
Mental functions of a brain and directions of personality, or otherwise to
tell reference points according to which people are projected in external or
internal world, have values in psychological types of analytical psychology of
C. G. Yung. Namely mental functions are logics, ethics, sensorics, intuition,
and reference points of personality are introversion and extraversion, that
forms a design of psychological types.
If to not consider reference points of personality and to consider only four
mental functions of a brain then it is possible to speak about functional types
of analytical psychology, that from the view point of analytical physiognomy
means the analysis of physiognomic parameters of eyebrows and mouth which
correspond with mental functions, and supposes the analysis of physiognomic
parameters of eyes in the second turn. Namely functional types form the reduced
chart of a human personality that allows to analyze functional displays of
people, and then to correlate functional displays to reference points of
introversion and extraversion which concretize projections of functions in
external or internal world.
To functional types in a context of analytical physiognomy there correspond
conditional symbols of human faces in which eyes have no value, and also to
functional types there correspond symbols of the canon of changes ijing or
tetragrams which are formed by combinations of four lines, that is shown in the
table.
Tetragrams of the canon of changes ijing differ from
hexagrams by absence of middle pairs of lines or middle digrams which
corresponds with physiognomic parameters of eyes. The remained four lines correspond with physiognomy of eyebrows and mouth the same as top and bottom digrams in hexagrams:  digrams at the level of eyebrows correspond with obvious ethics, and at the level of a mouth correspond with obvious sensorics;  digrams at the level of eyebrows correspond with active logics, and at the level of a mouth correspond with active intuition;  digrams at the level of eyebrows correspond with active ethics, and at the level of a mouth correspond with active sensorics;  digrams at the level of eyebrows correspond with obvious logics, and at the level of a mouth correspond with obvious intuition. Numbers in cells of the shown table correspond to numbers of a magic square, namely sums of numbers of all verticals and horizontals in the table possess mathematical ratio that is magic property. The shown magic numbers are serial numbers of functional types of analytical physiognomy. 
For the analysis of psychological transactions, it is necessary to apply the ring chart in which functional types of analytical physiognomy are located according to mathematical ratio of numbers with tetragrams of the canon of changes ijing in a magic square, that corresponds with a metaphysical structure of a human personality and allows to analyze transactions of mental functions of a brain.
The information on transformation of the square
table of functional types of analytical physiognomy in the ring chart in
which principles of a magic square
are observed, look on pages of this website in other section which has
the name circles of emotions. Transformation of the square table to the ring chart can be considered as the decision of a circular quadrature as in a magic square there are mathematical ratio of numbers in verticals and horizontals, and also in the ring chart there are mathematical ratio of numbers or serial numbers of functional types. For example, serial numbers of harmonious and contrast functional types are not even numbers, and serial numbers of obvious functional types are even numbers. 

In the shown ring chart to each functional type there corresponds a tetragram
of the canon of changes ijing and serial number, and also serial numbers of
four derivative psychological types which correspond with derivative hexagrams
ijing. For example, 9th functional types has derivative 62nd, 15th, 16th, 2nd
psychological types.
And also mental functions are specified for each functional type in the shown
chart. For example, 16th functional type possesses active ethics and obvious
sensorics.
According to the shown ring chart of functional types of analytical physiognomy
it is possible to analyze psychological transactions.
Harmonious 1, 5, 9, 13 functional types have harmonious interrelations
with other types as obvious mental functions counterbalance functional displays
of other types.
Contrast 3, 7, 11, 15 functional types have contrast interrelations as
active mental functions do not counterbalance functional displays of other
types.
Explicit 4, 8, 12, 16, and also 2, 6, 10, 14 functional types have
ambiguous interrelations as obvious mental functions counterbalance, and active
mental functions do not counterbalance functional displays of other types.
Interrelations of explicit and contrast functional types are essential for
analyses as harmonious types in any case possess harmonious interrelations with
any other types.
Explicit types.
812, 610, 214, 416, 68, 1012, 24, 1416, 212, 814, 410, 616, 48,
1216, 26, 1014 pairs have the counterbalanced interrelations as active
rational mental function (logics or ethics) of one functional type is
counterbalanced by obvious rational mental function of the second functional
type, or active irrational mental function (sensorics or intuition) of one
functional type is counterbalanced by obvious irrational mental function of the
second functional type in all pairs. Namely if rational function is active in
one type then rational function is obvious in the second type, and also if
irrational function is active in one type then irrational function is obvious in
the second type, that counterbalances functional displays in pairs.
28, 1016, 612, 414 pairs have equivalent interrelations as rational
functions of both types are obvious or irrational functions of both types are
obvious, and also rational functions of both types are equivalent or irrational
functions of both types are equivalent in all pairs. For example, 2nd functional
type has the obvious irrational sensorics and 8th functional type has the
obvious irrational intuition, and also the active rational logics of 2nd
functional type is equivalent to the active rational logics of 8th functional
type.
1214, 46, 810, 216, 816, 412, 210, 614 pairs have inadequate
interrelations as rational functions of both types are obvious or irrational
functions of both types are obvious, but rational function of one type is
inadequate to rational function of the second type or irrational function of one
type is inadequate to irrational function of the second type in all pairs. For
example, 12th and 14th functional types have obvious rational logics, but the
active irrational sensorics of 12th functional type is inadequate to the active
irrational intuition of 14th functional type.
Contrast types.
1115, 711, 37, 315 pairs have equivalent and inadequate interrelations
as active rational functions or active irrational functions of both types are
equivalent, but also active rational functions or active irrational functions of
both types are inadequate in all pairs. For example, 11th and 15th functional
types have active rational logics that corresponds to equivalent mental
functions, but the active irrational intuition of 11th functional type is
inadequate to the active irrational sensorics of 15th functional type.
311, 715 pairs have twice inadequate interrelations as active
rational functions and active irrational functions of both types are inadequate
in all pairs.
Explicit and contrast types.
In interrelations of explicit functional types with contrast types also rational
or irrational mental functions can be equivalent if active function of one type
is identical for active function of the second type, or can be inadequate if
active function of one type is not identical for active function of the second
type. Or adjacent rational and irrational mental functions can be
counterbalanced if obvious function of one type counterbalances active function
of the second type.
Besides in interrelations of explicit, contrast, harmonious types it is possible
to consider variants in which active functions are counterbalanced by equivalent
or inadequate obvious functions. For example, the active sensorics of 12th
functional type is counterbalanced by equivalent obvious sensorics in
interrelation with 16th functional type, but is counterbalanced by inadequate
obvious intuition in interrelation with 13th functional type, that in essence it
is possible to consider as different variants of interrelations.
The following page results the information on properties of the listed interrelations of functional types of analytical physiognomy.
