12th September 1986
Communicable Insights
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Geometry of connectivity
In this annex to Comprehension of Appropriateness,
the arguments of the previous annex can be clarified and taken a step further
using the work of Ron Atkin on q-analysis, namely the theory and application
of mathematical relations between finite sets. He has applied this to the analysis
of communication patterns within complex organizations. (38, 39, 40).
The perceptual significance of this approach is well-illustrated by visual
sensitivity to colours resulting from the three primary hues (red, green and
blue). These may be represented on a simple triangle (see Figure 7).
| Figure 7: Ccomprehension of insights based on triangular model of Ron Atkin | |
 |
0-dimension vision: |
Here the vertices (O-simplexes) represent the primary hues, the sides are twofold combinations (1-simplexes), and the combination of the three hues makes the central white (2-simplex). The 2-simplex, together with all its faces, forms a simplicial complex KY (X) where X is the vertex set (red, green, blue) and Y is the set of seven perceived colours.
Now to be able to see all the colours, a person's vision needs to have the ability to function in the triangle as 2-dimensional "traffic" on that geometry, moving from location to location adjusting to the complexity of the geometrical structure which carries the visual traffic. It however the person's vision is limited to 1-dimensional traffic, then white could not be perceived because the visual traffic of seeing is then restricted to the edges and vertices only. Similarly, if the person's colour vision is only O-dimensional, then it is restricted to the vertices. It can only see one vertex colour at a time and never a combination (as represented by an edge). If vision was 3-dimensional, it would allow traffic throughout the geometry, but would perceive other colours as well, calling for a fourth vertex in order to contain the full range of combinations.
If the geometry represents concepts or languages (or modes of socio-economic organization) instead of colours, then it would be expected that some people, in relation to that set, would have O-dimensional comprehension (i.e. sensitive to isolated primary issues only) and others would have 1-dimensional comprehension (i.e. only sensitive to binary combinations of primary issues). The latter would be unable to maintain attention to three concepts simultaneously in order to perceive the threefold combination (the central, integrated "white" issue). The threefold issue may then be termed a 2-hole in the pattern of communication connectivity amongst those involved. For 2-dimensional traffic however, the issue complex is coherent, comprehensible and well integrated. For the 1-dimensional traffic, it feels less secure as a whole, since the latter may only be experienced sequentially through a succession of experiences ("around the edges") from which the shape of the whole may be deduced but not experienced For O-dimensional traffic, the integrated concept does not exist, since experience is disconnected.
"Generally speaking it seems to be confirmed that action (of whatever kind) in the community can be seen as traffic in the abstract geometry and that this traffic must naturally avoid the holes (because it is impossible for any such action to exist in a hole). The holes therefore appear strangely as objects in the structure, as far as the traffic is concerned. The difference is a logical one in that the word "q-hole" describes a static feature of the geometry S(N), whilst the world "q-object" describes the experience of that hole by traffic which moves in S(N)" (38, p. 75).
As an "object" this phenomenon is an obstacle to communication and comprehension and obliges those confronted with it to go "around" in order to sense the higher dimensionality by which it is characterized. Communications "bounce off" such objects. As a "hole" this phenomenon engenders, or is engendered by, a pattern of communication. It appears to function both as "source" and "sink". Atkin suggests that, in some way which is not yet fully understood, such object/holes act as sources of energy for the possible traffic around them. From the initial research it would appear that such objects/holes are characteristic of communication patterns in most complex organizations. It seems highly probable that they can also be detected in any partially ordered pattern of communication. As such "societal problems", "human needs", and "human values" merit examination in this light from the perspective of different languages and modes of socio-economic organization.
Very concretely, Atkin has investigated situations in which the "vertices" (which could themselves be n-simplexes in a multidimensional geometry) are individuals or offices linked together through various committees. They could also be governments or disciplines. There will then be a lot of O-traffic and 1-traffic within and between offices due to the details of their intra-and inter-office (bilateral) operations. This traffic will circulate around the holes/objectswhich they constitute. Any n-level traffic can only be encompassed, or be brought to rest, by an (n+1)-level body (e.g. an executive or a committee). If the latter does not exist, such traffic will continue to circulate around the q-objects in the structure and, according to Atkin, may be defined as noise. An "empire builder" (or any elite), for example, in such an organizational system will carefully create many q-holes underneath him (at the n-level), so that subordinate bodies answerable only to his appointees, are trapped in the flow of noise between them (38, p. 129). Atkin notes that even though the geometry may not have been rendered explicit, such structures generate the feeling throughout a community of some "power behind the scenes" acting to outwit the formal structure. The special value of q-analysis is that it can clarify why action/discussion in connection with (development) issues tends to be "circular" in the long-term, however energetic it may appear in the short-term. As such it shows how social change is blocked by the way in which conceptual traffic patterns itself around the sensed core issue which is never confronted as such because the connectivity pattern is inadequate to the dimensionality of the issue. This would explain why so many issues go unresolved and why the process of "solving" problems becomes institutionally of greater importance than the actual "elimination" of the problem.
