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Joy in the Present
      

1979

The Territory Construed as the Map

In search of radical design innovations in the representation of human activities and their relationships

- / -


Prepared in 1979 in connection with the Forms of Presentation sub-project of the Goals, Processes and Indicators of Development (GPID) project of the United Nations University. Printed in Transnational Associations, 1982, 2, pp 80-89. Also in: Forms of Presentation and the Future of Comprehension (1984)

Introduction

This paper explores the possibility of a new approach to the representation of any complete ranges of human activity or concern. The justification for doing so has been discussed elsewhere (1, 2, 3). The intention is to provide a much improved overview of their degree of relationship and a feel for the dynamics between them. A particular concern is to reflect adequately the degree of lack of relationship, indifference, mutual irrelevance, or distortion of perspective characteristic between those active in such different fields.

The tentative nature of these investigations must be stressed. At this time it appears that three distinct approaches must be clarified. Then, by interrelating them and allowing each to modify the interpretations to which the others give rise, a basis for the new representation sought emerges.

The prime concern here is not one of logic or rigour since, to the extent that these have been called for, they have been utilized in more conventional responses to the problem (e.g. classification schemes, general system theories, world models, etc.). Rather the concern is to provide a convenient, comprehensible representation - capable of embodying all the detail and precision required - which will provoke reflexion, discussion at many levels, and feedback on the perceived relationships between the fields represented. The concern is to create a communication tool to fulfil a need not met by conventional explanations, information frameworks and systems. Given that the conventional approaches are unable to provoke their users into formulating better (as opposed to more precise) questions, the tool sought should enable users to formulate those questions for which they did not know that they needed the answers.

The three approaches are examined separately in Parts 1 to 3 below. In Part 4 their interrelationship is explored.

Part 1: Ordering distinctions

In this approach the point of departure is the concept of a complete range of human activity or concern, namely a totality which is divided up by making distinctions, whether in a series or nested. Aspects of this question have been explored elsewhere (1), especially the relationship of the act of distinguishing to cognition.

Two much used representations of such breakdowns are the list and the matrix:

List: A list does not order the relationships between its elements except in relation to nested sub-lists or in the case of a list in series form. This does not imply that such relationships are lacking, merely that they cannot be reflected in the list form. Note that a list is in fact a series of "points", but it is not necessary to conceive of it as such. The points could be represented as areas on a surface. It is only in the matrix that the manner in which the total area is cut up becomes explicit.

Matrix: The cells of a matrix may be thought of as sub-areas of the area representing the totality which the matrix attempts to reflect. The sub-areas are of course positioned with respect to column and row communalities. It is now interesting to ask why the area is bounded in such a limiting manner. For the rectangular/square form is one of the simplest. It provides a (paned) "window" through which the totality may be perceived. But it raises questions about the "wall" in which the window is set and the position of the observer in relation to the observed on the other side of the window.

Now to the extent that the matrix is complete in its coverage, there really should not be any "wall". The matrix should in such cases in effect "wrap around" the observer; all is window and nothing is implict, unexplicated or excluded. If this is not so then the wall should be conceived as wrapping around the observer, possibly with other windows corresponding to other partial views of the external totality to which the observer may turn his attention.

From this point of view the conventional two dimensional matrix raises the question of the conceptual significance of crossing the encompassing boundary. It is irrational and unmeaningful because the "wall" is unrecognized. There is almost a flavour of danger of "failing over the edge" as sailors feared with the early "flat earth" models (quaintly conceived in the East as supported on the back of a primordial elephant or tortoise).

If it is assumed that the matrix is complete, then it should be possible to represent it without such an arbitrary external boundary. If the external boundary is eliminated then the matrix takes the form of a closed surface (wrapped around the observer). By what procedure can a two-dimensional matrix be so modified and to what does it give rise ?

Consider a 2-by-2 matrix. The simplest symmetrical figure which retains the same number of areas is the tetrahedron. It provides four "windows" on the external universe for any observer positioned within.

