17 December 2004 | Draft
using geometry to embody developmental integrity
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Case for multi-dimensional accounting
"Three sets of books": shadow of the "bottom line" approach?
Spreadsheet to torus
Synergetics and tensegrity
"Sustainability" through "golden mean accounting"?
Towards a "semantic dome"
Construction of "semantic shelters" or memetic vehicles"?
It is universally accepted that the most basic form of accounting lies in the single answer to the question "what does it cost?" A more elaborate approach, leading to that figure, is to itemize in a list the costs which total to that single budget figure. The great historical innovation in ensuring control over financial accounts was the shift to double entry bookkeeping, subsequently taking the form of the spreadsheets that are basic to the project and program management of any modern institution. Spreadsheets facilities have of course been embodied into spreadsheet software.
The following text is concerned with how the third dimension is reflected in an actual geometrical representation of accounting -- moving beyond one-dimensional "budgets", and two-dimensional budget lines and spreadsheets. It is correct that standard spreadsheets offer 3-D graphics in addition to 2-D displays -- as a means of obtaining an overview of sets of datapoints. The focus here however is on the potential significance of the actual geometry in integrating disparate (or potentially incommensurable) preoccupations of an organization in such a manner as to heighten the coherence and integrity of the operation.
The only resources relating tangentially to this possibility seem to be materials referenced by Robert Grace (The Over-all Picture, 2000). The exercise here is intended to be suggestive of possibilities -- as a stimulus to imagination and creativity -- rather than implying closure on a well-defined new method.
Chris Lucas (Multidimensional Economics, 1999) outlines a complexity-based economics in the light of the following assessment.
Vahe Poladian, et al (Time is Not Money: The case for multi-dimensional accounting in value-based software engineering, 2003) argue that:
Richard B. Dull and David P. Tegarden (A Comparison of Three Visual Representations of Complx Multidimensional Accounting Information, 1998) have investigated the relationship between three visual representations (two-dimensional, three-dimensional fixed, and three-dimensional rotatable) of multidimensional data, and the subjects' ability to make predictions based on the data (namely "cognitive fit"). Output of a momentum accounting system was simulated and graphics were rendered based on that information. They concluded:
David Ellerman (Double-Entry Bookkeeping: The Mathematical Formulation and Generalization, 1986) explores the lack of any mathematical exploration of standard double entry bookkeeping which might enable its generalization:
In arguing for "a more flexible approach to logic chains", Réal Lavergne (Results-Based Management and Accountability for Enhanced Aid Effectiveness, 2002) states:
Xavier Bry and Jean-François Casta (Synergy Modelling and Financial Valuation: Contribution of Fuzzy Integrals, 2003) point out that financial assessments are characterized by: the importance of the role assigned to human judgement in decision making, the use of qualitative information and the dominant role of subjective evaluation. They examine the specific problems raised by the modelling of synergy between the assets of a firm:
"Triple-entry bookkeeping": Henning Kirkegaard (The Logic of Double-Entry Bookkeeping) proposes a new understanding of the inherent uncertainties of double-entry bookkeeping system in the light of the study on triple-entry bookkeeping by Yuji Ijiri (Momentum Accounting and Triple-Entry Bookkeeping: Exploring the Dynamic Structure of Accounting Measurements. American Accounting Association, 1989). He stresses that for five centuries the questions about the causes of claims and agreements have been left unanswered in accounting since double-entry bookkeeping has only two logical measurement points.
He concluded that:
The term triple-entry bookkeeping has not been extensively used although various approaches are taken to resolving the time-based uncertainties in accounting.
