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This paper explores the possibility of a new approach to the representationof any complete ranges of human activity or concern. The justificationfor doing so has been discussed elsewhere (1, 2, 3). The intention is toprovide a much improved overview of their degree of relationship and afeel for the dynamics between them. A particular concern is to reflectadequately the degree of lack of relationship, indifference, mutual irrelevance,or distortion of perspective characteristic between those active in suchdifferent fields.
The tentative nature of these investigations must be stressed. At thistime it appears that three distinct approaches must be clarified. Then,by interrelating them and allowing each to modify the interpretations towhich 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 extentthat these have been called for, they have been utilized in more conventionalresponses to the problem (e.g. classification schemes, general system theories,world models, etc.). Rather the concern is to provide a convenient, comprehensiblerepresentation - capable of embodying all the detail and precision required- which will provoke reflexion, discussion at many levels, and feedbackon the perceived relationships between the fields represented. The concernis to create a communication tool to fulfil a need not met by conventionalexplanations, information frameworks and systems. Given that the conventionalapproaches are unable to provoke their users into formulating better (asopposed to more precise) questions, the tool sought should enable usersto formulate those questions for which they did not know that they neededthe answers.
The three approaches are examined separately in Parts 1 to 3 below.In Part 4 their interrelationship is explored.
In this approach the point of departure is the concept of a completerange of human activity or concern, namely a totality which is dividedup by making distinctions, whether in a series or nested. Aspects of thisquestion have been explored elsewhere (1), especially the relationshipof the act of distinguishing to cognition.
Two much used representations of such breakdowns are the list andthe matrix:
List: A list does not order the relationships between its elementsexcept in relation to nested sub-lists or in the case of a list in seriesform. This does not imply that such relationships are lacking, merely thatthey cannot be reflected in the list form. Note that a list is in fact a seriesof "points", but it is not necessary to conceive of it as such. The pointscould be represented as areas on a surface. It is only in the matrix thatthe 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 thearea representing the totality which the matrix attempts to reflect. The sub-areasare of course positioned with respect to column and row communalities. Itis 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 questionsabout the "wall" in which the window is set and the position of the observerin relation to the observed on the other side of the window.
Now to the extent that the matrix is complete in its coverage, therereally should not be any "wall". The matrix should in such cases ineffect "wrap around" the observer; all is window and nothing isimplict, unexplicated or excluded. If this is not so then the wall shouldbe conceived as wrapping around the observer, possibly with other windowscorresponding to other partial views of the external totality to whichthe observer may turn his attention.
From this point of view the conventional two dimensional matrix raisesthe question of the conceptual significance of crossing the encompassingboundary. It is irrational and unmeaningful because the "wall" is unrecognized.There is almost a flavour of danger of "failing over the edge" as sailorsfeared with the early "flat earth" models (quaintly conceived in the Eastas supported on the back of a primordial elephant or tortoise).
If it is assumed that the matrix is complete, then it should be possibleto represent it without such an arbitrary external boundary. If the externalboundary is eliminated then the matrix takes the form of a closed surface(wrapped around the observer). By what procedure can a two-dimensionalmatrix be so modified and to what does it give rise ?
Consider a 2-by-2 matrix. The simplest symmetrical figure which retainsthe 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 emphasizesany functional continuity between the aspects associated with the individualsub-areas or facets (the "panes"). But at the same time it drawn attentionto the discontinuities between the areas associated with the edges. Theyare not smooth transitions but are marked by sharp angles. It may thenbe asked (if reality is continuous in contrast to our conceptions thereof)whether such a representation suggests others which would reflect a lesserdegree of discontinuity between aspects. And indeed there are, for thegreater the number of symmetrically disposed surface areas ("panes"), thelarger the angle between adjacent areas and the closer the approximationto 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 onlythrough the "distorted discontinuities" of the most unspherical figuresthat it may be grasped to any degree.
A compromise may be considered however. Even a tetrahedron may be projectedonto a circumscribed sphere. This cuts up the surface of the sphere intofour (spherically) triangular areas. More complex figures would of courseresult in more complex patterns on the surface of the sphere. The challengeis of course to maintain continuity but the realities of the discontinuitiesbetween extant conceptual frameworks may suggest that any such goal isidealistic. Disturbing factors are:
(a) Unequal development: Clearly a particular cell of a matrix mayitself 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 associatedsphere. (The intermediate three-dimensional figure would of course be asymmetricalto a corresponding degree).
(b) Gaps: Assuming that the original ma-trix was incomplete to theextent of missing one row, for example, then its "presence" could be indicatedby 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 unrelatedmatrices which each encompassed aspects of the reality to which an observercould be sensitive, then their representation on the sphere surface wouldgive rise to patterned non-contiguous zones separated by unmarked (shaded)areas reflecting the discontinuity between them. (The rules for projectingthe plurality of intermediate three-dimensional figures onto the surface wouldbe more complex than before). The manner in which these disturbing factorsare handled indicates the freedom associated with this representational approach.Clearly distinct matrices could either give rise to distinct spheres or couldbe incorporated onto a single sphere as non-contiguous zones (case c). Onthe other hand, the possible articulation into many nested levels of a particularcell in a matrix (case a), could be handled by representing the latter ona separate sphere if the totality of its special perspective needed to bestressed. List elements, re-presented by areas (see above), could be disposedaround the surface of a sphere on the basis of a projection of a three-di-mensionalfigure 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 theboundary is eliminated, however, the question of what is contiguous towhat is raised. Also in a two-dimensional matrix there are two types ofcontiguity (row and column) between cells. But, considering the simpleexample of a 2-by-2 matrix transformed into a tetrahedral surface, thevalidity of juxtaposing particular areas may be questioned.