The continuity of surface area of the three dimensional figure emphasizes any functional continuity between the aspects associated with the individual sub-areas or facets (the "panes"). But at the same time it drawn attention to the discontinuities between the areas associated with the edges. They are not smooth transitions but are marked by sharp angles. It may then be asked (if reality is continuous in contrast to our conceptions thereof) whether such a representation suggests others which would reflect a lesser degree of discontinuity between aspects. And indeed there are, for the greater the number of symmetrically disposed surface areas ("panes"), the larger the angle between adjacent areas and the closer the approximation to a continuous surface, namely a spheroid.

However, the greater the number of distinct areas (whatever they signify), the more difficult it is to comprehend the totality with any precision. The patterning of the surface area may be readily scanned but it is only through the "distorted discontinuities" of the most unspherical figures that it may be grasped to any degree.

A compromise may be considered however. Even a tetrahedron may be projected onto a circumscribed sphere. This cuts up the surface of the sphere into four (spherically) triangular areas. More complex figures would of course result in more complex patterns on the surface of the sphere. The challenge is of course to maintain continuity but the realities of the discontinuities between extant conceptual frameworks may suggest that any such goal is idealistic. Disturbing factors are:

(a) Unequal development: Clearly a particular cell of a matrix may itself be broken down into more sub-cells than is yet possible with its neighbours. such differences would be reflected in the surface patterning of the associated sphere. (The intermediate three-dimensional figure would of course be asymmetrical to a corresponding degree).

(b) Gaps: Assuming that the original ma-trix was incomplete to the extent of missing one row, for example, then its "presence" could be indicated by an appropriate number of (shaded) areas on the surface of the sphere - if their "absence" from the total pattern had been remarked of course.

(c) Zones: Assuming that originally there were two or more unrelated matrices which each encompassed aspects of the reality to which an observer could be sensitive, then their representation on the sphere surface would give rise to patterned non-contiguous zones separated by unmarked (shaded) areas reflecting the discontinuity between them. (The rules for projecting the plurality of intermediate three-dimensional figures onto the surface would be more complex than before). The manner in which these disturbing factors are handled indicates the freedom associated with this representational approach. Clearly distinct matrices could either give rise to distinct spheres or could be incorporated onto a single sphere as non-contiguous zones (case c). On the other hand, the possible articulation into many nested levels of a particular cell in a matrix (case a), could be handled by representing the latter on a separate sphere if the totality of its special perspective needed to be stressed. List elements, re-presented by areas (see above), could be disposed around the surface of a sphere on the basis of a projection of a three-di-mensional figure with the appropriate number of sides. If the list was not "complete" then gaps in the spherical surface would be required (case b).

Pattern of contiguity

In a matrix it is clear how the cells relate to one another. Once the boundary is eliminated, however, the question of what is contiguous to what is raised. Also in a two-dimensional matrix there are two types of contiguity (row and column) between cells. But, considering the simple example of a 2-by-2 matrix transformed into a tetrahedral surface, the validity of juxtaposing particular areas may be questioned.

(a) Enantiodromia: A strong objection that may be made to juxtaposing cells at opposite boundaries of a matrix is that they obviously reflect extreme poles of distinction. And yet there is much to suggest the intimate relation-ship of extremes (4). Whether it is the French phrase "les extremes se touchent", traditional Chinese concepts of the continuous transformation from yin into yang and vice versa, or the classical Greek dramatic notion of enantiodromia (T.S. Eliot, The Four Quartets: We shall not cease from exploration. And the end of all our exploring, will be to arrive where we started, And know the place for the first time), in all cases there is a functional continuity which the matrix form conceals. On the other hand the matrix itself may be missing rows and/or columns, in which case juxtaposition would be inappropriate.

(b) Valency: In a two-dimensional matrix, all cells have a valency of 4 (neglect-ing the boundary question discussed above). The better known three-dimensional closed figures may have surface elements of valency 3, 4, 5, 6, 8 and 10, although not all combina-tions are possible this implies a grea-ter richness than can be adequately captured by a matrix, and a richness whose continuity is maintained in its projection onto a spherical surface.

(c) Linkage lines: In a two-dimensional matrix, the links between cells of the same row or column are clear. Such strings of areas may also be present on the three-dimensional closed fi-gures, although partial strings are then also feasible.

(d) Matrix projection: Although it is acceptable to portray a map of the globe as a "matrix" of latitude/longitude cells, despite the distortion, a less distorted representation is achieved by using other projections which de-part from the rectilinear mode. These clarify to different degrees the time relationship between the areas as projected from the position of the observer. It is possible that representation of matrices could benefit from being seen in this light.