"Quadruple entry bookkeeping": On behalf of the International Monetary Fund, Cornelis N Gorter and Manik L Shrestha (Bookkeeping Conventions and the Micro-Macro Link. Review of Income and Wealth, Vol. 50, No. 2, pp. 181-201, June 2004) point out that the formal accounting logic of the national accounts and other macroeconomic statistics is not always well understood. In addition, the relation between macro statistics and micro accounting data often is not clear. They summarize the main bookkeeping conventions at the macro level:
Harry Postner (Winter of Our Discontents: A Personal View of the National Economic Accounts, 2001) discusses the relationship between economic accounting and commercial accounting:
Multidimensional or matrix accounting: A multidimensional accounting system uses existing company data to look at the organization in multiple ways. Different users require diverse perspectives or dimensions of information, which are not possible to furnish under the sole concept of double-entry accounting. But designers of computer-based accounting systems in the past thirty years have tended to focus on producing existing information cheaper, or faster. Few questions have been asked about whether better accounting information could be produced by using a computer -- whether cost-effective, computer-based accounting systems can be used to generate better accounting information than existing transaction processing accounting systems. There have been few studies of these issues beyond:
Examples of multidimensional accounting include:
Such vector accounting (or property accounting) provides a valuation-free description of the property transactions underlying the value transactions of ordinary accounting, thus avoiding their valuation controversies. According to Ellerman, it is called property accounting because it keeps accounts directly in terms of the stocks and flows of the underlying property rights. It attempts to stake out the objective territory that involves no valuation in order to delineate the real issues of valuation. Property is understood to change by: transactions between parties and appropriations ("or, metaphorically, with Nature"). He states:
Ellerman criticizes the model of Ijiri (above) because of the lack of balance sheet equation, the lack of any equity accounts, nonclosure and unworkability of temporary accounts, nonbalancing trial balance, and the use of scalar accounts rather than vectors. These are maintained and generalized in the vector accounting model.
Subsequently Ellerman (Introduction to Property Theory: The Fundamental Theorems, 2002) develops his approach using directed graph theory.
The metaphor of the "bottom line" has become fundamental to many aspects of new discourse and reporting regarding sustainable development and corporate social responsibility. The following "bottom lines" are to be understood as cumulative or nested, namely "triple bottom line" reporting includes both double and single bottom line reporting:
Double bottom line: Sustainable development and concerns about corporate social responsibility have over the past decades forced attention on the double (or dual) bottom line. This tends to signify the need to reconcile the financial bottom line with the social bottom line -- possibly with the aid of a "social audit". It could be argued that the double bottom line was first articulated internationally through the call for "structural adjustment with a human face" -- in response to the strictures of traditional IMF and World Bank practices. There is however some confusion in the terminology in that a more sophisticated approach to social responsibility tends to be acknowledged in triple or quadruple bottom line reporting -- and the environmental dimension may even be acknowledged as double bottom line reporting [more]. These distinctions are tentatively made in Table 1 where the interpretations of Scheme A tend to be more conservative than Scheme B.
Triple bottom line: More recently, the Global Reporting Initiative guidelines for "triple-bottom-line reporting" broaden financial reporting into a three-dimensional model for economic, social and environmental reporting [more]. This focuses corporations on the environmental value added (or destroyed) -- in addition to the economic and social values of the double bottom line. Narrowly conceived, the term "triple bottom line" is then used as a framework for measuring and reporting corporate performance against economic, social and environmental parameters. More broadly understood, the term is used to capture the whole set of values, issues and processes that companies must address in order to minimize any harm resulting from their activities and to create economic, social and environmental value [more]. The "triple bottom line" of sustainability reporting can be disaggregated into a "five capitals model" in the following way: economic (manufacturing, financial), social (human, social), environmental (natural). As noted in the Sustainability Accounting Guide (2003):
It has been estimated that 45% of the world's top companies publish triple bottom line reports. The triple bottom line may be understood as "social responsibility", taking into account issues such as globalization and the impact of multi- national companies, in terms of their responsibilities to the communities in which they work.
Quadruple bottom line: This form of reporting embraces a further component - governance. It represents the emergence of sustainability reporting through which reporting is aligned more closely with underlying management practices and measures of corporate performance. The trend to quadruple bottom line reporting has been accelerated by major company collapses that have focused attention on governance and social responsibility. Corporate social reputation is increasingly recognized as having less to do with earnings and more to do with reputation across a broad array of stakeholders. However, in the "bottom line indicators race", technology has also been proposed instead of governance (Sustainable Energy Watch Global Report for RIO+10). But quadruple bottom line reporting may be better understood in terms of "ethical responsibility" (as distinct from social responsibility") as the focus on employees, on stewardship and on leadership fostering and nurturing employees. This takes account of the challenge to ethics indicated by in boardroom disclosures. As noted by Nasir Butrous and Ellen McBarron (A Call for an Ethical Focus in Business, 2004), many organizations judged to be socially responsible for their philanthropic and community work have been found to have made unethical decisions; support unethical values and in fact have acted unethically. The quadruple bottom line adds a new dimension to the running of the company quite separately from the bottom, dual and triple bottom lines. The ideas of ethical leadership foster the internal democracy of open management.