(a) Enantiodromia: A strong objection that may be made to juxtaposingcells at opposite boundaries of a matrix is that they obviously reflect extremepoles of distinction. And yet there is much to suggest the intimate relation-shipof extremes (4). Whether it is the French phrase "les extremes se touchent",traditional Chinese concepts of the continuous transformation from yin intoyang and vice versa, or the classical Greek dramatic notion of enantiodromia(T.S. Eliot, The Four Quartets: We shall not cease from exploration. Andthe end of all our exploring, will be to arrive where we started, And knowthe place for the first time), in all cases there is a functional continuitywhich the matrix form conceals. On the other hand the matrix itself may bemissing rows and/or columns, in which case juxtaposition would be inappropriate.
(b) Valency: In a two-dimensional matrix, all cells have a valencyof 4 (neglect-ing the boundary question discussed above). The better knownthree-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 agrea-ter richness than can be adequately captured by a matrix, and a richnesswhose continuity is maintained in its projection onto a spherical surface.
(c) Linkage lines: In a two-dimensional matrix, the links betweencells of the same row or column are clear. Such strings of areas may alsobe present on the three-dimensional closed fi-gures, although partial stringsare then also feasible.
(d) Matrix projection: Although it is acceptable to portray a mapof the globe as a "matrix" of latitude/longitude cells, despite the distortion,a less distorted representation is achieved by using other projections whichde-part from the rectilinear mode. These clarify to different degrees thetime relationship between the areas as projected from the position of theobserver. It is possible that representation of matrices could benefit frombeing seen in this light.
(e) Complementarity: In some matrices, complementary pairs of cellsare evident. Such complementarily may be even more evident in the symmetryof three-dimensional closed figures, in relation to the points raised in Part2.
The three-dimensional closed figures discussed in Part 1 are ideal abstractionsin an important sense distinct from that al-ready mentioned. It is a factthat all but the simplest structures (not excluding the cube, for example)are not of themselves stable. If the vertices play no structurally stabilisingrole they collapse. Intuitively this suggests the importance of attentionto design techniques which could ensure the inherent stability of structurescon-forming to such patterns.
These problems have been extensively in-vestigated by Buckminster Fullerand others. Their relevance to the concerns of this paper have been discussedelse-where (5, 6, 7).
Of special relevance is the concept of counterbalancing counteractingforces as a basis for maintaining the pattern in question. This is achievedthrough ten-segrity structures. It suggests that com-plementary opposedfactors should be specially positioned in relation to one an-other. Thispattern of contraints may be used to design a spherically symmetrical representation(5).
In thic approach the concern is to make use of some surface which canbe 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 possiblythe Egyptians, as reported by Francis Yates (8). It is only comparativelyrecently in the 17th century that it went out of favour with the westernscientific revolution and the widespread use of pa-per as a crutch formemory. There is little current concern with memory (particularly withthe increasing number of information services and references tools) otherthan in the form of gimmicks to meet the chal-lenge of examination, orin relation to speed reading etc. On the other hand these gimmicks, currentinvestigations 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 discussedelsewhere ( 1 ).
A recent paper proposes the use of a sperical surface to model the bodyof knowledge and its development (10). The concern did not extend to problemsof comprehension. As Yates reports, this de-mands the use of "hooks" whichusefully trigger the imagination through non-intellectual processes, howeverirrational and unsystematic they may appear. Thus favoured "surfaces" includedbuilding complexes which enabled some to use over 120,000 memory locationsin a structured comprehensible relationship to one another. The productionof a suitable representation can be seen as a problem of design, namelya 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-singlyapparent.
As a design problem, any initial attempts are bound to contain manyweaknesses. These could however be progessively reduced following experiencewith the representation, discussion and feedback. Part of the merit ofthis approach (for some at least) lies in reflecting on the design problemitself and the disciplined pattern of decisions which need to be made.It is likely that there are several alternative patterns which could leadto equally useful and thought provoking results.
Decision 1: The surface used for the representation shall be a sphericalone. This has the merit of built-in continuity which, through the absence ofa boundary, does not give undue privilege to any position on the surface. Beingfinite and rounded it has a certain "graspable" quality; the form of the wholeis intuitively comprehensible as a gestalt. This quality is absent from conventionaltabular (or matrix) presentation which provide an abstract framework lackingany focus for comprehension. The same is true of more complex surfaces (althoughthere are merits to the use of a torus, for example).
Decision 2: The surface shall be broken up into a pattern of two interweavingforms: "land" and "water". Clearly a uniform surface would not provide any "grip"for the imagination. Simply inscribing a regular latitude/longitude grid patternwould also stress the abstract and alienate the imagination. The land-and-watercoding appeals to the imagination because of the widespread familiarity withthe terrestrial globe, its various surface features, and their relationshipto the observers own location and those of others of whom he is aware. It hasan organic quality which is encountered in fictional fantasy worlds (of Tolkien),science fiction, or humour (see Fig. 1 and 2; are they conceived as continentson 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.Links Books, 1972.