(e) Complementarity: In some matrices, complementary pairs of cells are evident. Such complementarily may be even more evident in the symmetry of three-dimensional closed figures, in relation to the points raised in Part 2.

Part 2: Complementary

The three-dimensional closed figures discussed in Part 1 are ideal abstractions in an important sense distinct from that al-ready mentioned. It is a fact that all but the simplest structures (not excluding the cube, for example) are not of themselves stable. If the vertices play no structurally stabilising role they collapse. Intuitively this suggests the importance of attention to design techniques which could ensure the inherent stability of structures con-forming to such patterns.

These problems have been extensively in-vestigated by Buckminster Fuller and others. Their relevance to the concerns of this paper have been discussed else-where (5, 6, 7).

Of special relevance is the concept of counterbalancing counteracting forces as a basis for maintaining the pattern in question. This is achieved through ten-segrity structures. It suggests that com-plementary opposed factors should be specially positioned in relation to one an-other. This pattern of contraints may be used to design a spherically symmetrical representation (5).

Part 3: Comprehensible code

In thic approach the concern is to make use of some surface which can be suitably "coded" to provide "hooks" onto which concepts can be "hung" in such a way as to facilitate comprehension of the patterns as a whole. The emphasis is therefore on providing a trigger for memory and comprehension. This preoccupation has a long history going back to the Greeks, and possibly the Egyptians, as reported by Francis Yates (8). It is only comparatively recently in the 17th century that it went out of favour with the western scientific revolution and the widespread use of pa-per as a crutch for memory. There is little current concern with memory (particularly with the increasing number of information services and references tools) other than in the form of gimmicks to meet the chal-lenge of examination, or in relation to speed reading etc. On the other hand these gimmicks, current investigations of memory prodigies, and the reports of the ancient art, all emphasize the importance of suitable "hooks". The relation to com-prehension, as exemplified by the Eastern practice of the mandala (9), is discussed elsewhere ( 1 ).

A recent paper proposes the use of a sperical surface to model the body of knowledge and its development (10). The concern did not extend to problems of comprehension. As Yates reports, this de-mands the use of "hooks" which usefully trigger the imagination through non-intellectual processes, however irrational and unsystematic they may appear. Thus favoured "surfaces" included building complexes which enabled some to use over 120,000 memory locations in a structured comprehensible relationship to one another. The production of a suitable representation can be seen as a problem of design, namely a series of decisions about the relationship between form and content (11). This involves a struggle for a "best fit". As the design is "firmed up" to completion, its value as a tool for improved comprehension becomes increa-singly apparent.

As a design problem, any initial attempts are bound to contain many weaknesses. These could however be progessively reduced following experience with the representation, discussion and feedback. Part of the merit of this approach (for some at least) lies in reflecting on the design problem itself and the disciplined pattern of decisions which need to be made. It is likely that there are several alternative patterns which could lead to equally useful and thought provoking results.

Decision 1: The surface used for the representation shall be a spherical one. This has the merit of built-in continuity which, through the absence of a boundary, does not give undue privilege to any position on the surface. Being finite and rounded it has a certain "graspable" quality; the form of the whole is intuitively comprehensible as a gestalt. This quality is absent from conventional tabular (or matrix) presentation which provide an abstract framework lacking any focus for comprehension. The same is true of more complex surfaces (although there are merits to the use of a torus, for example).

Decision 2: The surface shall be broken up into a pattern of two interweaving forms: "land" and "water". Clearly a uniform surface would not provide any "grip" for the imagination. Simply inscribing a regular latitude/longitude grid pattern would also stress the abstract and alienate the imagination. The land-and-water coding appeals to the imagination because of the widespread familiarity with the terrestrial globe, its various surface features, and their relationship to the observers own location and those of others of whom he is aware. It has an organic quality which is encountered in fictional fantasy worlds (of Tolkien), science fiction, or humour (see Fig. 1 and 2; are they conceived as continents on a "flat earth", and if so, why ?; how distant are they from each other ?).

