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===6.3. A Projective Point of View===
===6.3. A Projective Point of View===
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A necessary connection between signs and reflection gives the TOI its critical function as a transitional object in the development of inquiry. In the form of a TOI, I address my reflection as if it were the reflection of another. On the off chance that it renders me a bit more critical, as I eye both its sources of authority and its styles of presentation, I can regard the record of this reflection as a partially alienated object, an artifact of unknown origin, or a work of uncertain provenance. And so the very existence of a sign, that takes after another in a search for its meaning and ultimately takes its place in tracing the traces of that process of inquiry, is intimately bound up with the act of reflection.
There is, moreover, a connection between the act of reflection and the psychological mechanism called "projection" that is useful to notice here. As it happens in practice, the effect of reflection is frequently achieved, not directly, by means of a deliberate effort to observe and to evaluate one's own conduct, but more indirectly, through the initial observation and the subsequent criticism of another's behavior, finally followed up by the often delayed afterthought and usually reluctant insight that the properties ascribed to the other's behavior can also apply to one's own.
The relationship between the isolated components of behavior in this sort of "projective" situation amounts to a familiar kind of sign relation. In regard to the properties possessed in common, the other's pattern of behavior is an icon, at first unrecognized, of one's own form of conduct. The introspective act of recognizing and assimilating the significance of such a relationship is referred to as "retracting" or "re owning" the projected attributes and descriptions. To sum things up in these terms, the retraction of a projection can bring about, in its composite fashion, the ultimate effect of a critical reflection, namely, the elicitation and application of a valid description to one's own conduct.
Before the usefulness of this insight can be appreciated, it is necessary to resolve an interdisciplinary conflict over the use of the term "projection" and to sort out the relationship between the psychological and the mathematical concepts of "projection".
O time, thou must untangle this, not I.
It is too hard a knot for me t'untie.
Twelfth Night: Viola—2.3.39-40
There are a couple of contingencies surrounding the trials of learning from one's own experience, issuing from and bearing on the complexity of that very experience, that appear to be tangled up with each other. Echoing the mythology of the Gordian knot, the Herculean Hydra, the Laocoonian serpert, and the Persean Medusa, each of which accounts of perverse polymorphism seems to reflect a variant aspect but to capture a sheer fragment of the underlying archetype, these two factors can be addressed by means of the following allegory:
1. The Knot. It is frequently difficult to learn anything at all from the encounter with one's own experience, especially while one is still faced with the full complexity of that experience.
2. The Knife. One tends to establish a personal array of mental or conceptual "frames", "planes", or "sections" that one can reliably and reductively "chart", "map", or "project" one's experience on.
The relationship between these two factors is such that the Knot leads to the Knife as its adaptive or expedient remedy, but that the Knife affords only a transitory relief for the problems bound up in the Knot, and further, an excessive reliance on any fixed array of armaments and stratagems under the emblem of the Knife has the contrary tendency to worsen the troubles experienced under the category of the Knot.
Thus, it is fair to say that the difficulty of learning from the full complexity of one's own experience is a problem condition that partly leads to and partly arises from the very configurations of artificial sections and arbitrary coordinates that one contrives to project one's experience on and to judge one's experience by, respectively. Although one's idealizations, simplifications, and other pet schemes of reductive representation can serve to render one's experience initially manageable, they can ultimately and adversely interfere with seeing the obvious.
In this setting, it is possible to bring about an accommodation between the mathematical and the psychological concepts of "projection" and to reconcile their discordant uses of the term within a concerted paradigm. For example, in dealing with the joint configuration space of a multiple agent system, one considers this "yoked extension space" (YES) to fall within a "common extension" (CE) of all the single agent state spaces. Each agent involved in such a system "projects", in a geometric sense, the total action of the system on its own "section" of the whole CE, its "local outlook", "mental plane", personal "frame of reference" (FOR), or "point of view" (POV).