The elements of the triangle may also be used to represent different modes of socio-economic organization comprehensible under different conditions. It is possible for a person or an organization to conduct all its communication in terms of one of these modes or frameworks. Communications in terms of other modes or frameworks would be incomprehensible and to some degree inconceivable. It is possible to envisage a different paradigm, corresponding to the 1-dimensional traffic, which would permit movement between the primary modes via intermediate modes. This would correspond to the mind-set of a polyglot or a polymath, for example. Presumably more complex paradigms could also be envisaged. Atkin analyzes much more complex situations in exploring information flows through the committee structure of a complex organization. He is especially concerned with how information on substantive issues gets moved around through appropriate committees without it being necessary to confront core issues or bring them into focus, namely the bureaucratic technique of handling information overload by avoiding use of that information.
Q-analysis gives precision to the recognition that traffic of different degrees of content connectivity finds (or creates) its appropriate level in any psycho-social communication conmplex, presumably including a language. Communicable insights are level-bound, especially where they are of high connectivity. In other words, at the level within which we can communicate, concepts cannot necessarily be anchored unambiguously into terms and definitions which "travel well". Precision introduces distortion which is only acceptable locally within any communicating society - although "locally" must be interpreted in the non-geographical sense in which all nuclear physicists are near neighbours, for example.
The relation between two personal or institutional structures, conceived as a multidimensional backcloth, carries whatever traffic that constitutes the communication between them. If this backcloth changes by becoming dimensionally smaller, then its geometry loses vertices and the consequent connectivity properties. This is first indicated by the failure of higher dimensional traffic which the geometry can no longer carry. Such 4-traffic, for example, must then move through the structure to some new haven of 4- dimensionality or it must change its nature and become genuine 3-traffic. This process of reducing communication expectations in order to continue to live within the new warped geometry is the classical problem of compromising. The feeling of "having to compromise" is a painful one. It is the feeling of stress induced by the warping of the communication geometry, namely the direct experience of a structurally induced force, in this case a 4- force (38, p. 146-7). It is the feeling associated with the distortion of an unsatisfactory translation between languages. This approach clearly provides a very precise approach to understanding more subtle forms of structural violence. Atkin has applied it to an analysis of unemployment (38, p. 148).
Such considerations suggest the power of q-analysis in clarifying approaches to human and social development in general. Reducing the dimensionality of the geometry on which a person (or group) is able to live is an impoverishment associated with repressive forces. Expanding the dimensionality induces positive, attractive forces through which a sense of development and enrichment is experienced (38, p. 163). Q-analysis seems to be a valuable new language through which precision can be given to intuitive experiences and their communication, particularly since it provides an explicit measure of obstruction to change.
In the case of social development, it is probable that most continuing societal problems should be seen as holes/objects, especially given the well-established record of unfruitful action in response to them - however vigorous and dedicated. Typical examples are: peace/disarmament, development, human rights, environment, etc. Q-analysis could then provide understanding of why any action tends to be drawn into a vortex of futuility, however much it satisfies short-term political needs for visible "positive" action. The participants in the action find themselves "circulating" around a central concern of which they are unable to obtain an overview due to the geometries of the overlapping conceptual and organizational structures through which they work (or which they somehow engender).
The term "futility" used above is however only appropriate if the sole considerations were the elimination of suchproblems. In fact the existence of such problems is extremely important to the organization of society, to social development, and to the direct or indirect employment of many people. Just as the "defence" business is vital to the economy of many countries, so is the "social problem" business vital to many sectors of society. Eliminating social problems would be a disaster for many people, especially problem- oriented intellectuals, the employees of problem-solving agencies, or indeed those in need of stimulus and challenge.
