Need representation: lists and matrices (20)

Needs Communication: viable need patterns and their identification (Part #7)

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Clearly the most favored representations of a total set of human needs are the list and the table-matrix. However, both conceal the question of completeness, as noted below.

A list does not order the relationships between its elements except in relation to nested sublists or in the case of a list in series form. This does not imply that such relationships are lacking, merely that they cannot be reflected in the list form. Note that a list is in fact a series of 'points,' but it is not necessary to conceive of it as such. The points could be represented as areas on a surface. It is only in the matrix that the manner in which the total area is cut up becomes explicit.

The cells of a matrix may be thought of as subareas of the area representing the totality that the matrix attempts to reflect. The subareas are, of course, positioned with respect to column and row commonalities. It is now interesting to ask why the area is bounded in such a limiting manner, for the rectangular or square form is one of the simplest. It provides a (paned) 'window' through which the totality may be perceived. But it raises questions about the 'wall' in which the window is set and the position of the observer in relation to the observed on the other side of the window.

Now to the extent that the matrix is complete in its coverage, there really should not be any 'wall.' The matrix should in such cases in effect 'wrap around' the observer; all is window and nothing is implicit, unexplicated, or excluded. If this is not so, then the wall should be conceived as wrapping around the observer, possibly with other windows corresponding to other partial views of the external totality to which the observer may turn his attention.

From this point of view the conventional two-dimensional matrix raises the question of the conceptual significance of crossing the encompassing boundary. It seems irrational and unmeaningful because the wall is unrecognized. There is almost a flavor of danger of 'falling over the edge,' as sailors feared with the early 'flat earth' models.

If it is assumed that the matrix is complete, then it should be possible to represent it without such an arbitrary external boundary. If the external boundary is eliminated, then the matrix takes the form of a closed surface (wrapped around the observer). By what procedure can a two-dimensional matrix be so modified, and to what does it give rise?

Consider a two-by-two matrix. The simplest symmetrical figure that retains the same number of areas is the tetrahedron. It provides four 'windows' on the external universe for any observer positioned within.

The continuity of surface area of the three-dimensional figure emphasizes any functional continuity between the aspects associated with the individual subareas or facets (the 'panes'). But at the same time, it draws attention to the discontinuities between the areas associated with the edges. They are not smooth transitions but are marked by sharp angles. It may then be asked (if reality is continuous in contrast to our conceptions thereof) whether such a representation suggests others that would reflect a lesser degree of discontinuity between aspects. And indeed there are, for the greater number of symmetrically disposed surface areas ('panes'), the larger the angle between adjacent areas and the closer the approximation, to a continuous surface-namely, a spheroid.

However, the greater the number of distinct areas (whatever they signify), the more difficult it is to comprehend the totality with any precision. The patterning of the surface area may be readily scanned, but it is only through the 'distorted discontinuities' of the simpler and most unspherical figures that it may be grasped to any degree (e.g., those corresponding to the simpler matrixes). A compromise may be considered, however. Even a tetrahedron may be projected onto a circumscribed sphere. This cuts up the surface of the sphere into four (spherically) triangular areas. More complex figures would, of course, result in more complex patterns on the surface of the sphere.

The challenge is to maintain continuity, but the realities of the discontinuities between extant conceptual frameworks may suggest that any such goal is idealistic. Disturbing factors are:

1. Unequal development: Clearly, a particular cell of a matrix may itself be broken down into more subcells than is yet possible with its neighbors. Such differences would be reflected in the surface patterning of the associated sphere. (The intermediate three-dimensional figure would naturally be asymmetrical to a corresponding degree.)
2. Gaps: Assuming that the original matrix was incomplete to the extent of missing one row, for example, then its 'presence' could be indicated by an appropriate number of (shaded) areas on the surface of the sphere-if their 'absence' from the total pattern had been remarked, of course.
3. Zones: Assuming that originally there were two or more unrelated matrixes that each encompassed aspects of the reality to which an observer could be sensitive, then their representation on the sphere surface would give rise to patterned noncontiguous zones separated by unmarked (shaded) areas reflecting the discontinuity between them. (The rules for projecting the plurality of intermediate three-dimensional figures onto the surface would be more complex than before.)

The manner in which these disturbing factors are handled indicates the freedom associated with this representational approach. Clearly distinct matrixes either could give rise to distinct spheres or could be incorporated onto a single sphere as noncontiguous zones (case 3). On the other hand, the possible articulation into many nested levels of a particular cell in a matrix (case 1) could be handled by representing the latter on a separate sphere if the totality of its special perspective needed to be stressed. List elements, represented by areas (see above), could be disposed around the surface of a sphere on the basis of a projection of a three-dimensional figure with the appropriate number of sides. If the list was not 'complete,' then gaps in the spherical surface would be required (case 2).

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