Challenges to Comprehension Implied by the Logo
of Laetus in Praesens
University of Earth Alternative view of segmented documents via Kairos

14 January 1997

Sustaining the Coherence of Dialogue through Apartness

Patterns of systematic configuration of entities through hypertext

- / -

A. Patterns of cognitive coherence
B. Category organization
C. Organization of web pages
D. 'Knitting' a configuration together
E. Speculative conclusion


Information overload has been a concern for many years. With the advent of Internet and the Web, concern has increased. The problem has been directly related to stress in managers and managerial ineffectiveness. It has resulted in dangerous over-simplification of issues to maintain a semblance of effective governance. The significance for the further fragmentation of knowledge is as yet unclear -- although concerns about the effectiveness of educational systems is now widespread. It is however clear that the ease with which people can now 'surf' through documents disguises inability to absorb the content of individual documents and to assemble insights from a set of hyperlinked documents into a meaningful whole. To this extent, learning is therefore inhibited rather than augmented -- as was proclaimed as the promise of such facilities. Integration of knowledge across disciplines, however vital, runs the risk of becoming a hopeless cause.

Electronic mail and software-supported conferencing have increased tremendously the potential for dialogue around the world. They have also increased the possibility of junk mail and spurious interventions in electronic conferences. It cannot yet be proven that software helps to increase the significance of a conference beyond what is possible in face-to-face mediated settings. Most electronic dialogues meander with little sense of their own historic message trail and with little, if any, pattern of cross-referencing between comments. There is little sense of integration or the emergence of any higher conceptual order.

Many commentators have indicated that the Web is just in its infancy. Many new tools are being rapidly developed to search the millions of websites automatically. Tools are available to test and map the integrity of hyperlinks within and between websites. Groupware is considered a vital software growth area. Mind-mapping software is available and is being further developed. This paper explores a further extension of some of these techniques.

A. Patterns of cognitive coherence

In designing a website, stress is conventionally placed on the importance of a suitably hierarchical structure. This is normally associated with the use of sub-directories, possibly to many levels. This procedure makes good sense in terms of the administrative task of maintaining a website. Beyond simple division into topic areas, this does not however address theissue of the cognitive coherence of the pattern of linkages between the documents so ordered and the meanings these should ideally convey -- especially when the hyperlinks transfer the user between different topic sub-directories, or to other sites. There is a marked tendency for hyperlinks to meander in a variety of directions. In theory a user could 'surf' on and on across an infinite plain of hyperlinks. This paper is concerned with how meaning might emerge from such journeying if closed curvature was a feature of the pattern of hyperlinks. It follows from an earlier paper on the possibility of a spherical organization of categories.

Trivial examples

As an introduction to what follows, consider three trivial examples:

Triangular pattern

More complex is the case of a set of three documents. Several situations may arise. 

This case is far from being as trivial as it may appear. The comprehension challenge of a communication triangle has in fact been the subject of extensive commentary by mathematician Ron Atkin:

A user may be able to follow the argument of Document A but be unable to understand the relevance of the hyperlink to Document B. This reduces experience of the geometry to the equivalent of the first 'trivial' example -- whether or not the user clicks mechanically on to the second or third document and understands its content in the same way.

A user may be able to follow the conceptual significance of the hyperlink pathway from one document to the next, but have no sense of the triangular significance structure soframed. It is as though the pathway was a tunnel which provided no overview of the triangular geometry. In effect the user is reduced to the geometry of the second 'trivial' example.

Finally the user may indeed be able to hold the significance of the triangular pattern as a whole, as a gestalt. In effect this triangle then becomes a basic learning module.

Regular (symmetrical) structures

Further exploration of hypertext pathway configurations can usefully start with the geometry of the Platonic solids. These are the most primitive 3-D approximations to a sphere. They are also the most readily comprehensible because of the symmetry and regularity. The surfaces are defined by polygons, notably triangles (by which other polygons may be constructed).

