|Exegesis Volume 5 Issue #25
Exegesis Digest Sat, 15 Apr 2000
Date: Wed, 12 Apr 2000 22:30:26 -0700
From: "William D. Tallman"
Subject: Time 5
In the fourth of this series, I considered the problem of describing the fundamental attributes of a cyclical process, and suggested that any process exists as the result of a focus of interest, a question asked, that the concept of process itself is defined by our awareness of and attention to some matter of interest. I showed that few, if any, of the customarily recognized attributes of process were truly archetypal, that they depended on some manifest process, such that might serve as a benchmark or a relatively universal human experience. I suggested that a closer inspection of process yielded the recognition that it was comprised of subprocesses and so contained within it the potential of being a larger process to any one of these, just as it itself is seen as part of a even larger process.
I put forth the idea of describing parts of a process as mechanisms that serve as functions, so that these parts could be seen primarily in the context of a given Process of Interest (POI). I stated that the relevance of these to the description of a temporal dimension lay in the manner in which these functions were connected serially, and showed that there was no inherent structure that might serve to define these connections. I observed that there were other types of connections and that connections could exist between functions not of the same set hierarchy, and that not all series of connected functions could serve to describe the temporal dimension.
Finally, I suggested that perhaps the most available form of archetypal description arose from the recognition of the order of serial connection, such as would be identified by numbering. I stated that this implied the necessity of trying to discern if the numbers themselves had intrinsic significance, such that could be applied to the functions to which they were assigned. I observed that this appears to have been long recognized as indeed being true, and began by declaring that the number one (1) referred to the POI itself and was relevant only to the context of the larger process within which the POI existed.
With this post, we initiate the consideration of the intrinsic nature of the counting numbers. We begin with the Number two (2).
The fundamental significance of this, or any other, number will be most easily seen as it represents the sum of the serially connected functions of interest, and so imparts it's descriptive value to the POI itself, as opposed to any part thereof. There are many conceptual representations of the Number two: ebb and flow, both sides (hemispherical views) of an object, positive and negative polarity, etc. We can contemplate these from our own experience and get some sense of what they mean to us.
The ebb and flow is analogous to going forth and returning. As we journey from one place to another, we experience the unfolding panorama of the environment such that all parts thereof reveal themselves first to our approach according to the direction of our travel. We get our initial sense of these parts in this way and so create our first comprehension of them, such that proffers a first level of understanding of each of these parts. All subsequent repetitions of this journey, that is, the travel in the same direction from and to the same places, will provide the opportunity to elaborate that understanding in terms of detail, but, in general, nothing new is added.
The return journey, however, traveling the same route and witnessing the same environment, is observed to be entirely different. Everything is new. The panorama of the environment reveals only those parts of the environment that appear the same from both directions to be recognized as being the same as they were in the first journey. Subsequent repetitions of this second journey provide, as before, more detail, but nothing new.
These two journeys, taken alternatively, make possible the recognition that the panorama is the same for both directions, but the views thereof are complementary, such that we come to understand that, for any given part of the environment, both views serve to provide a (more) complete experience and therefore a fuller understanding of each of these parts. Now, we understand that we may not actually have a complete experience of any given part, because there may be aspects that are not available to either direction of travel, especially true of those parts that may be some distance from the traveled route. Nevertheless, the opportunity to recognize that a compilation of views from both directions definitely increases the fullness of our witness thereof, generates the notion of completeness.
At this point, we are speaking of witnessing both sides of any given object, which is the second mentioned representation of the Number two. We come to understand that neither side is complete in itself, that both sides are necessary to the object of interest, from whence we can come to understand that all sides are equally necessary. We come to realize that nothing reveals itself completely to any one point of view, and we discover that even if complimentary points of view, as one might acquire having traveled in both directions, are apparently different enough to display contradiction and/or incompatibility, they are both nevertheless necessary to the object itself.
So we come to recognize polarity, or fundamental difference, because this difference arises as a consequence of comparison. We experience our response to these differences and recognize that the appearance of incompatibility can generate the illusion of relative virtue, where one view is chosen as superior to the other. Now, the concept of polarity is often understood in its scientific sense, where it defines the direction of energy flow and identifies the function of an energy terminal. We are accustomed to assigning judgments of desirability to this concept, with the intent to describe the presence or absence of that which is considered desirable (or that which is undesirable in the absence of that which is).
This, of course, has nothing to do with the scientific usage. In fact, before the mechanisms of electricity were identified, the direction of flow was established as being from positive to negative; subsequent understanding identified this as wrong, that the flow was the other way. Now, that which flows (the electron) is understood to have a negative charge and the whole system of analysis developed around that convention works just fine. The reason for this is that polarity is a display of symmetry, which suggests that neither pole can exist in the absence of another.
This is not to say that polarity is completely identical except for "handedness", for it is not (for instance, the square root of a positive number is real, but of a negative number is imaginary, where real and imaginary are not a polar dual). Nevertheless, at some level, all polarity only exists in the context of its opposite.
In consideration of these examples, we might suggest that an intrinsic property of the Number two is that of *completeness*. Thus, each part of a two part process is the completion of the other. I suggest that a process must have, by definition, at least two parts, and that, in like fashion, a cycle must have two parts as well.
The corollary of this is that any two connected functions define a process, if (probably 'and only if') the two functions are peers, that is, that one is not a subset of the other. This is not, however, a definition of a cycle, for two connected functions define a cycle if and only if they are recursively connected, that is, that they have a double connection, one on each end.
What do we make of all this?
Well, having in mind these descriptions, one now has the basic tools with which to identify the existence of a process, and it can be determined that there exists a temporal dimension of some metric, the measure of which is Two. We know that two non-peer functions do not necessarily comprise a process, although they can when otherwise defined, but that lies outside our interests here. We can surmise that the nature of the serial connection of two peer processes may describe the basic metric of a process.
Taken together, the metric and the measure (here, two) contribute to the complete description, and thus to a definition, of a process. In application, then, we can suggest that the nature of the connections that create a process tells us of the manner in which we can understand the POI as an entity in its own right. So we have the tools to not only identify the existence of a process, but to establish a fundamental descriptive attribute thereof. And these tools are those that establish the dimension of time.
With the measure of two, we can identify the connection that generates that measure as *the primary definition of the purpose of the process*.
Consider, though, that nothing has been said about the functions (here, two) that contribute to the nature of that connection. They do not have to have anything more in common than that they are peer. They do not have to have equal length or equal power. It is entirely possible for a process to have more than one of these series of two functions, where one is larger than the other. An example might be a situation where a function that appears to have a major part in a process requires another much smaller function to complete that part of the process: the major function may have longer duration of operation, may have greater complexity, etc. So, not all two-function processes have "halves" equal in duration. The POI may contain several such attributes, but each of these contributes to an illumination of the fundamental purpose of the POI.
It would seem intuitively obvious that equality of duration should be a signature of connected processes that are a metric of time, but this is an assumption, I suspect. It would suggest that duration is a necessary attribute of any description of the temporal metric, and this may not be so. I will suggest that this is an issue in a post later in this series.
In the next post, I will consider the Number three (3).
End of Exegesis Digest Volume 5 Issue 25
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