In the process of analysis, there seems to be a bias amongst humans for the use of dichotomous methods to break-down a whole into it's aspects. These methods are highly successful in that they enable a high degree of consensus when used to make maps of reality (where maps are designed to be very explicit (EITHER/OR) to enable cross-cultural use - thus ground maps with areas marked in blue are read by interpreting the blue as water).
The success of this method for analysis has also been used for synthesis, based on the assumption that once the parts of a whole have been explicitly listed, so one just needs to put them together again to get back to the whole.
Careful consideration of the use of dichotomy to synthesize has led the author to the opinion that the only method that can successfully combine previously dichotomized data is in fact trichotomous in form.
We can demonstrate the distinctions between dichotomy and trichotomy by starting with a whole, say in the form of an integer - 2.
We can break 2 down into two parts, 1 & 1. But the process of putting the 1s back together consists of the parts (1,1) and the process of summation (+). What this process does is combine the two parts into one 'space' - a 'space' we label as '2'. This process of recombination requires the two parts and a temporal component - the use of summation. Thus, in simply form, addition is the process of packing 1s into a single space (as is multiplication but in a more refined manner).
For a more detailed analysis, consider the process of repeated dichotomization on a whole. To describe this process, consider the use of six dichotomies; this will give sixty-four possible ‘states’, or ‘parts’, that make-up the whole.
These sixty-four parts are in an explicit form - they are 'all there is' and have been derived using EITHER/OR methods. In simple terms they are lifeless; like the parts on a garage floor after the engine of a car has been stripped-down (although perhaps in a little more order in that contextual considerations emerge as the analysis process functions. Consideration of contexts leads one to lay-out the parts in an ordered fashion, with parts from a common area being grouped together).
From the engine analogy we 'know' that putting the parts back together requires something more than just putting everything back where we found them; position options in placement, if not considered, can lead to what was a smooth running engine turning into a rough, or even non-, running engine.
This is where we come face-to-face with what I will call BOTH/AND logical states as compared to EITHER/OR logical states.
In these BOTH/AND states we are dealing with process as well as form; we are combining two 'things' into the same 'space' and there is the strong suggestion (as we shall see, more like 'fact') that these combinations sometimes do not work, simply because we have assumed a dichotomous thought process whereby we just stick the parts together, assuming they will work. What this does NOT do is recognize that the concept of wholeness is based on the integration of parts rather than just the summation of parts.
Thus the car engine does not 'exist' until it is turned-on; prior to this act it is just a block of ordered parts combined with some theoretical considerations - everything in an EITHER/OR state.
One of the 'best' (simplest) methods of symbolizing EITHER/OR analytical methods is the use of a set of symbols derived from China - the concept of 'yin' and 'yang'.
In this system, 'yin' is symbolized as a broken line -- --, and 'yang' is symbolized as an unbroken line '-------'. These symbols represent the two elements of *any* dichotomy; they act as templates.
Thus the sequence of 'yes' followed by 'no' is symbolized by :
-- --
-------
Where the derivation process starts at the bottom and moves upwards.
This process captures EITHER/OR states, where each step in the derivation is EITHER yin OR yang. (thus each step is the answer to a yes/no type question).
We now consider states where BOTH/AND conditions exist. In these states BOTH yin and yang occupy the same 'space' until an EITHER/OR determination is made.
Thus the symbol:
-- -- -------
can be symbolized as -- - -- , representing a 'BOTH' state where the explicit determination has not yet occurred. (To resolve a BOTH/AND state we just translate it into explicit EITHER/OR-ness through the adding of a dimension (another dichotomy). This process however leads to *two* forms emerging and it is up to the user to determine which one they wish to use - thus their intent dictates the path that follows. In the above digram, reversing the yin/yang order does not change the BOTH/AND symbol.)
What we find is that, in using this new symbol, there are four possible ‘combinations’ of digrams that can be compressed into three monograms:
-- -- becomes -- -- -- -- -- -- becomes -- - -- ------- ------- becomes -- - -- -- -- ------- becomes ------- -------
These lines can be used to translate six-dichotomy symbols into trichotomy symbols. Thus the dichotomously-derived symbol:
-- -- -- -- -- -- ------- ------- ------- becomes the trichotomously-derives symbol: -- -- -- - -- -------
With this conversion system in mind, we find that to convert sixty-four dichotomously-derived symbols we need twenty-seven trichotomously-derived symbols.
