We here apply dichotomous analysis to the generic concept of a whole. Since dichotomy emphasizes distinction (A/~A), and analysis emphasizes separation, the first 'cut' of the whole separates whole and parts (and thus a 1:many type of dichotomy - we have in fact copied the whole to enable the cut without destroying the whole):
----------------------- | WHOLE | PARTS | -------\------/-------- | WHOLE | -----------------------
The next cut is applied to both elements, but what can we cut 'whole' into since we have already got parts? The answer is aspects of the whole. Applying the same cutting to PARTS gives us aspects of the parts (this intuitively maintains the 1:many type dichotomy):
----------------------------- |WHOLE|ASPECTS|PARTS|ASPECTS| | |(whole)| |(parts)| ----\---/---------\----/----- | WHOLE | PARTS | -----------\------/---------- | WHOLE | ----------------------------- Fig 1. The whole/parts dichotomy developed over three levels.
This method of analysis, through continuous cutting, if developed to the nth degree, introduces us to a continuum, as the ability to cut runs out. The continuum is another word for a whole, and so we are back at the beginning. However, the linking of the continuum with wholeness implies that each level of the dichotomy-tree thus developed, shows the continuum aspects of the whole in finer detail in a left-to-right (or right-to-left) sequence. By also adding symbols representing contraction and expansion, the aspects of the continuum move from one 'pole' to the other 'pole' and can still be read left/right or right/left.
Using the above as an example, the discrete cutting nature of dichotomy takes us bottom-up, refining all the way by cutting at each level. But analysis of traditional teaching methodologies suggests that the process of describing wholeness follows a horizontal pattern. Here, we study the whole, followed by aspects of the whole, followed by the closer analysis of those aspects that are removable - parts, followed by aspects of the parts, the latter manifest in the transitions and transformations that occur between parts; how they influence each other.
We thus find that the apparent discreteness inherent in dichotomy in fact helps to create a model of any continuum; any whole. This should work in reverse, where analysis of a continuum should create a hierarchy of dichotomies. We in fact find this in, for example, music and physics.
The above model of dichotomy, and the resulting emergence of a continuum, suggests that the discrete/continuous dichotomy is, like expand/contract, a fundamental characteristic of the dichotomy process.
In considering the base template, fig 1, a pattern emerges when we analyze the descriptive characteristics of each cell, or state. These patterns stem from the consideration that a dichotomy developed past the 1:1 state of level 1, is in fact a set of states that represent the mixing of the two elements of the initial dichotomy. Level 2, for example, introduces states that represent the actions of element A within the context of element B, and visa versa.
What this shows is that, when using dichotomous analysis, I use the initial dichotomy to analyze itself; I feed it back into the process of analysis by using it as the context for further analysis.
This development allows me to introduce another dichotomy of a more refined character that lets me symbolize this. Thus, each level of a tree can symbolize the continuation of the initial, but gross, dichotomy, or the introduction of a new dichotomy (refined) that functions within the context of the original dichotomy (and is the continuation of that dichotomy but in an implicit form).
How many dichotomies can one possibly have? The answer is: as many as one wishes as long as they are contextually valid; that they are either identical in meaning with the original or they operate within the original's context.
As we shall see, mathematics is the manifestation of detailed dichotomous analysis where the dichotomies used are in fact 'marked' using numbers. For example, consider the dichotomy of manic/phobic. Observation of reality, using the manic/phobic dichotomy as context, suggests that things are not so extreme (A or B). We can therefore express this by doubling-up the words:
manic / phobic manic+manic/manic+phobic/phobic+manic/phobic+phobic
and thus introduce variations to the extremes. Further development of this will of course become somewhat 'messy' unless I can either:
(a) introduce words that encapsulate the doubling-up(refined dichotomies) or, (b) we can introduce a form of shorthand like this: manic / phobic ^ we insert numbers here to get a range. manic......0.......phobic -3 -2 -1 0 +1 +2 +3
this is the same as adding alternative word-based dichotomies to display the increasing levels of mania or phobia. (mania 1, mania 2, ...) and turns fig 1, for example, into a number line extendable into Cartesian coordinates. (This is expanded in the mathematics section.