What does the POV of an agent consist in? Generally speaking, agents are not dumb. They are not limited to a single view of their situation, nor are they restricted to a single scenario for its ongoing development. They can entertain many different possibilities as candidates for the so called and partly self describing "objective situation" and they can envision many different ways that these potential situations might be developing, both before and after their passage through the moment in question. Furthermore, under circumstances favorable to reflection, agents can invoke POV's that help them to contemplate many different possible developments in the constitution of these very same POV's.
Now, it is conceivable that all the POV's entertained by a single agent are predetermined as having the same collection of generic characters, and thus that this invariant constitution is what really limits the range of all possible POV's for the agent in question. If so, it leads to the idea that this invariant constitution defines a "uniquely general POV", a "highest order meta POV", or a "consummate POV" of the agent involved. Still, the only points of access and the only paths of approach that an agent can have to its own consummate POV, if indeed such a goal does make sense, are through the agency and the medium of whatever POV's it happens to have at each passing moment in its developmental history. Consequently, a persistent enough search for a good POV opens up the investigation of each agent's prevailing "point of develoment" (POD).
In the best of all possible worlds, then, being under the influence of one POV does not render an agent incapacitated for considering others. Of course, there are practical limitations that affect both the capacity and the flexibility of a particular POV, and there can be found in force both logical constraints and resource constraints that leave a POV with a narrowly fixed and impoverished character, one that the agent opting for it can fail to represent reflectively enough within the scope of this POV itself. In particular, the "finite information constructions" (FIC's) that are accessible from a computational standpoint are especially limited in the kinds of POV's they are able to attain.
This means that POV's and POD's have recursive constitutions and recursive involvements with one another, calling on and referring to other POV's and POD's, both for the exact definitions that are needed and also for the more illuminating elaborations that might be possible, both those belonging to the same agent, reflexively, and those possessed by other agents, vicariously. A large part of the task of building a RIF is taken up with formalizing POV's and POD's, in part by analyzing their intuitive notions in terms of their implicit recursive structures and their referential involvements with each other, and in part by exploring their potential relationships with the previously formalized concepts of "objective concerns" (OC's).
In settings where recursion is contemplated, it is possible to conceive of a distinction between "well founded" recursions, that lead to determinate definitions of the entities in question, and "buck passing" recursions, that lead one down the "garden path" to an interminable "run around". The catch, of course, is that it is not always possible to implement an effective procedure that can accomplish what it is possible to conceive. Thus, there are cases where the imagined distinction does not apply and times when the putative difference is not always detectable in practice.
In this connection, there are two or three fundamental questions that need to be addressed by this project:
1. What makes a POV or a POD "well founded"?
2. Can "buck passing" POV's and POD's be tolerated?
3. How should they be treated and regulated, if tolerated?
A tentative approach to these questions is tendered by the pragmatic theory of sign relations, where the "definitive" and the "elaborative" aspects of recursion correspond to the denotative and the connotative components of reference, respectively. Although it is always useful to organize the connotative realm in the species of a determinate ordering or a well founded hierarchy, there is found in these parts generally a greater tolerance for the baroque proliferation of circuitous references and a broader acceptance of provincial, dialectic, and private coinages.
If all thought takes place in signs, as a tenet of pragmatism holds, then mental space is a space of signs and their interpretants, in other words, it is a connotative realm.
In this perspective, that is to say, in the POV of the present project and in the current opinion of its author, a POV is associated with an abstractly defined, but concretely embodied and frequently distributed, "section of memory" (SOM), where the signs constituting it are stored. In this rendition, a SOM is a curve, surface, volume, or more general subspace of the total memory space, in other words, a subset of memory that can be treated, under the appropriate change of coordinates, as being swept out by a set of variables, and ultimately addressed as being generated by a list of binary variables or bits. Working under the assumption that agents can engage in non trivial developments, it must be granted that they have the ability to change their POV's in significant ways between the successive POD's in their progress, and thus to move or jump from one SOM to another, as dictated by will or as constrained by habit.
