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1986

Mapping Networks

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Published as Section YF in the Encyclopedia of World Problems and Human Potential (1986)

Analysis of networks

The data collected together in the sections of this publication has been deliberately organized in a manner which stresses the interrelationships between the entities within a section and between those in different sections. (Each section is characterized by entities of a different type, and several types of relationship may exist between the same two entities). In effect. therefore. the entities and relationships in each section constitute a network. possibly composed of many subnetworks. Similarly. since entities in each section may be linked to those in other sections, the whole is constituted by a system of interlinked networks in which the relationships have a limited number of distinct meanings. The entities and relationships are currently held in computer files in a form which should facilitate analysis of these networks. It is hoped that the availability of data in this form will encourage the development of new types of analysis more appropriate to the structural complexity portrayed, especially since both the quantitative data and the mathematical functions representing the nature of particular relationships under different conditions (which are a precondition for the application of current methods of quantitative analysis of social systems). are absent and in most cases unavailable.

As Francois Lorrain notes (1) the abstract notion of a network is undoubtedly called to play a role in the social sciences comparable to the role played in physics by the concept of euclidean space and its generalizations. But the poverty of concepts and methods which can currently be applied to the study of networks stands in dramatic contrast to the immense conceptual and methodological richness available for the study of physical spaces. A whole reticular imagery remains to be developed. At this time a network is understood to contain simply nodes and links and little else. An attempt to define anything like a reticular variable results in very little. This is not surprising, since to succeed would require the establishment of a general mathematical theory of networks which as yet has been little developed. In contrast to this situation. consider the multitude of spatial variables which are available: coordinates, length, surface, volume, curves. classes of curves. classes of surfaces, parameters of curves, parameters of surfaces, and so on, and all these in a space of any number of dimensions and manifesting any type of curvature.

1. Social Networks

The types of network which occur in the social sciences are of such a diverse nature that only a purely formal definition of this notion is of sufficient generality.

A network is constituted by a certain set of points. In the social sciences these points may represent any or all of the following: individuals. groups. organizations. beliefs, roles. etc. In this exercise they represent: international organizations, multilateral treaties world problems. strategies, concepts (human development, integrative, patterns). metaphors, symbols, modes of awareness, values. Such points may represent the existence of entities at the present time, or they may represent the existence of entities at some past or future time (or such points may also be used to represent intervals of time).

The points in a data set may be linked by one or more kinds of relationship. In this exercise three basic types of relationship are distinguished:

In the first case above a relationship is further defined by the types of entity between which it occurs, namely whether they are of the same type, or whether they are of different types. In the second and third case, a relationship is further defined by distinguishing the direction of the relationship, which is further developed in the third case by distinguishing several ways in which A can act upon B.

2. Analysis of Networks

Classical mathematics. summarizing Francois Lorrain's (1) remarks. is not able to handle complex structural features characteristic of social systems. Organization is best depicted as a network. The mathematical theory of networks derives largely from certain branches of topology and abstract algebra rather than from analysis. which underlies classical mathematics. The theory of graphs is often presented as a kind of general theory of networks with numerous possible applications in the social sciences. However, other than in the area of operations research. the theory of graphs has not proved itself to be very useful in sociology. The reason is probably that the theory has mainly been developed in the context of relatively limited problems in such a way that the results collected under the graph theory label, although numerous and of great interest, have little unity. In addition, the theory rarely handles networks with several distinct types of relationships each with its own configuration of links. It is precisely such networks which are of most interest in sociology. The theory also tends to exclude networks in which some of the points have links back to themselves when it is often just such networks which are important in representing social structures.