Figs. 1 and 2 Humorous mapping exercises.
Reproduced from : Rebus Heaviwait and Emmanuel Lighthanger. Projex. New York, Links Books, 1972.
Fig 2

Decision 3: The two-fold distinction on the surface shall be used to carry the basic two-fold distinction in human activity and concerns. Here care is required because of the problems of label words at this level of abstraction (1). It is not a question of adequate definition, because this simply introduces the vicious circle of the definition of the words used in any definition, etc. ignoring the question of comprehension. The words used here are therefore to be considered as pointers only. The basic distinction is between what can be comprehended (by the reader/observer) as common to what is denoted by the labels in earth of the following lists:

  • "land": rational, intellectual, conscious, order, recognized "left brain", yang, practical, expressed, etc
  • "water": irrational, emotional, unconsciuous, disorder, unrecognized, "right brain", yin, "impractical", repressed, etc
This is not in any way meant to suggest that one is `` better" than the other, just as it would be ridiculous to suggest that land is better than water.

Decision 4: The land masses shall represent activity performance rather than the activity as a subject eg performing chemical operation and associated symbol manipulation, rather than "chemistry" as a body of knowledge; praying rather than prayer; etc. This removes the need to consider subjects which are not associated with a pattern of activity, and renders other subjects subordinate to the pattern of activity with which they are associated. It is a move from a noun-focus to a verb-focus (and is thus more process oriented). Subsequent investigation may suggest that this decision should focus more on the notion of the "body of knowledge" rather than "activity performance". Revision of the design sequence would then be required or the advantages of an alternative design considered. It is possible that some mixed notion ("disciplined order" ?) would be preferable whose specification might itself raise problems of labelling, definition and comprehension.

Fig. 3: ICC - Information coding classification
Reproduced from : I. Dahlberg, International Classification. 9 (1982), 2, p.87-93.

AREAS

 

1

 

2

 

3  

 

4

 

5

 

6

 

7

 

8

 

9

 

1

FORM &

STRUCTURE. AREA

11

Logic

12

Mathematics

13

Statistics

14

Systemology

15

Organization

16

Metrology

17

Cybernetics (Contr. & automat.)

18

Standardization

19

Testing &

monitoring

2

ENERGY   & MATTER

AREA

21

Mechanics

22

Physics of

matter

23

Gen. & tech.

physics

24

Electro-

nics

25

Physical

chemistry

26

Pure

chemistry

27

Chemical

technol. &

engg.

28

Energy

sci. &

technol.

29

Electrical eng.

3

COSMO &

GEO-AREA

31

Astronomy

& astro-

physics

32

Astronau-

tics & space

research

33

Basic geo-

sciences

34

Atmospher

sci. & tech.

35

Hydrospher.

& oceanol.

sci. & tech.

36

Geological

sciences

37

Minig

38

Materials

sci. & me-

tallurgy

39

Geography

4

BIO-AREA

41

Basic

biol. scien-

ces

42

Microbio-

logy &

cultivation

43

Plant

biology &

cultivation

44

Animal

biology &

breeding

45

Veterinary

sciences

46

Agriculture

& horticul-

ture

47

Forestry &

wood sci. &

technol.

48

Food

science &

technol.

49

Ecology

& envi-

ronment

5

HUMAN AREA

51

Human biology

52

Health &

theoretical

medicine

53

Pathology

& medi-

cine

54

Clinical

medicine &

cure

55

Psychology

56

Education

57

Profession,

labor,

leisure

58

Sports

59

Household

& home-

life

6

SOCIO-

AREA

61

Sociology

62

State  & politics

63

Public

admini-

stration

64

Money  &

finances

65

Social  aid,

social poli-

tics

66

Law

67

Area plan-

ning, urba-

nism

68

Military

sci. & tech.

69

History

7

ECONOMICS & TECHNO-

LOGY AREA

71

Gen. & natl.

economics

72

Business

economics

73

Technology

in general

74

Mechanical

& precision

engg.

75

Building

76

Commodi-

ty sci. &

technol.

77

Vehicle sci.

& technol.

78

Transport.

technol. &

services

79

Utilities

& service

econom.

8

SCIENCE & INFORMA-TION AREA

81

Science of

science

82

Information

sciences

83

Informatics,

computer

sci.

84

Information

in general

85

Communi-

cation sci.

