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Challenges in Applying Mathematical Insights

to Comprehension of World Problems and Communication amongst International Organizations about Strategic Responses

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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


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

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.

Challenge 1: Feedback loop analysis

In the case of several databases, notably Problems and Strategies, there is an interesting challenge of analyzing feedback/feedforward loops. This concerns situations where, for example, Problem A aggravates Problem B, which aggravates C, which aggravates A; similarly when Strategy A, facilitates B, facilitates C, facilitates A. (see discussion)

Crude programs have been developed by UIA to identify such loops up to the size of 7 links. The question is whether more efficient algorithms could be designed to allow for dynamic analysis in response to user requests -- and of longer loops. Relevant to this question is whether data must necessarily be reformatted, or transferred to separate tables, to facilitate this process. The UIA has not been able to make use of packages designed for network analysis for this purpose, notably because of the limited sizz of the networks for which they tend to designed.

Such analysis is important to assist in determining patterns of redundancy in the link structure, notably in the light of the fact that any Problem, for example, may be nested within one (or more) broader Problems. It is redundant, for example, to indicate links from all narrower Problems when a single link from a broader Problem suffices. Possible errors may be signalled, for example, when many, but not all, narrower problems are indicated as aggravating another Problem.

Challenge 2: Identification of intersecting feedback loops

In seeking to shift the level of analysis from isolated Problems to Problem loops, routines have also been designed to identify intersecting loops, where loops have two Problems in common. Of interest are situations where several loops intersect in this way to define a structure more clearly displayed in three dimensions.

In this process, attention has to be given to situations denoting possible error conditions where loops have more than two elements in common. One question is what kinds of error of this type should be detected. And again the challenge is to be able to identify loops and flag possible errors by more efficient algorithms in response to users queries and editorial changes. More interesting, as explored below, is to see such loops projected as circles onto the surface of a sphere (or possibly a torus) with intersections between loops according to whether differently oriented circles intersect. Of interest in this case is whether the nodes defining the circles can be positioned in (or can define) zones corresponding to their thematic significance.

Challenge 3: Displaying loop intersect structures

The challenge for UIA "hyperlink editors" is how to hold a comprehensible overview of complex conceptual structures, adding or subtracting links from them in the light of new information and flagged potential errors. This comprehension challenge is also that of users (notably policy-makers) in seeking to dialogue about Problem and Strategy complexes.

At this stage the UIA has developed crude routines to identify sets of 3 intersecting loops and display them as mutually orthogonal regular polygons effectively forming a polyhedron. These structures have been generated as VRML files that can be viewed through free plug-ins to Netscape and Internet Explorer browsers. They are suitable to generation on the fly in response to user requests and parameters. The surfaces can be coloured and the nodes (Problems, say) can be turned into hotlinks to descriptive text profiles extracted from the database. The structure then serves as a kind of cognitive map through which the database may be entered and explored. (see demos via see)

Other visual metaphors have been generated under parameter control in the same way to display complex organizations. In particular a spherical metaphor can be generated in which polygons defining the surface of the sphere have been used to denote particular organizations in the system. A solar system model has similarly been used in which each plant is a different Organization in the complex (as in the case of the UN system of bodies).

The challenge in using the spherical metaphor is to identify ways of distributing loops (some of which may intersect) onto the surface of a displayable sphere. Issues in this process are how to position the nodes and lines to avoid (or appropriately code) overlap that is unrelated to actual intersection between loops. This problem has been extensively explored in two dimensions for printed circuit board design. The optimization considerations have also been extensively explored in operations research - designing delivery truck routes. In VRML terms, patterns of intersections define polygons fundamental to the display process.

The challenge may be seen in terms of iterative "massaging" of the loops into the most uncluttered configuration. For display purposes a distinction might be made between "local" loops restricted to particular portions of the surface and "great circle routes" effectively circling the sphere. Users might wish to turn off display of local loops or highlight great circle routes. (In two dimensions the display problem can be described as that of designing an algorithm to take subway stations and lines linking them, held as nodes and links in a database, and design comprehensible maps - but to do this in three dimensions).

