these support the LSI. Results indicate that rather than attempting to identify the largest or smallest relevant scales and work down or up from there, the LSI dictates a strategy of focusing directly on the most important or interesting scales. An example is given from a hierarchical state factor model of ecosystem responses to climate change.