A final disadvantage of the theory of graphs is that it only offers a fairly limited number of means of global analysis of networks. It seriously neglects an important aspect 01 the study of any type of mathematical structure. namely the level of transformation relations between graphs. Because of its composition, a category possesses a richer structure than a simple graph, and it is therefore possible to define more rigorous and fruitful criteria of transformation (namely the concepts of function and functional reduction). In addition a set of points and a set of relations can be treated in their totality and simultaneously, in contrast to the methods of graph theory which considers individual paths between particular points in the graph. In the universe of categories (the universe of objects and relationships). transformations between categories may also be considered as relationships within a category whose objects are themselves categories, and so on. All this emerges from consideration of the global structure resulting from the manner of composition which relates the relationships themselves, thus providing a dialectic of levels of structure and a new imagery of networks. At all levels of this universe, the functional relationships between categories play a central role. They are the fundamental instruments which may be used in the exploration of structural complexity and the tools for extraction of information in global studies.

3. Use of graph theory methods

Despite the limitations noted above, graph theory methods have been applied to the analysis of social structures although such applications are not very common (see references below).

The image of a "network or web" of problems (or organizations, etc; to represent a complex set of interrelationships is a fairly familiar one. This use of "network", however, is purely metaphorical and is very different from the notion of a network of concepts as a specific set of linkages among a defined set of concepts. with the additional property that the characteristics of these linkages as a whole may be used to interpret the semantic significance of the concepts involved.

4. Some features of graphs

Using graph theory, a number of characteristics of networks can be determined. Points 1 to 3 below are concerned with the shape of the network. 4 to 8 with interactions within the network.

  1. Centrality: A measure (in topological not quantitative terms) of the extent to which a given entity (eg a problem) is directly or indirectly "related" via links to other entities (ie, the extent to which it is "distant" from another entity). One can speak of a "key" problem or of an organization being "central" to the concerns of a particular complex. It may also be considered a measure of the degree of "isolation" of the entity. A systematic analysis of the centrality of entities in a network could indicate where new entities are necessary to bridge gaps and link isolated domains.
  2. Coherence: A measure of the degree of "interconnectedness" or "density" of a group of entities. This may be considered as the degree to which a system of problems is "complete". Differences in density would reduce the tendency for more highly coherent problem systems to appear more self-reinforcing in comparison to less organized parts of the network. In some respects this is an indication of the degree of "development" of a problem system.
  3. Range: Some entities are directlY related to many other entities, others to very few. The range of an entity is a measure of the number of other entities to which it is directly related. Range could be considered an indication of the "vulnerability" of a problem to the extent that a high range problem would be less vulnerable to attack than a low range problem, since it has more relationships anchoring it to its problem environment and preserving it in existence. High range points are therefore either key points in resistance to problem change or else key points in terms of which orderly change can be introduced.
  4. Content: The "content" of a relationship between entities is the nature or reason for existence of that relationship. Simple graphs have only one link between any two entities; multigraphs have two or more links, each of different content.
  5. Directedness: A relationship between two entities may have some "direction" (ie, A to B, or B to A). There may be several types of directedness. Two types are important for this project: A is a sub-element of 8; A acts on B. In a multigraph, one link may point from A to 8 and the other from 8 to A.
  6. Durability: A measure of the period over which a certain relationship between entities is activated and used. At one extreme, there are the links activated only on a "one-shot" basis (eg a single crisis), at the other there are links, and sets of links, which are considered stable over centuries (eg between the more permanent problems).
  7. Intensity: A measure of the strength of the link or bond between two entities. Two problems may be said to be "strongly bound together". In some cases, the intensity is a measure of the amount of the "flow" or "transaction" between the entities. The link from A to B may be strong, and that from B to A, weak.
  8. Frequency: A link between two entities may only be established intermittently.
  9. Rearrangeability and blocking: A connecting network is an arrangement of entities and relationships allowing a certain set of entities to be connected together in various possible combinations. Two suggestive properties of such networks, which are extensively analyzed in telephone communications, are: (a) rearrangeability (a network is rearrangeable, if alternative paths can be found to link any pair of entities by rearranging the links between other entities); (b) blocking (a network is in a blocking state if some pair of entities cannot be connected).

