|Exegesis Volume 5 Issue #27
Exegesis Digest Wed, 10 May 2000
Date: Sat, 6 May 2000 13:57:38 -0700
From: "William D. Tallman"
Subject: Time 6
In the fifth of this series, I began the analysis of Number as a proper metric of cyclic process, with the idea that it may also be effectively used as a metric of process in general. I will not repeat the structure of arguments that comprise the basis for this work, as it has probably been adequately presented in previous segments. I will, however, mention some of the ideas presented in the last post, as they will be carried forward for further investigation and usage.
In the contemplation of the application of Number as a metric, we observed that the dividing points created thereby may be expected to have intrinsic significance. In the case of the archetypal cycle, we assumed for this level of analysis that the beginning and ending of a cyclical Process of Interest (POI) are appropriately connected; we recognize that in a specific application this is not the case, but it is the iterative nature of the cyclical process that is of interest here. The relevance of this is that the connection itself is not an intrinsic part of the POI, for it represents the interface between the POI and the larger context within which it exists.
This has an interesting result. We are accustomed to the symmetry between the number of arcs in a circle and the number of points dividing these arcs: two arcs comprise a complete circle when they are connected by two points, and the general case is that [n] number of arcs are generated by [n] number of points. In this case, however, the number of arcs is generated by [n -1] number of points. For our purposes, the arcs represent the application of the metric of Number as it generates a specific number of segments in the temporal dimension of a POI. The establishment of these segments generates a number of points equal to one less than the number of segments, and so we have two numbers to address in any given POI.
The Number two (2) implies also the Number two minus one, or one (1). Likewise, the Number seven (7) also implies the relevance of the Number six (6), etc., etc. The second integer is a metric of the internal structure of a given POI, a structure which is generated by the applied temporal metric itself. It seems obvious, at least to me, that there is some potential for confusion here, especially when the same metric is applied to both of these aspects of the general cyclic process; we might also view them as attributes, and acknowledge that they are related, but in doing so we are well advised to limit ourselves to that acknowledgment. We cannot automatically infer a specific significance to the second attribute (the interior connections); that significance, whatever it may or may not be, is of fundamental interest to our analysis, however.
In the analysis of the Number two (2), we identified the single interior point of connection. I suggested that the Number two (2) speaks of completeness and that it identifies the nature of the purpose of a given POI. Earlier in this series, I suggested that the purpose of a process may be one of the most useful things we can know.
There are, of course, arguments that the purpose of a process is integral with its fundamental nature, and the expansion of this notion is part of the foundation of teleology, which appears not to be as well considered presently as it was formerly. The teleological view is not necessary here: we can easily assume that a process has a purpose without erecting a large structure of cosmic analysis thereon. The recognition that any given POI has power in its larger context, such that it creates some change therein, is valuable in and of itself and requires no further elaboration; it does not, however, rule out such an exercise.
Thus, the purpose of a process is an intrinsic part of its nature, and it is a descriptive aspect of any definition thereof; beyond that, it becomes a part of the larger mass of relevant data we might obtain from observation and analysis. The point here is that purpose is a singular concept: although it may have multiple manifestations, it also may have only one. The insight of interest here is that there is a correlation between the nature of the primary significance of the Number, and the nature of the structure that the Number generates within the POI itself. A singular significance and a single division.
We shall see if this correlation holds true in further analysis.
The next Number of interest is three (3). The application of that measure generates the first fully interior segment, bounded fully by other interior segments. We can reasonably expect that this is a contributor to the significance of that measure, I think.
For the first time, there exists a segment that does not partake of the larger context of the POI. It might be observed that this segment has something of the nature of the internal dividing point generated by the measure two (2). Accordingly, we might ask if this is a further manifestation of the Number one (1), and we could arguably be on solid logical ground in doing so. There is a problem here, however: in so doing, we manage to establish a third relevant type of Number, and that must be justified, especially in light of the fact that it already has an applied metric. It is part of the measure of three (3). Nevertheless, the point is not easily dismissed, I think, even though it does not warrant the same treatment as that of the internal division(s).
What we can do is observe that there is a commonality of function here. The single division in the measure of two (2) connects a single segment preceding and a single segment following. This third segment in the measure of three (3) expands that function but on a different level. Segments and division points are not peer entities, but segment and segments are. We can observe that the single division point *connects* the two segments in the measure of two (2), and the single fully interior segment in the measure of three (3) *observes* the other two segments. It remains to discover what this may mean.
