Challenges in Applying Mathematical Insights
to Comprehension of World Problems and Communication amongst International
Organizations about Strategic Responses
- / -
: Feedback loop analysis
: Identification of intersecting feedback
: Displaying loop intersect structures
: 2D to 3D transformations
: Public access and participation in decision-making
: Management of electronic messaging streams
: Consensus vs Intractable differences
: 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 (http://www.un-intelligible.org/docs/overview.php#orga).
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
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
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
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
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
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:
Spherical Configuration of Categories: to reflect systemic patterns of
environmental checks and balances 1994 (https://www.laetusinpraesens.org/docs/catspher.php)
Visualization: Graphics environment for exploring relationship networks
Visualization: Network maps (more)
Visualization: Holistic network mapping using NETMAP (more)
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:
Selection and filtering to limit the numbers (with some appropriate rationalization)
Personal "one-to-one" contact (or delegation of such contact to several
Group "one-to-many" contact (collective briefings and consultations): potentially
limited to 1,000 people, although extendable through video conferencing
and "fire-side chat" techniques
Serial representations (succession of presentations by NGOs to intergovernmental
assemblies): heavily constrained by agendas
Distribution of position papers to decision-makers: heavily constrained
by the quantity of reading matter to which each such person is exposed
E-mail or equivalent contact: again heavily constrained by overload, but
much more easily managed through filters and standard responses or automatic
onward forwarding to "more appropriate" respondents
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:
Supplying petitioners with topic keys to trigger such filters
Identifying patterns of message redistribution to appropriate responding
units, in the light of the pattern of Problems or Strategies with which
the agency is dealing
Determining under what conditions, and from what point, to respond automatically
with a standard "blocking" message of acknowledgement
Determining possibilities for responding automatically with a proactive
message requiring further input from the petitioner to elicit further response
Determining under what conditions messages should be channelled into a
listserver / discussion forum from which some form of consensus is required
before the views can be taken into account
Determining how to detect and monitor various ways of abusing the resulting
system and to report on such abuses transparently
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
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:
- Discovering richer patterns of comprehension to reframe polarization
1998 (67k) [text]
- Spherical configuration of interlocking roundtables: electronic enhancement
of global self-organization through dialogue patterns 1998 (43k) [text]
- Reframing relationships as a mathematical challenge: Jerusalem as a
parody of current interfaith dialogue 1997 (22k) [text]
- Envisaging the art of navigating conceptual complexity 1995 (47k) [text]
- Towards a web framework for synthesis in dialogue: insight capture from
the flow of conference interventions 1996 (74k) [text]
- Clarification of a mathematical challenge for systems science 1994 (17k)
- Configuring strategic dilemmas in intersectoral dialogue [text]
- Analysis: vicious cycles and loops [text]
- Comprehension: social organization determined by incommunicability of
- Distinguishing levels of declarations of principles [text]
- Representation, comprehension and communication of sets: the role of
number 1979 (130k) [text]
- Spherical Configuration of Categories: to reflect systemic patterns
of environmental checks and balances 1994 [text]
- Visualizing relationship networks: international, interdisciplinary,
inter-sectoral 1992 [text]
- Visualization: Graphics environment for exploring relationship networks [text]
- Visualization: Network maps [text]
- Visualization: Holistic network mapping using NETMAP [text]
- Coherent organization of a navigable problem-solution-learning space
1996 (23k) [text)]
- Sustaining the coherence of dialogue through apartness; patterns of
systematic configuration of entities through
hypertext 1997 (26k) [text)]