5. Implications of artificial intelligence research

In considering the possibility of analyzing networks of problems (organizations, concepts, etc). it is important to benefit as much as possible from related work on artificial intelligence, and possibly pattern recognition. Artificial intelligence projects to simulate human personality or belief systems have had to develop mathematical techniQues and computer programmes which can handle and interrelate entities such as concepts and propositions, some of which may be positively or negatively loaded to represent positive values and perceived problems (the credibility and importance of a belief in a network, and the intensity with which it is held. may also be indicated). Clearly the objective of such projects is not achieved once a simple inventory of entities can be examined. even if it is highly structured in the form of a thesaurus. Of particular interest is the work on "dialogues" with such belief systems, some of which are established over a period by extensive interviews with individuals and others which are specially constructed to simulate paranoia, for example (see references). Presumably it would be possible to conduct somewhat similar dialogues with the collective beliefs constituted by problemlatique networks such as might be developed during the course of this project.

6. Comment

Despite the available techniques noted above, and others which have been applied to non·social networks, much would seem to remain to be accomplished. as Francois Lorrain's (1) remarks indicated. in order to grasp networks in their totality.

The question is what it would be useful to know about networks at this time. What indicators would it be useful to attach to individual problems (organizations, ete) to indicate the characteristics of their relationship to the network(s) in which they are embedded? What similar indicators would be useful in describing the relationships between relatively dense networks and the larger network in which they themselves are embedded? What sort of concept about networks need to be embodied in a network vocabulary so that such matters can be discussed intelligently and unambiguously in public debate? In other words, what are the elements of an adequate vocabulary of structure and in what disciplines has the basis for such a vocabulary already been established: chemistry. crystallography, architecture, design in general, etc?

What can be learnt from biologists about the growth and development of the many reticular structures they encounter (eg radiolaria)? More interesting perhaps, in which occupations do some individuals develop a special {instinctive or intuitive} sensitivity to the structural and dynamic characteristics of the networks with which, or within which, they work: airline pilots, urban bus drivers, electricity grid controllers, counter·espionage directors, factory process controllers, computer-based data network designer/controllers, telephone exchange designer/ controllers, institutional fund controllers, ete? What do such people say, or want to say. about their networks? Why has the term "networking" suddenly sprung into common use and consequently what could "to network" mean? It is questionable whether any adequate organizational response (a network strategy) to the world problem complex can be elaborated until such rich experience is collected together and matched to an elaborated, mathematically-based concept structure, and an associated vocabulary. A conceptual quantum jump is required to grasp problem (and other organized) structures in their totality and be able to communicate such insights. It is hoped that the availability of the data in this publication will help to stimulate such fresh thinking on the conceptual containment of societal networks.

Use of interactive graphics

1. Description

The suggestion has been made above that the representation of the relationship between theoretical entities (concepts, organizations, problems, ete) could best be accomplished using methods based on graph theory. network theory and topology. The relationships registered in this project could be plotted manually as networks. However, particularly since the relationships are already coded on computer tape in a suitable format, there are three major disadvantages to this manual approach:

These three difficulties can be overcome by making use of what is known as "interactive graphics" (29). This is basically a television- type screen attached to a computer. The user sits at a keyboard in front of the screen and has at his disposal what is known as a light-pen (or some equivalent device) which allows him to point to elements of the network of concepts displayed on the screen and instruct the computer to manipulate them in useful ways. In other words the user can Interact with the representation of the conceptual network using the full power of the computer to take care of the drUdgery of:

In effect the graphics device provides the user with a window or viewpoint onto the network of concepts.

