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In the sixth of this series, I suggested that the points connecting the parts of a process have an intrinsic significance complimentary to the parts themselves. Thus, the temporal dimension of process is complex, rather than simple: the application of any proper temporal metric must take this into account, and provide meaningful information about the relationship between the parts of a process and the points that connect those parts. This relationship, as expressed by the metric Number, is given as n:(n - 1); other metrics should be expected to generate appropriate meaningful analogous expressions, one might presume.

I suggested that (n - 1) provides insight into the archetypal meaning of (n), such that (n) represents any given Number. The source of this temporal complexity is the interaction between any Process of Interest (POI) and the larger contextual process of which it is a part. An analysis of the relationship between the intrinsic nature of a POI and its manifestation within a larger context produces another relationship, further complicating the archetype of temporal dimension: in addition to n:(n - 1), we can derive n:(n + 1). The relationship n:(n - 1) expresses the difference between the structure of an archetypal cyclical process, and its manifestation, such that one of the points of connection between the process parts takes on the role of interface between the POI and its larger context, leaving (n - 1) connection points in the internal structure of the POI.

The relationship n:(N + 1) expresses the reality that the interface point is manifest in two places, at the beginning and at the end of the POI, thus creating (n + 1) connection points. Having pointed this out, I must address the question of the significance of this second expression, but we must realize that this expression arises out of the condition of manifestation which is unique to any given POI. The short answer to the question, then, is that it is fundamentally dependent on the uniqueness of the given POI, and so is not a consideration proper to an archetypal analysis. It is important to recognize, however, that any practical application of Number as a temporal metric to any given POI must address this second expression, and so we can expect some resonance between the specific meaning of the second expression and the structure of archetypes of the metric of Number; this is not the same as an archetypal significance.

The most obvious clue to the significance of the second expression is that its measure, (n + 1), suggests an incremental increase in the general complexity of the POI itself. We can observe that the presence of the POI in the larger context serves to divide that larger context into two (2) parts: that which precedes and that which follows; this suggests that the interaction between the POI and its larger context is itself complex, at the very least it is duplex, an expression of the Number two (2). The result of all this is the recognition that the analysis of a given POI must address an hierarchy of levels in the temporal dimension, and so is not so simple as the contemplation of the meaning of a single Number as a temporal measure. Nevertheless, the analytical tools presented here are appropriate to the task, however complex it is allowed to become.

Turning again to the analysis of specific Numbers, the Number four (4) is the first factorable integer, containing within it the Number two (2). We should expect this to figure prominently in the archetype of four (4), and so it does. Each of the parts inherent in the Number two (2) is itself so divided, and this serves to provide a deeper insight into the POI, for it illuminates the structure of parts as functions or subprocesses, such as we discovered in the analysis of the Number three (3). In this case, the measure is the Number two (2) in its most fundamental iterative form, and so we can turn to the previous analysis of the Number two (2) and expect to find the Number four (4) an expansion of the Number two (2).

I spoke of going forth and returning in that analysis, such that the fundamentals of perspective were acquired. In the cyclic format, the measure of the Number two (2) is the most primitive expression of the temporal dimension of a POI in its own right (the Number one (1) representing identity which has meaning only in the larger context of which the POI is a part, and so not having significance in terms of the POI itself). In that regard, then, the Number two (2) represents completeness. The dynamic role of the Number two (2), however, addresses the functional aspect of the POI, showing something of its essential nature: the only internal point of connection is at the center of the POI. The simplest significance of function is purpose, and so this is the primary significance of the Number two (2).

When we apply this to the each of those parts, we can expect to discover something of the nature of the purpose of each part in its own right, and so we also discover another aspect of the internal structure of process itself. Within the POI is another going forth and returning as the initial two parts are seen to functionally interact. The primary going forth now has its own purpose, as does the primary return, and now we have the interaction of these two additional internal purposes. The question now arises concerning the nature of the relationship between these purposes, specifically between the primary purpose and the interaction between the internal purposes. We can reasonably view these two both as peers and as parts of an hierarchy (micro/macrocosm), but we must recognize that those are distinct relationships. Primary purpose and internal interaction are roughly peer attributes, but the evaluation of the several purposes as such must be in terms of an hierarchical relationship.

In the first instance, we can reasonably expect to gain some insight into the nature of the primary purpose by an investigation into the nature of the internal interaction, and we discover that the two internal purposes are indeed about the reasons for going forth and returning. The first of the internal purposes is about what is intended in going forth, as the second of these is about what arises as a result of having gone forth in the (sub)process of returning. These are archetypal significances, of course, and so provide only clues as to the reality of their manifestation in the POI. In the second instance, we can expect to discover in the nature of the relationship between the two internal purposes how the POI itself might interact with such other process in the larger context with which it might find itself in direct interaction.

A third approach is to disregard hierarchical concerns and contemplate the three internal connection points as de facto peers. Without the tools of analysis presented here, this approach is probably the most intuitively obvious, and we discover that it produces the view that the relationships here are evidently intractable. In this approach, we are forced to contemplate the conclusion that the relationships we have already determined as being hierarchical are in fact inherently antagonistic when regarded as peers. Interestingly enough, it appears that this is exactly the approach that has produced the most common astrological views of Aspects generated by this construction.

Astrology literally concludes that these relationships of purpose are at "cross purposes", and that the relationships between them are inherently fractious. The Aspect of the Square is deemed intrinsically difficult, and it is generally thought, so it seems, that the virtue of the Aspect lies squarely (oops, sorry... ;) ) in its fundamentally difficult nature. We are commonly adjured to regard the Square as an opportunity to gain in strength, internal integrity, stability, etc. Unfortunately, there is no commonly accepted notion that the Aspect provides any insight into how it might do so.

Turning to the analysis of derived expressions, we can assess the value of (n - 1) and come up with the perspective of the "odd man out", which further enforces the negative conclusion. In other applications, the Number three (3) yields qualities of stability (the tripod) and primitive resonance (see analysis given in this series). In a common four (4) based figure, the T Square, we find the "odd man out" intuitively obvious, but when the idea of hierarchy is taken into account, we come up with the idea that the balancing connection point at the base of the T has the quality of a monitor/controller, dictating the dynamics of the T Square function. This idea is, I believe, well regarded and often used; what is of interest here is that the idea is easily generated by the tools of analysis I've presented in this series of posts.

In the next post, I will look at the Number five (5) and will begin to draw some general observations about the use of Number as the temporal metric of process, and attempt to show how they may be utilized as analytical tools. I will also take a more rudimentary look at other Numbers and suggest how they may be treated in accordance with the ideas set forth here.

Comments?

wtallman