(pseudonyms for John McHale and Magda McHale, respectively)
|Fig. 1: Marxyland||Fig. 2: Anotherland|
Decision 3: The two-fold distinction on the surface shall be used tocarry the basic two-fold distinction in human activity and concerns. Here careis 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 introducesthe vicious circle of the definition of the words used in any definition, etc.ignoring the question of comprehension. The words used here are therefore tobe considered as pointers only. The basic distinction is between what can becomprehended (by the reader/observer) as common to what is denoted bythe labels in earth of the following lists:
Decision 4: The land masses shall represent activity performance ratherthan the activity as a subject eg performing chemical operation and associatedsymbol manipulation, rather than "chemistry" as a body of knowledge; prayingrather than prayer; etc. This removes the need to consider subjects which arenot associated with a pattern of activity, and renders other subjectssubordinate to the pattern of activity with which they are associated. It isa 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 onthe notion of the "body of knowledge" rather than "activity performance". Revisionof the design sequence would then be required or the advantages of an alternativedesign 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.
Cybernetics (Contr. and automat.)
Gen. and tech.physics
Astronau-tics and spaceresearch
Atmosphersci. and tech.
Materialssci. and metallurgy
Microbio-logy and cultivation
Plantbiology and cultivation
wood sci. &
Health & theoretical
State and politics
Social aid,social poli-tics
Area planning, urbanism
ECONOMICS and TECHNOLOGY AREA
Gen. and natl.economics
|76 Commodity sci. and technol.||77
Vehicle sci.& technol.
SCIENCE and INFORMATION AREA
Information in general
Religion and secret teachings
The "fields of human activity" denoted by the land masses could be interpretedto 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 typesof role. Only by further investigation will the implications of this designdecision become apparent.
There is an obvious design problem of determining which level of " humanactivity" is to be mapped by the surface areas themselves and which levelscould be more appropriately indicated by (a) features on those areas, whether"natural" or "artificial", or (b) by "natural" or other activities occurringon or over such surfaces, or (c) by making use of one or more other sphericalsurfaces (a point raised in Part 1). This question will be considered inPart 4
Decision 5: It follows from Decisions 3 and 4, that the water massesshall 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 bodyof water, would thus be used to represent an "irrational" discontinuity in anordered approach. The distinctions implied by the size and nature pf the bodyof water (ocean, inland sea, lake, river, marsh, stream, etc) will need to beclarified by subsequent design decisions even if their possibilities can beintuited at this point.
Two basic design problems must be faced at this point namely:
The conceptual procedure whereby a matrix is formulated gives rise to cellsof 'equal importance' or 'weight'. By this is meant thateach category (cell) is equally distinct from the other categories (cells).Of course, if some quantitative measure is attached to the cells than therewill be inequalities. But these may be considered secondary (at least for themoment).
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 subdivisionof the spherical surface. The relationship of the matrix cells might also beconsidered 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 thesocial sciences, the humanities, or other modes of activity shows the weaknessof this presupposition and the difficulty which would be encountered in formulatingsuch a matrix. Even classification science, by definition neutral to the varietyof fields of activity, generates a variety of competing matrices (although theyare usually lists). In fact Fig. 3 constitutes the most recent effort to coverthe complete range with a minimum of distortion. But of course it is not designedto highlight the hiatus, in the minds of the practitioners, between the differentfields. 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 alongthe discontinuities between the areas on the spherical surface. However thisdoes not imply a regular pattern of "canals", for the degree of hiatus willvary between different "land" areas, giving rise to anything in width betweena river and an ocean. On the other hand, some possible lines of hiatus willbe eliminated as a result of the rational binding together of two areas (e.g.where a suitable paradigm ensures the appropriate meshing). Furthermore, alarge category (e.g. a particular science) may be fragmented by a "networkof waterways" into sub-areas due to the mutual hostility between its constituentschools of thought.
The question is then does the Part 1 procedure suggest a means of decomposingthe 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 geodesicsubdivision of the surface of a sphere (Fig. 4). It may be used to decomposethe surface as finely as is required by the (ability to "resolve conceptually") the presence of nested sub-categories in a given zone (and not necessarilyin another). It may be based on many of the three-dimensional figures to whichthe Part 1 procedure gives rise.
These steps indicate that it is possible to depart from the "simplistic" idealsubdivision of the spherical surface and to respond to local variations. Butthe areas so delineated, however small, are still bounded by "straight" lines(i.e. on the curved surface). It is a valuable indication (preserving the classificatoryprecision 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 resultingin a ragged, "realistic coastline". This raises the question of how to determinewith 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 ofactivity which "incorporates" a sub-area across the original boundary into itsown domain. This opens the possibility to the indication of a ("political")switch of allegiance or empire building, neither of which is foreign to thedynamics between disciplines, for example.
Despite these possibilities however some nagging questions remain. They maybe illustrated by imagining that in the absence of the conventional globalmap information was nevertheless available on all the land masses. This couldbe presented in list or matrix form. Despite the lack of any global perspective,inhabitants of the land masses could be consulted on their relationships withneighbouring territories and the barrier constituted by any intervening bodyof water. The problem is how to solve the question of scale, distance and directionon the basis of such interviews. How can any group associated with a particularpattern of activity be objective about the relative size of the land surfaceby which the activity is denoted ? There would be an obvious tendency to inflatethe 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 pointof declaring its existence to be a 'pure fantasy of fevered minds"). Inthis 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 providea rational basis for positioning the boundaries between fields of activityand this is considered in Part 5. At this point some available indicatorsmay be considered as a guide to refining a map in terms of size of surfaceareas as a measure of relative importance.
