Dichotomy

Comes from the Greek dichotomia, from dichotomos, divided, from dich-, in two + temnein, to cut.

My own research shows that the process of dichotomous analysis, one of the main tools humans seem to use to make maps, has a set of properties that are often projected onto the object under analysis, leading to the confusion of map and territory. Here is the list of properties, taken from "The Sense of Dichotomy":

The Principle of Dichotomy

A fundamental tool used in prediction is the derivation of a classification system. In Western civilization, we can trace this back to the works of Aristotle (1) and the concept of dichotomy. A dictionary describes dichotomy as:

"1. (logic) division into two classes, one positive, the other negative. 2.(botony) a mode of branching by repeated bifurcation"

As will be shown, these are somewhat 'gross' representations.

The concept of dichotomy allows for the enabling of a frame of reference, a universe of discourse, where classes are created such that, for example, an object is symbolized as either being in 'A' (in the class) or in '~A' (outside the class). We can therefore symbolize the universe of discourse by the symbol '1', and thus:

    
                              A U ~A = 1

The symbol 'U', from set theory, represents the concept of Union.

For any class, 'A', that includes less than the whole universe, what remains in 1 is '~A'. This is the aristotlian approach linked with logic in the above definition.

What is implied here is the 'wholeness' of 1, the universe of discourse within which I make my indications of A/~A. This simple process can then be applied to each element of this dichotomy where the element takes on the mantle of the universe of discourse and I can, for example, form B/~B within the context of ~A. The latter in fact shows the emergence of hierarchic forms based on dichotomous processes and this is the approach linked with botony in the above definition. The latter introduces the concept of indication in that the emphasis is on an aspect of the whole rather than an independent entity.

The use of negation(~), as is found in Aristotle's A/~A, leads us into the two forms of dichotomy, dichotomies of opposition and dichotomies of complementarity (the latter being an abstraction of the bifurcation concept mentioned in the above definition. Working backwards, the two elements join into one. What also needs to be considered is that dichotomies can be read as either two extremes that have the same absolute values (like the two ends of an axis - the linear point view) or as text and context, where one element forms the context(background) for the emphasized other(forground). This implies that their absolute values are NOT the same, at least qualitatively if not quantitatively).

Dichotomies of opposition are used more in analysis, and where the two elements are often destructive when combined. (Exclusive OR). Dichotomies of complementarity are used more in synthesis, where the two elements are seen as parts of a whole with the whole emerging when the parts join - (Inclusive OR) - with the final whole being the universe of discourse.

However, it needs to be noted that the destruction of the elements in a dichotomy of opposition is in fact more a transformation; for example, matter/anti-matter join into a burst of energy, just as minus and plus join to become zero (neutral). However, there is no hierarchic change of level. As found in dichotomies of complementarity, I can often recover the elements from the whole whereas the union of oppositional elements cannot be reversed from the result.

Closer examination of the dichotomization process also suggests that dichotomy has in fact three types of dichotomous contextual relationships that affect states (four if you consider position as important e.g. many:1 as well as 1:many):

One : One
This is the conventional logical and 'scientific' point of view with a single context, relational analysis bias. e.g. in the dichotomy of Positive/Negative there is a one:one bias in that text and context for both elements are considered equal. This is the common type for dichotomies of apparent opposition, where each element is treated as a whole and context is almost ignored (or else very 'gross'). In dichotomies of complementarity, each element is treated as a part with the context being the whole (aka the next level in the hierarchy). In a mathematical sense, the absolute values of each element are equal.

One : Many
One context to many - hierarchy analysis. This seems to 'map' the current model of the hemisphere functions of the brain and suggests a representation of a 'balanced' state. e.g. in the dichotomy of Individual/Sociological there is a bias in that the context of Individual is singular (one state) whereas the context of Sociological implies many states (hierarchy). In a mathematical sense, the absolute values of each element are never equal.

Many : Many
'Un-scientific' point of view due to weakness in prediction - too many variables; a hierarchy to hierarchy. This is usually 'removed' by treating both elements as 'ones' of a higher class - the act itself showing hierarchic thinking - or else using the process of idealization to extract one element from each 'many' and treat them using dichotomous analysis of the one:one type, and then doing the same for other elements. The fuzzyness of the degree predictabilty is manifest in the 'fact' that, mathematically, the comparison of the absolute values of each element could be equal or not - context is a strong influence here.

