In analizing a whole, using dichotomy, the first step is to seperate it by looking for aspects. These come in two forms, removable (parts) and non-removable. To retain the structure of the whole we first copy it and dissect the copy.

The process of dissection lead to the emergence of a binary tree that reflects the possible analytical steps through time. Bottom-up this is:-

+-----+--------------------+-----+--------------------+
|Whole|Aspects of the whole|Parts|Aspects of the Parts|T3
+-----+--------------------+-----+--------------------+
|   Whole                  |     Parts                |T2
+--------------------------+--------------------------+
|                         Whole                       |T1
+-----------------------------------------------------+

When we consider dynamics, the process of contraction and expansion, then
the above diagram is reflected to allow for them, thus:

+------+---------+-------+---------++---------+-------+---------+------+
| Exp  |   Exp   |  Exp  |  Exp    ||   Con   |  Con  |  Con    | Con  |
|Whole | Aspects | Parts | Aspects || Aspects | Parts | Aspects | Whole|T3
+------+---------+-------+---------++---------+-------+---------+------+
|   Exp Whole        Exp Parts     ||     Cont. Parts |  Cont. Whole   |T2
+----------------------------------++----------------------------------+
|      Expansive Whole             ||          Contractive Whole       |T1
+----------------------------------++----------------------------------+

A cognitive analysis easily links the different types at T3 with the 
trigrams of the I Ching, going left to right:

Creative   - concern with Expansive wholes
Joyous     -    "     "   Expansive aspects of wholes
Clinging   -    "     "   Expansive parts
Arousing   -    "     "   Expansive aspects of parts/wholes
Gentle     -    "     "   Contractive aspects of parts/wholes
Abysmal    -    "     "   Contractive parts
Keep Still -    "     "   Contractive aspects of wholes
Receptive  -    "     "   Contractive wholes

An extension of this occurs when we analize another categorization system based on dichotomy, the MBTI. This is a system of personality typing and has it's roots in the set of dichotomies derived by Carl Jung.

When analized at the same level of derivation as the above trigrams, we find that we can place certain behavioural characteristics in the same manner as we have done with the I Ching:

The Receptive : Advocates/Disciples - Identity seekers, concerned with 
                                      developing wholeness through the 
                                      following (internalization) of a creed.

Keeping Still : Mentors             - Identity seekers, concerned more
                                      with developing a relationship
                                      with a whole rather than internalizing
                                      it.

The Abysmal   : Conservators        - Security seekers, concerned with
                                      the overall protecting by distinction
                                      of parts of the whole.

The Gentle    : Monitors            - Security seekers, concerned with
                                      the monitoring of these aspects
                                      in the form of formal relationships
                                      (contracts etc)

The Arousing  : Engineers           - Solution seekers through the 
                                      developing of models based on
                                      the relationships of parts (
                                      an expansive bias)

The Clinging  : Organizers          - Solution seekers through the
                                      developing of maps of distinctions
                                      (parts)

The Joyous    : Players             - Sensation seekers through the
                                      development of external relationships

The Creative  : Operators           - Sensation seekers through the
                                      integration of inner with outer
                                      (expansive wholeness)

If you take the formal MBTI symbols (I/E,N/S,T/F,J/P) (four dichotomies) and map them 'logically' you do NOT get the above corresponding patterns. These patterns emerge through semantic analysis based on whole/parts dichotomous analysis.

If we then take the standard types of number we use, we find that we can place them in the same order as the above:

Positive whole numbers = positive (expansive) wholes bias
         irrational numbers = aspects of the whole bias (relational)
         rational   numbers = parts bias
         complex    numbers = aspects of the parts/whole bias (relational in
                              the form of transitions/transformations)

This is then reflected for negative numbers.

We can then group all of these for comparison:

General whole/aspects concept:

+------+---------+-------+---------++---------+-------+---------+------+
|Whole | Aspects | Parts | Aspects || Aspects | Parts | Aspects | Whole|T3
+------+---------+-------+---------++---------+-------+---------+------+
           (Expansive)                      (Contractive)


Mathematics:

    +---------------------------------------------------------------+
    |       |       |       |       |       |       |       |       |
    | whole |irratio|ration |complex|complex|ration |irratio| whole | T3
    |       |nal    |al     |       |       |al     |nal    |       | 
    +---------------------------------------------------------------+
                Positive (Exp).     |       Negative (Con).

