Examples of Integrated, Multi-set Concept Schemes
Annexes to Patterns of N-foldness
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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
. 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
Number after decimal
- when 0 signifies: general contextual extracts
- "non-zero" : number of elements in the concept set described
in that extract.
Order of items within such groupings is not significant, except
that occasionally related items have been placed together, especially for
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.
used to separate and sequence extracts with the same initial number;
The extracts within each of the following Annexes were selected in the light
of the following considerations:
General contextual extracts (prefix 0)
Brief indication of the general approach.
- Remarks touching on the problem of comprehension.
- Remarks concerning the use of number or geometry as an ordering aid.
Concept set extracts (non-zero prefix)
- Any clear identification of a complete set generally indicated by a reference
to a number of elements.
- Duplicate references to the same set were included when this might assist
comprehension of the set,
- Sufficient contextual material was given, when available, to assist comprehension
of the significance of the set within the concept scheme.
- 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.
0: UNU/GPID Project: It is appropriate to employ the same presentation
method to the GPID concept scheme as it is now emerging.
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.
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.
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
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,
5: Genetic code: This recent fundamental breakthrough in the biological
sciences groups a number of concept sets in a highly integrated pattern.
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.
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
6: Movement and dance notation: This concept scheme is one of the
most widely accepted frameworks through which understanding of dance is
9: Chinese art of war: This traditional scheme is even now considered
basic to ordering perceptions of strategy and tactics.
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.
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.
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.
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.
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.
15 : Systematics: 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.
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.
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.
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.
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.
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"
- 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