Quintuple bottom line: As noted above, there is an emerging consensus recognizing "governance" as the key factor in quadruple bottom line reporting. However another candidate is spirituality -- as reflected in the "spirit in business" movement, or as articulated by Sohail Inayatullah (Spirituality as the Fourth Bottom Line, 2003). Spirituality may indeed be understood as fundamental to a more enlightened form of governance -- as exemplified in "faith-based governance". If however spirituality is considered distinct from governance, then it would need to be allocated to a fifth bottom line. For Inayatullah, spirituality means four interrelated factors.
In what follows, the question is whether such "bottom line" notions can be integrated with greater precision into a new geometry suggestive of a system of accounting -- spherical accounting.
Before exploring how spherical accounting might work, it is useful to note how parallel accounting systems tend to exist in practice -- independently of any implementation of triple or quadruple reporting as advocated above. In fact the following examples in many ways constitute a shadow form of what is recommended with respect to corporate social responsibility. They represent a marked tendency to maintain parallel sets of books as illustrated by the following:
In such circumstances it is not surprising that software is advertised as: "Maintains five independent sets of financial information on each asset and allows analysis by displaying three sets of books side by side" [more].
In relation to the emergence of governance as the focus for quadruple line reporting, it is interesting to note the following comment, and controversy, on the potential for abuse of electronic voting during the 2004 presidential elections in the USA:
Whilst steps may indeed be taken to implement triple and "higher" forms of bottom line reporting -- with their own "sets of books" and audits -- it would be naive to imagine that these "white books" would not be obliged to continue to coexist with their shadowy analogues ("black books") to which reference is made above. For example, although (as noted above) "45% of the world's top companies publish triple bottom line reports", there is little debate concerning the relationship between such a response to "corporate social responsibility" and the tax avoidance practices of such corporations -- many are alleged to pay very little tax in practice. It might even be asked whether such reports are used as a "good citizen" disguise for tax avoidance.
The following table may therefore prove to be a useful reminder that public debate and reporting may be ignoring an unstated reality (whose scope Transparency International continues to document):
This table benefitted from the insights of Nadia McLaren
There is now an extensive literature on the relevance of metaphor to strategic thinking -- and hence the need for empowering metaphors to enable more effective strategies. The question to be asked in relation to the challenge of the times is: what kind of metaphoric trap is strategic thinking entrapped in?
The suggestion here is that in relation to accounting, as a fundamental tool of management, the world's initiatives are trapped in a disempowering, impoverished metaphor. This might be described in terms of the oversimplistic "geometry" that leads to expressions like "budget lines" and "bottom lines". This is an extension of the kind of thinking dependent on "bullet points" in strategic presentations. Such thinking tends to avoid more contextual articulations of any value to strategic understanding. In fact there is a dramatic split between:
From this perspective, it might be argued that the economic preoccupations of business and development are well-served by "closed-system" thinking that is articulated through spreadsheets. Such thinking reinforces tendencies to grid systems, notably in urban planning. Distinct from this mode of thinking is that associated with more "open systems" of less predictable behaviour. Typically these include the ecosystems of the natural environment -- the "pattern that connects". They also include the kind of thinking pioneered by Christopher Alexander (A Pattern Language: Towns, Buildings, Construction , 1977) in relation to urban environments.
It might be argued that the developmental mode is essentially two-dimensional and is an excellent tool for appropriately limited purposes. The second is in some ways three-dimensional -- as presented imaginatively through photographs and representations of a spherical Earth. The argument here is that sustainable development is the challenge of the interaction between two geometries -- the plane and the sphere -- and the nature of the transitions and transformations required to shift from one to the other.
This theme has of course been explored in several works of fiction well-known to mathematicians (Edwin A. Abbott. Flatland : A Romance of Many Dimensions, 1884; Dionys Burge, A Fantasy About Curved Spaces and an Expanding Universe, 1965; Ian Stewart, Flatterland: Like Flatland, Only More So, 2002) [more].
It is of course clear in geometrical terms that the two-dimensional may be very well suited to local perspectives and issues -- laying out a garden or a town, a small business. But it would appear to be extremely problematical in dealing with global issues -- environmental degradation, depletion of natural resources, the clash of civilizations -- where the three-dimensionality of some form of spherical approach is more isomorphic with the shape of the world and how it may need to be understood. This consideration relates to work on "cognitive fit" (cf Ritu Agarwal, et al. Cognitive Fit in Requirements Modeling: A Study of Object and Process Methodologies, Journal of Management Information Systems, 1996). "Cognitive Fit" is defined as the degree to which a particular diagramming technique is representative of a problem space, notably in accounting systems (cf Roberta Ann Jones, et al. An Empirical Investigation of the Cognitive Fit of Selected Process Model Diagramming Techniques; Cheryl Dunn, et al. An Investigation of Localization as an Element of Cognitive Fit in Accounting Model Representations, Decision Sciences Journal, 2001).