MBTI:

+--------+------+---------+--------+-------+----------+------+--------+
|Operator|Player|Organizer|Engineer|Monitor|Conservate|Mentor|Advocate|T3
+--------+------+---------+--------+-------+----------+------+--------+
  (XSTP)  (XSFP)   (XNTJ)   (XNTP)   (XSTJ)   (XSFJ)   (SNFJ)  (XNFP)

(X means either I or E. These apply at level T4).

I Ching:

+--------+------+--------+--------+------+-------+---------+---------+
|Creative|Joyous|Clinging|Arousing|Gentle|Abysmal|KeepStill|Receptive|T3
+--------+------+--------+--------+------+-------+---------+---------+
       (Yang based)               |           (Yin based)


We now consider the concept of the trigrams as manifesting the different
ways you can mix two elements (i.e. yin/yang). We find that we can use
mixing terms to decribe the whole/aspects/parts concepts:

+-------+------+-------+------+------+-------+------+-------+
| Blend | Bond | Bound | Bind | Bind | Bound | Bond | Blend |T3
+-------+------+-------+------+------+-------+------+-------+
           (Expansive)        |        (Contractive)


Thus, anything dealing with wholeness can be described using terms
analogous to the concept of blending.

Anything dealing with aspects of the whole can be described using
terms analogous to the concept of bonding (relational)

Anything dealing with parts can be decribed using terms analogous
to the concept of bounding (boundary, distinction, etc)

Anything dealing with aspects of parts (how they influence each
other or the whole - transitions/transformations) can be described using
terms analogous to the concept of binding.

Thus, these terms represent invariant contextual terms for any form of dichotomy, and are the fundamental elements for the creation of 'meaning'. I suggest that the template of which these are part is a template that exists in the brain and it is this contextual template that enables the ease in which we make analogies. For example, in the various 'maps' listed above, all cells in the left-most position deal in some way with expansive blending (wholeness).

In the context of the I Ching, the sometimes excessive number of possible associations made to a specific trigram stem from this template. For example any contractive bounding concept can be linked to the trigram of The Abysmal.

The use of the mixing terms favours the introduction of dynamics over the more static 'whole/parts' terms, but overall a mixing term is synonomous with a 'whole/parts' term.

If one can recognize the possibility that the mixing template has neurological foundations, then one can see how the knowledge of this can be used for a more refined approach to prediction systems, and one can also see how many of the esoteric typologies, constructed using dichotomy, continue to flourish.

The advantage of the I Ching is it's symbolism. It easily encapsulates the different forms of dichotomy as well as easily conforming to the mixing concept and it already has a refined degree of analysis down to level T6, the sixty-four hexagrams. (The MBTI only explicitly goes to level T4). Furthermore, all of the analysis done so far on the I Ching (context etc) is applicable to all of the other dichotomously derived maps.

If we create a full binary map of the I Ching, and place the trigrams at level t3, we can infact find the roots of many concepts by using the yin/yang symbols to work backwards. Thus, putting the MBTI system at T3 we can trace backwards to the root personality types which emerge as being identity seekers and sensation seekers. The other two types (sollution and sensation) emerge from these fundamentals at another level. This suggests a path of personality development ( which I will not go into here).

In summary, the mixing template is a template of context that emerges from the use of dichotomy in the process of categorization.. Thus, maps of 'reality' based on dichotomy will not necessarily be valid since any map based on dichotomy will seem to 'ring bells' and generate a sense of 'value' even if, in 'reality', there is none.

At the same time, there is the possibility that humans have adapted to the environment by internalizing it's characteristics, and thus the mixing template exists 'out there'.

This not only validates the ability of mathematics to symbolize reality but also validates the more esoteric typologies as well (but only in the context of typology not the methods (i.e. planetary influences etc)). At the same time, it shows that there are gaps in the manner in which we interpret reality and perhaps with the knowledge of the template as background, we can develop a more practical approach to development.