1984

## Periodic coaction coordinate system

### Examples of Integrated, Multi-set Concept Schemes (Annex 16)

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See other Examples of Integrated, Multi-set Concept Schemes. The concept scheme described here is discussed in the paper on: Patterns of N-foldness: comparison of integrated multi-set concept schemes as forms of presentation. This was prepared for a sub-project meeting of the Forms of Presentation group of the Goals, Processes and Indicators of Development (GPID) project of the United Nations University (UNU). The annexes were published in Patterns of Conceptual Integration. Brussels, UIA, 1984, pp. 161-204

The following extracts describe briefly a generalization of the notion of periodicity as reflected in the classification of elements. It is claimed to be a scientifically based pattern of a universal kind which is displayed in some respect by all of human knowledge and experience. The extracts are from:

• Edward Haskell (Ed). Full Circle. New York, Gordon and Breach, 1972 (prepared in connection with the 1972 International Conference on Unified Science)

1.1 "The (0,0) coaction may be placed at the origin if there are no coactors. But in actual systems it must be interpreted as a third "axis", the scalar zero circle....How do you decide whether a coaction has net (+) or (-) or (0) effect ? You must have a reference, which is the state of the system before the coaction is initiated, or a reference point must be picked. This then establishes the (0,0) state and is, of course, neutral to all coactions. Its value is thus plotted as the radius of a circle, the zero-zero circle (0,0)." (Cassidy, p 6-7)

2.1 "In the cybernetic analysis of the more complex and organized systems we recognize two distinct kinds of factors. There is the work component or components, which we shall designate by X, and the governor, or controller, which we shall designate Y. Of course, the governor does work too (strategic work), and we have simplified the relationships very greatly. There will be cases of a system made up of sub-systems, one controlling in some respects, not in others, and so on." [p. 5)

3.1 "Now the processes that characterize X may. in the interaction with Y, be accelerated or in some way enhanced C+), or may be unaffected (0), or may be decreased (-). Similarly, the processes that Y undergoes." (p. 5)

4.1 In the four quadrants of the coaction coordinate system, there are the following conditions:

X (0 to +), Y [0 to +3 - X (0 to + ), Y (O to +)

X (0 to -), Y (0 to +) - X (0 to -), Y (0 to -) (p. 7)

8.1 Ignoring the (0,0) coaction (see 1.1, above), the eight remaining coactions fall on axes of the coordinate system or within its quadrants, as follows:

+ * symbiosis - - synnecrosis

+ 0 commensalism - 0 amensalism

* - parasitism - * prédation

0 - allopathy 0 + allotrophy (p. 7)

9.1 When the possibilities indicated (see 2.1 above) are cross-tabulated, it becomes evident that there are nine and only nine of the qualitatively different coactions. In (+, +) both gain. If X and Y represent two organisms, this might be called symbiosis, or mutualism. The relation (+, 0) may be illustrated by the case of an older brother (Y) who, without knowing it (0), sets a constructive example (+) to a younger (X). This may be called commensalism. (Cassidy, pp. 5-6)

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