A connection point is a marker with a single dimension: that of location. A segment is an entity of two dimensions and possesses area, within which an indeterminate number of points can be located. A point possesses no substance, but an area does, and so is a suitable venue for locational change. The relevance of this is that the observer may reside in an area and have a range of views as a result of different attitudes, and cannot do so at a single point. The observer in this first fully internal segment can see in both directions, can have multiple (here, only two, perhaps) simultaneous views.
This internal segment can be viewed as a function in its own right, and so possesses the nature of a process as well. As such, it can be observed to have its own independent existence and purpose, but not peer to the POI itself. As the POI interacts with its own peers in the larger contextual process, this third segment interacts as peer with the other two segments, each of which connect with the larger context.
What do we make of this?
We might suspect that this third segment displays something of the "how" to the "what" addressed by the attribute of purpose. The concept of "how" is, I think, not as concise as that of "what". We are better advised, I suggest, to see how some fundamental of the concept of function itself might be illuminated by the Number three (3).
We can observe that there are some correspondences that can be identified, and these may be fruitful to contemplate. The third segment has the same relationship to the POI as the POI has to its own larger context, and so there is established a manifestation of cosmic hierarchy. The larger context is the macrocosm and the third segment is the microcosm. I will be so crass as to introduce a new term here: the orthocosm, that is, the POI itself. This, interestingly enough, generates the same number of cosmoses (cosmii?) as the Number of interest here: three (3).
We now have a correspondence between the measure of the temporal metric and the measure of the hierarchical metric, which we might identify as that of the cosm (further evidence of crassness on the part of the author < grin > ). The source of this manufactured word is a derivation from cosmism, which is the view that the universe is a rational and inherently knowable structure, etc.. etc.. The appropriateness of this source lies in the hierarchical structure of macro and microcosm that assumes the validity of that view, and it is this hierarchy that we are addressing here.
So I've presented two (related) manufactured words, neither of which are directly relevant to the subject of interest here: the metric of the temporal dimension. Although these areas are not of specific interest, they do have power with regards the POI, and that the measure of three (3) invokes them *is* of interest here. Accordingly, its appropriate to investigate what sort of effect cosmic hierarchy might have on the POI.
I suggest that the primary matter is the manner in which these hierarchical attributes interact. We can observe that they do not do so directly, because they are not peers (by definition), but they do so indirectly via mutual influence, most relevant here upon the orthocosm, the POI itself. The object of interest here is how these influences may or may not have commonalities: it is assumed that they do because they are produced by fundamentally identical mechanisms (the relationship between a process and a subprocess where there is no intervening hierarchy), and they have the orthocosm (the POI) in common. Specifically, it is the similarities that are of interest, as the differences can be of some indeterminate number of divergent causes. The focus is on how these similarities influence each other.
There is a ready made concept that is directly applicable here, and it is that of *resonance*. Because we are interested in the presence or absence of similarities, it is the presence or absence of resonance that is the core issue here. Resonance implies dissonance, of course, but that implication is not supported here. The phenomena of dissonance has its own mechanisms and they are not of equal relevance to those of resonance; the sources of dissonance are probably more varied and widespread than those of resonance, and those sources may be the subject of another Number measure.
Another aspect of the structure generated by the Number three (3) is that of the two inner divisions which delineate the central inner segment. They serve to define that segment to the other two, which are connected to the larger contextual process. Taken together, they represent the primary attributes of a function: the input and the output; and they act as such to the extent that the central inner segment is indeed a subfunction, a process for which the POI is the larger context. For the POI itself, these two attributes must be presumed to operate simultaneously, and so the manner in which they do so is a legitimate concern. Here again, we are interested in the presence or absence of resonance,
This particular quality, in its presence or absence, is usefully descriptive of the subprocess that generates it. To the extent that we can discern any answer to the question "how" in that subprocess, we are probably justified in suspecting that the quality of resonance between these two portal markers suggests that the subprocess is intrinsically indigenous to the POI and so any such answer would seem to be inherently valid. A lack of resonance between these markers would suggest some dysfunctionality in those regards, I would think. And so the presence or absence of resonance between the two portal markers bounding the central subprocess speaks directly to the nature and efficacy of the POI.
As I have said, it is probably somewhat futile to seek a comprehensive answer to the "how" of the POI in the temporal measure of three (3), but from the above analysis, we might be able to perceive something of real import concerning the effectiveness and robustness of the POI: these qualities may be considered generally proportional to the presence of resonance between the inner markers that connect the temporal segments created by the measure of three (3).