Will the future see present approaches to global accounting as somewhat akin to the "flat earth" mindset of centuries past? Why was it so difficult to demonstrate the sphericity of the globe and to enable its circumnavigation? The challenge for mapmakers of the past was to ensure a relationship between surface measurements and the shape of the world -- using appropriate approximations. To what extent is the nature of this challenge recognized in the case of any accounting system that claims to be global, whether geographically or in terms of an inclusive attitude to all sectors of human activity?
A particular property of a two dimensional representation of reality is the nature of its boundaries. A spreadsheet is apparently well bounded -- with a limited number of columns and rows. But more columns or rows can be easily added. Similarly an urban grid plan is bounded -- but further streets can be added whenever required. This is in fact the essence of development as widely conceived. Green belt zones can always be "cleared" as a basis for further development. No inherent limits are integrated into strategies based on a two-dimensional approaches to accounting. Such strategies are essentially unconstrained by any higher dimensionality.
Even the discussions of multidimensional accounting, as a generalization of double entry bookkeeping, imply an unbounded grid -- even though the array is multidimensional. In an urban context, the contrast is especially evident between a gridwork of streets and a neighbourhood focused on a square -- where the focus is meaningful to all in the area as a "centre of gravity". This is a form of constraint on the unboundedness of the grid.
By contrast with a grid, the three-dimensionality of a sphere is inherently constrained -- although the surface is described as "finite but unbounded". The constraining features of a sphere reflect the additional constraints on two-dimensional thinking imposed of necessity by triple, quadruple and possibly quintuple bottom line thinking in response to the challenge of living on a sphere rather than on an infinite plane -- as developers tend to continue to assume.
The shift towards quadruple and higher forms of accounting can be understood as an effort towards completeness. Elsewhere (Needs Communication: Viable need patterns and their identification, 1980) it was argued that:
The "wrapping" called for must necessarily be undersood as the introduction of curvature. Can sustainable accounting be designed without the forms of curvature that will take account of all the feedback loops essnetial to sustainability? In contrast to the feedback loops that figure on systems diagrams, the requirement in the case of sustainability is surely for mutually constraining loops associated with distinct value flows -- to which the double, triple and quadruple bottom lines point.
A simple exercise in geometry can be used to transform the spreadsheet -- as a sheet -- into a torus (namely a doughnut shape):
What purpose might this shape serve in understanding the financial viability of an organization? Clearly, when displayed graphically, any strictures in the torus might provide a way of sensing the health of the organization -- perhaps to be expressed as "constipation" or "bloat" at certain points.
If the spreadsheet of an organization were to be displayed in this way, it would raise the interesting question of the stability of a torus under dynamic environmental conditions. Most striking is the comparison with the viability of a smoke ring. The integrity of a smoke ring is sustained by movement around the circular bands around the doughnut shape.
Toroidal dynamics are of fundamental interest in nuclear fusion research -- in the search for new sources of energy. Spheromaks are easily formed, self-organized magnetized plasma configurations -- sometimes called magnetic vortices, magnetic smoke rings, or plasmoids (Paul M Bellan. Spheromaks: A Practical Application of Magnetohydrodynamic Dynamos and Plasma Self-Organization, 2000)
In terms of the challenge of relating disparate elements, significant to double or triple bottom line insights, the advantages of this kind of approach would appear to be modest.
In the light of the arguments for multidimensional accounting, the existence of "sets of books", and the promotion of multiple "bottom line" reporting, it is worth considering alternative ways of framing possible future approaches -- especially now that there is both a need, and a willingness, to make extensive use of computer visualization facilities.
For example, it could be assumed that:
Although such a system adjusts relatively rapidly through the redistribution of tensions and pressures along various value streams, this takes time. There are lags typical of those recognized in "momentum accounting". In the sense the sphere may hold the temporal dimension, in a manner reminiscent of longitude.
The extensive work of R Buckminster Fuller (Synergetics: the Geometry of Thinking, 1975) on synergetics provides a formalization and integration of many of the elements noted above. Fuller has described it in the following terms:
Fuller has described synergetics as a form of universal accounting system (cf Amy C. Edmondson. A Fuller Explanation: A Quick Comparison: "Synergetics Accounting" ).