In the case of human development, Atkin shows how the individual can be defined in terms of a multidimensional geometry requiring a minimum of four levels (38, p. 111). By relating this geometry to that of society, Atkin introduces an 8-level scheme (38, p. 162) within which the degree of integration or eccentricity of communication can be clarified in terms of developmental or anti-developmental forces.
Concerning such levels, the question arises as to whether their hierarchical order is fixed. Preoccupations associated with Schumacher's "small is beautiful", for example, may well modify the order. The ordering may be a question of orientation in which the "top" and "bottom" elements selected depend on the preferred concept and direction of development (e.g. "top-down",, "bottom-up"). This would be more consistent with the concept of order as an (existential) choice as discussed above in connection with the various fourfold "languages".
In such a multidimensional geometry it is clear that, whether in the case of an individual, a group or society as a whole, it is not possible to eliminate "underdevelopment" as associated with low dimensionality. Such a geometry will necessarily continue to have traffic of very low-level connectivity co-present with that of increasingly higher level connectivity. The simplest illustration arises from the continual birth of infants who will, when resources permit, continue to be educated through to the level of connectivity to which they can respond. But there will always be communication at both low and high- connectivity levels, especially about socio-political issues. The question is then how such learning communication between these different levels of connectivity can weave itself together within a social structure.
It is the status of the holes/objects in relation to development which could provide an interesting point of departure for further investigation. As noted above, it is not a question of attempting vainly to eliminate such holes, especially when some of them may arise from alternative concepts of "development". Rather it is a question of how configurations of holes can be identified and/or designed. It is such configurations of holes which provide the minimum structure (and communication dynamics) to stabilize and give form to the co-presence of the differing "answers" to the challenge of development.
In effect such holes exist at a lower connectivity-level than the "macro-hole" of higher connectivity constituted by the world problematique at this time. This macro-crisis hole "absorbs" the development initiatives of society by engendering the immense volume of action/communication traffic around the hole so defined. This draws attention to the developmental implications of the probable presence of holes of yet higher dimensionality than can be readily sensed or made the subject of acceptable public (consensual) communication.
How then are "better" holes to be engendered within such configurations? Now from one point of view it is necessary to avoid introducing an element of evaluation, because from each hole the perception of other holes will be distorted so that no communicable assessment can be usefully formulated. On the other hand, it may prove to be the case that, at the level of the configuration as a whole, more than one such configuration can be identified/designed in order to interrelate the perspectives associated with the set of holes. And at this level, without privileging any particular hole, more adequate interrelationships between the elements making up the holes can be identified.
Expressed differently, introducing evaluative judgements into the relationships
between the holes within a particular configuration can only contribute to
the dynamics between such holes in terms of perceived advantage/disadvantage.
Excessive emphasis on this runs the risk of tearing the configuration apart.
The identities associated with the holes can be respected in each of the configurations
in a series constituting progressively more adequate or richer formulations
of the relationships between "developments". There is consequently a
multiplicity of concepts of development operative in society. Individuals and
groups may "progress" from one to another, possibly with a general
tendency towards those of higher connectivity. But other individuals and groups
will emerge and find the concepts of lower connectivity more meaningful before
moving on, if they do, to those of higher connectivity. (In this sense the "ontogenesis"
of an individual tends to repeat the "phylogenesis" of his/her society).
Society in this sense is the arena within which individuals and groups refine
their concept of development.
Frameworks as frozen portions of learning cycles
In different ways the previous sections suggest that it might befruitful to consider the apparent isolation of languages or modes of socio-economic organization as being due to an inability to understand how to move between such frameworks. Although each framework constitutes a rich learning environment, it becomes a trap if no way can be found to exploit the advantages of other frameworks when they may be more appropriate. In a sense each framework provides a mode of information processing which is effectively a frozen portion of a larger learning cycle. Each such portion, just as with an organ in the human body, processes certain kinds of information in a manner significant for the whole, but within the prevailing paradigm there is no means of transferring the significance extracted to other contexts within the whole where it may be of value.
