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Clarification of a Mathematical Challenge for Systems Science

Paper prepared for the Annual Meeting of the International Society for Systems Sciences (Amsterdam, 1995)

Preliminary analysis
Clarifying the larger challenge
Related issues
Further clues

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Data has been collected and partially ordered on some 12,000 'world problems' as perceived by the universe of international organizations. The unique feature of this data set is that some 120,000 relationships have been identified between such problems -- effectively constituting a complex network of systemic relationships. The data is published as part of the Encyclopedia of World Problems and Human Potential (1994).

The partial ordering of the data has taken the form of distinguishing hierarchical relationships between problems where possible, namely establishing relationships to those which are more general ('broader') and to those which are more specific ('narrower'). A given problem may however point to several more general ones. Where such identification of levels seems questionable, problems may simply be identified as 'related' to others. Clearly broader/narrower and related/related relationships are reciprocal.

From a systemic perspective, of greater interest are other relationships whereby a given problem is identified as 'aggravating' one or more other problems. These too are reciprocated through 'aggravated by' relationships. There are some 30,000 aggravating relationships. Also of interest, but rarer, are cases of problems 'reducing' other problems, and in turn being 'reduced' by others. These may be seen as different types of feedback loop.

The question of interest concerns useful ways of analysing the data, especially that on aggravating relationships. There are several reasons:

  • the data is prepared through what amounts to a hypertext editing process that can generate redundant relationships which it is difficult to identify in a linear editing environment; more powerful techniques are required to identify them
  • even when redundancies are removed the resulting network is exceedingly complex and does not lend itself to visual inspection, especially when local properties of the network (in systemic terms) may be easily confused with global properties of greater significance
  • since it represents a global system of relationships, it is useful to ask in what way may the network be manipulated, preserving its topological properties, in order to render its global properties more comprehensible.
ological properties, in order to render its global properties more comprehensible.

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