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Applying Mathematical Insights to Comprehension of World Problems


Challenges in Applying Mathematical Insights
Challenge 1: Feedback loop analysis
Challenge 2: Identification of intersecting feedback loops
Challenge 3: Displaying loop intersect structures
Challenge 4: 2D to 3D transformations
Challenge 5: Public access and participation in decision-making
Challenge 6: Management of electronic messaging streams
Challenge 7: Consensus vs Intractable differences
Challenge 8: Exclusive possession of territory

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The following interrelated challenges derive from ongoing work at the Union of International Associations (UIA) on a number of databases we maintain on an intranet, and publish in hardcopy, or on CD, and increasingly serve dynamically over the web ( The databases are World Problems, Strategies-Solutions, International Organizations, International Meetings, Human Values, Human Development, etc. In each database the number of profile records numbers from 5,000 to 150,000. In total the number of (hyper)links within, and between, these databases exceeds 1.5 million. Many have (hyper)links to external websites. The profiles and links are designed to reflect the conflicting views of a wide variety of consistencies - not an "authorized" version promulgated by the editors in the light of their own research and models. The role of the editors is to "clean up" the information received and insert relevant (hyper)links in the light of information available.

The UIA is an international nonprofit research institute that derives its ongoing income through acting as an information clearinghouse. It was created in 1910 and has been based in Brussels since that time. The challenges identified below relate currently to several contracts, notably one partially funded by the European Commission (DG XIII: Information) and focussing on Problems and Strategies in areas of biodiversity, and another on health and environment.

The UIA databases are maintained through text database software produced by Revelation Technologies and applications written and maintained by UIA. The common file structure has remained essentially unmodified since 1985 through a long series of application upgrades. Increasingly files are maintained through DOS windows on Win98. The data is served dynamically through the Windows version of Revelation (OpenInsight) which is shortly to be available in a Java-oriented flavour - still using the same file structure common to the DOS and Windows versions. The CGI scripts are written in Revelation's flavour of Basic, which is common to both the DOS and Windows versions and will in future interface with plagtform independent jRev (and use of Java Beans).

Some of the earlier points have been outlined in greater detail in a 1994 paper: Clarification of a Mathematical Challenge for Systems Science /mathsys_x_h_1

All the challenges below call for sharper definition in mathematical terms to distinguish between what is feasible with existing maths and what calls for new developments.

Augmenting human intellect: The fundamental importance of interactive graphics, in whatever form, is its ability to facilitate understanding. Progress in understanding is made through the development of mental models or symbolic notations that permit a simple representation of a mass of complexities not previously understood. The challenge is to discover ways of using the computer to augment human intellect and the capacity to comprehend complexity.

Graphics environments for exploring relationship networks: Because of the overwhelming volume of data, it is becoming increasingly clear that conventional means of presenting such data do not respond adequately to the needs of an important category of users. Users associated with the policy elaboration process need new information tools which help them to get an overview of the maze of data. Options need to be presented for discussion in terms of a context of explicitly interrelated issues -- in contrast with the present tendency to disguise this complexity by reducing it to a linear agenda of issues. Users need "maps" of the pathways between text entries, especially in complex subject areas. Such maps provide a sense of context which is lost in many hierarchical presentations of data in linear text form. It is only from such maps that users can quickly obtain an adequate overview of data in an unfamiliar area to guide their efficient use of conventional information tools. Such maps are of value precisely because they are richer than simple hierarchically structured thesauri.

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