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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.

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.

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 POVs in significant ways between the successive PODs 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 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 POVs in significant ways between the successive PODs 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.

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.

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 POVs and PODs, 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.

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 POVs and PODs, 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.

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.

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.