On the basis of the informatics-cybernetic approach proposed by the author, the main historical stages of the “matrix” global evolution of a multidimensional system-educated person mastering a new basic information technology are presented. System education is understood as a sufficient level of education of the individuals composing it (to ensure the production, social, cultural and other processes of selfcontrolling of an element of the corresponding tier of the hierarchical-network system of the Humankind). It is indicated that all such elements form a triangular matrix of dimensions from 2×2 to 6×6 and beyond.