Summary of the properties of dichotomy

There is a subtle distinction here. Although hierarchy implies relationships, they are fixed. The emphasis on relational and hierarchical emphasises the dynamic and static concepts.

from continuity comes the ability to use wave analogies and the concepts of parts and aspects as harmonics of the whole; the whole treated as if an octave. The continuum also emphasizes the concept of bias rather than absolutes. What should be noted when making a wave-biased analysis is that the use of sine/cosine based functions will always have an aspectual, analog character compared to the tan based functions that are more discrete.

each element of a dichotomy exists within the context of the other and both exist within the context of a whole. In dichotomies of complementarity the elements can enfold back into the context; they can occupy the same space. Dichotomies of opposition, although in the same context, cannot occupy the same space, thus suggesting these dichotomies have their elements treated as wholes.

This has an interesting consequence when considering dimensional maps based on orthoganal relationships. It suggests that the derivation of information using orthoganal relationships, and thus a bias to contextual independence, infact hides the hierarchic relationships and thus the contextual dependence. The process of orthoganal emphasis is in fact the emphasis on dichotomies of extremes expressed geometrically where attempts are made to avoid hierarchy. For an example, in the MBTI we find that the supposed orthoganal dichotomies hide the underlying context-dependent dichotomies that form the hierarchy.

Here we find that the states generated within each hierarchic level have specific descriptive characteristics analogous to terms used to describe types of mixing. Although these terms can get more complex the more levels we go through, they are found to be hybrids of four mixing types combined with the characteristics of (5). The four types are Blend, Bond, Bound, and Bind. These characteristics are the root of dichotomous meaning in that objects with dichotomous roots that the individual finds as 'valued' will enable the ellicitation of the same meaning when other objects have the same characteristics (and thus become also 'valued'). This valuation often occurs out of 'real time' context since the only context in the template is mixing.

For example, astrologically-based descriptions of one's persona, since they are based on the dichotomies of fire/water and air/earth, will ellicit mixing responses that have previously been set off by more dichotomy-based 'common sense' descriptions of persona (e.g. MBTI or tests using the 'BIG-5', or just a degree of self-reflection). This resonance can then favour the individual declaring that there is something of value in astrology, not realizing that it is the dichotomous roots of both systems that is resonating and creating 'meaning'; they treat the metaphor (Astrology) as if 'fact'.

The 'wave' nature previously described introduces probability concepts and the suggestion that the moment we make a dichotomy we inherit one of it's properties - the normal distribution curve.

Using dichotomy, one can never get a whole picture, only a very refined picture. Thus any model that has dichotomous roots will be found to have a degree of incompleteness. Since most of scientific 'fact' is symbolized mathematically, and since mathematics is founded on dichotomy, all of the models within Science will show a degree of incompleteness; as will any other models developed within any other dichotomously-derived system of analysis.

Godel found this in Mathematics. Heisenberg found this in Physics. Yeats emphasized this, as did Lao Tsu in 450 BC - you cannot 'cut' the whole. On the other hand, this statement is made within the context of dichotomy and so there may be something else that can help resolve the incompleteness 'problem'.

As we build our 'whole', so the degree of complexity increases and the information turns apparently entropic. However, patterns emerge within this apparent chaos that show a degree of stability and from the complexity can emerge 'new' behaviours.

Thus the use of the sense of dichotomy will lead to the emergence of the above characteristics within the object under consideration not as a result of the intrinsic nature of the object but due to the nature of the sense. Just as the eye does not hears pictures nor the ear see sounds so the abstract sense of dichotomy too has it's forms of representations and it's limits. What is implied by this is that 'meaning' is only valid within the initial context of dichotomy. The proposed template is a template of metaphor-derived meaning based on whole, part, aspect analysis. Thus all dichotomously derived systems of analysis are metaphors for whole/aspect analysis - which is what the basic neurology deals with. Of interest is the observation that (point 13), since mathematics has dichotomous roots, and since chaos and complexity have emergent properties, so these properties should exist within the overall brain system.


A note on dichotomous contextual development