A number of possible indicators are available:
Both types of data would fail to distinguish between the various patternsof activity often associated with different kinds of social grouping (e.g.organizations) or cultural group (e.g. communities). Clearly a varietyof sources would have to be used to obtain a rough indication of surfaceareas as a stimulus to feedback.
A second question concerns overlapping patterns of activity (e.g. anoccupation 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 surfaceapproximations are based on some indicator like world man-hours per yearper activity, some very basic activities might acquire undesirable prominenceon the total surface (e.g. sleeping, food consumption, etc.). One approach,if desired, is to use a logarithmic relationship between man-hours andsurface area. But would this destroy the desirable iconic value of sucha map ? With regard to the degree of relationship between land areas, itshould be possible to make some use of citation analysis. Clearly the frequencyof citation of papers in neighbouring fields would be high. A frequencyanalysis could then lead to a suitable pattern of juxtaposition of fields.Of course citation information is only available for certain fields ofactivity and covers only a few publications, but it could neverthelessprovide some valuable ("quantifiable") guidance particularly for the naturaland social sciences. Possibly an analogous "citation" approach could bedeveloped on the basis of a rigorous interview technique in order to coverother fields.
The preceding paragraphs are an indication of design problems to be confrontedin the light of different kinds of information available. It is appropriateto view this problem in terms of the probable confusion in the minds of theearly cartographers confronted on the one hand with religious and philosophic(ideal) models of the structure of the world, and on the other with a jumbleof facts, opinions and rumours based on travellers and investigators with differentkinds of axe to grind.
Doris Lessing: Briefing for a Descent into Hell
|The world was spinning like the most delicately tinted of bubbles,all light It was the mind of humanity that I saw, but this was notat all to be separated from the animal mind which married and fused withit everywhere. Nor was it a question of higher or lower... I watched a pulsingswirl of all being, continually changing, moving, dancing, a controlledimpelled dance, held within its limits by its nature, and part of this necessitywas the locking together of the inner pattern in light with me otherworld of stone, leaf, flesh and ordinary light..|
And on this map or plan that showed how myriads of ridiculously self-importantidentities were reduced to a few, was another, different, but, in someplaces, matching pattern, of a stronger, rarer light (or sound) that variedand pulsed and changed like the rest but connected direct, made a linkand a bridge, a feeding channel, between the outer (or inner, accordingto how one looked at it) web of thought or feeling, the pulsating bubbleof subtle surrounding colour, and the solid earthy watery globe of Man.Not only a link or a bridge merely, since this strand of humanity wasopen like so many vessels open to the rain, but part of the shimmeringweb of fluid joyful being, which was why the scurrying, hurrying, scrabbling,fighting, restless, habng, wanting little patches of humanity, the crustsof lichen or fungi growing here and mere on the globe, the sea's children,were, in spite of their distance from the outer shimmering web, neverthelesslinked with it always, since at every moment the glittering tensionof singing light flooded into them, into the earthy globe, beating onits own delicious pulse of joy and creation.
This investigation has so far clarified a number of aspects of the designproblem. Attempts at producing crude maps could be made. But it is possiblethat, by plunging further into the implications of the spherical framework,some useful insights and clues may be obtained to improve map design. Thatis the aim of this Part, which raises questions without necessarily supplyingadequate answers.
Given the distinct land masses of Part 4, one may ask what "spreads"or "stretches" any such field of activity over the spherical surface toits boundary. Why is "mathematics" in one part and "art" in another ?
Suppose that each such field could be defined in terms of different combinationsof a limited number of distinct "elements" of perception or cognition. Thenhow many elements are required at a minimum to enable the complete range ofactivity fields to be specified ? What kinds of elements and combinations arewe talking about ? And how does this relate to the geometry of the sphere?
It is important to note that in denoting a field of activity by an area,this opens up possibilities which are absent when it is definedas a point -- as in a list, a classification scheme, or even a matrix(where a "cell" is in effect a point in an array). Such a field may beconceived as composed of points with a common characteristic. But towardsany boundary of the field the "strain" increases on the specificationsof the point in terms of the common characteristic (exemplified by themore central points of that field). The boundary is the location wherethe points shift allegiance to minimize the strain.
This suggests that the land mass denotation of field of activity reflectsvery adequately the crudity and rigidity of conventional conception ofsuch activities. It corresponds to the Aristotelian either/or approach.The possibility that there might be some functional continuity across suchboundaries is excluded. Attempts can made to extend the boundary of a fieldto encompass a neighbouring field, but the possibility that the natureof the field changes as one moves over it is excluded. Althoughin fact, as with border cultures anywhere, the activities on each sideof the border may have more in common than with their respective centralpositions. This of course makes a matrix representation crude and unsubtleAlso information must be placed in either one cell or another, but notbetween.
Expressed in term of the sphere, it would be much better to be ableto indicate the type of activity by some function of the position of apoint on the sphere. Transition from point to point would then give functionalcontinuity emphasising continuous " transformation" from one activity toanother. The "artificial" regrouping of points into areas to which a conventionallabel is attached, and the emergence of discontinuities between areas,would then be understood as arising from an inability to handle such functionalcontinuity - an inability with which we are obliged to live. (There isa temptation to think of such artificial areal rigidifications as conceptual"tectonic plates" floating slowly around on an underlying semi-fluid continuousmagma which wells up at the discontinuities... or as "macrons" (14)).
If this line is followed further, it may be asked how points might bedefined in these terms. What function or coordinate scheme could be usedto "spread", the complete range of activity "elements" over the sphericalsurface ? Is it, for example, possible to use any 4-fold scheme (e.g. Jung,Parsons, etc) such that from a given point moving "north", "south", "east", or "west" moves one to activities with a greater amount of "quality A","B", "C" or "D" respectively ?