The five cases which follow (tetrahedron, octahedron, cube, icosahedron, dodecahedron) are of increasing complexity and exhaust the set of Platonic solids (Figures 1a to 5a). In this exploration the vertices are considered to be documents and the edges are the hypertext links between them. The resulting conceptual sets are best understood from the pattern of hypertext links between them (Figures 1b to 5b). Another way of seeing them is through the net diagrams derived from rolling the solids across a surface (Figures 1c to 5c), although the hypertext links are duplicated in this representation.

The succession of cases raises the question what kind of gestalt emerges at each stage. If, for example, 8 concepts constitute a set that needs to be understood as a gestalt (a macro-concept), are the hypertext links between them appropriately mapped by a cube? How can the pattern of hypertext links be usefully traversed to get a sense of the gestalt? Is there an order to the learning journey represented by the cubic structure as a whole?

Also of great interest is the way in which the hypertext links are increasingly restricted to the periphery of the structures, as these increase in complexity. The centre is increasingly unoccupied because the links are between contiguous, or near-contiguous, documents. The more complex structures therefore hold understanding of macro-concepts or learning modules in which there are distinct discontinuities between non-proximate documents. It is essential to go through certain documents to understand the relevance of the more distant documents to which these are linked. This confirms the need to acquire understanding of some concepts before understanding their relevance to others. Nevertheless the pattern of links loops back on itself as a framework for the gestalt. There are multiple entry points to the gestalt, but no particular exit point.

Coherence, Apartness and Circuits

Can stages in coherent understanding be usefully represented by such hyperlinked structures of lower-level understandings? The sequence of structures of increasing complexity is alsointeresting because of the degree of distance between concept documents in a structure. In the more complex structures some documents are quite distant from others. Their apartness is significant to the ability of the structure to hold variety. Apartness is effectively a measure of variety.

One of the challenges of the Internet and of e-mail systems (especially in the case of Intranets) is the ability of everything, and everybody, to be linked to everything else. This leads directly to overload and may be perceived as anarchy, however much such communication is extolled as a democratic ideal. It does not lead to insight however democratic it may appear. The understanding of total togetherness implicit in the truism 'everything is linked to everything' undermines any integrative insight. Diversity can only be held by appropriate apartness. The structures identified above suggest a way of exploring appropriate apartness through which higher order concepts can be held and sustained in any learning module or in an ongoing dialogue.

The sequence of structures may suggest that the more apartness than can be built into a structure, the greater its ability to carry disparate insights coherently -- unity within diversity. The structures may be seen as conceptual gene-pools (meme-pools) of different complexity. However such structures then constitute an increasing challenge to comprehension, however well particular sub-elements may be understood.

A learning module may be usefully understood as made up of sub-modules that lock together. The sub-modules (partial learnings) can be related to the hyperlink pathways which constitute sub-circuits -- often triangles, squares, hexagons or regular polygons. It is these learning circuits which, as circuits, are necessarily self-reinforcing.

Perhaps more interesting than the 'local' circuits, to be found binding together particular segments of the periphery, are the circuits which effectively traverse the structure as a whole. These are the different hyperlink pathways around the periphery. Structurally they relate to the 'great circle' pathways around any spherical representation of the original solids. A minimum of three such pathways is required to maintain the integrity of a structure. Maybe it is such 'Grand Tours' which T S Eliot's famous phrase best describes: '...discovering it for the first time...'.

What is intriguing about this approach is that it points to the value, possibly even the necessity, of working with structures in which total transparency is not available from any point. Rather there is a sense of opaqueness, accompanied by a recognition that this would disappear from a different perspective (at the expense of losing the clarity of the current perspective). In a complex dialogue, this would reflect the ability of different people to hold the understanding essential to particular threads of the discussion.

B. Category organization

Since the emphasis here is on the cognitive challenge of representing and understanding complexity, this issue with regard to category organization is how to divide up the universe of knowledge. Ideally the user should be able to move between a representation based on 3, 4...8, 10...30...N categories -- to 'zoom' through levels of complexity.

This raises the question, addressed in an earlier paper, of how to present the user with N categories, notably if the user has particular views on how knowledge should be spread across categories. Sets of predefined categories, for a given N, may be offered to the user, or the user may adapt any one of these sets, or introduce a new one.

In this context each category would be associated with a document (or with a hierarchically organized set of documents). The focus of this paper is on the representation of the relationship between such categories.