In the West part of the difficulty lies in the conception of learning as a linear process resulting in a shift in comprehension from A to B. It is only in the insights of Western poets that there is any recognition that, as stated by T S Eliot : "The end of all our exploring will be to arrive where we started and know the place for the first time". Gregory Bateson does however makes a strong case for the essential discontinuity of the learning process as a "zigzag dialectic between form and process" (17, p. 194). If the zigzag is considered as occuring around a learning cycle however, marrying in the Eastern bias towards recurrence, this cycle can then be subdivided into sufficiently detailed elements to be of significance for organizational operations. Jantsch discusses cyclical organization in terms of the system logic of dissipative self-organization:
"Hypercycles, which link autocatalytic units in cyclical organization, play an important role in many natural phenomena of self-organization, spanning a wide spectrum from chemical and biological evolution to ecological and economic systems and systems of population growth. The cyclical organization of a system may itself evolve if autocatalytic participants mutate or new processes become introduced. The co-evolution of participants in a hypercycle leads to the notion of an ultracycle which generally underlies every learning process". (41, p. 15)
The question then becomes how many discontinuous phases (Jantsch's "participants") it is useful to distinguish in the cycle. Too few and the incompatibilities between them are too fundamental, too many and the distinctions between them are too subtle. The operational significance of this conceptual constraint has been explored in earlier papers from which it is apparent that significance is lost if more than about 7 categories are used (42), unless the total breaks down into sub-sets based on simple (e.g. 2,3,5) factors (43).
A novel approach to the learning cycle in relation to action has been taken by Arthur Young (44) as a consequence of his experience as the inventor of the Bell helicopter (whose three-dimensional movement is notoriously difficult to control. He established the vital learning-action link through a new interpretation of the operational significance of the set of 12 "measure formulae" through which material phenomena are observed, acted upon and controlled in physics and engineering. These he portrays as corresponding to a series of phases in a learning-action cycle. Of special interest for the development theme is the significance he attaches to the sequence of movement around the cycle: one direction involving essentially unremembered experience-without-learning, the other involving conscious-learning-action. His approach has been adapted and modified to further emphasize the action-learning significance (Section KD, 1). It is interesting that the philosopher Stephane Lupasco also attaches importance to the analysis of such measures in terms of the polarities they constitute and the types of energy with which they are associated (45, p. 26).
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Place Figure 8 here [see subsequent version at https://www.laetusinpraesens.org/docs/learnstr.php)
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This approach clarifies how portions of such a cycle are vulnerable to institutionalization (as specialized, independent answer domains, or habital responses) to the extent that there is no learning bridge across the discontinuities. The problem of (social) integration is thus intimately related to the functioning of (collective) learning cycles. It seems probable that needs (and their satisfiers) also relate to different portions of such cycles, as would ranges of incompatible development goals or alternative visions of desirable futures. In each case the point to be emphasized is that such seemingly incompatible fragments are "frozen" portions of a cycle with which individuals or groups identify. None are of lasting significance in their own right, especially insofar as they hinder the collective learning process which must take place through them.
The facilitative and obstructive factors to further learning (i.e. successful "struggle" in marxist terms) at each stage in the cycle are probably linked to patterns of complementarity and incompatibility between the stages according to their memberships of (2,3, or 4-member) sub-sets in the cycle (e.g. preceding and succeeding stages in the cycle are in conflictual relationship since they would correspond to thinking of the opposite hemisphere). Answers given from any part of a cycle are of course "questionable" as perceived from other parts of the cycle.
A single cycle is probably not a sufficiently concrete representation of the complexity to be encompassed by an adequate meta-language. Where several cycles interlock to form a sphere, the nodes are effectively combinations of cyclic phases. The relationships of challenge and harmony between such nodes have been discussed in earlier papers concerning Fuller's tensegrity concept.
The acid test of learning cycles however, is whether they can encompass the discontinuities between the major political tendencies by which the world community is seemingly divided. Any such relationship posited must necessarily be highly controversial, but the controversy should be patterned according to the aspects of the learning challenges involved. This has been explored elsewhere (11, 46)
(c) Wholeness and the implicate order
The previous sections consider how various essentially complementary frameworks might be fitted together, in effect a "bottom-up" approach. Further insight into the information processing problem may be obtained by assuming than it is biasesin man's current mode of thought (especially in the case of Western man) which cause such frameworks to be perceived as separate in the first place.
As a theoretical physicist, David Bohm is concerned with the illusory nature of fragmentation (47, 48) and the manner in which distinct fragments emerge from wholeness in movement (49). He sees the perceptual problems with which he deals as being as relevant to a more healthy response to psychosocial fragmentation as to the problems of fundamental physics. The value of Bohm's perspective for understanding healthy individual development has in fact been recently stressed by a physician Larry Dossey (50).
