On cognitive foundations of big data science and engineering

Big data are one of the representative phenomena of the information era of human societies. A basic study on the cognitive foundations of big data science is presented with a coherent set of general principles and analytic methodologies for big data manipulations. It leads to a set of mathematical theories that rigorously describe the general patterns of big data across pervasive domains in sciences, engineering, and societies. A significant finding towards big data science is that big data systems in nature are a recursive n-dimensional typed hyperstructure (RNTHS). The fundamental topological property of big data system enables the inherited complexities and unprecedented challenges of big data to be formally dealt with as a set of denotational mathematical operations in big data engineering. The cognitive relationship and transformability between data, information, knowledge, and intelligence are formally revealed towards big data science.