It is interesting to consider the operation and development of an organism in mathematical terms. ERoEI (Energy Return/Energy Invested) is a mathematical expression that is in common use in discussions of such issues as the supply of oil. It is simplistic , so misleading, as it is dealing only with the rate of using energy embedded in the system extracting and supplying the oil: the EI term together with the rate of energy supply: the ER term. It is an expression of the oil supply situation at some, unidentified stage. The numbers will change with developments. ERoEI was a very high value in many oilfields, including the Middle East. However, it is now so low where fracking is used that the process is hardly worthwhile.
ERoEI is a measure of the oil extraction process used by many commentators despite its unrealistic consideration of energy alone and the assumption that the energy input, the chemical energy in the oil is free. There for it is only a limited measure of the energy cost of the process as represented by EI compared to the energy output, ER. It does not take into account the materials irreversibly used in the process. In addition, it is only a measure of the operation of energy provision. The operation of industrialized civilization entails many other processes. The manufacture of an airliner is another operational process and this is subject to continual scrutiny by specialists in the company without reference to a simplistic mathematical expression such as ERoEI.
However, it is an aid to understanding of the operation and development of an organic or inorganic organism to formulate a mathematical expression that does represent what invariably happens. Materials (solids, liquids and/or gaseous) are input into the organism at a rate that varies over time.
Processes in the organism carry out a range of activities while transforming the rate of inputs that then provide rates of (solid, gaseous and/or liquid) outputs. In mathematical terms, the activities can be represented as functions of the rates of the inputs. The rates of the outputs can be represented as functions of the activities. These functions continually change over time. That is the development of the organism. The functions can be mathematical expressions that approximate what happens to a degree. Often what happens is fuzzy so the approximations are not very good.
However, the principles outlined here about the relation between the operation and associated development of organic and inorganic organisms are sound even though most people do not understand that they always apply in natural and technological physical operations. Economists certainly do not because they believe money flow is the determining factor. Medical people do understand many of the aspects of operation and development while all people have some knowledge of how their bodies behave over time. Engineers have understanding of the operation of machines and appreciate the development that these machines will wear out (due to friction). Biologists and botanists understand this coupling of processes in their fields without needing to use mathematical models. On the other hand, climatologists strive to produce mathematical models that mirror operations of the climate in the endeavour to predict developments under the input of greenhouse gases. Geologists aim to gain understanding of the vast forces acting underground that have over time affected developments such as mountain ranges. These are some examples of where specialists have understanding of operations and developments. But society at large, and the leaders in particular, do not take the holistic consequences of these principles into due account. Yet they do understand that they cannot be immortal.