He can instruct the computer. via the keyboard, to:

  1. Move the window to give him, effectively, a view onto a different part of the network - another conceptual domain;
  2. Introduce magnification so that he can examine (or "zoom in" on) some detailed sections of the network;
  3. Introduce diminution so that he can gain an overall view of the structure of the conceptual domain in which he is interested;
  4. Introduce filters so that only certain types of relationships and entities are displayed - either he can switch between models or he can impose restrictions on the relationships displayed within a model, ie he has a hierarchy of filters at his disposal;
  5. Modify parts of the network displayed to him by inserting or deleting entities and relationships. Security codes can be arranged to that (a) he can modify the display for his own immediate use without permanently affecting the basic store of data. (b) he can permanently modify features of the model for which he is a member of the responsible body, (c) and so on;
  6. Supply text labels to features of the network which are unfamiliar to him. If necessary he can split his viewpoint into two (or more) parts and have the parts of the network displayed in one (or more) part{s). He can then use the light pen to point to each entity Of relationship on which he wants a longer text description leg the justifying argument for an entity or the mathematical function. if applicable. governing a relationship, and have it displayed in an adjoining viewpoint);
  7. Track along the relationships between one entity and the next by moving the viewpoint to focus on each new entity. In this way the user moves through a representation of "semantic space" with each move, changing the constellation of entities displayed and bringing new entities and relationships into view;
  8. Move up or down levels or "ladders of abstraction". The user can demand that the computer track the display (see point 7) between levels of abstraction, moving from sub-system to system. at each move bringing into view the context of the system displayed;
  9. Distinguish between entities and relationships on the basis of user- selected characteristics. The user can have the "relevant" (to him) entities displayed with more prominent symbols, and the relevant relationships with heavier lines;
  10. Select an alternative form of presentation. Some users may prefer block diagram flow charts, others may prefer a matrix display, others may prefer Venn diagrams (or "Venn spheres" in 3 dimensions) to illustrate the relationship between entities. These are all interconvertible (eg the Venn circles are computed taking each network node as a centre and giving a radius to include all the sub-branches of the network from that node);
  11. Copy a particular display currently on the screen. A user may want to keep a personal record of parts of the network which are of interest to him. (He can either arrange for a dump onto a tape which can drive a graph plotter. a microfilm plotter, or copy onto a videocassette. or, in the future. obtain a direct photocopy);
  12. Arrange for a simultaneous search through a coded micro- film to provide appropriate slide images or lengthy text (which can in its turn be photocopies);
  13. Simulate a three-dimensional presentation of the network by introducing an extra coordinate axis;
  14. Rotate a three-dimensional structure (about the X or Y axis) in order to heighten the 3-D effect and obtain a better view "around" the structure;
  15. Simulate a four-dimensional presentation of the network by using various techniques for distinguishing entities and relationships (eg "flashing" relationships at frequencies corresponding to their importance in terms of the fourth dimension);
  16. Change the speed at which the magnification from the viewpoint is modified as a particular structure is rotated;
  17. Simulate the consequences of various changes introduced by the user in terms of his conditions. This is particularly useful for cybernetic displays;
  18. Perform various analyses on particular parts of the network and display the results in a secondary viewpoint (eg the user might point a light-pen at an entity and request its centrality or request an indication of the interconnectedness of a particular domain delimited with the light pen.);
  19. Use colour (when a colour screen is available) to distinguish between different concepts or networks of relationships on the same display. Several hundred colour codes are available under computer control (3);
  20. Experiment with the generation of paths for the construction of hypothetical larger conceptual units (eg organizations) from available smaller units. as suggested by equivalent work on computer-assisted design of complex organic syntheses (2).

In every current use of interactive graphics there is some notion of geometry and space, but the geometry is always the three dimensional conventional space. There is no reason why "nonphysical spaces" should not be displayed instead - and this is the domain of topology. The argument has been developed by Dean Brown and Joan Lewis (3):