C. Organization of web pages

In earlier papers on the spherical organization of categories, the emphasis was placed on the actual visualization of any such sphere. Whilst this is increasingly feasible in a Web environment, it demands a higher order of technology than many currently possess. There are also some special algorithmic challenges to be dealt with. Much of interest may however be accomplished by ensuring the 'spherical' organization of the hyperlink pathways, without actually having to visualize the structure mapped out by the configuration of pathways. Visualization can then be an optional additional feature.

One approach to configuring hypertext documents is now discussed. It arises from the challenge of finding meaningful ways to organize the web addresses (URLs) of increasing numbers of international organizations (currently 1,300), currently classified into some 800 subjects. As of January 1996 these are clustered under 100 categories, ordered by an 'integrative matrix' originally inspired by the ICC system of Ingetraut Dahlberg (see).

The following discussion takes into account the possibility for the user of shifting between category sets composed of different numbers of categories.

1. Configuration-N Web pages

If N was 20, this would give rise to a web document containing information of the form:

Each of these lines would provide hyperlinks to individual pages with content appropriate to each category, as follows.

2. Category-N/M Web pages

For a given category, say medicine, there would be a page, providing title information (eg Medicine) plus synonyms or keywords (including non-English variants). Formally the page would be Category-20/19 in this example. 

The actual content of the page would in this example be the URLs of international organizations clustered under that category. Users could then hyperlink to the relevant websites.

Clearly there would be a total of 20 pages of this type.

3. Overview Web page

This page would list out the Configuration-N pages, where N might run from 3 to 100 or more. Each line of the page would provide a hyperlink to an individual Configuration-N page (described above). It is from this page that the user would choose through how many categories the universe of knowledge was to be viewed.

4. Overview table

Of greater importance to those concerned with the organization of knowledge would be the information in the following table. For each topic or subject (arbitrarily numbered), this indicates where it is allocated within different configurations. Namely if N is 4, under what Category-4/? is Medicine to be found, or if N is 56, under what Category-56/? is Medicine to be found.

  Config-10 Config-12 Config-48 Config-56
Topic136     48/16 56/23
Topic7     48/16 56/9
Topic291     48/5 56/23
Topic58     48/39 56/8

It is also possible to present this page as a Web table and to enable a user to click on:

The special challenge of this page is how to distribute knowledge relating to a given topic between cells corresponding to a particular subdivision of the universe of knowledge. In effect this table defines a kind of conceptual 'gear box'. It wouldrequire continuing comment and review.

5. Topic-X pages

Within the above framework, each topic is 'stretched' or 'constrained'. This requires a context within which to comment on the semantic significance of the placement of the topic within any particular Configuration.

This commentary would be presented on a Web page for the topic (eg Medicine313, where 313 was an arbitrary topic number attached to a label of purely indicative significance). On this page there would be commentary on Medicine313-4/48, Medicine313-23/56, etc, as required. Each of these would provide a hyperlink to the relevant Category-N/M page (described above). Ironically, presented in the form of subscripts and superscripts, such topic descriptors might then be termed 'iso-topics' because of similarities of the notation to that of isotopes.

6. Topic index page

This page of alphabetically ordered topics would provide a user with a way of hyperlinking to the Topic-X pages (described above). Note that this would provide users with access to topics which might easily use the same descriptor, although having quite distinct significance. They would appear as, for example, Medicine313 and Medicine512.

D. 'Knitting' a configuration together

The first part of this paper has discussed the importance of configuring categories into structures. The second part has discussed the practicalities of presenting such information on Web documents. This can be usefully undertaken independently of the requirements of the first part. 

Missing so far is any discussion of how, once a decision has been made to work with a configuration of say 20 categories, the Category-20/M pages should then be interlinked or 'knitted' together into the kind of structure described in the first part of the paper. This might possibly be a dodecahedron of 20 categories, since it has 20 vertices.

In the case of these 20 categories, how are the hyperlinks between the respective documents of Configuration-20 to be determined? Note that this is not a question of hierarchically ordered information, which might indeed be provided by other types of hyperlink from any given document. The question concerns the relationships between 'peer' categories, notably of a cross-disciplinary nature.