The purpose of this exercise in "cognitive geodesics" is essentially one of comprehension of complexity relating to interlinked thematic topics. Thus, also of interest is the possibility of constraining nodes or links into predefined areas on the sphere corresponding to themes (environment, security, etc). Alternatively these zones might emerge as a result of the massaging process or exclusions made by user choice (excluding thematic "continents" from a global representation).

The UIA has briefly explored display of data using a powerful package for analyzing transactions. NETMAP is a e package that analyzes very large and complex networks of relationships and presents the result in a special circular graphic form. The approach permits new patterns of relationship to be discovered between people, organizations, or problems. Users can interact with the display to obtain more or less detail, or derive displays based on other criteria. It offers unique possibilities for navigating through hundreds of thousands of entities and relationships whilst retaining both a sense of context and without loss of detail.

See also discussion in:

Challenge 4: 2D to 3D transformations

Much conceptualization of international Problems and Strategies is undertaken through what are effectively two-dimensional frameworks typically portrayed as lists or tables. There is a heavy investment in related displays as typified by menu design on the web. Of interest therefore is the ability to transform 2D displays into 3D displays such as to hold the relationships between the parts but, hopefully, to open up new degrees of freedom. There is also a corresponding need to collapse a 3D display into 2D to facilitate certain modes of communication constrained by less-costly technologies.

This transformation has been explored by the UIA, notably in relation to the issues of the Rio Earth Summit of 1992. The cognitive contents and relationships of a 2D matrix was displayed on the net diagram of a regular polyhedron which could then be folded up into 3D. This transformation can be considered as conceptually linked to the challenges identified above. (see discussion and figures)

Of special interest is the way in which the polygons can be understood as defining dialogue arenas. These may be treated as isolated to the disadvantage of effective policy-making. They may also be treated as feeding into each other where the sides are effectively part of feedback loops. Such 2D and 3D structures therefore hold understanding of necessary relationships between distinct dialogues. The 3D variant provides a sense of integration that is absent in the 2D variant that has to be folded up to lock its external links into place. Such links could be used as a guide to controlling electronic communication protocols between participants in large groups.

Challenge 5: Public access and participation in decision-making

Central to the widespread current debate on "civil society" is the question of public access to decision-making arenas relating to thematic areas. This is as true within a country where the focus is on access to government decision-makers, as at the international level where the concern is with access to international decision-making. In the latter case the focus may be on "NGO access". These lobbying and representation issues are all modern equivalents of the ancient pattern of "petitioning the sovereign" - as most recently seen when 4 million Jordanian citizens were accorded the right to personally greet their new king.

There is an intriguing mathematical challenge associated with the public participation and access processes now enshrined in a new international convention (Aarhus, 1998). There is little challenge for 10 bodies (or less) to seek representation before a decision-maker or a decision-making body - whether for an address, to have a personal interview, or to distribute position papers or other messages. And there is little challenge for the authority to receive such numbers.

However the situation changes radically as the numbers increase. It is significantly different when there are 100, 1000, 10,000, 100,000, 1,000,000, or 10,000,000. It is estimated that there are 10,000 lobbyists in Brussels, for example. UN-ECOSOC is in transition from 1,000 to 10,000 NGOs seeking access, as is UNESCO.

On the decision-makers side, the response to such pressure for access may be handled by various techniques:

The process may be rationalized by encouraging petitioners to form clusters and coalitions so that they make collective representations rather than individual ones. This may well be perceived as restrictively manipulative by one or both sides.

The challenge is to find fruitful ways of modelling (and simulating) this democratic access problem in order to move beyond the request for simplistic solutions that primarily accord advantages to the skilled and the well-resourced - and notably ignore vulnerability to questionable techniques of facilitating / privileging such access that have long been developed by business. The focus would be on filters, switching messages, topics and diversity of topics, degree of transparency, and quantitative constraints on limited attention resources. Any simulation should facilitate testing for abuse of access processes.

For the future, aspects of this challenge might be understood in terms of increasing the sophistication with which e-mail communications are filtered and channelled into a governmental system. This means:

Challenge 6: Management of electronic messaging streams

In some electronic conference situations there is a need to ensure that the sequence of input messages builds into a pattern of coherence. It is such a pattern that then represents the meaningful synthesis of exchanges between participants. At present many conferences suffer from inability to make much sense of the continuing flow which may contain many valuable insights that are easily lost. New participants may be obliged to read a large backlog of communications in order to develop a contextual understanding enabling them to contribute appropriately.