"Both geometry and topology deal with the notion of space, but geometry's preoccupation with shapes and measure is replaced in topology by more abstract, less restrictive ideas of the qualities of things...Being more abstract and less insistent on fine points such as size, topology gives a richer formalism to adapt as a tool for the contemplation of ideas.. Concepts can be viewed as manifolds in the multidimensional variate space spanned by the parameters describing the situation. If a correspondence is established that represents our incomplete knowledge by altitude functions, we can seek the terrae incognitae, plateaus, enclaves of knowledge, cusps, peaks, and saddles by a conceptual photogrammetry. Exploring the face of a new concept would be comparable to exploring the topography of the back of the moon. Commonly heard remarks such as "Now I'm beginning to get the picture" are perhaps an indication that these processes already play an unsuspected role in conceptualization.. By sketching tentative three-dimensional perspectives on the screen and "rotating them on the tips of his fingers". one internalizes ideas non-verbally and acquires a sensation of sailing through structures of concepts much as a cosmonaut sailing through constellations of stars. Such new ways of creating representations break ingrained thought patterns and force re-examination of preconceived notions. A mapping is a correspondence is an analogy. Teaching by analogy, always a fertile device. can be carried out beautifully by topological means....Topological techniques are useful at even the most advanced levels of scientific conceptualization......

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. There is nothing new in the use of models to represent psycho-social abstractions. Jay Forrester (4), making this same point with respect to social systems. states:

"Every person in his private life and in his community life uses models for decision making. The mental image of the world around one, carried in each individual's head. is a model. One does not have a family, a business, a city. a government. or a country in his head. He has only selected concepts and relationships which he uses to represent the real system. The human mind selects a few perception, which may be right or wrong. and uses them as a description of the world around us. On the basis of these assumptions a person estimates the system behaviour that he believes is implied..The human mind is excellent in its ability to observe the elementary forces and actions of which a system is composed. The human mind is effective in identifying the structure into which separate scraps of information can be fitted. But when the pieces of the system have been assembled, the mind is nearly useless for anticipating the dynamic behaviour that the system implies. Here the computer is ideal. It will trace the interactions of any specified set of relationships without doubt or error. The mental model is fuzzy. It is incomplete. It is imprecisely stated. Furthermore. even within one individual, the mental model changes with time and with the flow of conversation. The human mind assembles a few relationships to fit the context of a discussion. As the subject shifts, so does the model. Even as a single topic Is being discussed. each participant in a conversation is using a different mental model through which to interpret the subject. And it is not surprising that consensus leads to actions which produce unintended results. Fundamental assumptions differ but are never brought out into the open."

These structured models have to be applied to any serially ordered data in card files, computer printout or reference books to make sense of that data. Is there any reason why these invisible structural models should not be made visible to clarify differences and build a more comprehensive visible model? The greater the complexity, however, the more difficult it is to use mental models. For example. in discussing his examination of an electronic circuit diagram, Ivan Sutherland writes (5): .

"Unfortunately, my abstract model tends to fade out when I get a circuit that is a little bit too complex. I can't remember what is happening in one place long enough to see what is going to happen somewhere else. My model evaporates. " I could somehow represent that abstract model in the computer to see a circuit in animation, my abstraction wouldn't evaporate. I could take the vague notion that "fades out at the edges" and solidify it. I could analyze bigger circuits. In all fields there are such abstractions. We haven't yet made any use of the computer's capability to "firm up" these abstractions. The scientist of today is limited by his pencil and paper a!,d mind. He can draw abstractions, or he can think about them. " he draws them, they will be static, and if he just visualizes them they won't have very good mathematical properties and will fade out With the computer, we could give him a great deal more. We could give him drawings that move, drawings in three or four dimensions which he can rotate, and drawings with great mathematical accuracy. We could let him work with them in a way that he has never been able to do before. I think that really big gains in the substantive scientific areas are going to come when somebody invents new abstractions which can only be represented in computer graphical form. ..

The availability of devices to restructure information in this way would seem to offer some hope that insights could emerge which respond more adequately to the recorded complexity of societal structure, whilst at the same time being more easily comprehensible to the uninitiated because of the ease with which such devices can be used as educational tools to develop understanding and comprehension of the same structural data from which the research insights are being derived. Such displays of course lend themselves to videotape recording for wider distribution.

