Representation, Comprehension and Communication of Sets: the Role of Number (original) (raw)

1978

Abstract and Contents

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Reproduced with the permission of the Secretary of the Commonwealth Science Council (CSR) by whom it was originally commissioned. Presented to a meeting on forms of presentation of the Goals, Processes and Indicators of Development (GPID) project of the United Nations University (Geneva, October 1978). Originally published in 3 parts in International Classification, 5, 1978, 3, pp. 126-133; 6, 1979, 1, pp. 15-25; 6, 1979, 2, pp. 92-103. Also published by the United Nations University as working paper HSDRGPID-22/UNUP-133 in 1980 [also searchable PDF version]

Abstract: Examines the cognitive and other factors which tend in practice to limit the number of elements distinguished in a set, particularly for sets fundamental to social science and policy formation, such as: human needs, values, principles, problems. It is argued that the number of elements so distinguished influences significantly both the relationships perceived between the elements and the qualitative characteristics manifested by them, irrespective of the content of the set. Such effects are important in the case of the more abstract sets for which the ambiguity of verbal descriptors creates considerable problems of comprehension and communication, especially when the set of elements is used as the basis for the elaboration of a group of cooperating institutions. The representation of such sets in traditional symbol systems and in modern 2 and 3-dimensional forms, is reviewed both as a source of constraints on set formulation and as a guide to the formulation and comprehension of the more complex sets through which the problems of society can be better contained.

Contents

1. Introduction
2. Context
3. Constraints on number elements in a set
4. Representation of sets: introductory comment
5. Representation of sets: review of types

1. Lists
2. Thesauri
3. Tables/Matrices
4. Diagrams
5. Yantras/Mandalas
6. Other techniques
7. Three-dimensional constructs
8. Mathematical notations

6. Involvement of the observer/creator of the set

1. Introduction
2. Laws of form
3. Logical "curvature"
4. Self-reference and time
5. Number and time

7. Number and logic

1. Beyond 2-term mogic: multi-term systems
2. Logic of inter-paradigmatic dialogue
3. Number and N-term systems

8. Comprehension and number

1. Problems of comprehension
2. Comprehension, remembering and mnemonic aids
3. The quagmire of number symbolism: the past
4. The quagmire of number symbolism: the present
5. Encyclopedic memory systems
6. Augmented comprehension
7. Convergence of concept triangle elements: a limiting condition

9. Qualitative characteristics of sets

1. Characteristics of multi-term systems
2. Clarification of specific sets

10. Representation of multi-term sets

11. Implications

Annexes 1. Clarification of terminology
2. Example of an elaboration of a number-based sequence of systems
3. Clarification of specific sets
4. Symbol generation
Notes
References