In this comparison, what is visualized as the geometric structure of a "cone" is commonly implemented through the data structure of a "tree", that is, a set of memory addresses (along with their associated contents) that are accessible from a single location, namely, the "root" of the tree, or the literal "point" of the POV.
Typically, but not infallibly, an agent can reduce the complexity of what is projected on its personal POV by employing a reductive hypothesis or a simplifying assumption. Often, but not always, this idealization is arrived at by picking one agent to treat as "nominal", in other words, whose actions and perceptions are regarded as "natural", "normal", or otherwise unproblematic. Usually, especially if one is a "mature" agent, this nominal agent is just oneself, but a "novice" agent, unsure of what to do in a novel situation, can chose another agent to fill the role of a nominal guide and to serve as a reference point.
It would be nice if one could ignore the sharper edge of knowledge that is brought to light at this point, and fret but lightly over the smooth and middling courses that gloss the conformal plateaus of established knowledge. However, it is the nature of the inquiry into inquiry that one cannot forever restrict one's attention to the generic, nominal, or unexceptional case, well away from the initial conditions of learning and the boundary conditions of reasoning. Still, for the purposes of a first discussion of POV's and POD's, I limit my concern to the nominal case, where the reductive strategy indicated is useful to some degree and where the nominal agent of choice is none other than oneself.
Under default conditions of operation, then, each one's POV embodies the reductive assumption that one's own particular actions and perceptions are "nominal", that is, natural, normal, or otherwise "not a problem". Relative to this ordinary setting, each one's POV is normally configured for tracking the more problematic courses of other agents and the drift of the residual system as a whole. Therefore, the natural setting of a POV can be pictured in terms of the perceptual "gestalt" it facilitates.
In unexceptional circumstances one always takes one's own agency and one's own experience for granted. This is tantamount to assuming that a synthetic balance is already in effect between the claims of conduct and the trials of bearing. Given this much free reign in arranging the play of forces, the artificial state of accord that results can present itself to be a neutral context of interpretation and the superimposed scene of rapport that prevails can pretend itself to be the unquestioned background of instrumental activity that is implicated in every notable objective contemplated or observation performed. Cast in the role of a stationary stage for the action, there is a whole body of interactions that reside in dynamic equilibrium with each other and that make this proving ground appear to be at rest, but the whole contrivance merely acts to place in relief and to render more obvious whatever else in the way of phenomenal experience is thereby permitted to figure against it as representing an object worthy of inquiry.
Loosely speaking, and operating under the usual anthropomorphism, one can say that an agent projects the joint state trajectory, the course that the whole system takes through a sufficiently well defined CE, onto a trajectory through its own proper space, the residual state space that is encompassed by its chosen POV. Strictly speaking, in another sense, all that is known of an agent is just what is projected on its space, and thus one can say that an agent is wholly constituted by this projection.
The difference between the two senses of "projection" can now be rationalized as follows. A psychological projection begins when a mathematical projection is employed to deal with a complex experience, that is, an overwhelmingly complicated trajectory of the total system. But the default assumption that one's own actions are not significantly implicated in what happens can occasionally turn out to be unjustified.
In a case of "psychological" or "transverse" projection, the significant aspects or motivating features of a problematic situation are attributed to the other actors, while one's own collusion in the relevant character of the total situation is ignored, denied, or otherwise relegated to the peripheral background of the configuration kept in focal awareness, the figure that is currently being attended as a content of consciousness. This form of strategic reorganization usually occurs reflexively among the automatic processes of perception, in spite one's full knowledge or token recognition of the times when it is just as likely that the salient quality of the situation is due to one's own conduct, and even when it is equally possible that the complexion of the moment cannot be resolved into separate components and rendered accountable to individuals at all.
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===6.4. A Formal Point of View===
===6.4. A Formal Point of View===
