- 1:30 PM

Fisher Information as a Metric for Sustainability

Arunprakash T. Karunanithi1, Heriberto Cabezas2, and Christopher W. Pawlowski2. (1) Department of Civil Engineering, University of Colorado Denver, 1200 Larimer Street, Denver, CO 80217, (2) National Risk Management Research Laboratory, U.S. Environmental Protection Agency, 26 West Martin Luther King Drive, Cincinnati, OH 45268

The important question in sustainability is not whether the world is sustainable, but whether a humanly acceptable regime of the world is sustainable. We propose Fisher Information as a metric for the sustainability of dynamic regimes in complex systems. The quantity now known as Fisher Information was developed by Ronald Fisher as a measure of indeterminacy. Following Fisher's work, we have developed a form of Fisher Information which is a measure of order. Order refers to the fact that orderly dynamic systems seem about the same with repeated observation. For example, a tree is a complex dynamic system. But it still looks like a tree from day to day, season to season. Hence, it posses order because its measurable properties do not vary wildly from one observation to the next. These systems, however, can undergo regime changes. Birth and death are two extreme examples of regime change. There are also more subtle dynamic regimes such as a good or poor health. In general, when a system changes dynamic regime, order in the measurable variables of the system also changes. Consequently, our form of Fisher Information which is a measure order changes as well. Changes in the Fisher Information are, therefore, indicative of a change in regime. Hence, we hypothesize that a requirement for the sustainability of a dynamic regime is that the Fisher Information should not change with time. We have obtained meaningful results from Fisher Information calculations using field data for: (1) climate change 2) the ocean around Bering Strait changing ecophysical regime, and (3) the degree of order in the socio-political systems of nation states. These are very different systems leading credence to the generality of the concept. Additionally, we hope to demonstrate how to do a Fisher Information calculation from data.