This raises the question of how to structure such a synthesis in practice without losing the value of a free-flowing exchange through "heavy" facilitation. Many groupware packages are now being developed to facilitate collaborative exchange. The purpose of this note is to look at ways of using existing web facilities -- and others to be envisaged -- to respond to this challenge.

Web pages could be used in a non-conventional manner, as follows, by distinguishing different "levels" (Levels 1 to N) of synthesis or coherence -- but without impeding the free-flow of contributions a t the "lowest" level (Level Z). Note that this approach could even be applied independently of any involvement (or knowledge) by contributors at Level Z. In the field of documentation, such such synthesizing functions are performed to some degree by indexers and writers of "abstracts". In many physical conferences they are performed by "report" writers and compilers of "communiqués".

See further discussion in: Towards a web framework for synthesis in dialogue: insight capture from the flow of conference interventions 1996 (74k)

Challenge 7: Consensus vs Intractable differences

Implicit and explicit in relation to the above challenges is how consensus is to be usefully understood when dealing with requisite variety (intractable differences, or incommensurable criteria), typical of competition for resources and moral high ground within the international community. This challenge is actually implicit in an interpretation of the title of the Union of International Associations. Where "associations" are understood as links, "international" implies across some conceptual boundary, and "union" has the significance best understood in symbolic logic. In society as a whole however "consensus" needs to be enriched by mathematical insights into the richer ways in which the integrity of a whole can be recognized.

Consensus does not have to mean everybody subscribing to the same set of things or to the same strategy - this single-factor approach needs to be understood as a simplistic limit condition. More interesting is to be able to articulate, and render comprehensible, frameworks in which this limit condition is apparent as an option (or perspective legitimate for some) but in which other forms of "agreement" may effectively maintain the integrity of relations between a set of elements. For example it is unnecessary for everyone to subscribe to A if they subscribe to B or C, provided that B and C in some way follow from A - in ways that those subscribing to B and C may not choose to recognize. Complex patterns of integration can be constructed through limited allegiances of this form. The question then becomes how to hold such patterns so that the perspective from B or C, seemingly incompatible, can be legitimated.

This challenge raises interesting questions of perspective and horizon effects on a surface onto which cognitive maps of distinct groups are projected. What is the complex surface which legitimates zones that each have reason to argue that their own perspective is unique and "correct" -- and that other perspectives are necessarily "incorrect" -- in the same way that the globe serves to justify simultaneously contradictory statements about the position of the sun?

These questions are notably of relevance to the (meta)organization of dialogues and sets of dialogues, especially those based on electronic communications involving a range of inter-sectoral, interdisciplinary or inter-faith issues with participants having different knowledge bases.

Aspects of the associated challenges for comprehension and communication have been explored in:

Challenge 8: Exclusive possession of territory

Many dramatically severe problems for the international community are associated with how property (territory) is understand to be held or possessed. The approach universally taken by those involved is that either the territory belongs to A or to B and many conflicts arise from competing exclusive claims. This "exclusion principle" approach is about the simplest that it is possible to take in mathematical terms. It would be good to have richer approaches on the table even if they are systematically ignored.

The most concrete example of a more complex approach is that based on the condominium formula used for half a century by the governments of France and the UK as co-sovereigns of the Anglo-French Condominium of the New Hebrides (1914-1980). The two governments governed the territory through parallel administrations. A number of countries continue to use parallel systems for religious and secular litigation. In such cases it could be said that the same territory is held by the two in defiance of the exclusion approach. Other examples may be seen in the case of multiple passport holders effectively entitling a person to two or more distinct nationalities.

The challenge is to articulate richer ways in which a single territory may be held by two (or more) parties. Possibilities include subdividing the territory, alternation of responsibility for a territory (using a variety of time-based techniques), allowing people to hold one or other (or both) nationalities on the same territory, or more complex patterns.

The formula should be on the table for discussions relating to Kashmir, Kurdistan, Northern Ireland, Kosovo, Macedonia, Cyprus, Sudan, Burundi, Sri Lanka, Gibraltar, Malvinas, Taiwan, Palestine/Jerusalem, etc.

See also discussion in:


Anthony Judge:

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