But although Fuller has articulated this extensive, and much-cited formalization, this does not focus specifically on semantic content -- of the type required by the distinct value flows discussed earlier. In arguments analogous to the economic reduction to financial flows (noted earlier), he stresses their reduction to energy flows. However in the 1970s, Fuller promoted a World Game approach (still promoted through the World Game Institute) that emphasized "total energy accounting" based on a 25-year "economic accounting" [more]. It is essentially a programme for the Design Science Revolution. It is conceived as an Integrative Resource Utilization Planning Tool. This called for:
The formalization does however stress the value of exploring such system representations through polyhedra having various properties and interrelationships -- and capable of transformation from one to another. This is most evident in his work on the vector equilibrium (cuboctahedron) and tensegrity [more | more | more].
Bonnie Goldstein DeVarco (Energetic Architecture - Buckminster Fuller's Geometry of the Sphere, 1997) notes the anticipation of some of Fuller's geometric insights by the so-called "Father of Accounting", Luca Pacioli (De Divina Proportione, 1509, illustrated by Leonardo da Vinci). A glass rhombicuboctahedron half-filled with water is the focus of a widely analyzed contemporary painting of Pacioli -- held to epitomize the deep Renaissance connection between art and mathematics. Pacioli is a key figure in the recognition of centro-symmetrical polyhedra [more]. Pacioli's own mathematical work had been preceded by that of Leonardo of Pisa, (1170-1250), also known as Fibonacci, to whom the Republic of Pisa awarded a yearly salary for his advice on accounting and related matters -- following his vital role in collating the Arab and Indian insights into mathematics for Europeans (Liber abaci, 1202).
Although the relevance of Fibonacci series in relation to financial markets has been widely explored [more], there do not appear to be any direct references in current financial accounting to the shared concern of Fibonacci and Pacioli with the Golden Mean. This "golden ratio" of any two consecutive numbers in the Fibonacci sequence is a proportion that is an important phenomenon in music, art, architecture and biology. The question is whether this ratio, as expressed in polyhedra, can be in any way understood as vital to new insights into sustainability accounting -- especially given the ease with which virtual polyhedra can now be constructed (cf George Hart, Virtual Polyhedra) [more], and linked to data of significance to policy-making and management (as has been done with the databases of the online Encyclopedia of World Problems and Human Potential).
The possibility is perhaps usefully emphasized by the current restriction of representation of "multi-dimensional accounting" to one of the simplest polyhedra, the cube -- as in the Sustainability Accounting Guide (2003).
Perhaps ironically, the only reference to "golden mean accounting" is in an early Western poem concerning Japan [more]. However the group associated with the 'San Francisco' Model of Economic Adjustment, in discussing their study of Multi-Dimensional Hyperbolae and the General Utility Problem (by Kurt Roemer, Newtonian Economics, 1985, Chapter 4), do explain the function of the Golden Mean in order to conclude that:
The importance of a "golden mean" is recognized metaphorically, as stressed in 2004 with regard to doing business in China by a leader of the China Society of Economic Reform [more]. Similarly David Hiley (Striking a Balance between Budget Extremes, 1999) in discussing Responsibility Centered Management (RCM) argues:
Similar metaphoric recognition is given in the case of the well-known alternative commuity, The Farm:
Severyn T. Bruyn (Civil Republic: Beyond Capitalism and Nationalism) also focuses on the metaphorical insight, arguing optimistically:
The challenge in moving beyond metaphor does indeed lie in "a lot of details". Given David Ellerman's approach to "vector accounting" [above] -- using directed graph theory to handle distinct forms of property ("property accounting") -- it is tempting to forsee a link to Fuller's formalization of polyhedral energy systems in terms of vectors (Synergetics: Explorations in the Geometry of Thinking. 1975: 420.00, 513.00, 521.00). However any such approach needs to be set in the context of other formal approaches to polyhedra (cf Branko Grünbaum. Are Your Polyhedra the Same as My Polyhedra?).
Also of great potential interest is the approach of Stafford Beer (Beyond Dispute: The Invention of Team Syntegrity, 1994) from the perspective of management cybernetics (as mentioned below). The geometric representation of dynamic systems, integrating the insights of Fuller and Beer has been usefully summarized by Curt McNamara (Systems Coupling and Precession, 2001; Geometrical Systems Mapping, 2002). Beer was also responsible for the development of a Viable Systems Model [more] that has colour-coded systemic features similar to those identified by Edwad de Bono (Six Thinking Hats, 1987; Six Action Shoes, 1991).