We can observe that the correlation between the secondary metric and the quantitative nature of the primary temporal metric continues to hold. Resonance, the primary quality of the Number three (3), is a quality of relationship, of connection. It implies the existence of two entities of interest; the question arises whether it implies more than two entities. I suggest that the answer is no: the quality of resonance is always reducible to the relationship between two entities, even though more than two may be involved. With multiple entities, a complex of resonances is generated which is characterized by the nature of the interaction between and amongst the several two-entity resonances. Thus, the correlation here is characterized by the measure of n - 1 (3 - 1 = 2).
Incidentally, it seems obvious that these connecting markers of division between the various segments of a POI can be regarded as 'cusps', which would most likely be the relevant astrological terminology. I avoid using that term, as it is already rather well defined by astrological usage. I do so because I don't want the assumptions created by that usage to have any part in this analysis, for they would at the very least muddy the waters, and more likely would create an insurmountable amount of confusion. Nevertheless, the recognition of this correspondence is itself useful, such that it allows the astrological usage and attendant understanding to be illuminated however it may by the analyses presented here.
Having said that, however, we can observe that our conclusions here are in line with the traditional interpretation of the measure of three as a means of observing functional effectiveness. The Aspect of the Trine is commonly regarded as a relationship of powerful harmony, and the Planets involved reinforce each other according to other parameters as appropriate. The placement of the Planets in Sign involve (typically) those of a single Element and so emphasize the trinary Modes.
The Modes lend themselves to several formal sorts, but probably the most relevant to this series is in terms of temporal nature. The Cardinal Sign has no temporal dimension: everything is in the present moment. The Fixed Sign has a single temporal dimension: the past continues to be represented according to the standards and ideals that are the refinement of tradition. The Mutable Sign has a dual temporal dimension: the past and the present combine to make possible the concept of potential, of what is possible, thereby creating the future.
> From another perspective, the Cardinal/Fixed/Mutable trio span duration itself, from none at all to eternity: The Cardinal Mode has no time, the Fixed Mode has time and deals with duration, and the Mutable Mode is timeless and deals with the eternity of endless change. It's interesting to observe that it is the middle Mode, bound by the other two, that possesses duration and is therefore concerned with process. Thus it demonstrates the property of being the principal identifying internal function of the astrological cycle of Modes; the other two serving as links to extra-Modal considerations.
Obviously, there are other formal sorts that are useful for the application of Number to astrological thinking; these were given as examples. They should serve to demonstrate the potential for generating insight that is one of the useful applications of archetypal and abstract concepts. It bears repeating, however, that these matters require diligent and somewhat rigorous contemplation: one has to keep at it, perhaps over a period of time, and one has to continually be vigilant in the disposal of limiting preconceptions, such that the reality of what is sought might show forth in its own right.
In the next of this series of posts, I will look at the Number four (4), and address the property of structural complexity that is fundamental to Number as a metric. At this point, I don't know how much more individual analysis of Number measures will be useful: it depends on how clearly I think I am able to present the relevant material. In any case, there are other issues to bring forward, and this series is already far longer than I'd envisioned when I began.
Date: Mon, 08 May 2000 22:40:12 GMT
From: Bill Sheeran
Subject: Re: Exegesis Digest V5 #26
> People develop a personal orientation to north, south, east & west, that
> reflects what is probably a universal cultural orientation. This
> orientation of the psyche is continually reinforced by diurnal motion, = for
> everyone. But is there any evidence that we have a psychic orientation = to
> the midpoints of the four quadrants? Just a thought on this last point, rather than evidence.
Assume an ideal square room, with a door in the middle of one of the walls. Stand in the middle of the room, and face the door. It is hard not to notice the corners of the room. The four walls and the four corners scream out eight. Sixteen is pushing it from a visual point of view. Not the most sophisticated thought experiment admittedly, but I would imagine that if geometric archetypes exist, the diagonal demanded by a rectangle (or square) is surely one of them.
Given that you mentioned the Celtic tradition, it is interesting to note that the Celtic New Year started on or around one of the cross quarter days, Samhain (today celebrated on November 1st, but originally the period bisecting the Autumn Equinox and Winter Solstice, around November 6th). This suggests a conscious psychic attunement to the number eight, given that the Celts are hardly likely to have not attributed significance to the equinoxes and solstices.=20
Another interesting peripheral point is that for the Celts, there were five directions - N, S, E, W and the Centre. One might wonder whether their astronomy/astrology contained an orientation towards the zenith and circumpolar stars, given that the obvious unique extended orientation in space of a centre point is a vertical one. Unfortunately, this is an area in which I am ignorant. =20
All the best,
Bill (Sheeran) =20
End of Exegesis Digest Volume 5 Issue 27
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