Clearly it would be important to avoid being trapped by any particular4-fold scheme which effectively stresses the qualities characteristic ofthe field of activity within which it was formulated. Rather the principleof a 4-fold scheme would be accepted and the challenge of determining whatcontent emerges from a 4-fold cut could be faced. This problem is discussedelsewhere (1). Basically the difficulty is one of avoiding the labellingtendency, the assumptions associated with labelling, the tendency to prematureconceptual closure, and the problem of comprehension. From this emergesthe possibility of taking whatever can be comprehended (without labelling)by the reader/observer as common to a wide range of 4-fold cuts. This isuncomfortable because of the elusive quality such as is found in the significanceattached by Chinese philosophical texts to "north", "south", "east", and"west" (16) (Note that, even more than in the West, the Chinese emphasizethe arreal as well as the directional character. This suggests a transformationfrom the "compass" circle representation to the spherical arcal which wouldcreate zones such as "north west", "south south east" to whatever levelof detail was required. How they would be located as areas on the sphereremains to be explored. On the other hand labels may be attached for convenience,although the challenge to comprehension should be stressed whenever possible.
The geometry of a sphere also suggests a more elegant scheme namelyin terms of radial coordinates. This effectivity transforms "north / south"and "east / west" into two angular measures. The challenge to comprehensionof enantiodromia (see above) has of course to be faced. The relationshipbetween angle and meaning has been explored by several authors (17, 18,19) but the conclusions are at best tentative; much remains to be done.
It should not however be forgotten that the purpose of this exerciseis to obtain an adequate `` conceptual surface". The sphere has comprehensiblecharacteristics but by choosing it, it is immediately necessary to allowmore complex phenomena (which are distorted by a spheric representation)to be projected onto it. The consequence is a necessary loss of (simplistic)neatness, emphasizing the value of the "realistic organic" map of Part3. But the line of investigation can be extended further (without losingthe link back to Part 3 and 4) by confronting the problem of differentlevels of abstraction and comprehension. It remains a design decision asto the level of abstraction at which the "fields of activity" are conceivedand allowed to "impact" on the surface of the sphere. But what happensto the levels which are less abstract or more abstract, once such a decisionis made ? Where do they get "put" ? Those which are less abstract may perhapsbe allowed to "affect" the topography and geography of the sphere, andsuch design possibilities are briefly discussed in Part 6. Those whichare more abstract and less comprehensible may possibly be projected intothe socio-cultural life which could be designed onto the sphere. This approachis not considered further in this paper. Although it could be very meaningfulas a communication tool and provides a rationale for the tendency to usecartoon, fictional and legendary characters to illustrate psycho-socialdynamics. An alternative is to nest a number of other spheres concentricallywithin that already discussed, according to the number of levels of abstractionit is desired to represent. With this approach, the most abstract (i.e.most central) sphere would reflect a minimum number of distinctions whoserelationships would be relatively clear and simple, but whose content wouldconstitute a challenge to comprehension and would be impossible to defineor label satisfactorily (1). At other levels, comprehension and labellingwould be less of a challenge but the relationship pattern would be increasinglycomplex and difficult to define or to comprehend as a totality. Considerthe successive shells of the I Ching elements with 2, 4, 8, 16, 32 and64 components (16). The patterning of the latter is very complex, in factone is reminded of the Chladni standing wave interference patterns (20).
If any more abstract spherical shells were omitted, their content andits relationships would have to be projected onto whatever less abstractshells were retained in the representation, or be left as "uncaptured"by it. Such projections would of course tend to complexity the patterning.Note that some clues to comprehending the nature of such a representationmay be obtained by reflexion on the successive electron shells of atomsand the patterning of "orbital clouds". This is an impressive conceptualmodel of the relationships between successive levels of distinction. Itis possible to see how many levels are required before N distinctions havebeen effectively made, namely how many levels are required before N distinctconcepts can be effectively represented (1). The representation/comprehensionproblem of this shell approach has, interestingly enough, been confrontedin the problem of representing the complete range of colours. Not onlydoes Johannes Itten (21) suggest that the complete range can be representedby points throughout a sphere (defined by latitude and longitude), buthe chooses to consider the basic colours as regrouped into 62 zones onthe surface of the sphere (5 x 12, plus 2 Polar zones of black and white).He also chooses to consider the remaining colours as grouped in 3 innershells. The whole scheme is structured so that complementary and contrastingcolours are immediately evident. He also indicates the complexity and richnessarising from colour "chords" of 2, 3, 4 or 6 tones based on the apexesof (three-dimensional) figures inscribed within the colour sphere (cf.Part 1). It is interesting that the representation of the range of coloursis not yet understood or accepted, and that the analogous problem for sounds,odours, tastes and textures in far from being solved.