Collectively these approaches address the real-world challenge of ambiguity and uncertainty as noted by J G March (Ambiguity and accounting: the elusive link between information and decision making, 1987). The point to be stressed is the generalization from accounting in purely financial terms, through accounting for "flows" based on incommensurable "value currencies", to "accounting" for flows of information (essentially meaning) that are fundamental to system viability or sustainability.
Fuller's insights into the redistribution of energy in systems enabled him to invent an architectural structure, for which he is best known -- namely the geodesic dome. But in this exploration of the possibility of spherical accounting, which is consistent with many of these insights, the question is raised as to whether it is possible to develop what amounts to a "semantic dome", or perhaps a "memetic dome" . This would not be constructed from physical materials. Rather it would be a virtual dome, integrated with and reflecting the contents of an information system of which it represented the "accounting".
However, despite this use of "dome" and the focus on semantic integration, this metaphor is not explicitly related to the geodesic and systemic insights of Fuller. Other distinct tools inspired to some degree by the same metaphor include:
These various approaches are significant in relation to the emergence of the semantic web -- specifically to the challenge of ontologies as a key enabling technology for the semantic web. Ontologies are formal and consensual specifications of conceptualizations that provide a shared understanding of a domain. (cf Haoxiang Xia, Yanzhong Dang. Toward a Semantic- Web- Services- enabled Knowledge Ecosystem Some Research Issues, 2003). Such work is seen as the underpinning of the emergent global brain (cf Simulating a Global Brain: using networks of international organizations, world problems, strategies, and values, 2000).
Specifically missing from these insights into a "semantic dome" are the systemic relationships between distinct semantic content as value flows -- fundamental to dynamic accounting in a functioning system, in contrast with the static descriptive analysis characteristic of knowledge ontologies. The former is vital to the operacy of sustaining the viability of a functioning psycho-social system -- whereas the latter is more concerned with learning about it and understanding it as an observer.
The contrasting semantic "flows" capable of holding the requisite variety to govern a complex system may perhaps be usefully described in terms of "languages" (12 Complementary Languages for Sustainable Governance, 2003). This recognition of distinct epistemological frameworks has been explored by Edward de Bono (Six Thinking Hats, 1987; Six Action Shoes, 1991).
Within the community of those developing knowledge tools for the emerging semantic web of the 21st century there is a marked belief in the possibility of uniformity and compatibility, however it is to be achieved. On the one hand, in addition to technological standardization, the challenge of interoperability addressed by computer-based ontology tools does indeed deal with terminological incompatibilities -- but on the questionable assumption that key terms do have similar referents, whether within or across cultures (but see Systems of Categories Distinguishing Cultural Biases, 1993).
On the other hand, the accounting systems concerned with interrelating different value flows do indeed recognize that the flows are distinct (and even incommensurable) and that it is less beneficial (even when possible) to reduce them to a common currency. But such accounting systems (whatever the number of "bottom lines") do not address the strategic challenge of the fundamental dilemmas engendered by these value flows -- with their different appeals and calls on quite distinct resources. And yet it is dealing with these dilemmas that is fundamental to the way in which the psycho-social system adapts to the future.
The possibility and role of incommensurable semantic content is neither recognized nor addressed. Whilst the web can indeed enable users to locate disparate information and to navigate between unconnected zones of semantic space, the designs for a semantic web do not acknowledge those challenges of epistemologically disparate content for which imposition of uniform semantic rules and processes would be rejected. A small indication of the challenge is recent steps to abandon the multilingual web domain names promoted since 2000 by the Multilingual Internet Names Consortium (MINC).
There would appear to be an assumption of an emergent degree of universal order and seamlessness -- a semantic continuum -- when there is every possibility that knowledge space may be troubled by increasingly chaotic dynamics and cleavages disruptive of the normalization favoured by those who feel empowered to "encourage" it. The conflicts, only too evident in the geopolitical and social spheres, may simply be replicated or echoed in knowledge space -- where they have already long been active, as is evident in the challenges of faculty politics, interdisciplinarity and transdisciplinarity. These challenges persist despite efforts at universal classification of knowledge, notably as pioneered by Paul Otlet, founder of the Union of International Associations, and reflected in his final vision (Monde: Essai d'universalisme, 1935) -- now seen by historians as an early visionary of the internet (cf Union of International Associations -- Virtual Organization Paul Otlet's 100-year Hypertext Conundrum?, 2001).
