es1.htmld transactional contention points that evoke a dialectic resolution as displayed in specific topicalization. Topic focus specifies the domains of topic, as well as the specific parameters of the setting and their function in interactional exchanges. The delimitation of topic focus mechanisms is accomplished through the use of mathematical notations derived from ESNOSYS.

Display repertoire relates the participant to topic focus and thereby characterizes "the individual". Thus, the individual participant is defined by means of the performative record that he produces in transactions. Display repertoire thus defines "personal.''

Constitutive exchanges relate participants to each 6ther and characterize their dealings. The basic format of constitutive exchanges is that of an alternating exchange of transactional moves.

Transactional engineering deals with the understanding and control of transactional settings and exchanges. It involves a functional analysis of situated performances of participants in actual settings. It analyses the principles of interactional functioning through the SAOROGAT method (viz. Self-Analytic Objective Reporting of On-Going Authentic Transactions). It deals with the concerns to which other such disciplines or psychotherapy, religion, and education have traditionally addressed themselves. It analyzes the functional characteristics of the instructional and SOFW (Standard Face Work registers.) It describes the radicalist register and how it relates to such concerns as personal adequacy, raising awareness, liberation,' and awakening.

Each of the five basic formal components will now be separately elaborated.

7. ETHNOSEMANTIC OUTLINES. (ESO's)

7. (i) ESO's are patterns of arrangement. These patterns are practically describable in terms of the mathematical properties of spaces (i.e. systems of geometries).

A geometry is the specification of the properties of a space. In other words, it describes the possible location of elements within it and their possible paths or changes in location over time.

Ethnosemantics is the specification of the interconnections that are possible between concepts, by reference to standardized procedures existing within a social group. In other words, these interconnections allow the derivation of topicalization ( cf. connected discourse , sentence, utterance, assertion).

By assuming that these conceptual interconnections (called conceptualizations) are made up of labeled elements (e.g. words, titles, topics, phases, paraphrases, coded references, identified signals, etc.), Lt is possible, then, to investigate the structure of these interconnected elements or points through the ESNOSYS notation system which will now be described.

ESNOSYS stands for Ethnosemantic Notation System. It is a "sub-language" (in programming "language") that is equivalent to geometry or algebra (particularly matrix algebra).

In geometry, the simplest or most basic element is the point. In two-dimensional spaces (e.g. drawings on a page) the simplest figure is the line. Thus, we derive

ESNOSYS RULE 1:

Conceptualizations are situated elements

In other words, conceptualizations have deictic properties - - they identify, localize and particularize, just as points on a sheet of paper can be individually labeled arid situated by specifying their coordinate values (as on a graph, for instance).

In the example, points can be situated on a page, but where are conceptualizations situated? This is specified in

ESNOSYS RULE 2:

Conceptualizations are situated elements in ethnosemantic

space.

Geometries are abstract, symbolic universes or manifolds. Figures are formal relationships among situated elements. Elements are hypothesized entities (cf. "theoretical existence") and formal relationships are patterns of arrangements and their derived interconnections. Yet, through these formal, abstract, hypothesized, theoretical elements and relationships, we derive such practical, concrete, actual benefits that mathematics, physics, and engineering have reified in technology and civilization. Thus, practicality includes the abstract and the concrete. Reification, actuality, and reality are the functional products derived from the geometries.

Ethnosemantic spaces are abstract, symbolic universes or manifolds. Conceptualizations are labeled entities that are situated in this space. Through a mechanism, called topic focus, these labeled elements can be selectively interconnected into a restricted arrangement, called topic domain. Topic domains are thus describable in terms of geometric figures or algebraic matrices. Topics, like geometric figures, are formal relationships among situated labeled elements, which themselves are abstract conceptualizations. Yet, through these symbolic entities and their relationships we derive such practical, concrete, actual benefits as a novel, a poem, a prayer, an intellectual production, and instructions that inform, warn, confuse, and clarify.

ESNOSYS RULE 3:

Conceptualizations are situated labeled elements interconnected in ethnosemantic space.

In geometry, the line connecting two points is the simplest or most basic operational procedure. The simplest topical constitution is the arrangement of two connected conceptualizations. This simplest ethnosemantic arrangement is called the contention point. Thus, the simplest geometric figure is the line connecting an arrangement of two points (line operational procedure); the simplest operational procedure in ethnosemantics is the formation of a contention point by connecting two conceptualizations.