Whilst the shell approach was, ironically, much favoured by traditionalreligious philosophers (whether concerned with the structure of the cosmosor of man) and does have iconic merit due to its spheric symmetry, it neverthelessposes serious problems to comprehension. The same information can be representedby "deconcentricating" the shells and treating each as a planet in orbitaround a central sun (presumably not a binary star!). The approach of Part3 and 4 can then be applied to each independently in terms of the contentof the level of abstraction decided. The structural richness of the solarsystem model, with which there is increasingly widespread familiarity,provides conceptual "hooks" on which to hang even more of the dynamicsit is desired to capture in a representation. Clearly the planets mustmove in orbit, they must spin, etc. These stabilizing characteristics,which have traditionally constituted severe obstacles to comprehension,are even more difficult to comprehend in the shell model (electron "spin",etc.). They also raise interesting questions about the adequacy of a simplespherical representation without "spin" (implying "poles", "diurnality"etc.) or "revolution" (implying "seasons") around a central predominating"function". Clearly it is not adequate simply to use separate and unrelatedspherical models to represent different sets of functions at differentlevels of abstraction (as is the conventional approach of disciplines concernedwith different levels of abstraction). There is a responsibility (whose?) to show their relationship by some means. The solar system model isstructurally rich (Even greater richness can of course be obtained by usinga .. galaxy ~ structure as a basis for a representation. as discussed elsewhere(22)) and, ironically again, has been used traditionally to relate differentfunctions (e.g. gods, qualities and planets) to facilitate comprehensionby the populace.
Hopefully it is now clearer how the design problems might be compartmentalizedand structured. The design objective is to provide a representation withinwhich one could structure one's thinking according to the level of abstractionat which one wished to function. This would not prevent, but rather encourage,consideration of the perspective at other levels of abstraction as appropriate.
It is to be hoped that Parts 3, 4 and 5 have given a better understandingof how "conceptual markers" might be used within some "terrestrial" or"solar" representation. It should be apparent that a step by step designapproach is possible with many options. Many of the options can be designedinto the representation without necessarily asserting themselves aggressivelyon the attention of the observer/user - who may be as sensitive or insensitiveto the variety and complexity as are people with regard to their ordinaryenvironment.
The stage is therefore set for the design team to create a world inwhich the familiar elements used in the representation are interrelatedin a manner which reflects, as much as possible, what is understood ofthe relationships and characteristics of the psycho-social phenomena theydenote. The design team may put into the design "kit", for use as "conceptualmarkers" as many features of the "real world" as are considered usefulin carrying an understanding of what needs to be represented. The designchallenge is to "feel out" the iconicity of different design options. Amajor difficulty is to resolve problems of level of abstraction and todetermine where to ¢< put,. certain phenomena (e.g. as a geological,climatic, or social feature, or on a separate planet). A "poor" designwould have the doubtful value of a literary metaphor. A "good" design wouldbe highly isomorphic and would raise interesting questions. How isomorphicand how iconic it is possible to be remains to be discovered. The designproblem is as much art as it is science, and that is how it should be toresult in a significant representation (for the absence of either leavesus where we now stand).
It is interesting to reflect on how many distinctions and relationshipsare built into any conventional concept of the world and our labellingof its elements and processes (on the basis of education or experience).Of course part of the design problem here is matched in the differentconcepts of the world held in nonwestern cultures and languages. Thisdoes not prevent communication, however much it is distorted, but it disguisesheavily the subtle differences in understanding (1).
In Fig. 6 some indication is given of the variety of features which could beconsidered in the design. It is worth bearing in mind the procedures used tointerrelate objectively such features in the "real world" (e.g. topography andtriangulation surveying). The stages and processes by which such techniqueswere discovered, and to consider the extent to which analogous problems arenot to be faced in designing or understanding the representation.
|Fig. 6: Metaphoric mapping features|
|Continent, wind, mountain (chain), storm, peninsula, flood (plain),island, desert, watershed, swamp, valley, jungle, plateau, grassland, ocean,forest, strait, sea, estaury, river|
Their have been a number of experiments which can be considered in thedirection of producing "conceptual maps". A basic distinction must be drawnbetween those which are point-oriented and those which are area-oriented.In the point-oriented case, one may cite arrow-diagram experiments in classification(23). A similar technique has been used to produce metabolic/biochemicalpathway charts (24). More generally there is the production of systems(flow) diagrams of various kinds (25). The limitations of this approachare apparent from the visual drabness of the basic flow chart of the Clubof Rome sponsored, highly, significant Limits to Growth project(26). Equally "academic" are social network diagrams, although these usuallyshow people linkages. Related to these, but focused on concepts are beliefnetworks (27) and "mental models" (28).
A very crude and partial move towards an area-oriented presentation has beenmade in the UNESCO science policy information thesaurus, SPINES (29). This isreally a compromise between the point and area forms as are the Venn diagramtype figures used innovatively for international organization memberships byUNCTAD. Of a very different kind are so-called "mental maps" (31) of peoplesperceived distortion of geographical areas with which they are (un)familiar.Other examples may be found (25).
|Paradox of the Complete Map|
from Lewis Carroll's Sylvie and Brumo Concluded 1893
|Paradox of the Inclusive Map|
posed by Josiah Royce, in The World and the Individual, 1899
'That's another thing we've learned from vour Nation.' said Mein Herr."map-making"
But we've carried it much further than you.
What do you consider the largest map that would be really useful ?'
'About six inches to the mile.'
'Only six inches!' exclaimed Mein Herr.
'We very soon got to six yards to the mile.
Then we tried a hundred yards to the mile.
And then came the grandest idea of all!
We actually made a map of the country, on the scale of a mile tothe mile!'
'Have vou used it much ?' I enquired.
'It has never been spread out, yet.' said Mein Herr: 'the farmers objected:they said it would cover the whole country, and shut out the sunlight!So we now use the country itself, as its own map, and I assure you itdoes nearly as well.'
