In the act of analysis or the making of a prediction, we recognize that as an object moves through time, so it is open to influences that can lead to change. Change is distinguished when the nature of the object is detected to be different when compared to it's existence in a previous timeframe. These changes may be obvious and extreme, or manifest in the development of subtle biases.
To be able to predict an object's future, I rely on information about it's current and previous contexts. From this data I then extrapolate possible futures. I can reinforce my prediction from information about other similar objects in other similar contexts, and applying that information to the current situation.
How, though, do I ensure the 'same conditions'? For only in the 'same conditions' can my prediction take on a degree of surety.
I can set-up an experiment in a laboratory with tight controls on 'conditions' but what happens in the 'real world'? What are the predictions of falling objects when we step out of the laboratory and have to include wind resistance and tidal influences? What actually happens as we move through time?
As we move through time, we determine an object's state based on previous contexts (Fig 1).
(o) T6
(o) T5 ^
(o) T4 |
(o) T3 |
(o) T2 |
(o) T1 |
X
Fig 1. An object's observed path through time. The context at T6 is
the sum of texts and contexts from T1 to T5.
By doing this, an interesting pattern emerges if we take into consideration all previous contexts and use the generic dichotomy of change/no_change. What we find is that irrespective of the value of the separating moments, after, for example, six timeframes the object has travered a path within a binary tree of possibilities ('o' in Fig 2).
+---------------------------------------------------------------+
||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| T6
+---------------------------------------------------------------+
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |o| T5
+---------------------------------------------------------------+
| | | | | | | | | | | | | | | | o | T4
+---------------------------------------------------------------+
| | | | | | | | o | T3
+---------------------------------------------------------------+
| | | | o | T2
+---------------------------------------------------------------+
| | o | T1
+---------------------------------------------------------------+
| o | T0
+---------------------------------------------------------------+
Fig 2. A diagram of all the possible paths within six time-frames.
The symbol 'o' represents the apparent straight path from figure 1.
In fig 2 we start at T0. If a change occurs we move left (CHANGE), if not we move right (NO CHANGE). If we stay in NO CHANGE positions (marked by 'o' in fig 2), then after six time-frames, even though our object has not changed, in relation to time and what could have happened, we find it at the extreme right-hand position (T6). This position reflect a specific 'state'.
At time T6, if we consider the previous contexts (T1 - T5) as affecting our current state, then there are sixty-four possible alternative positions, in only one of which the object is located.
We should note that the above process need not be in consecutive time frames. It is possible for us to consider concepts relavent to T3 before concepts relavent to T2, but the latter will emerge such that formalization leads to the same format; everything 'finds' it's place. Furthermore, we could hold our consideration at T3 and come back to it at a later time to pick-up where we left off; but the act of dichotomization attaches the frame (fig 2) to the object under analysis.
What this development implies is that, when considering any system of classification based on pairing (a dichotomy e.g. CHANGE/NO CHANGE), as we move through time taking into consideration all previous contexts, then all possible comparisons will naturally emerge, forming a binary tree as shown in fig 2.
Since we are concentrating on the specific situation, the possible paths are explicitly unobserved and all we 'see' is the path experienced, as shown in fig 1.
If we consider only the events at each timeframe, then each frame is considered as independent of all others, and thus there is only one context applicable, the one that is part of that timeframe concerned. This implies that each frame is considered to be independant from all previous frames with the exception of it's position in the sequence of frames (the only context is time with each moment being 'seperate' from every other).
By deciding to take into consideration previous contexts, we move into the realm of dependence. Within this context, variations emerge that influence the degree of information available. If, for example, we considered only the previous two contexts, and numbered these as we developed and summed the contexts, so we would discover the emergence of a Fibonacci sequence, as shown in fig 3. If we chose to consider *all* previous contexts, then a binary sequence emerges.
frame 1 2 3 4 5 6 7 8 9 10 12 ....
system
1 frame 0 1 1 1 1.... (independence)
2 frames 0 1 1 2 3....(Fibonacci sequence)
3 frames 0 1 1 2 4 7....(Tribonacci sequence)
4 frames 0 1 1 2 4 8 15....
5 frames 0 1 1 2 4 8 16 31...
6 frames 0 1 1 2 4 8 16 32 63...
..
n frames 0 1 1 2 3 8 16 32 64 128 256 512 1024 etc
Fig 3. Emergence of the binary sequence from a Fibonacci sequence
when concidering previous contexts.
We can determine the degree of development by dividing one element by it's predecessor. In the Fibonacci sequence, as we move up the scale, so this value oscillates around 1.618. At the binary sequence the development factor is 2.