ESNOSYS RULE 4:

The first, simplest ethnosemantic operation is the evocation of contention points by interconnecting two conceptualizations

Contention points are discourse mechanisms relating to topic focus and register. The creation of a contention point is a standardized procedure. In geometry, standardized operational procedures allow the creation of figures. For example, the 3-cornered figure known as the triangle can be drawn by arranging three points in any pattern (viz.: situating them anywhere on the page) and interconnecting them such that each point connects with two other points.

It is possible to say that the connection of points 1 and 2 raises the contention point. of "How to complete the operation to draw a triangle?" The resolution of this contention point is attained when (a) point 3 is added to the pair arrangement and (b), it is situated such that it interconnects with 1 and 2 separately.

The arrangement of two conceptualizations as an interconnected pair raises standardized contention points.

This illustration shows four contention points and their resolutions. In Square 1, the contention point can be paraphrased something like this:

"What role relationship characterizes the mother-child relationship?" In Square 2: "What is a primary positive emotion that often characterizes the mother-child relationship?" In Square3: "What characterizes the relationship between mother and child when they don't get along?" In Square 4: "What is a primary function of being a mother in relation to her child?" It is not necessary to assume that there is a limitation to the number of contention points that a particular pair of conceptualizations can evoke. Therefore) the number of possible triangular resolutions of two conceptualizations is indeterminate just as the number of different-shaped triangles that can be drawn is indeterminate. The resolution of contention points is the next level of ethnosemantic operation (the first was: pairing two conceptualizations). This operation is evocative and is accomplished through the mechanisms of discourse dialectics. In practice, any person who talks can perform resolutions to contention points. The set of resolutions performed by an individual to particular contention points is a parameter of display repertoire and is thus indicative of personal contention. Triangular resolutions specifies topic, hence topicalization work, (i.e. what people say, write, think), is characteristic of individual participants (see "role type").

These considerations lead to

ESNOSYS RULE 5:

The second ethnosemantic operation is the resolution of contention points by the evocation of a third conceptualization that is connected to the other two.

7. (iv) In geometry, there are two ways of building more complicated figures Thus, starting with a 3-cornered figure in two-dimensional space (i.e. on paper), one can expand the number of points in an arrangement to four, (quadrangle), five (pentagon), six (hexagon), and more to an indeterminately large number that approximates a circle. This operation represents an arithmetic progression of a number of corners from 3 to an indeterminately large number, and is referred to as a horizontal expansion. The other way of expanding the number of points in an arrangement is to add dimensions to space. Thus, by using triangular cardboard cutouts (or child construction equipment) one can build a three-dimensional version of the triangle, known as the pyramid. Similarly, the three-dimensional pyramid can be expanded to a fourth-dimensional pyramid. These are called vertical expansions, and they, too, have no determinate number.

Consider now-some contrastive features of horizontal and vertical expansions. To assist in the presentation, we shall use perspective drawing techniques to illustrate differences in arrangements with three- and four-dimensional figures.

Table of Correspondences Between Geometric and Ethnosemantic Parameters

ETHNOSEMANTIC COROLARIES

ESNOSYS allows the derivation of ethnosemantic corollaries along the logic of correspondence it establishes between geometry and ethnosemantics. The empirical investigation of ethnosemantic outlines, topic structures, and other discourse mechanisms, will now be illustrated.

Corollary 1:

the standard level of conceptual organization is formally represented by the triangular arrangement.

Corollary 2:

the standard conceptual unit of topic is constituted by the triangular arrangement of three concepts.

Corollary 3:

non-standard topical arrangements (i.e. non-triangular) require changes in the dimensionality, connectivity, and curvature of arrangements of concepts. These types of changes are called gaps. (Understanding is opening gaps.

Corollary 4:

standard topical domains are constituted by means of triangular fragments whose arrangement is elaborated in accordance with group membership specifications.

Corollary 5:

the connectivity (viz.: level of conceptual organization) of a topical domain is a measure of its degree of sophistication.

Corollary 6:

an individual's level of practical understanding can be expressed as a function of the degree of sophistication of his actual topical domains (i.e. the connectivity of his topical domains).

Corollary 7:

the standard organizational structure of constitutive exchanges is a three-dimensional manifold; the basic transactional unit is a three-dimensional solid (viz..: move, legitimization, ratification: organized in a time sequence), (or: The 7opology of standard constitutive exchanges is a three-dimensional surface organized by a sequential arrangement [time] ).