'Let us imagine that a portion of the soil of England has been levelledoff perfectly and that on it a cartographer traces a map of England. Thejob is perfect; there is no detail of the soil of England, no matter howminute, that is not registered on the map; everything has there its correspondence.
This map, in such a case, should contain a map of the map, which shouldcontain a map of the map of the map, and so on to infinity.'
Clearly there is little to prevent the "design" (in the sense of thispaper) of animated representations based on geographical or even socio-culturalsystems. Initially it would only be necessary to use the computer powerto "explore" the topography in detail. Later "climate", "erosion", "plantspecies In "animal species Is can be added in together with their interrelationships.The possibility of growth, or geological or species evolution (from a "primeval"condition) could be explored. It is clear that, in contrast with conventionalsimulations, the dynamics of the representation impose a powerful and necessarydesign constraint which facilitates `` right brain" comprehension by non-specialists.The computerized display in fact constitutes a powerful design tool beyondits current uses for "computer aided design" of physical systems.
The problem is not so much the hardware but rather the information on the fieldsof human activity. This currently has built in blindspots or distortions dueto the focus and interest of the investigating disciplines. Currently an attemptis being made to remedy this with a view to such a mapping exercise. This isbeing done with data on 8,000 "international" organizations covering thecomplete spectrum of human activities which have achieved international significance.This is obtained from the Yearbookof International Organizations (34), itself derived from a data base incommon with the Yearbook ofWorld Problems and Human Potential which was conceived with such a mappingexercise in mind (3).
Much can of course be learnt from the conventional discipline of mapdesign (35) and from structures in nature (36).
This unconventional approach to classification should be compared withthe long series of approaches in the past (37, 38, 39). The record of howsocieties have chosen to see the universe/environment decomposed into categoriesis extremely instructive. E I Samurin examines over 200 such attempts (37).
As is to be expected no classification exercise bears a very happy relationshipto any of its predecessors or contemporaries. The new rejects the old andviews its inadequacies with considerable disdain. This attitude, temperedwith defensiveness, also tends to characterize the relationship betweenadvocates of the different schemes today - which are the basis of the computerizedinformation systems of international agencies competing for financial resources.
What is missing is a sense of continuity not as a form of historical lip-service- but of the evolution of classification patterns. Now the design approach advocatedin this paper provides such a linkage. For, if the exercise were to be conductedin terms of the framework of any given period of the past, it would be seenhow the "land masses" would be differently located with respect to one another.The geological evolution of the earth may therefore be used to suggest the basisfor a series of maps which record successive conceptual decompositions from"primitive" to complex. Continuity is respected.
... Against other people's maps
"... Boaz-Jachin doubted that his father's map would be of any use tohim. He had remembered it as large and beautiful.
Now he thought of it as small and cramped, too neat, too calculated,too little cognizant of unknown places, of the night places waiting beyondthe day places, of the somewheres dropping from the open wombs of nowheres.He felt lost as he had not done since being with the lion.
'Maps,' he said softly. 'A map is the dead body of where you've been.A map is the unborn baby of where you're going.
There are no maps. Maps are pictures of what isn't I don't want it.'
'That's beautiful,' said the girl "There are no maps" What don't youwant ?'
'My father's map,' said Boaz-Jachin. 'That's good,' said the girl. 'Isit yours ? Do you write ? It sounds like the beginning of a poem: "Myfather's map is..." What is it ?'
'His,' said Boaz-Jachin. 'And he can keep it.'
Hopefully this paper demonstrates that there is a practical approachto this very difficult problem and that much could be learned from suchan exercise.
This sort of approach opens up for discussion the whole question ofthe value of the conventional western scientific approach of distinguishingsets of factors or conditions, and displaying them in a matrix or classifyingthem in some way. This widespread tendency detaches the observer from thephenomena in a manner 'which can conceal inability to relate to them, tofully comprehend them or to understand their relationship to other suchsets. How can the " scientific", act of classification be related to thenon-scientific need for representation and comprehension of complexity- given the variety of perspectives, information preferences, and tolerancesfor complexity ?
Clearly there is a paradox associated with such mapping in that themap is inadequate if the mapping activity does not figoure on it. Whilstamusing (see "paradoxes"), the paradox embodies problems which we resolvesimplistically at present and thus suffer the consequences of the inappropriatenessof our collective action. Alastair Taylor in concluding an article on Processand structure in Sociocultural systems (40) makes the point that:
" What we have to recognize is our shared involvement in a fundamentalconceptual shift - a multirelational transformation from a nation-stateparadigm progressively to a global construct comparable to the shift ofperspective from the Mercator projection - rectilinear and emphasizingtwo-dimensional "flat" space - to, say, an orthographic projection, atonce curvilinear and recognizing new spatial relationships. Perhaps thetraditional concept of space itself requires to be assessed anew. The nation-stateparadigm tended to view space as a void, an empty receptacle to containpieces of "property", so that space was largely a matter of "place" and~ location", and what lay beyond the property lines was either no-man'sland or, alternatively, open to entrepreneurial grabs" and exploitation.But a very different way of perceiving space is to regard it as a plenum- an ordering constituent of a macrocosmic system in which field forcesare omnipresent and omnio-operative, acting upon all material phenomenaand maintaining a dynamic, energizing, as well as balancing, field itis in the context of a plenum or field we need to approach the orderingof our planetary and extraterrestrial spaces alike".
And, strangely enough, C.H. Waddington in his concluding remarks tothe same book is forced into the geographical metaphor which is the themeof this paper in order to convey the complex notion of an epigenetic landscapein relation to evolution.
