TAPe is based on group theory, Lie algebra, heterarchy of elements, antitransitivity, linguistic means of interrelations between elements, etc.
It is essential to understand that the brain, while performing calculations, does not make use of the traditional mathematics with its roots, integrals, functions — after all, it is not a computer dealing with 1's and 0's. But should we draw a parallel with computers, the brain rather deals with elements and symbols that constitute a system, a kind of "alphabet" that we decided to call languagemathics. We use this newly coined term as we are convinced that it allows describing the essence of brain processes used to perceive information in the most accurate manner. What can be conventionally referred to as language elements ("letters") interact with one another according to mathematical laws, thus generating new, more complex elements ("words" and "sentences"). In TAPe’s languagemathics, we denote elements using such categories as operators, filters and groups (depending on their hierarchy or, more precisely, heterarchy) — the elements themselves are called T-bits. And it is this process of the elements interacting with one another on different levels that the Theory of Active Perception describes.