2. Implications of computer augmentation of intellect

There are important intellectual implications emerging from work on advanced computer systems. Of particular interest is the work of Douglas Engelbart's team at the Center for Augmentation of Human Intellect (Stanford Research Institute) which is a centre for the US ARPA Data Network (which links the computers of major universities in the USA). Engelbart has worked on the means of creating an "intellectual workshop'· to facilitate interaction between conceptual structures (6). He considers that:

"Concepts seem to be structurable, in that a new concept can be composed of an organization of established concepts and that a concept structure is something which we might try to develop on paper for ourselves or work with by conscious thought processes, or as something which we try to communicate to one another in serious discussion..A given structure of concepts can be represented by any of an infinite number of different symbol structures, some of which would be much better than others for enabling the human perceptual and cognitive apparatus to search out and comprehend the conceptual matter of significance and/or interest to the human. But it is not only the form of a symbol structure that is important. A problem solver ;s involved in a stream of conceptual activity whose course serves his mental needs of the moment The sequence and nature of these needs are quite variable, and yet for each need he may benefit significantly from a form of symbol structuring that is uniquely efficient for that need. Therefore, besides the forms of symbol structures that can be constructed and portrayed, we are very much concerned with the speed and flexibility with which one form can be transformed into another, and with which new material can be located and portrayed. We are generally used to thinking of our symbol structures as a pattern of marks on a sheet of paper. When we want a different symbol-structure view, we think of shifting our point of attention on the sheet, or moving a new sheet into position. With a computer manipulating our symbols and generating their portrayals to us on a display, we no longer need think of our looking at the symbol structure which is stored - as we think of looking at the symbol structures stored in notebooks, memos, and books. What the computer actually stores need be none of our concern, assuming that it can portray symbol structures to us that are consistent with the form in which we think our Information is structured. A given concept structure can be represented with a symbol structure that is completely compatible with the computer's internal way of handling symbols, with all sorts of characteristics and relationships given explicit identifications that the user may never directly see. In fact, this structuring has immensely greater potential for accurately mapping a complex concept structure than does a structure an individual would find it practical to construct or use on paper. The computer can transform back and forth between the two-dimensional portrayal on the screen, of some limited view 01 the total structure, and the aspect of the n-dimensional internal image that represents this "view". " the human adds to or modifies such a "view", the computer integrates the change into the internal-image symbol structure (in terms of the computer's favored symbols and structuring) and thereby automatically detects a certain proportion of his possible conceptual inconsistencies. Thus, inside this instrument (the computer) there is an internal-image, computer-symbol structure whose convolutions and multi-dimensionality we can learn to shape to represent to hitherto unattainable accuracy the concept structure we might be building or working with. This internal structure may have a form that is nearly incomprehensible to the direct inspection of a human (except in minute chunks)."

These insights have been incorporated into the design of an operational computer system which is now being developed so that it will be possible to use computer devices as a sort of "electronic vehicle with which one could drive around with extraordinary freedom through the information domain. Imagine driving a car through a landscape which, instead of buildings, roads, and trees, had groves of facts, structures of ideas. and so on, relevant to your professional interests? But this information landscape is a remarkably organized one; not only can you drive around a grove of certain arranged facts, and look at it from many aspects, you have the capability of totally reorganizing that grove almost instantaneously. You could put a road right through the center of it, under it, or over it, giving you, say, a bird's eye vIew of how its components might be arranged for your greater usefulness and ease of comprehension. This vehicle gives you a flexible method for separating, as it were, the woods from the trees." (7)

3. Conclusion

Application of this kind of technology to an understanding of the world problem complex has not been attempted. As explained above, such devices offer a means of developing improved conceptual (and associated organizational) structures to contain the complexity with which humanity has to deal at this point in time. Of vital importance is the ability of these devices to portray the information in a more meaningful (or "iconic") form than emerges from conventional quantitative studies. This is particularly important in communicating with the informed public but specially so with the policy-making community, as Harold Lasswell notes (8):

"Why do we put so much emphasis on audio-visual means of portraying goal, trend, .condition, projection. and alternative? Partly because so many valuable participants in decision-making have dramatizing imaginations They are not enamoured of numbers or of analytic abstractions. They are at their best in deliberations that encourage contextuality by a varied repertory of means, and where an immediate sense of time, space, and figure is retained."