86

Mass-com-

munication

87

Printing &

publishing

88

Communica-

tion engg.

89

Semiotics

9

CULTURE

AREA

91

Language

& linqui-

stics

92

Literature

& philology

93

Music

& musico-

logy

94

Fine arts

95

Performing

arts

96

Culture

sci.i.n.s.

97

Philosophy

98

Religion

&  secret teachings

99

Christian

Religion

The "fields of human activity" denoted by the land masses could be interpreted to include: walking, hating, philosophy, economics, welding, chemistry, drama, meditation, etc. They could have been restricted to intellectual disciplines (12), or more broadly to occupations (13). They could have been extend to types of role. Only by further investigation will the implications of this design decision become apparent.

There is an obvious design problem of determining which level of " human activity" is to be mapped by the surface areas themselves and which levels could be more appropriately indicated by (a) features on those areas, whether "natural" or "artificial", or (b) by "natural" or other activities occurring on or over such surfaces, or (c) by making use of one or more other spherical surfaces (a point raised in Part 1). This question will be considered in Part 4

Decision 5: It follows from Decisions 3 and 4, that the water masses shall be used to represent human activity which is not "consciously" and "rationally" ordered in the manner associated with land masses. A land mass split by a body of water, would thus be used to represent an "irrational" discontinuity in an ordered approach. The distinctions implied by the size and nature pf the body of water (ocean, inland sea, lake, river, marsh, stream, etc) will need to be clarified by subsequent design decisions even if their possibilities can be intuited at this point.

Two basic design problems must be faced at this point namely:

  • the determination of the relative size of any land mass or body of water, even if attention is restricted to surface area.
  • the disposition of the land or water areas in relation to one another; the pattern they constitute on the surface of the sphere.
At this point it is necessary to draw together the threads emerging from the three approaches and to return to insights from Parts 1 and 2.

Part 4: Integration

The conceptual procedure whereby a matrix is formulated gives rise to cells of "equal importance" or "weight". By this is meant that each category (cell) is equally distinct from the other categories (cells). Of course, if some quantitative measure is attached to the cells than there will be inequalities. But these may be considered secondary (at least for the moment).

Using the argument of Part 1, the matrix categories may be given equal "land" areas (in Part 3) on the surface of a sphere, at least as a first approximation. If the matrix attempted to reflect all fields of human activity (see Fig. 3, for example), then this could be considered an indication of the desired subdivision of the spherical surface. The relationship of the matrix cells might also be considered an adequate indication of the disposition of the areas on the surface.

This procedure of course presupposes that :

(a) the matrix is complete,

(b) all activity is rationally ordered

(c) the relationships between such activ­ities are rationally ordered.

The current lack of relationships between the natural sciences, or with the social sciences, the humanities, or other modes of activity shows the weakness of this presupposition and the difficulty which would be encountered in formulating such a matrix. Even classification science, by definition neutral to the variety of fields of activity, generates a variety of competing matrices (although they are usually lists). In fact Fig. 3 constitutes the most recent effort to cover the complete range with a minimum of distortion. But of course it is not designed to highlight the hiatus, in the minds of the practitioners, between the different fields. One may also ask what aspects of human activity are omitted from a « subject field »matrix with its built in emphasis on the study mode.

In the light of Part 3 therefore, «water » areas are likely to be evident along the discontinuities between the areas on the spherical surface. However this does not imply a regular pattern of « canals », for the degree of hiatus will vary between dif­ferent « land » areas, giving rise to any­thing in width between a river and an ocean. On the other hand, some possible lines of hiatus will be eliminated as a re­sult of the rational binding together of two areas (e.g. where a suitable paradigm en­sures the appropriate meshing). Further­more, a large category (e.g. a particular science) may be fragmented by a «ne­twork of waterways » into sub-areas due to the mutual hostility between its consti­tuent schools of thought.

The question is then does the Part 1 procedure suggest a means of decom­posing the surface further to delineate where discontinuities may arise between sub-categories. There is in fact a well-de­veloped tech nique for doing so. This is the geodesic subdivision of the surface of a sphere (Fig. 4). It may be used to decom­pose the surface as finely as is required by the (ability to « resolve conceptually » the) presence of nested sub-categories in a given zone (and not necessarily in ano­ther). It may be based on many of the three-dimensional figures to which the Part 1 procedure gives rise.