Returning to the 1:1 type of dichotomy, if we consider just the mixing of the first two elements, then at this point a question arises as to how many basic ways can I describe the mixing of two things (excluding mathematical representations)? After all, it is somewhat inefficient to pile one on top of the other and just say 'another mix'. The answer, with the help of a thesaurus, is that there are (basically) four ways:
I can - blend them - making a new whole. bond them - making a whole with aspects (relational). bound them - making a whole with clear parts. bind them - making a whole composed of parts influencing each other rather than 'stuck to' each other. Using the model in fig 1, I can replace the whole/parts terms with terms derived from mixing: blend (WHOLE) bond (ASPECTS) bound (PARTS) bind(ASPECTS) \ / \ / blend (WHOLE) bound (PARTS) \ / blend (WHOLE) Fig 2. The whole/parts dichotomy developed using mixing terms over three levels. From this: A whole is analogous to a blending. An aspect of a whole is analogous to a bond to the whole. A part of a whole is analogous to a bound, a separation (forming a boundary between whole/part). An aspect of a part is it's influence on other parts, or even to the whole, in the context of the part's uniqueness. Thus, these aspects are analogous to a bind where we deal with influences of separate entities on each other; they seem to be invisibly tied whilst moving through time.
Previously, I emphasized the presence of contraction and expansion in the process of dichotomous analysis. In the context of mixing, these become ways, or directions, of mixing - I can mix inwards or outwards. Thus, I end up with eight ways that I can mix the two elements:
Expansive Contractive
Blending Blending
Bonding Bonding
Bounding Bounding
Binding Binding
Excluding the contraction/expansion elements, we have a template of
the following for:
+-------------------------------+
| | | | |
| BLEND | BOND | BOUND | BIND |
| whole |aspects| parts |aspects|
+-------------------------------+
| BLEND | BOUND |
| whole | parts |
+-------------------------------+
| BLEND |
| whole |
+-------------------------------+
Fig 3a. The base template
When we include the expansion/contraction dichotomy, we get the
full template:
+---------------------------------------------------------------+
| | | | | | | | |
| BLEND | BOND | BOUND | BIND | BIND | BOUND | BOND | BLEND |
| | | | | | | | | F3
+---------------------------------------------------------------+
| | | | |
| BLEND | BOUND | BOUND | BLEND | F2
+---------------------------------------------------------------+
| | |
| BLEND (expand) | BLEND (contract) | F1
+---------------------------------------------------------------+
| X | F0
+---------------------------------------------------------------+
Fig 3b. The mixing template
The introduction of the expand/contract dichotomy requires the mirroring of the the base template (fig 3a) giving fig 3b.
Fig 3b stops at level F3, but there is nothing to stop me developing finer levels. However, I find that, rather than form the new levels through simple linear development I can in fact develop the basic eight 'types' found at level F3, by using contextual considerations rather than continued level by level development. Thus I can have, for example, the concept of contractive bonding within the context of contractive binding. This allows me to develop refined 'forms' without the process of explicit derivation; I am practicing refinement through the use of feedback.
Using this feedback process, I can move from 8 gross types at F3 to a possible 64 refined types at level F6, bypassing the developmental levels of F4 and F5.
As will be shown, what this means is that when I try to describe something that has been created from dichotomous roots, I will unconsciously use words that have a strong analogous connection to the descriptions of mixing given above. Blend and whole (to merge and become 'one'), Bond and relation (to form a bond with X), Bound(ary) and part(e.g. dichotomisation), bind and influence (transition / transformation) - a 'binding' contract.
These mixing terms act as invariant context markers when used in the template of fig 3b. Thus, no matter what the nature of a specific dichotomy, it's combination with other dichotomies within the same context will lead to the expressions of meanings being influenced by the mixing terms. This allows for the ease of making analogies across differing disciplines that have dichotomous roots; it is the template that causes a degree of syntactic and semantic resonance and thus 'understanding'. (As we go deeper so our terms become refined and more complex, but these basic terms set the context for the complexities that follow)
What this implies is that any dichotomously-derived typology is in fact a metaphor for the template.
In the creation of a dichotomy tree one can go as deep as one wish (or am able to do). But when the number of points become too many one finds that one can represent them as harmonics, with the emergent continuum analogous to an octave and the process of dichotomisation being the simple creation of harmonic relationships. Thus a form of wave representation is possible within *any* form of dichotomous processing.
Overall, the principle of dichotomy can be used as a method of analysis and classification of any system in that it maintains both relational and hierarchical characteristics within the context of wholes, parts, and their aspects; the fundamental forms of description. Furthermore, when taken past the 1:1 format, dichotomy has within it emergent qualities that allow for the apparent expression of 'meaning' in that subjects with common dichotomous roots 'resonate', irrespective of their 'real' nature. These degrees of 'meaning' become more refined only at levels of more than three degrees of dichotomous analysis, equivalent to dimensions greater than 3 or 4 (since any dichotomy can be represented as an axis. This suggests that humans can experience dimensions greater than 3 through 'feeling'; as we analyze dichotomously so we are building a whole that has emotional markers creating an overall 'feeling' of value; akin to the concept of intuition.)