For Bohm: "the widespread pervasive distinctions between people (race, nation, family, profession, etc.), which are now preventing mankind from working together for the common good, and indeed, even for survival, have one of the key factors of their origin in a kind of thought that treats things as inherently divided, disconnected, and 'broken up' into yet smaller constituent parts...considered to be essentially independent and self-existent." (49, xi).
Attempting to live according to the notion that the fragments are really separate is then what leads to the growing series of extremely urgent crises with which society is confronted. "Individually there has developed a widespread feeling of helplessness and despair, in the face of what seems to be an overwhelming mass of disparate social forces, going beyond the control and even the comprehension of the human beings who are caught up in it." (49, p. 2). And yet the seeming practicality and convenience of the process of divisive thinking about things supplies man with "an apparent proof of the correctness of his fragmentary self-world view."
Basing his investigations on insights from the current state of physics, Bohm focuses "on the subtle but crucial role of our general forms of thinking in sustaining fragmentation and in defeating our deepest urges toward wholeness or integrity". (49, p. 3). He arrives at the conclusion that "our general world view is itself an overall movement of thought, which has to be viable in the sense that the totality of activities that flow out of it are generally in harmony, both in themselves and with regard to the whole existence." (49, p. xii). This view implies that "flow is, in some sense, prior to that of the 'things' that can be seen to form and dissolve in this flow". (49, p. 11). Thus the "various patterns that can be abstracted from it have a certain relative autonomy and stability, which is indeed provided for by the universal law of the flowing movement". (49, p. 11).
Of special relevance to the question of human and social development, is that the above- mentioned desirable harmony "is seen to be possible only if the world view itself takes part in an unending process of development, evolution, and unfoldment, which fits as part of the universal process that is the ground of all existence." (49, p. xii). This has the merit of grounding the concept of development in movement from which appropriate conceptual and social forms temporarily arise, rather than, as is presently done, starting from some "thing" (e.g. a society, a community, or a person) which has to be stimulated into a process of movement and change that is then called "development" (under certain conditions).
Bohm cautions against the expectations of quick remedies: "To ask how to end fragmentation and to expect an answer in a few minutes makes even less sense than to ask how to develop a theory as new as Einstein's was when he was working on it, and to expect to be told what in terms of some programme, expressed in terms offormulae or recipes...What is needed, however, is somehow to grasp the overall formative cause of fragmentation, in which content and actual process are seen together, in their wholeness". (49, p. 18).
As he notes, this confronts us with a very difficult challenge: "How are we to think coherently of a single, unbroken, flowing actuality of existence as a whole, containing both thought (consciousness) and external reality as we experience it?" (49, p. x). The approach he suggests requires looking at the challenge in a new way. Instead of aiming for some reflective correspondence between "thought' and "reality as a whole" the process of thinking about reality as a whole can more usefully be thought of as a kind of "dance of the mind" (determining, and being determined) which functions indicatively. (49, p. 55-6).
Bohm explores the implications of quantum theory as an indication of "new order". The questions he raises are also relevant the emergence of any new psychosocial order. He demonstrates that in the past recognition of new patterns of order has involved attention to "similar differences and different similarities" (49, p. 115), namely the "irrelevance of old differences, and the relevance of new differences" (49, p. 141). The radical transformation of understanding brought about by quantum theory, for example, results from recognition of the way in which modes of obsevation and of theoretical understanding are related to each other.
For Bohm, however, comprehending the new order bears some resemblance to artistic perception. He uses Piaget's distinction between assimilation (understanding, render comprehensible) and accommodation (adaptation, fitting to a pattern) as the basic modes of intelligent perception. This artistic perception then begins by "observing the whole fact in its full individuality, and then by degree articulates the order that is proper to the assimilation of this fact." (49,p.141) Thus it does not begin with abstract preconceptions as to what the order has to be, which are then "adapted" to the order that is observed.