Traditionally "ontology" has been the most fundamental branch of metaphysics -- the study of being or existence as well as the basic categories thereof [more]. As such it has strong implications for the conceptions of reality notably where this is determined by theology. "Ontology" has been borrowed by computer science for the purpose of formulating an exhaustive and rigorous conceptual schema within a given domain, a typically hierarchical data structure containing all the relevant entities and their relationships and rules (theorems, regulations) within that domain [more]. The very fact of such borrowing may be considered as a metaphoric illustration of the challenge.
These issues are given dramatic current significance in the light of the strategic impact of the semantic challenges inherent in:
The nature of the challenge of "semantic discontinuity" was explored on the occasion of the United Nations Earth Summit (Rio de Janeiro, 1992) in Configuring Globally and Contending Locally: shaping the global network of local bargains by decoding and mapping Earth Summit inter-sectoral issues (1992). This specifically focused on the challenge of configuring meaningfully the "inter-sectoral strategic dilemmas of sustainable development", whether as a matrix or as a 3D icosidodecahedral structure. The latter representation was used in order to take advantage of the systemic insights developed by Fuller as synergetics. Of relevance are more recent hypotheses regarding the role of tensesgrity (Jim Nystrom. Tensegrity as the agent of phase transitions, 1998; Donald E. Ingber, The Architecture of Life, Scientific American, Vol. 278, 1998, 1).
As was stated then (Summary of analysis on the occasion of Earth Summit, 1992):
Spherical accounting thus points to ways of using unavoidable fundamental disagreement as an essential feature of the design of organizations adapted to the turbulent conditions of the 21st century (cf Using disagreements for superordinate frame configuration, 1994). The challenge of strategic balancing under such conditions, using Fuller's insights into tensegrity, has been articulated elsewhere (cf Implementing Principles by Balancing Configurations of Functions: a tensegrity organization approach, 1979). The point to be stressed is that "incommensurables" and "disagreements" are then distributed into a polyhedral configuration of polarities rather than fused into a single polarity -- thus opening up a large spectrum of possibilities for negotiation and the "management of disagreement".
Tensegrity structures clarify ways in which individual bargains need to be interlocked using local elements of disagreement ("compression elements") within the global network of agreement ("tension elements"). Tensegrity structures are effectively patterns of sustainability. The challenge is to find useful ways to encode such patterns to offer insights into the strategies of sustainable development. [more]
Management cybernetics, notably as developed by Stafford Beer [more], resulted in a particular application of Fuller's tensegrity insights to integration of diverse perspectives (Beyond Dispute: The Invention of Team Syntegrity, 1994), a syntegration process, and a World Syntegration Action Plan (Origins of Team Syntegrity, 199?; World in Torment: a time whose idea must come, 1992). As further developed by the Syntegrity Group for the syntegration process, syntegrity combines the notions of synthesis and tensegrity -- itself a combination of tension and integrity (cf Allenna D Leonard. Team Syntegrity Background, 2002).Team syntegrity is a suite of structured group processes based on cybernetic principles for decision-making and consensus building. It optimizes the effectiveness and efficiency of information exchange while integrating various points of view. As used by the Systems and the Information Society Network (2001-2), to explore frameworks considered useful "to account for the complexity of social and organisational activities in the new information society", the "syntegration protocol" was described as:
Shann Turnbull (The competitive advantages of stakeholder mutuals, 2000) introduces the related concept of "social tensegrity" as a method for efficiently managing the problems created by the limited, inconsistent and contrary operating characteristics of people. It uses the contrary characteristics of humans to improve self-governance and it is an emergent property of organisations established with holonic architecture:
On the larger scale a "semantic dome" (or perhaps a "memetic dome") may be envisaged in a manner analogous to that of Buckminster Fuller's ambitions for protective physical domes for cities and regions. Such semantic shelters ("memetic shelters"?) may be seen in the pressure to adapt "star wars" information systems (sustaining "nuclear shields" or "umbrellas") to include protection from semantic content associated with information and memetic warfare (Missiles, Missives, Missions and Memetic Warfare: Navigation of strategic interfaces in multidimensional knowledge space, 2001).
Of much greater interest is the development of semantic shelters for (virtual) communities, neighbourhoods, households or individuals (cf Dynamically Gated Conceptual Communities: emergent patterns of isolation within knowledge society, 2004), notably as illustrated by emergence of "renaissance zones" during the forseen periods of social breakdown (cf Renaissance Zones: experimenting with the intentional significance of the Damanhur community, 2003). The development of "memetic vehicles" as a further possibility may depend on a generalization of understanding of the function of a "wheel" -- integrating the flows characteristic of "spherical accounting" for project management -- to provide a form of "traction" through semantic space (cf Metaphors as Transdisciplinary Vehicles of the Future, 1991).
