The advancement of a mathematical model of sustainable development

Earth System Analysis was postulated as a theory by Hans-Joachim Schellnhuber in 1998 as a way to characterise the Earth System—the coupled relationship between the environment and humans. Within this theory is the notion of Geocybernetics—management of the Earth System in order to achieve strategies and mechanisms of co-evolution between the environment and humans. This is regarded as the concept and application of sustainable development. However, whilst fundamental definitions in Earth System Analysis are presented for the coupled relationship between the environment and humans, no such definitions exist for sustainable development within the Earth System context. Consequently, this paper presents a mathematical model of sustainable development that provides for the fundamental abstraction of the key concepts and parameters necessary for sustainable development to occur. The model utilises basic mathematics to detail these concepts and parameters, as well as the conditions required for sustainable development to occur. The model presented is, in some regards, a work in progress, and further refinements will be made given the nature of the research performed to this point, i.e. the fundamental mathematical definition of sustainable development and its application. However, the research conducted thus far has made it reasonable to communicate the findings made up to the present point. The paper also provides a brief example of the application of the model to an environmental impact assessment of a metro rail scheme in India, for the purpose of evaluating the level of sustainable development (if appropriate) for the project under consideration.

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