From dissecting ignorance to solving algebraic problems

Engineers and scientists are increasingly required to design, test, and validate new complex systems in simulation environments and/or with limited experimental results due to international and/or budgetary restrictions. Dealing with complex systems requires assessing knowledge and information by critically evaluating them in terms relevance, completeness, non-distortion, coherence, and other key measures. Using the concepts and definitions from evolutionary knowledge and epistemology, ignorance is examined and classified in the paper. Two ignorance states for a knowledge agent are identified: (1) non-reflective (or blind) state, i.e. the person does not know of self-ignorance, a case of ignorance of ignorance; and (2) reflective state, i.e. the person knows and recognizes self-ignorance. Ignorance can be viewed to have a hierarchal classification based on its sources and nature as provided in the paper. The paper also explores limits on knowledge construction, closed and open world assumptions, and fundamentals of evidential reasoning using belief revision and diagnostics within the framework of ignorance analysis for knowledge construction. The paper also examines an algebraic problem set as identified by Sandia National Laboratories to be a basic building block for uncertainty propagation in computational mechanics. Solution algorithms are provided for the problem set for various assumptions about the state of knowledge about its parameters.