Network maps

1. Acceptability of network maps

It is now considered quite acceptable in many major cities to print and make available to the general public (often on notice boards or in tourist literature) various schematic maps: the subway (underground, or metro) network; the urban bus network; and the suburban railroad network. Travellers are also accustomed to exposure to documents showing the airline network. Other kinds of network are mapped for the benefit of workers in specialized sectors (eg oil pipeline networks. electricity distribution networks, telephone networks, military communication networKs. goods distribution networks, etc). The most complex map of thIS type would seem to be that used to summarize (on a surface 100 x 132 cm) the relationships between over 1000 biochemical compounds involved in metabolism (See: Gerhard Michael Biochemical Pathways. Mannheim, 80ehringer Mannheim GmbH. 1974; also, but less complex: 0 E Nicholson. Metabolic Pathways. Colnbrook. England, Koch-Light Laboratories, 1974).

The point is that people are now very familiar with such maps in one form or another and use them, like road maps, to organize their thinking about the movement of themselves or items with which they are concerned between distant points embedded in a complex network. No such network maps are currently available to show the relationships between distant points representing particular features of the social system. As a result thinking about the social system and its problems is somewhat chaotic, as would be any discussion about travel in the absence of adeQuate maps to provide the necessary frameworks for such discussion.

2. Reasons for the lack of societal network maps

  1. There is much confusion concerning the kinds of entities that can be distinguished in the social system, due to overlapping systems of categories, needs, and the maze of associated terminologies. .
  2. Where clarity emerges, it is usually in relation to one particular entity (eg one holding company and its network of subsidiaries, or one government agency and its associated bodies); any maps produced then have that body as the central reference point.
  3. Much of the required information is scattered through a variety of reference books and no research has justified its systematic organization.
  4. Systematic sociological research in the past inverts the focus so that, for example, instead of determining how many organizations (problems, etc) there are in a sample in order to determine the number per capita. the mean number of personal relationships to such entities is determined on a per capita basis, so that there is no means of determining how many distinct entities there are to which the relationships are established.
  5. Where such information is collected it is often considered secret because of its political or economic significance. Examples are (a) the collection of data on organizations in every country by the civil or military intelligence units; and (b) the secrecy associated with the subsidiaries owned by a major (multinational) corporation at anyone time and their interrelationships.
  6. Where the data can be collected. and there is a strong case for doing so, there is often reluctance to do so because of the problems of data handling. This is best seen in the (non-societal) case of mapping ecosystem food webs in which animal species are embedded. There is a multiplicity of inter-specific "food chains", together with many branches and cross-connections among food chains making a structure of interactions called "food webs". The complexity of these food webs is such that no one has yet worked out the complete pattern of food relationships and interactions in any natural community. The relationships between 50 species in a given community results in a diagram so full of lines that it is difficult to follow and this only represents one quarter of the 210 known species in a "simple" community. (David Pimental. Complexity of ecological systems and problems in their study and management. In: KEF Webb (Ed) Systems Analysis in Ecology. New York. Academic. 1966, p.15-35).
  7. Where the research has been done. there is a reluctance to produce maps because of the tiresome, time-consuming and often costly nature of the task of doing so. particularly when the networks are complicated.

3. Psycho-social significance of maps: a parallel

The current ability to map the societal system may be usefully compared to that of the European geographical mapping ability during the Middle Ages and earlier. The changing psycho-social significance and status of maps, since such early times, provides many clues for understanding the present situation. Maps in that period were often closely guarded secrets, for military and economic reasons. And just as the understanding in Europe of non European continents was very limited at that time, so today there are only a few well-known problem areas (such as: population, food, peace, etc). Each such territory (or "feudal state") is more or less poorly controlled by a few major organizations (the "cities") with a few well-established links between them (the "roads" or "rivers"). The relations between these feudal states are the limit of concern. Few people travel long distances and when they do, in the absence of readily available maps. they use "experts" to guide them from point to point. Other continents are only vaguely known (and are widely held to be populated by mythical monsters). Each group is content with artistic or impressionistic two-dimensional maps centred on its own organization (or field of concern), confidently held to be the prime mover in the social system as perceived from that point of reference. The significance of any three-dimensional representation is not recognized and a flat-earth perspective prevails.