The question of the underlying kinds of metaphor through which the geographicalordering of the world is understood has recently been explored by AnneButtimer stresses the need for new metaphors at this time (33).
There is a tantalisingly elusive relationship between the metaphor andcurrent techniques for investigating and representing macrodynamics. Thisis itself interpreted in terms of catastrophe theory, namely the theoryof the transitions of attractors (macrons) in a phase space, which is thebasis of the geometry of macrons as it has developed so far (14). The interestingquestion is what macron patterns the mind chooses to recognize under differentcircumstances. The ramifications of this question are discussed elsewhere(1), and it is interesting that the same authors are cited by Erich Jantschin considering the archetypal implications of the decomposition of a wholein relation, to modes of learning, evolution of consciousness, and methodsof inquiry (41). For example von Franz, a Jungian scholar, states of thetime-bound qualities of the first four numbers: "One comprises wholeness,two divides, repeats, and engenders symmetries, three centers the symmetriesand initiates linear succession, four acts as a stabiliser by turning backto the one as well as bringing forth observables by creating boundaries,and so on ,' (42, p. 74). Jantsch notes that it is the transitions betweenthese four basic qualities that symbolize how a gestalt system maintainsits nature (to comprehension ?) in the presence of many temptations tobecome formalized. And it is the first step from one to two which constitutesthe "original sin" of formal division which, according to Pankow (43, p.35) "separates the two sides of complementarities and treats them as identities".
He relates this to the work of Spencer Brown (44) and concludesthat "Therein lies a formal justification for the ultimate complementarily ofthe search without (in the physical world) and the search within (in our ownexperience), for what we approach, in either case, from one side or the other,is the common boundary between them (Spencer Brown, p. XIX)" (41). Such investigationssuggest an intriguing link between the ecosystem design elements of this paperand the traditional notion of both Eastern and Western religious disciplinesconcerning the importance for the individual to cultivate an ¢¢ innerspiritual garden". Venturing further, one can see the challenge to society ofthe collective re-creation of a "Garden of Eden I" in the sense of this paper,which goes beyond that of simple metaphor, as a design challenge to scienceand art intertwined. Although, as A. Korzybski stressed, "the map is not theterritory", the territory we know may certainly be construed as a very powerfulmap.
The first and most obvious type of change in an embryo is that it developsinto an adult form; this is relatively long-lasting, but is in fact alwaysundergoing slow processes of change, which lead eventually to senescenceand death. This implies that the phase space in which the system is modeledcontains a surface with a general slope which will guide any trajectorytoward the adult state, and final death. However, we have also to takeaccount of the fact that different parts of an embryo develop into differentorgans - liver, kidney, brains, muscles, and so forth. This situationcan be described by supposing that superimposed on the general slope isa radiating system of valleys, which direct some trajectories tomove along toward the kidney, another set to move along toward liver,and so on. An attractor surface modeled in such a manner is called anepigenetic landscape.
A description in these terms suggests many questions which it might beprofitable to study. At what point do various valleys branch off fromone another ? Do two valleys which have once become separate from oneanother ever later come together and fuse again ? But perhaps the mostimportant questions for most practical purposes relate to the shapes ofthe valleys in cross section and the height of the mountain watershedsbetween them.
There is no reason why a valley should not have the shape of a very narrowcanyon with precipitous and possibly high walls; or alternativelybe characterized by the gentler contours, leading down to broad watermeadows through which the river meanders, which are characteristicof what geologists would regard as an old, mature earth form.
To avoid having to use the only metaphorical name of a "valley", forwhat is really a characteristic of an attractor surface in a multidimensionalspace, I have coined the word "chreod". The cross-sectional shape of thechreod describes the reaction of the system to fluctuations affectingit. In a chreod with a canyon-like shape. It will be very difficult todivert the developing system from the very bottom of the valley. If thisis done by a strong enough influence, the system will immediately findits way back to the bottom as soon as the influence ceases. Such a systemis very stable in Holling's terms. On the other hand, if the chreod hasthe shape of a broad river floodplain, it will be very easy todivert the system from the very lowest point and it will return thereonly after meandering at random for quite some distance. This is a systemwith little stability in Holling's terms.
On the other hand, the resilience of the system depends not on the shapeof the river valley or chreod, but on the height of the watersheds oneach side of it. These indicate the maximum fluctuation which the systemcan absorb while remaining within the same chreod. Anything greater thanthis will push the system out of this chreod over the watershed. Now Hollingsuggests that it is very unstable systems (i.e., those corresponding tobroad valleys), which are most resilient (i.e., have the highest watersheds).In a very general way, in epigenetic landscapes comparable to old maturedearth forms, this may be true; but the connection is not necessary. Infact, in newly formed landscapes, developed for instance in regions ofthe earth recently subject to considerable uplift, one may find deep valleyswhich are very narrow in a cross section, such as the Grand Canyon. Ifone is trying to design and produce in a relatively short time a systemin which it is of the first importance that it remain in its own chreodand not be pushed over a watershed into something quite different, thenthe simplest plan would be to make a very deep valley and a narrow one.The objection to this is not that its stability necessarily robs it ofresilience, but that it allows very little variation among the individualsin a population passing along it. One could say that it produces a greatdeal of turbulence in the stream at the bottom. The social ideal wouldseem to be to allow a great deal of individual variation, in a maze ofmeandering streams in a flat valley bottom, but at the same time to havehigh watersheds on each side to prevent the system's being flipped outof that chreod into some unknown country.
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