What is noticable in fig 3 is that, starting from frame 0 of each sequence, we have the beginnings of a binary sequence that is extended by one frame for each sequence. What ends the sequence is where we find the next binary sequence number - 1 rather than the next binary number. Numerically, this is a way to determine which context ratio is applicable for a given system, with the emergence of the binary sequence emphasising maximum detail as well as maximum stable developmental energy. I give this feature the overall name of the Context Ratio.
A good area of research for this is the stock market, based on the dichotomy of profit/loss. As we shall see, to go beyond a development factor of 2:1 leads us into the world of complexity, attractors, and increasing chaos implying that the window of 1.6 to 2.00 is a window of stable development. Lower than 1.6 is decay and above 2.00 is unstable but allows for 'emergence' of possibly profitable new forms.
The principle of dichotomy functions within the development ratio set by the binary sequence. This emerges since in dichotomy the previous action, both text and context, becomes the whole context of the next action and is thus 'cut' into two.
As we move through each frame, we are moving from a gross state to a more refined state in that 'meaning' is becoming more precise since our assessments of the current state use all of the previous states as context. Thus what distinguishes refined from gross is an increase in the number of states at a level resulting in finer descriptive choices, since each state associates with a specific description of whatever is under dichotomous analysis.
This development of 'meaning' seems to be the standard form found in any serial process. In fig 2 we find that, even though we have detected no change through six timeframes, we have in fact moved into a cell which is one of sixty-four we could possibly been in. This results from the passage of time and nothing else.
In traditional 'logic' time is never explicitly considered since the dichotomous analysis emphasizes a 50/50 point of view (to cut into two) , equivalent to being always at level 1. Time, however, emphasizes possible variations in contexts, as we saw in fig 1, where an apparent choice of 'no change' leaves one in an 'unbalanced (extreme)' position when seen in the framework of the whole. Time introduces 'reality'.
This shows that at each level developed within a dichotomy-tree the implicit relationships go beyond one:one. If we hold one state as constant then as we develop so other states develop at each level and the one:one condition becomes a one:many condition. Thus direction gives us inductive and deductive characteristics and dichotomy develops hierarchic undertones.
We now consider the overall format of dichotomy trees. The difference between the format used in fig 2, when compared to the more common representation of binary trees, for that is what dichotomy trees are, is that in these common systems the emphasis is on the relationships between the nodes rather than each node's specific context. Nodes are symbolized as 'dots' connected by lines, as in fig 4:
o o o o o o o o
o o o o
o o
o
Fig 4. An apparently expanding tree.
Considering fig 4, only when we emphasize contextual boundaries, as in the boarders in fig 2, does the contracting, or contextual bounding, nature become manifest. The introducing of these markers shows the emergence of hierarchy in that the scope of each cell is only equal to those cells at the same level.
Starting at the bottom of fig 4, it is easy to draw connecting lines, but only when I give each node a 'domain' of operation, defined by a boarder around it does the emphasis that I am working in small and small units become explicitly clear. The lines in fact symbolize context in a relational form ('horizontal' links) whereas the establishment of boarders represents context in a hierarchic form ('vertical' links).
Comparing figs 2 and 4, so-called 'context-free' behaviour (fig 4) appears as expansive whereas context dependent behaviour (fig 2) appears contractive. A single unconnected node in fig 4 can be considered as 'context-free' but when placed in a structure like fig 2 it always has a context. Thus the 'whole' is both relational and hierarchic but founded on hierarchic to be of 'value'; relational links can be broken but 'value' maintained as long as hierarchy is maintained.
An element that only exists in a relational context, when freed of those links becomes 'random' in that it has no 'position' whatsoever. Therefore, in thought processes, hierarchic thinking will reflect dependency biases - where the concept of randomness is treated wearily or even denied. Relational thinking, on the other hand would allow for the existance of totally independent elements (i.e. 'random' events).
From this comes the concept that identity ('non-randomness') has two sides. Identity in the form of relational links and identity in the form of positional links. Relational links are those links that give an element a sense of 'purpose' in that the breaking of the links introduces a degree of instability - an identity crisis; the links define the context for identity but the element maintains a degree of independence.
Positional links get around this breakage problem by an element being embedded in a context. They are more dependence based in that any relational links can be broken and yet a form of 'identity' remains; there is still the part-to-whole aspect in that one cannot move outside of the core context.
As a result of these concepts we find creativity being divided into two types - innovative (expansive, out-of-context approach), and adaptive (contractive in that it always stays within the overall context).
What this emphasizes is that expansion and contraction are fundamentals within the context of dichotomy and that context supplies identity. (as we shall see, using these distinctions recursivly, which is what we do when we use the I Ching, leads to the emergence of a continuum).
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