Under such conditions. it is easy to understand the psychological and communication difficulties which make it impossible to achieve any general galvanization of political will in response to world problems. Each sector is content with its own sketchy local map (if any is held to be required) of the problem environment, and there is little concern for whether such local maps mesh together with those of neighbouring territories or into a general map of the region. Communication therefore frequently breaks down and moments of solidarity are soon forgotten. Warring between feudal territories is common. The state called "energy". clashes with that called "environment". Alliances are formed and each state has imperialistic ambitions: "development" wants to incorporate "environment"; "environment" lays claim to the territory of "development". and all are claimed by the territory called "peace". Lacking maps, assemblies of individuals and groups from different problem territories are pathetic. The people from "heavy rainfall" areas cannot understand the constant harping on water by people from "desert" areas; the people from "arctic" areas cannot relate meaningfully to those from "tropical" zones.

The history of the evolution of geographical perceptions. and the tools that have been required to move humanity towards a global perception, indicate the kinds of difficulty which have to be faced. (The much-used NASA photograph of Earth from space is only significant as a symbol because people know that they can relate its features to the map of the world in their own atlas in order to be able to locate their home town, for which they also have a detailed local map, to which they can relate their personally acquired knowledge.) Local maps are needed which mesh into global maps, so that each can see his place in any world problem strategy and so that global decision-making can relate to the tactical problems of groups as perceived in each community.

Problem maps (bound together into "atlases") are needed to help individuals see and appreciate the relationships. distances and differences between problem territories. And it should be possible to relate these to organizational (and other) maps. just as any atlas has contour maps, climatic maps and political maps of the same region. Individuals, whether students, executives. researchers, or policy makers. have at least as much need for such visual devices to orient themselves in the social system as they have for road and other currently available maps.

Hopefully it will be possible to reach a stage at which such maps can be produced as standard conference documentation as a means of providing background documentation for debates, and in order to sharpening the focus of debate. Clearly the debate itself should lead to proposals for the amendment of such maps (as a result of the recognition of: new issues. relationships between problems, proposals for organizations or programmes. or new relationships between organizations, ete). New versions of such maps, or hypothetical maps (eg of organizational systems) could be fed into later sessions of the same meeting or used as one form of summary of the achievements of the meeting.

4. Production of network maps

Once the information on societal entities is held on computer it becomes possible to overcome many of the obstacles to map production noted above. Computers are currently used to plot out electronic circuit diagrams and other types of network. onto large charts. The computer programmes handle the tedious problem of designing such charts, including the use of appropriate colours to distinguish between different features of the network (or networks) on the same chart. (Artists, designers and communications psychologists can also introduce an aesthetic component to facilitate comprehension)·.This approach has the considerable advantage that different designs (based on the same data) may be tried or used for different purposes. Some designs may be highly simplified, others may be very complex. New maps can be easily produced if the original data is modified. The data base used may be the same as that used for interactive studies of the network so that both approaches may be integrated under the control of a researcher.

However, although the computer program~~s e.xist !or the production of twO-dimensional maps. there are difficulties still to be overcome in the representation of three (or n) dimensional networks on a two-dimensional surface, if such complex representations are necessary. Some of these mathematical and associated problems (of projections) have been examined by geographers Interested in producing a more accurate representation. of the spherical Earth on a map. Experiments have been made with a number of alternatives which each have their advantages. The data collected together on computer for this publication should encourage and facilitate similar experiments in societal network map production.

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