Tuesday, July 5, 2016

The failure of finite elements

Engineers and mathematicians, with a core competence in building complex structures from elemental and standardized components, have had a tough time with domains not amenable to prescriptive and deterministic logic. These include high energy physics, biology, economics and artificial intelligence. The idea that the behavior of a system cannot be predicted by its components is foreign to most disciplines and the applications of such hard sciences, supported by engineering and technology.

In complex organisms such as companies, it has long been recognized that outcomes cannot be predicted by an analysis of its components, however standardized they may be. The “rules of engagement,” if not defined in elegant and closed form mathematics, appear to be less relevant for those seeking precision. However, there is almost nothing in today’s world that could be defined so precisely and the recognition of this concept is possibly the first positive step toward embracing reality.

The interplay between physicists wanting to prove century old predictions and engineers standing ready to prove anything by heavy and complex machines, has been costly to society. The interplay between biologists and chemists wanting to influence systems with precise and targeted therapy and engineers standing ready to do so, has been costly to society. The interplay between economists looking to apply statistical precision to the unknown and engineers ready to build models to whatever is needed, has been costly to society.

Complex systems cannot be broken down to finite elements for the behavior of the system does not emanate from its components.