The difference between the two systems is that the trichotomous system includes BOTH/AND states, the specific order of which is not determined until the user shows ‘intent’ - how you wish to analyze.
What is 'interesting' about this process is that certain trichotomy symbols contain more than one dichotomy symbol; a number of symbols occupy the same space. For example, in using symbols composed of six dichotomies (hexagrams), some symbols translate without conversion (one : one - there are eight of these) whereas most trichotomy symbols ‘contain’ 2,4, or 8 dichotomy symbols.
What this implies is that there are certain parts that cannot share space with other parts unless both parts are in some way 'tuned'. By this I mean that the combination of contexts leads to a 'virtual' context emerging that is 'stable' for the lifetime of the relationships; some relationships will never 'work' simply because of their contextual differences which cancel each other out or raise 'extreme' conditions. Thus, in a 'perfectly' working system, parts work in their own context but the joining of the contexts of all of the parts is such that a stable 'virtual' context emerges.
This process is analogous to the concept of superposition with waves. In this state, at least two waves occupy the same 'space'. The constructive and destructive interference leads to the emergence of a 'virtual' wave that 'exists' as long as the two waves occupy the same space. Here, the virtual wave is like a 'whole' that is made-up of the two parts - the two 'real' waves.
Another analogy is with Cymatics - which studies the patterns created when sand, having been placed on a surface, starts to form whole patterns when the surface is made to vibrate. The generated patterns are maintained as long as the vibration continues and only changes when the harmonics of the vibration change (and the changes are whole changes). (This can serve as a model of consciousness where the surface becomes a sphere and the sand the neurons of the brain).
What I have done (see appendix I) is to create a conversion table that links dichotomy to trichotomy. Thus the process of refinement is to analyze a whole dichotomously, creating it's parts (explicit EITHER/OR states) and then to put the whole back together using trichotomy.
Thus in neural net systems, the path from input layer to hidden layer is dichotomous and the path from hidden layer to output layer is trichotomous.
In a 'full' system we have eleven layers each, with the following number of nodes (which have been derived from whole/aspects analysis and then linked to trichotomous synthesis):
1->2->4->8->16->32->64->27->9->3->1
the appendix shows the 64->27 connections. (The 'rule' is to differentiate all of the parts and then convert the symbols to trichotomous forms and then group all common forms. We can take this down, for example, to 4096 'part' states that link to 729 trichotomy states but these are just levels of refinement for the whole system. Of note is that we can jump from 8 symbols to 64 by combining the 8 symbols with each other. We find that the resulting meanings are the same as if we had derived the system line by line. This gives us nine layers).
In the model of dichotomous analysis devised by the author, the resulting parts can now be put back together in a more integrated way, and the use of the system using the MBTI allows for the 'tweeking' of conflicting interests to enable parties to operate in the same context, for it is this same context that is vital for proper operation and thus avoiding conflict and/or 'misunderstandings' - like who 'leads' in the dance.
In the context of consciousness we here see the linking of mind and brain where the analysis of the brain into parts does NOT give an overview of the whole - to do this requires the conversion of dichotomous analysis (DA) to trichotomous synthesis (TS); thus the mind includes a timing component that adds a degree of ‘thirdness’ (like Charles Peirce’s concept of firstness, secondness and thirdness which by it’s definition leads to firstness/thirdness oscillations where intent determines which is which (and both states are explicitly described by *two* dichotomy symbols). This oscillation does not appear until we move past the first iteration process where ‘firstness’ is the initial perception/sensation of an object, secondness is the dichotomous analysis of the object and thirdness is where these previous two concepts are combined to give a third. At this point, this 'third' becomes the 'first' for the next level of iteration).
Since the author's analysis of dichotomous analysis suggests that the method is hard-wired and is an adaption to 'out there' it follows that trichotomous synthesis is also from 'out there' and is the other end of the dichotomy process. Thus DA and TS form the whole that is DATS; the method used by humans (and other lifeforms) to 'map' reality and function within it.