In struggling to comprehend what the future may consider as self-evident as the wheel, it is particularly interesting to recognize the variety of different insights into the challenge (cf Darrell Mann and Simon Dewulf. Evolving The World's Systematic Creativity Methods, 2001). These are often mutually "hostile" and heavily patented (cf Future Coping Strategies: Beyond the constraints of proprietary metaphors, 1992). More interesting however is the possibility that they each represent a valid perspective lacking a common framework of requisite complexity to integrate them -- or that they are each slightly "out of focus" with respect to a more generic understanding for which current language is inadequate.
Walter Block. Compromising the Uncompromisable: The Austrian Golden Mean. Cultural Dynamics, July 1997, 9, 2, pp. 211-238.
Johan Bollen. Adaptive Hypertext Networks That Learn the Common Semantics of Their Users [text]
M Bromwich. Discussion of multidimensional accounting and distributed databases: their implications for organizations and society. Accounting, Organizations and Society 5(1), 1980, 125-128.
Xavier Bry and Jean-François Casta. Synergy Modelling and Financial Valuation: Contribution of Fuzzy Integrals, 2003 [text]
A. Charnes, C. Colantoni and W. W. Cooper. A futurological justification for historical cost and multi-dimensional accounting. Accounting, Organizations and Society, 1, 1976, 4, pp. 315-337.
David Ellerman. Generalized Double-Entry Accounting: Showing what is 'Double' in the Double Entry Method. 2004 [abstract]
David Ellerman. Introduction to Property Theory: The Fundamental Theorems, 2002 [text]
David Ellerman. Double Entry Multidimensional Accounting. Omega: International Journal of Management Science. 1986. 14, 1, pp. 13-22.
Ian Fraser. Triple Entry Bookkeeping - A Critique. Accounting and Business Research, Spring 1993, pp. 151-158
W. D. Haseman and A B Whinston. Design of a Multidimensional Accounting System, The Accounting Review, 1976, January, pp. 65-79.
Bo Hedberg and Sten Jönsson. Designing semiconfusing information systems for changing organizations. ACM SIGMIS Database archive, 13, 1982, 2-3 [text]
Michael R. Hyman. A Critique and Revision of the Multidimensional Ethics Scale. Journal of Empirical Generalisations in Marketing Science, Volume One, 1996. [text]
Y. Ijiri and E. C. Kelly. Multidimensional accounting and distributed databases: their implications for organizations and society. Accounting, Organizations and Society 1980, 5(1): 115-123.
Henning Kirkegaard. True Accounting - Myth or Possibility?
Peter Koenig. 30 Lies About Money: liberating your life, liberating your money. iUniverse, 2003
Bernard A. Lietaer:
Chris Lucas. Multidimensional Economics. 2006 [text]
Nick Mackinnon. The portrait of Fra Luca Pacioli, The Mathematical Gazette, 77, 1993, pp. 130-219.
Darrell Mann and Simon Dewulf. Evolving The World's Systematic Creativity Methods (Paper for the 7th European Association of Creativity and Innovation conference at the University of Twente, Netherlands, 2001) [text].
J. G. March. Ambiguity and accounting: the elusive link between information and decision making. Accounting, Organizations and Society, 1987, 12, 2, pp. 153-168
James J. Odell. Six Different Kinds of Composition. Journal Of Object-Oriented Programming Vol 5, No 8. January 1994 [text]
Luca Pacioli. Particularis de Computis Et Scripturis: 1494. Pacioli Society 1994
Proceedings of the Conference Accounting and Economics. Garland Publishing, 1996 In Honour of the 500th Anniversary of the Publication of Luca Pacioli's Summa de Arithmetica, Geometria, Proportioni et Propotionalita, Siena, 18-19 November 1992A reprinted issue of the journal Economic Notes, v.22, no.2, 1993, published by Monte dei Paschi di Siena,Italy).
Allan Savory. Achieving the Triple Bottom Line - Really. 1999 [text]
arkus Schwaninger. Managing Complexity: the path toward intelligent organizations. Systemic Practice and Action Research 13 (2), pp. 207-241, April 2000 [abstract]
Robert Emmett Taylor. No Royal Road: Luca Pacioli and His Times (Dimensions of Accounting Theory and Practice). Ayer, 1981
Jonathan Tennenbaum. Incommensurability and Analysis Situs. The New Federalist, June-July, 1997 [text]
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