**UPDATE (August 2015): See the attached PDF file for an updated, more thorough explanation of this topic by the author.
Reinin dichotomies were derived using group theory, a field of math I know very little about.
This site gives a thorough explanation. Unfortunately it is in Russian, and online
translators obviously don't do very well with the mathematical terminology. That said, maybe misutii and any resident mathematicians could help out.
I'll try to explain my current understanding of it as simply as possible. The idea is that the socion, with its dichotomies, is a
Klein 4-group. This means, given a few initial dichotomies, you can produce all other possible symmetric dichotomies. (I'm not sure what symmetric means in this context.)
New dichotomies can be formed by combining the original four dichotomies. If I, N, T, and J are represented by 1 (true) and their opposites by 0 (false), comparing them with the boolean operation of equivalence (=) yields new dichotomies. For instance, a type is "static" if I and J are both true or both false. Mathematically, I=J. (The above article uses the clumsy but equivalent notation (I & J) v (~I & ~J) instead.) Any other commutative (i.e. symmetric) operation, such as XOR, could also be used.
4C2 = 6 dichotomies are formed by comparing pairs of the original four dichotomies.
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Try this socionics test - ru.laser.ru
1. I am very interested in solving complex issues and unraveling a tangle of contradictions.