DS Achievements (обрывок)

**Hello, everyone!

I will list the objects and principles that were discovered and researched by Semyon Churiumov and me.

I think, his 2 main achievements are formalization of socionics structure and Parallelism Principle.

Socionics works with the structure, that can be fully described with mathematical language (Group Theory). Sciences that contain mathematical structure are called Formal. They have methodological differences from Empirical ones. They are abstract and can be advanced using theoretical methods.

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Basing on mathematical researches, Churiumov defined the strict order of types, relations and dichotomies. It is required for inner symmetry of the system.

Математические исследования показали, что соционические множества обладают алгебраическими свойствами. Первым это сделал Рейнин, обнаружив групповую природу признаков. Позже было обнаружено, что Типы, Отношения, Функции тоже можно рассматривать как алгебраические группы. 

Математические множества соционики обладают многими замечательными свойствами и различным образом связаны друг с другом.

Socion is strictly ordered set of 16 elements. These elements can manifest as 16 Types, 16 Relations and 16 Dichotomies.

Parallelism Principle states one-to-one correspondence between elements of these sets. Thus each Type corresponds to one Relation and one Dichotomy. Corresponding elements are isomorphic, they have identical structure and basing on this, also the same meaning (Archetype, semantic field).

Same principles effects 8 Information Aspects, 8 Model A Functions and 8 Dichotomies of the Functions/Aspects. This level can be called either Aspecton or Model A.

By definition algebraic group has to contain neutral element. This is 16th Reinin “Dichotomy” - Existence (Identity). It doesn’t divide the set, but unites it. 

Socionics algebra is also applied to Types and Relations due to strict order and binary coding of Socion Elements.

In terms of Group Theory Socion is algebraic group with binary operation logical equality. 

Socion and Aspecton (Model A) are similar sets.  

Соционика имеет дело со структурой, которая может быть полностью описана математическим языком, разделом общей алгебры - теорией групп. Науки, обладающие математическими структурами называются формальными и имеют методологические отличия от других. Они абстрагированы и могут развиваться теоретическими методами.

Parallelism Principle

There is a correspondence between main sets of Socionics. 

16 Types of Information Metabolism - 16 Intertype Relations - 16 Reinin dichotomy

8 Information Aspects - 8 Model A Functions - 8 dichotomies of each

Elements that correspond to each other are Isomorphic. Thus they have identical structure and meaning (Archetype).**