Trying to be effective (no matter who exactly and in what field) a person face the problem which inevitably destroys all our attempts to easily get to a desired goal. The problem is the existence of some insuperable barriers for our mind, anotherwords barriers for principles of thinking. They are our clue and main reason for research. Here we investigate these barriers and their features exposing the nature of mental process. We start from special structures which reflect the ways to define relations between objects. Then we came to realizing about what is the material our mind uses to build thoughts, to make conclusions, to understand, to form reasoning, etc. This can be called a mental dynamics. After this the nature of mental barriers on the required level of abstraction as well as the ways to pass through them became clear. We begin to understand why thinking flows in such a way, with such specifics and with such limitations we can observe in reality. This can help us to be more optimal. At the final step we start to understand, what ma-thematical models can be applied to such a picture. We start to express our thoughts in a language of mathematics, developing an apparatus for our Spatial Theory of Mind, suitable to represent processes and infrastructure of thinking. We use abstract algebra and stay invariant in relation to the nature of objects.