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Examples of Integrated, Multi-set Concept Schemes

Annexes to Patterns of N-foldness


The concept schemes identified here are 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). They were published in Patterns of Conceptual Integration. Brussels, UIA, 1984, pp. 161-204 [searchable PDF version]

Each concept scheme is the subject of an Annex listed below. The items within each Annex are ordered according to the number of set elements. This number is given as that portion of each (non-zero) item number before the decimal. The number after the decimal is a sequence number of no significance.

It should be stressed that the exercise is tentative and experimental.

Order within Annexes

Following the brief introductory references to the work[s) from which the items within each Annex were obtained, the items are ordered sequentially by a numeric code structured as follows:

Number before decimal
  • when 0 signifies: general contextual extracts
  • "non-zero" : number of elements in the concept set described in that extract.
Number after decimal
  • used to separate and sequence extracts with the same initial number;
Order of items within such groupings is not significant, except that occasionally related items have been placed together, especially for contextual extracts. Example: 12.2 indicates, the second extract containing information on a concept set of 12 elements. Some references to annex material in the introductory paper are made in the form 17.12.2, meaning Annex 17, item 12.2.

Extract criteria

The extracts within each of the following Annexes were selected in the light of the following considerations:

General contextual extracts (prefix 0)

  1. Brief indication of the general approach.
  2. Remarks touching on the problem of comprehension.
  3. Remarks concerning the use of number or geometry as an ordering aid.

Concept set extracts (non-zero prefix)

  1. Any clear identification of a complete set generally indicated by a reference to a number of elements.
  2. Duplicate references to the same set were included when this might assist comprehension of the set,
  3. Sufficient contextual material was given, when available, to assist comprehension of the significance of the set within the concept scheme.
  4. Extracts which seemed of questionable interest were included if there seemed some possibility that they might later prove to be of signi ficance in relation to corresponding extracts in other annexes.

In general, the extracts were selected in the spirit of a "data gathering exercise", namely they might (or might not) prove to be of interest in continuing, this investigation.

Annexes

  • Annex 0: UNU/GPID Project: It is appropriate to employ the same presentation method to the GPID concept scheme as it is now emerging.
  • Annex 1 : Geometry of Meaning: This is a modern effort to order a complex pattern of information on change and development in the light of physical concepts of dimensionality and control.
  • Annex 2 : Book of Changes : This is the 3000-year old Chinese I Ching which is conceived as encoding the complex pattern of changes in physical and social phenomena. It has been of considerable interest to Leibniz (philosopher), Jung (psycho-analyst)and western mathematicians, and its poetic expression has proved highly acceptable to a segment of western society.
  • Annex 3: Catastrophe theory: This is a new controversial way of thinking about change in all kinds of phenomena in the light of the mathematics of differential topology.
  • Annex 4: Tibetan Buddhism: This is a highly structured traditional scheme of concept sets which, because of both illiteracy and the absence of paper, uses powerful imagery to facilitate memorability and communicability,
  • Annex 5: Genetic code: This recent fundamental breakthrough in the biological sciences groups a number of concept sets in a highly integrated pattern.
  • Annex 6: Chinese Communist terminology: This is included because it illustrates the importance, in one major non-western political system of concept sets governed by number.
  • Annex 7: Tonal patterns of Rg Veda chanted poetry: The Rg Veda is, in terms of survival over 4000 years, the most successful active communication vehicle. The concept scheme interlinks many concept sets in a very powerful way.
  • Annex 6: Movement and dance notation: This concept scheme is one of the most widely accepted frameworks through which understanding of dance is ordered.
  • Annex 9: Chinese art of war: This traditional scheme is even now considered basic to ordering perceptions of strategy and tactics.
  • Annex 10: Art of colour: Artists achieve certain visual effects by selecting intuitively amongst a range governed by a perceptionoriented concept scheme distinct from the colour preoccupations of physicists and chemists.
  • Annex 11: Islamic cosmological doctrine: As in the case of Tibetan Buddhism, this concept scheme has been of special significance to Islamic culture for an extended period.
  • Annex 12: Language and transformational-generative grammars: Language itself should be rich in concept schemes which are themselves a form of language. This Annex, unlike the others, considers aspects of current thinking which have rendered superficial the traditional concept sets in this area.
  • Annex 13: Thermodynamics: This fundamental discipline is concerned with the description of change in physical processes. It has been applied by analogy to social processes. Its pattern of concepts is very well integrated. Unlike the other concept schemes, the concept sets are not explicitly set out. An attempt is made in this Annex to show how they might emerge for comparison with other schemes.
  • Annex 14: Periodic classification of chemical elements: This fundamental scheme is included because of the comprehensibility of the pattern governing the complexity of the information ordered.
  • Annex 15 : Systematics: This modern scheme, formulated by a philosopher- mathematician, is includstematics: This modern scheme, formulated by a philosopher- mathematician, is included because of the variety of phenomena it encompasses and the leads it offers to understanding number-governed patterning complexity.
  • Annex 16 : Periodic coaction coordinate system: This ambitious modern scheme is included because it Durports to order patterns of interaction in a variety of complex systems.
  • Annex 17 : Synergetics; geometry of thinking: This highly original and well- integrated scheme is included because of the multiplicity of concept sets it includes and the leads it provides as to how transformations between them may be accomplished.
  • Annex 18: Polygons and polyhedra: This Annex indicates the sets of polygons and polyhedra. It is significant in the light of the previous Annex as indicating how set elements can be interrelated in an integrated whole.
  • Annex 19: Topological features of polyhedra: Again, in the light of Annex 17, the number-governed sets associated with this material offer useful indi cations as to how such sets are interrelated in patterns.
  • Annex 20: Chladni patterns: This is included as a systematic study of the range of patterns arising form the vibration of a surface area. It is significant in that it indicates how a zone is "broken up" into sub-zones.
  • Annex 21: Levels of declarations of principles: This is a separate experiment in articulating principles based on different numbers of elements. (Although originally published with the other annexes, it formed the topic of a separate paper)

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