These steps indicate that it is possible to depart from the «simplistic » ideal subdi­vision of the spherical surface and to re­spond to local variations. But the areas so delineated, however small, are still bounded by « straight » lines (i.e. on the curved surface). It is a valuable indication (preserving the classificatory precision of Part 1) but lacks the organic quality sought in Part 3.

However, consider the ideal boundaries of the areas decomposed as in Fig. 5. If a giv­en boundary is « eroded » by the en­croachment of some irrational element. this may be indicated by selective removal of the smallest sub-areas, thus resulting in a ragged, « realistic coastline ». This raises the question of how to determine with precision which such areas to switch from land to water.

Fig. 4 Geodesic sub-division of a sphere.
Fig. 5 Erosion of ideal geodesic sub-division.

On the other hand, the encroachment may be that of a neighbouring field of activity which "incorporates" a sub-area across the original boundary into its own domain. This opens the possibility to the indication of a ("political") switch of allegiance or empire building, neither of which is foreign to the dynamics between disciplines, for example.

Despite these possibilities however some nagging questions remain. They may be illustrated by imagining that in the absence of the conventional global map information was nevertheless available on all the land masses. This could be presented in list or matrix form. Despite the lack of any global perspective, inhabitants of the land masses could be consulted on their relationships with neighbouring territories and the barrier constituted by any intervening body of water. The problem is how to solve the question of scale, distance and direction on the basis of such interviews. How can any group associated with a particular pattern of activity be objective about the relative size of the land surface by which the activity is denoted ? There would be an obvious tendency to inflate the importance of that with which one was familiar and, unless menaced by it, to diminish that of which one disapproved or was misinformed (even to the point of declaring its existence to be a "pure fantasy of fevered minds"). In this light, any map in likely to be the subject of considerable controversy (if in fact the procedure is held to be of any merit).

It may in future be possible to respond to this difficulty and provide a rational basis for positioning the boundaries between fields of activity and this is considered in Part 5. At this point some available indicators may be considered as a guide to refining a map in terms of size of surface areas as a measure of relative importance.

A number of possible indicators are available:

  •  occupational statistics
  •  educational statistics by discipline or occupation
  •  funds associated with sectors of economic activity
  • documents associated with particular "subjects" or disciplines.
But, however these might be used to obtain some first approximation to relative importance, they fail to detect the more prevalent types of activity e.g. walking, cafe activity, love-making, etc. These are better recorded by time-budget data where available. However time-budget categories would prove inadequate to the task of distinguishing the variety of human activities which emerge from the data above.

Both types of data would fail to distinguish between the various patterns of activity often associated with different kinds of social grouping (e.g. organizations) or cultural group (e.g. communities). Clearly a variety of sources would have to be used to obtain a rough indication of surface areas as a stimulus to feedback.

A second question concerns overlapping patterns of activity (e.g. an occupation which involves walking, which is itself also a leisure activity). Here the overriding or determining pattern must be considered to take precedence.

This however brings up a further question. If the relative land surface approximations are based on some indicator like world man-hours per year per activity, some very basic activities might acquire undesirable prominence on the total surface (e.g. sleeping, food consumption, etc.). One approach, if desired, is to use a logarithmic relationship between man-hours and surface area. But would this destroy the desirable iconic value of such a map ? With regard to the degree of relationship between land areas, it should be possible to make some use of citation analysis. Clearly the frequency of citation of papers in neighbouring fields would be high. A frequency analysis could then lead to a suitable pattern of juxtaposition of fields. Of course citation information is only available for certain fields of activity and covers only a few publications, but it could nevertheless provide some valuable ("quantifiable") guidance particularly for the natural and social sciences. Possibly an analogous "citation" approach could be developed on the basis of a rigorous interview technique in order to cover other fields.

The preceding paragraphs are an indication of design problems to be confronted in the light of different kinds of information available. It is appropriate to view this problem in terms of the probable confusion in the minds of the early cartographers confronted on the one hand with religious and philosophic (ideal) models of the structure of the world, and on the other with a jumble of facts, opinions and rumours based on travellers and investigators with different kinds of axe to grind.

Doris Lessing: Briefing for a Descent into Hell