The science of allocating such links is poorly developed. These links are most obvious in the systemic relations within complex systems, whether in nature or in processing factories. They are also evident in the functional relationships between divisions of complex organizations -- not the hierarchical relationships portrayed in organization charts. They are also characteristic of learning pathways, where Category A must be understood beforeCategory B and C, which together then constitute a learning sub-module through which Configuration 20 (say) may eventually be understood as a gestalt. The Union of International Associations has embodied a very large number of such horizontal 'functional' relationships into its Encyclopedia of World Problems and Human Potential (notably as hyperlinks on the CD-Rom version).

The issue here is not the insertion of such links but rather the insertion of particular links between categories, configured according to a pattern described in the first part of this paper. This might be termed a constrained mapping exercise. How are categories to be positioned in relation to one another so as to fit onto such a structure? Which categories should be considered proximate and which distant in any given case? Clearly this is a matter of further experiment for which HTML documents provide an ideal environment, whether on the Web itself or on a local computer.

One web-based experiment along these lines, undertaken by the author, involves provision of hyperlinks between pages for each of the 64 hexagrams of the Chinese I Ching. Each page has six basic links to some other document in that conceptual scheme according to the rules of that system. Together these constitute a framework of 384 transformational links.

E. Speculative conclusion

This paper moves between structural hypotheses, organization of categories and the practicalities of the organization of documents on the Web. The essential feature is the challenge to comprehension and provision of an appropriate vehicle for higher conceptual orderings. It offers an interface between what a user can easily know and what may prove a major challenge to understanding.

As a basis for further experiment the cognitive aspects of this approach suggests a number of interesting lines of research. It might be used to map living systems, whether species interactions in ecosystems in nature or interactions between roles in a human community. The emphasis here is less on the 'systemic' dimension and more on how to approach any understanding of what sustains the 'life' of such systems. 

The approach might also be used to provide a framework for disagreement in continuing conflicts, such as over Jerusalem, involving intractable parties. Since it avoids simplistic commitment to 'agreement', and endeavours to embody discontinuity, it may prove more capable of holding a higher degree of diversity than much explored 'agreement-systems' ('getting to yes'). Aspects of this have been explored in earlier papers on tensegrity, which relates to the construction in practice of the kinds of 3-D structures discussed in the first part of this paper. It may offer a new approach to 'squaring the circle'.

More a symbolic perspective, some of the figures presented suggest possibilities of their functional equivalence to easternyantras and mandalas, to the enneagram, or to use of pentacles in the western magical tradition, even to the ourobouros. Some figures recall symbols based on 'unfolding' petals of insight, whether of a lotus (eastern traditions) or of the rose-in-the-cross (western traditions). From a Jungian perspective, these all serve to knit together psychic functions important to personality integration. An individual could even create Web documents corresponding to distinct sub-personalities and explore how they might be linked as a framework for personality integration. The point being that the person can move between the documents along structured pathways, but the gestalt emerges through experience of the pattern -- only incidentally assisted by its actual visualization in two or three dimensions.

A great deal of work has been done on the transformations between 3-D structures of different types, for example how an icosahedron transforms into, or from, a tetrahedron -- via a range of intermediary structures. This may offer insights into ways in which a user can transform patterns of knowledge in order to unpack more detail, or to conflate detailed insights into a more comprehensible whole. It should also not be forgotten that there are far more complex semi-regular and other 3-D patterns which merit exploration, to say nothing of the potential significance of 4-D structures, as typified by the hypercube (currently of vital importance in the design of super-computers).

With the increasing need for software support in classifying conference interventions as they occur (through groupware), it may be that the approach suggested here could prove fundamental to holding the pattern of insights that emerges during the course of a dialogue. The ability to do so may prove to be a mark of sustainable dialogue. It may be the only means of pointing to transformations in that dialogue towards structures capable of providing comprehensible coherence to even greater diversity. A sustainable dialogue may prove to be one in which insights are somehow 'bounced' around a 3-D framework, much as nuclear plasma is contained in magnetic bottles to avoid 'quenching' -- a problem in most dialogues.

creative commons license
this work is licenced under a creative commons licence.