Bohm uses the differences between a lens system (in measurement processes) and a holographic system to show how by use of the former "scientists were encouraged to extrapolate their ideas and to think that such an (analytical) approach would be relevant and valid no matter how far they went, in all possible conditions, contexts, and degrees of approximation."(49,p.144). The advances in relativity and quantum theory imply, however, an undivided wholeness in which such "analysis into distinct and well-defined parts is no longer relevant." This is best illustrated by the hologram in which a whole pattern is somehow encoded into each part, no matter how small. The new order appropriate to our time could then be conceived as contained as a totality, encoded in some implicit sense into each region of space and time (49,p.149).
He elaborates an entirely new way of understanding order as "implicate", or enfolded, which he contrasts with "explicate" forms that are commonly observed and sought. The simplest example he gives is of a television image, carried by a radio wave in an implicate order, and then explicated by a receiver.
In more general terms, Bohm argues that the underlying wholeness in movement (the "holomovement"), noted above, acts like the radio wave to "carry" an implicate order. Under certain circumstances particular things (objects, phenomena, people, nations) can then be unfolded from this dynamic totality by a perceiver, but the holomovement is not limited in any specifiable way at all. As suchit does not conform to any particular order and is essentially undefinable and immeasurable. This means that no single theory can capture or contain phenomena on a permanent basis. Rather, each theory will abstract a certain aspect that is relevant only in some limited context, lifting it temporarily into attention so that it stands out in relief (49,p.151). Furthermore, any new order within which a multiplicity of such aspects are "integrated" is itself not a final goal (as in efforts at "unified science"), but rather part of a movement from which new wholes are continually emerging (49,p.157).
This approach is very helpful in opening up ways of conceiving development and new forms of social order. In providing a mathematical description of implicate order, for example, Bohm makes a useful distinction between: transformation, as a geometric rearrangement within a given explicate order, and metamorphosis, as a much more radical change (such as between a caterpillar and a butterfly) in which everthing alters, although "some subtle and highly implicit features remain invariant"(49,p.160). The former characterizes much development thinking, whereas the subtlety of the latter has hitherto made it appear non-operational or equivalent to catastrophe.
Given Atkin's use of simplical complexes to describe social organization, it is also interesting that Bohm suggests the extension of this technique in terms of "multiplexes" (49,p.166-7). His argument that phenomena need to be perceived as projections of a higher-dimensional reality for which appropriate algebras are required (49,p.188), relates to Thom's concerns with mathematical archetypes (49).
The challenge of Bohm's arguments lies in the manner in which they strike at the very root of the meaning of human and social development. His arguments highlight the extent to which both the physical and social sciences continue to rely on a Cartesian framework (if only in the familiar tabular/matrix presentations characteristic of social science papers) at a time when inherent weaknesses in the thinking behind such frameworks have been demonstrated. His most basic point is that the phenomena such as those which are the preoccupation of "development" (peoples, ideologies, groups, societies) are essentially derivative. "The things that appear to our senses are derivative forms and their true meaning can be seen only when we consider the plenum, in which they are generated and sustained, and into which they must ultimately vanish". (49,p.192) In this light, the basic flaw in present development thinking is the a priori recognition of certain distinct social entities which it now seems desirable to "develop".
It is precisely this conception (as argued on different grounds by the world-system theorists) which reduces development to "sterile" transformative operations and prevents any metamorphoses (to use Bohm's terms). For it is development which precedes and underlies such explicate social entities as a movement from which they have been unfolded: "what is movement" (49,p.203). Metamorphosis thus calls for ways of unfolding new, currently implicate forms from this holomovement, and enfolding into it those which are currently explicate, but are inadequate to the time. This is far removed from mechanistic efforts to "eliminate" undesirable structures and to "build" new ones from their components.
It should not be assumed that this implicate order is an inaccessible theoretical abstraction. Bohm argues that conscionsness itself operates by enfolding and unfolding and that "not only is immediate experience best understood in terms of the implicate order, but thatthought also is basically to be comprehended in this order". (49,p.204). This creates the possibility for "an unbroken flowing movement from immediate experience to logical thought and back" thus ending the fragmentation characteristic of the absence of any awareness of such movement (49,p.203). He argues that movement is itself sensed primarily in the implicate order and that Piaget's work "supports the notion that the experiencing of the implicate order is fundamentally much more immediate and direct than that of the explicate order, which...requires a complex construction that has to be learned" (49,p.206).
Different languages may thus be understood as different ways of unfolding the implicate order. Atkin's work suggests ways in which the intuitively sensed differences between such unfoldings may be articulated in mathematical terms which are highly relevant to the problems of information transfer in modern society.
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